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| United States Patent |
5,923,703
|
|
Pon
, et al.
|
July 13, 1999
|
Variable suppression of multipath signal effects
Abstract
Method and apparatus for formation of an autocorrelation difference
function of an incoming digital signal that reduces the effects of
presence of a multipath signal or of noise in an incoming digital
composite signal. An incoming digital composite signal, including direct
and multipath signals, is received that has a bit value transition
interval of length .DELTA..tau..sub.chip. Two or three consecutive bit
values b.sub.n-2, b.sub.n-1 and b.sub.n of the direct (ideal) signal are
examined. If a test condition for these bit values is satisfied, a first
non-uniform weighting function w1(t) is used to compute the contribution
of a time interval I.sub.n ={t'.vertline.t.sub.n-1
+.DELTA.<t'.ltoreq.t.sub.n +.DELTA.}, where .DELTA. is a selected time
value satisfying 0.ltoreq..DELTA.<.DELTA..tau..sub.chip, to first and
second autocorrelation functions AC#(.tau.;E) and AC#(.tau.;L) with
respective selected first and second time shifts .tau.=t.sub.E and
.tau.=t.sub.L (>t.sub.E) If the test condition is not satisfied, a second
weighting function w1 (t) is used to compute the contribution of the time
interval I.sub.n to AC#(.tau.;E) and AC#(.tau.;L). An autocorrelation
difference function .DELTA.AC#(.tau.)=AC#(.tau.;E) and AC#(.tau.;L) is
formed in which the effects of noise or of multipath signals is
suppressed, relative these effects in a conventionally computed
autocorrelation difference function
.DELTA.AC(.tau.)=AC(.tau.;E)-AC(.tau.;L).
| Inventors:
|
Pon; Rayman (1451 Poppy Way, Cupertino, CA 95014);
Martin; Kreg (19161 Cozette Ln., Cupertino, CA 95014);
Farmer; Dominic (1807 Golden Hills Dr., Milpitas, CA 95035)
|
| Appl. No.:
|
138767 |
| Filed:
|
August 24, 1998 |
| Current U.S. Class: |
375/150; 375/346 |
| Intern'l Class: |
H04K 001/00; H04L 025/08 |
| Field of Search: |
375/208,209,343,346,285,267,347
|
References Cited [Referenced By]
U.S. Patent Documents
| 4007330 | Feb., 1977 | Winters | 375/330.
|
| 4168529 | Sep., 1979 | Tomlinson | 364/715.
|
| 4203070 | May., 1980 | Bowles et al. | 375/317.
|
| 4203071 | May., 1980 | Bowles et al. | 375/343.
|
| 4608569 | Aug., 1986 | Dickey, Jr. et al. | 342/384.
|
| 4660164 | Apr., 1987 | Liebowitz | 364/728.
|
| 4862478 | Aug., 1989 | McIntosh | 375/200.
|
| 5091918 | Feb., 1992 | Wales | 375/11.
|
| 5101416 | Mar., 1992 | Fenton et al. | 375/1.
|
| 5164959 | Nov., 1992 | Cai et al. | 375/1.
|
| 5282228 | Jan., 1994 | Scott et al. | 375/344.
|
| 5390207 | Feb., 1995 | Fenton et al. | 375/1.
|
| 5402450 | Mar., 1995 | Lennen | 375/343.
|
| 5444451 | Aug., 1995 | Johnson et al. | 342/453.
|
| 5481503 | Jan., 1996 | Kuhn et al. | 367/100.
|
| 5488662 | Jan., 1996 | Fox et al. | 380/34.
|
| 5493588 | Feb., 1996 | Lennen | 375/343.
|
| 5495499 | Feb., 1996 | Fenton et al. | 375/205.
|
Other References
R. E. Ziemer & R. L. Peterson, Digital Communications and Spread Spectrum
Systems, MacMillan Publishing Company, New York 1985, pp. 149-447.
Alfred Leick, GPS Satellite Surveying, John Wiley & Son, New York, 2nd
Edition, 1995, and Ziemer and Peterson, op. cit.
W. M. Bowes, "Correlation Tracking," Charles Stark Draper Laboratory, May
1980.
|
Primary Examiner: Bocure; Tesfaldet
Attorney, Agent or Firm: Wagner, Murabito & Hao
Parent Case Text
This application is a divisional of 08/650,338 filed May 20, 1996.
Claims
We claim:
1. A method of formation of an autocorrelation difference function of an
incoming signal that reduces effects of presence of a multipath signal in
the incoming signal, the method comprising the steps of:
(1) receiving an incoming digital signal s(t) that can vary with the time t
and that has a digital signal bit period with a selected length
.DELTA..tau..sub.chip ;
(2) forming a first signal product difference
.DELTA.s.sub.1 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1(t+.tau.-t.sub.E ;qE)-s(t)S.sub.d
(t+.tau.-t.sub.L)w1(t+.tau.-t.sub.L ;qL),
where S.sub.d (t) is a selected reference signal, w1(t;q) is a first
selected, non-constant weighting signal that may depend upon one or more
parameters q, .tau. is a selected time shift, t.sub.E and t.sub.L are
first and second selected time values satisfying 0<t.sub.L -t.sub.E
<2.DELTA..tau..sub.chip ;
(3) forming a second signal product difference
.DELTA.s.sub.2 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1 (t+.tau.-t.sub.E ;qE)-s(t)S.sub.d (t+.tau.-t.sub.L)w1
(t+.tau.-t.sub.L ;qL),
where w1 (t;q) is a second selected weighting signal that may depend upon
one or more parameters q;
(4) selecting an integer n.gtoreq.2 and setting an accumulation A.sub.n-1
=0;
(5) examining the incoming digital signal bit value b.sub.n, for the time
interval defined by n.DELTA..tau..sub.chip
.ltoreq.t<(n+1).DELTA..tau..sub.chip, and the immediately preceding
digital bit value b.sub.n-1 of the reference signal S.sub.d (t);
(6) when b.sub.n-1 .noteq.b.sub.n, computing the contribution of the first
signal product difference over a time interval I.sub.n
={t'.vertline.t.sub.n-1 +.DELTA.<t'.ltoreq.t.sub.n +.DELTA.}, where
.DELTA. is a selected time value satisfying
0.ltoreq..DELTA.<.DELTA..tau..sub.chip, to an autocorrelation difference
function .DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and
adding this contribution to A.sub.n-1 to form A.sub.n ;
(7) when b.sub.n-1 =b.sub.n, computing the contribution of the second
signal product difference over the time interval I.sub.n to the
autocorrelation difference function .DELTA.AC#(.tau.;q) for the incoming
digital signal s(t), and adding this integral or sum to A.sub.n-1 to form
A.sub.n ;
(8) replacing the integer n by the integer n+1 and repeating steps (5), (6)
and (7) at least once;
(9) interpreting the accumulation A.sub.N for a selected positive integer N
as the autocorrelation difference function .DELTA.AC#(.tau.;q) for the
incoming digital signal s(t);
(10) determining at least one value t.sub.0 of the time shift variable
.tau. for which the autocorretation difference function
.DELTA.AC#(.tau.;q) changes sign; and
(11) interpreting the time value t=t.sub.0 as an estimate of the time at
which a signal, which is substantially free of the presence of a multipath
signal, was received.
2. The method of claim 1, further comprising the step of selecting at least
one of said weighting functions w1(t;q) and w1 (t;q) to be a notch
function.
3. The method of claim 1, further comprising the step of selecting at least
one of said weighting functions w1(t;q) and W1 (t;q) to be an anti-notch
function.
4. The method of claim 1, further comprising the step of selecting said
weighting function w1 (t;q) to be substantially zero everywhere.
5. A method of formation of an autocorrelation difference function of an
incoming signal that reduces effects of presence of a multipath signal in
the incoming signal, the method comprising the steps of:
(1) receiving an incoming digital signal s(t) that can vary with the time t
and that has a digital signal bit period with a selected length
.DELTA..tau..sub.chip ;
(2) forming a first signal product difference
.DELTA.s.sub.1 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1(t+.tau.-t.sub.E ;qE)-s(t)S.sub.d
(t.tau.-t.sub.L)w1(t+.tau.-t.sub.L ;qL),
where S.sub.d (t) is a selected reference signal, w1(t;q) is a first
selected, non-constant weighting signal that may depend upon one or more
parameters q, .tau. is a selected time shift, t.sub.E and t.sub.L are
first and second selected time values satisfying 0<t.sub.L -t.sub.E
<2.DELTA..tau..sub.chip ;
(3) forming a second signal product difference
.DELTA.s.sub.2 (t;.tau.;t.sub.E ; t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1 (t+.tau.-t.sub.E ;qE)-s(t)S.sub.d (t+.tau.-t.sub.L)w1
(t+.tau.-t.sub.L ;qL),
where w1 (t;q) is a second selected weighting signal that may depend upon
one or more parameters q;
(4) selecting an integer n.gtoreq.3 and setting an accumulation A.sub.n-1
=0;
(5) examining the incoming digital signal bit value b.sub.n, for the time
interval defined by n.DELTA..tau..sub.chip
.ltoreq.t<(n+1).DELTA..tau..sub.chip, and the two immediately preceding
digital bit values b.sub.n-1 and b.sub.n-2 of the reference signal S.sub.d
(t);
(6) when b.sub.n-2 =b.sub.n-1 and b.sub.n-1 .noteq.b.sub.n, computing the
contribution of the first signal product difference over a time interval
I.sub.n ={t'.vertline.t.sub.n-1 +.DELTA.<t' .ltoreq.t.sub.n +.DELTA.},
where .DELTA. is a selected time value satisfying
0.ltoreq..DELTA.<.DELTA..tau..sub.chip, to an autocorrelation difference
function .DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and
adding this contribution to A.sub.n-1 to form A.sub.n ;
(7) when b.sub.n-2 .noteq.b.sub.n-1 or b.sub.n-1 =b.sub.n, computing the
contribution of the second signal product difference over the time
interval I.sub.n to the autocorrelation difference function
.DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and adding this
integral or sum to A.sub.n-1 to form A.sub.n ;
(8) replacing the integer n by the integer n+1 and repeating steps (5), (6)
and (7) at least once;
(9) interpreting the accumulation A.sub.N for a selected positive integer N
as the autocorrelation difference function .DELTA.AC#(.tau.;q) for the
incoming digital signal s(t); and
(10) determining at least one value t.sub.0 of the time shift variable
.tau. for which the autocorrelation difference function
.DELTA.AC#(.tau.;q) changes sign; and
(11) interpreting the time value t=t.sub.0 as an estimate of the time at
which a signal, which is substantially free of the presence of a multipath
signal, was received.
6. The method of claim 5, further comprising the step of selecting at least
one of said weighting functions w1(t;q) and w1 (t;q) to be a notch
function.
7. The method of claim 5, further comprising the step of selecting at least
one of said weighting functions w1(t;q) and w1 (t;q) to be an anti-notch
function.
8. The method of claim 5, further comprising the step of selecting said
weighting function w1 (t;q) to be substantially zero everywhere.
9. Apparatus for formation of an autocorrelation difference function of an
incoming signal that reduces effects of presence of a multipath signal in
the incoming signal, the apparatus comprising:
a signal antenna that receives an incoming digital signal s(t) that can
vary with the time t and that has a digital signal bit period with a
selected length .DELTA..tau..sub.chip ;
a signal receiver/processor, including a computer, that generates a
selected digital reference signal S.sub.d (t), that examines a signal bit
value b.sub.n and the immediately preceding digital bit value b.sub.n-1 of
the reference signal S.sub.d (t), and that is programmed to:
(1) receive an incoming digital signal s(t) that can vary with the time t
and that has a digital signal bit period with a selected length
.DELTA.t.sub.chip ;
(2) form a first signal product difference
.DELTA.s.sub.1 (t;.tau.t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1(t+.tau.-t.sub.E ;qE)-s(t)S.sub.d
(t+.tau.-t.sub.L)w1(t+.tau.-t.sub.L ;qL),
where w1(t;q) is a first selected, non-constant weighting signal that may
depend upon one or more parameters q, .tau. is a selected time shift,
t.sub.E and t.sub.L are first and second selected time values satisfying
0<t.sub.L -t.sub.E <2.DELTA..tau..sub.chip ;
(3) form a second signal product difference
.DELTA.s.sub.2 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1 (t+.tau.-t.sub.E ;qE)-s(t)S.sub.d (t+.tau.-t.sub.L)w1
(t+.tau.-t.sub.L ;qL),
where w1 (t;q) is a second selected weighting signal that may depend upon
one or more parameters q;
(4) select an integer n.gtoreq.2 and set an accumulation A.sub.n-1 =0;
(5) examine the bit value b.sub.n, for a time interval defined by
n.DELTA..tau..sub.chip .ltoreq.t<(n+1).DELTA..tau..sub.chip, and the
immediately preceding bit value b.sub.n-1 of the reference signal S.sub.d
(t);
(6) when b.sub.n-1 .noteq.b.sub.n, compute the contribution of the first
signal product difference over the time interval I.sub.n
={t'.vertline.t.sub.n-1 +.DELTA.<t'.ltoreq.t.sub.n +.DELTA.}, where
.DELTA. is a selected time value satisfying
0.ltoreq..DELTA.<.DELTA..tau..sub.chip to an autocorrelation difference
function .DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and
adding this contribution to A.sub.n-1 to form A.sub.n ;
(7) when b.sub.n-1 =b.sub.n, compute the contribution of the second signal
product difference over the time interval I.sub.n to the autocorrelation
difference function .DELTA.AC#(.tau.;q) for the incoming digital signal
s(t), and adding this integral or sum to A.sub.n-1 to form A.sub.n ;
(8) replace the integer n by the integer n+1 and repeat steps (5), (6) and
(7) at least once;
(9) interpret the accumulation A.sub.N for a selected positive integer N as
the autocorrelation difference function .DELTA.AC#(.tau.;q) for the
incoming digital signal s(t);
(10) determine at least one value t.sub.0 of the time shift variable .tau.
for which the autocorrelation difference function .DELTA.AC#(.tau.;q)
changes sign; and
(11) interpret the time value t=t.sub.0 as an estimate of the time at which
a signal, which is substantially free of the presence of a multipath
signal, was received.
10. The apparatus of claim 9, wherein at least one of said weighting
functions w1(t;q) and w1 (t;q) used by said signal receiver/processor to
form said signal product is selected to be a notch function.
11. The apparatus of claim 9, wherein at least one of said weighting
functions w1(t;q) and w1 (t;q) used by said signal receiver/processor to
form said signal product is selected to be an anti-notch function.
12. The apparatus of claim 9, wherein said weighting function w1 (t;q) is
selected to be zero everywhere.
13. Apparatus for formation of an autocorrelation difference function of an
incoming signal that reduces effects of presence of a multipath signal in
the incoming signal, the apparatus comprising:
a signal antenna that receives an incoming digital signal s(t) that can
vary with the time t and that has a digital signal bit period with a
selected length .DELTA.t.sub.chip ;
a signal receiver/processor, including a computer, that generates a
selected digital reference signal S.sub.d (t), that examines a bit value
b.sub.n and the two immediately preceding digital bit values b.sub.n-1 and
b.sub.n-2 of the reference signal S.sub.d (t), and that is programmed to:
(1) receive an incoming digital signal s(t) that can vary with the time t
and that has a digital signal bit period with a selected length
.DELTA..tau..sub.chip ;
(2) form a first signal product difference
.DELTA.s.sub.1 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1(t+.tau.-t.sub.E ;qE)-s(t)S.sub.d
(t+.tau.-t.sub.L)w1(t+.tau.-t.sub.L ;qL),
where w1(t;q) is a first selected, non-constant weighting signal that may
depend upon one or more parameters q, .tau. is a selected time shift,
t.sub.E and t.sub.L are first and second selected time values satisfying
0<t.sub.L -t.sub.E <2.DELTA..tau..sub.chip ;
(3) form a second signal product difference
.DELTA.s.sub.2 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1 (t+.tau.-t.sub.E ;qE)-s(t)S.sub.d (t+.tau.-t.sub.L)w1
(t+.tau.-t.sub.L ;qL),
where w1'(t;q) is a second selected weighting signal that may depend upon
one or more parameters q;
(4) select an integer n.gtoreq.3 and set an accumulation A.sub.n-1 =0;
(5) examine the bit value b.sub.n, for the time interval defined by
n.DELTA..tau..sub.chip .ltoreq.t.ltoreq.(n+1).DELTA..tau..sub.chip, and
the two immediately preceding digital bit values b.sub.n-1 and b.sub.n-2
of the reference signal S.sub.d (t);
(6) when b.sub.n-2 =b.sub.n-1 and b.sub.n-1 .noteq.b.sub.n, compute the
contribution of the first signal product difference over a time interval
I.sub.n ={t'.vertline.t.sub.n-1 +.DELTA.<T'.ltoreq.t.sub.n +.DELTA.},
where .DELTA. is a selected time value satisfying
0.ltoreq..DELTA.<.DELTA..tau..sub.chip, to an autocorrelation difference
function .DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and
adding this contribution to A.sub.n-1 to form A.sub.n ;
(7) when b.sub.n-2 .noteq.b.sub.n-1 or b.sub.n-1 =b.sub.n, compute the
contribution of the second signal product difference over the time
interval I.sub.n to the autocorrelation difference function
.DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and adding this
integral or sum to A.sub.n-1 to form A.sub.n ;
(8) replace the integer n by the integer n+1 and repeat steps (5), (6) and
(7) at least once;
(9) interpret the accumulation A.sub.N for a selected positive integer N as
the autocorrelation difference function .DELTA.AC#(.tau.;q) for the
incoming digital signal s(t); and
(10) determine at least one value t.sub.0 of the time shift variable T for
which the autocorrelation difference function .DELTA.AC#(.tau.;q) changes
sign; and
(11) interpret the time value t=t.sub.0 as an estimate of the time at which
a signal, which is substantially free of the presence of a multipath
signal, was received.
14. The apparatus of claim 13, wherein at least one of said weighting
functions w1(t;q) and w1 (t;q) used by said signal receiver/processor to
form said signal product is selected to be a notch function.
15. The apparatus of claim 13, wherein at least one of said weighting,
functions w1(t;q) and w1 (t;q) used by said signal receiver/processor to
form said signal product is selected to be an anti-notch function.
16. The apparatus of claim 13, wherein said weighting function w1 (t;q) is
selected to be substantially zero everywhere.
17. A method of formation of an autocorrelation difference function of an
incoming signal that reduces effects of presence of a multipath signal in
the incoming signal, the method comprising the steps of:
(1) receiving an incoming digital signal s(t) that can vary with the time t
and that has a digital signal bit period with a selected length
.DELTA..tau..sub.chip ;
(2) forming a first signal product difference
.DELTA.s.sub.1' (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1(t+.tau.-t.sub.E ;qE)-s(t)S.sub.d
(t+.tau.-t.sub.L)w1(t+.tau.-t.sub.L ;qL),
where S.sub.d (t) is a selected reference signal, w1(t;q) is a first
selected, non-constant weighting signal that may depend upon one or more
parameters q and that is periodic with period equal to
.DELTA..tau..sub.chip, .tau. is a selected time shift, t.sub.E and t.sub.L
are first and second selected time values satisfying 0<t.sub.L -t.sub.E
<2.DELTA..tau..sub.chip ;
(3) forming a second signal product difference
.DELTA.s.sub.2 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1 (t+.tau.-t.sub.E ;qE)-s(t)S.sub.d (t+.tau.-t.sub.L)w1
(t+.tau.-t.sub.L ;qL),
where w1 (t;q;k) is a second selected weighting signal that may depend upon
one or more parameters q and that is periodic with period
k.DELTA..tau..sub.chip, where k is a selected integer .gtoreq.2;
(4) selecting an integer n.gtoreq.2 and setting an accumulation A.sub.n-1
=0;
(5) examining the incoming digital signal bit value b.sub.n, for the time
interval defined by n.DELTA..tau..sub.chip
.ltoreq.t.ltoreq.(n+1).DELTA..tau..sub.chip, and the immediately preceding
digital bit value b.sub.n-1 of the reference signal S.sub.d (t);
(6) when b.sub.n-1 .noteq.b.sub.n, computing the contribution of the first
signal product difference over a time interval I.sub.n
={t'.vertline.t.sub.n-1 +.DELTA.<t'.ltoreq.t.sub.n +.DELTA.}, where
.DELTA. is a selected time value satisfying
0.ltoreq..DELTA.<.DELTA..tau..sub.chip, to an autocorrelation difference
function .DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and
adding this contribution to A.sub.n-1 to form A.sub.n ;
(7) when b.sub.n-1 =b.sub.n, computing the contribution of the second
signal product difference over the time interval I.sub.n to an
autocorrelation difference function .DELTA.AC#(.tau.;q) for the incoming
digital signal s(t), and adding this integral or sum to A.sub.n-1 to form
A.sub.n ;
(8) replacing the integer n by the integer n+1 and repeating steps (5), (6)
and (7) at least once;
(9) interpreting the accumulation A.sub.N for a selected positive integer N
as an autocorrelation difference function .DELTA.AC#(.tau.;q) for the
incoming digital signal s(t);
(10) determining at least one value t.sub.0 of the time shift variable
.tau. for which the autocorrelation difference function
.DELTA.AC#(.tau.;q) changes sign; and
(11) interpreting the time value t=t.sub.0 as an estimate of the time at
which a signal, that is substantially free of the presence of a multipath
signal, was received.
18. A method of formation of an autocorrelation difference function of an
incoming signal that reduces effects of presence of a multipath signal in
the incoming signal, the method comprising the steps of:
(1) receiving an incoming digital signal s(t) that can vary with the time t
and that has a digital signal bit period with a selected length
.DELTA..tau..sub.chip ;
(2) forming a first signal product difference
.DELTA.s.sub.1 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1(t+.tau.-t.sub.E ;qE)-s(t)S.sub.d
(t+.tau.-t.sub.L)w1(t+.tau.-t.sub.L ;qL),
where S.sub.d (t) is a selected reference signal, w1(t;q) is a first
selected, non-constant weighting signal that may depend upon one or more
parameters q and that is periodic with period equal to
.DELTA..tau..sub.chip, .tau. is a selected time shift, t.sub.E and t.sub.L
are first and second selected time values satisfying 0<t.sub.L -t.sub.E
<2.DELTA..tau..sub.chip ;
(3) forming a second signal product difference
.DELTA.s.sub.2 (t;.tau.;t.sub.E ;t.sub.L ;qE;qL)=s(t)S.sub.d
(t+.tau.-t.sub.E)w1 (t+.tau.-t.sub.E)-s(t)S.sub.d (t+.tau.-t.sub.L)w1
(t+.tau.-t.sub.L ;qL),
where w1 (t;q;k) is a second selected weighting signal that may depend upon
one or more parameters q and that is periodic with period k.DELTA..tau.hd
chip, where k is a selected integer.gtoreq.2;
(4) selecting an integer n.gtoreq.3 and setting an accumulation A.sub.n-1
=0;
(5) examining the bit value b.sub.n, for the time interval defined by
n.DELTA..tau..sub.chip .ltoreq.t.ltoreq.(n+1).DELTA..tau..sub.chip, and
the two immediately preceding digital bit values b.sub.n-1 and b.sub.n-2
of the reference signal S.sub.d (t);
(6) when b.sub.n-2 =b.sub.n-1 and b.sub.n-1 .noteq.b.sub.n, computing the
contribution of the first signal product difference over a time interval
I.sub.n ={t'.vertline.t.sub.n-1 +.DELTA.<t'.ltoreq.t.sub.n +.DELTA.},
where .DELTA. is a selected time value satisfying
0.ltoreq..DELTA.<.DELTA..tau..sub.chip, to an autocorrelation difference
function .DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and
adding this contribution to A.sub.n-1 to form A.sub.n ;
(7) when b.sub.n-2 .noteq.b.sub.n-1 or b.sub.n-1 =b.sub.n, computing the
contribution of the second signal product difference over the time
interval I.sub.n to the autocorrelation difference function
.DELTA.AC#(.tau.;q) for the incoming digital signal s(t), and adding this
integral or sum to A.sub.n-1 to form A.sub.n ;
(8) replacing the integer n by the integer n+1 and repeating steps (5), (6)
and (7) at least once;
(9) interpreting the accumulation A.sub.N for a selected positive integer N
as the autocorrelation difference function .DELTA.AC#(.tau.;q) for the
incoming digital signal s(t); and
(10) determining at least one value t.sub.0 of the time shift variable
.tau. for which the autocorrelation difference function
.DELTA.AC#(.tau.;q) changes sign; and
(11) interpreting the time value t=t.sub.0 as an estimate of the time at
which a signal, that is substantially free of the presence of a multipath
signal, was received.
Description
FIELD OF THE INVENTION
This invention relates to a method for minimizing the deleterious effects
of multipath on incoming digital spread spectrum signals that are
encountered in signal receivers, using analysis of transitions of
consecutive bit values in the incoming signal.
BACKGROUND OF THE INVENTION
The effects of multipath are well known in communications systems.
Multipath is the term used to define the secondary signals that are
locally induced reflections of a primary signal that enter the receiver in
question a fraction of a second later than the direct path signal, and
because of the relatively short delay between the original signal and the
secondary signal, induce a type of destructive interference that results
in some type of impairment to the desired signal. In analog FM band
automobile receivers, the effects of multipath create an annoying flutter
that causes a loss of intelligibility. In television signals, the
impairment is called a "ghost" image. A similar impairment occurs in other
forms of analog communication. In digital systems, whether for speech or
for data transmission for other purposes, multipath basically adds noise
to the desired signal, resulting in either outright errors or at least,
much noisier data. In spread spectrum receivers, the effects of multipath
are generally found in the correlators used to achieve signal timing
synchronization. In GPS or GLONASS receivers, which seek to determine
location based on triangulation of range distances determined from time
delay measurements made from an orbiting constellation of satellites, the
effect of multipath is to induce comparatively large instantaneous errors
in the time of arrival measurements which translate into large errors in
the indicated positions. Removal of these errors is the subject of most of
the work done by previous workers in this field. Previous researchers have
sought to deal with the effects of multipath by attempting to estimate the
magnitude of the error introduced, and to subtract this error or to
otherwise compensate for its effects.
The methods employed to acquire and demodulate data from spread spectrum
transmissions is well known in the art. See R. E. Ziemer and R. L.
Peterson, Digital Communications and Spread Spectrum Systems, Macmillan
Publ Co., New York, 1985, pp. 419-447 for a discussion of acquisition and
demodulation of spread spectrum signals. A spread spectrum GPS receiver
must obtain both code and carrier synchronization in order to demodulate
the desired data successfully. Issues associated with tracking and
accurately demodulating a spread spectrum signal, once the signal is
acquired, are discussed in many references on GPS, such as Alfred Leick,
GPS Satellite Surveying, John Wiley & Sons, New York, Second Edition,
1995, and Ziemer and Peterson, op cit.
A GPS signal contains a 50 bit/second navigation message and a unique
spreading code (C/A) of length 1.023 kilobits, which is transmitted at a
frequency of about 1.023 Mbits/sec. Signal acquisition requires that phase
lock first occur with the radio frequency carrier and that the reference
or local replica signal be synchronized with the spreading code. In signal
synchronization, a local replica of the particular satellite code is
synchronized in time with the incoming satellite signal code.
Once the Doppler error in the downlink signal from the satellite is
appropriately compensated for and signal synchronization is obtained, the
navigation message in the 50 bit/second modulation that forms the
composite GPS signal (direct plus multipath) can be demodulated. This
navigation message contains data on the satellite ephemerides and time
pulses that indicate when the transmission originated from the satellite.
By measuring the difference between the local clock time and the indicated
satellite time of transmission, the time delay, and thus the instantaneous
distance from GPS receiver to satellite, can be obtained by multiplying
this time delay by the speed of light in the ambient medium.
Signal synchronization is performed using a signal correlator. The
correlator constantly compares the incoming signal with a local replica of
the desired signal; a microprocessor adjusts a time shift .tau. of the
local replica signal until satisfactory agreement is obtained. Because the
incoming signal and the local replica signal are substantially identical,
a measure of the degree of agreement of these two signals is often
referred to as an autocorrelation function. A variety of autocorrelation
functions AC(.tau.) are shown in various texts, and an example is shown in
FIG. 1A. An autocorrelation function AC(.tau.) can be described according
to one of the equations
##EQU1##
depending upon whether integration or summation of sampled values over a
suitable contribution time interval is used to compute the composite
signal autocorrelation function. The length T of the contribution time
interval used to compute the autocorrelation function in Eq. (1A) or (1B)
is often chosen to be N times the chip length .DELTA..tau..sub.chip, where
N is a large positive number.
Tracking the composite satellite signal requires maintaining signal
synchronization. The peak of the autocorrelation function is rounded, not
pointed, due to finite bandwidth effects, so that locating a true peak is
difficult. Receiver designers have, therefore, resorted to an
"early-minuslate" correlation tracking method, as discussed by W. M.
Bowles in "Correlation Tracking," Charles Stark Draper Laboratory, May
1980, by Fenton et al in U.S. Pat. No. 5,101,416, and by Lennen in U.S.
Pat. Nos. 5,402,450 and 5,493,588. In the early-minus-late tracking
method, a first correlator measures an equivalent autocorrelation function
when the local replica signal is shifted to an "early" time t.sub.E
relative to the position (.tau.=t.sub.P) of an ideal or punctual replica,
and a second correlator measures a second equivalent autocorrelation
function when the local replica signal is shifted to a "late" time
t.sub.L. Early and late replicas of the punctual autocorrelation function
AC(.tau.;P) are illustrated in FIG. 1B. By subtracting the late
autocorrelation function from the early autocorrelation function, a
correlation tracking function or autocorrelation difference function
.DELTA.AC(.tau.) with a zero crossing, corresponding to the
autocorrelation function peak can be developed, if the separations of the
early and late time shifts from the punctual time shift are chosen to be
equal. A representative early-minus-late tracking function
.DELTA.AC(.tau.) is shown in FIG. 1C.
If the tracking or time shift variable .tau. for the autocorrelation
difference function .DELTA.AC(.tau.) lies to the left (to the right) of
the zero crossing point, the system uses the presence of positive
(negative) values of .DELTA.AC(.tau.) to increase (decrease) the value of
.tau. and drive the system toward the zero crossing point for
.DELTA.AC(.tau.). The zero-crossing point is thus easily measured and
tracked, and the equivalent peak value and peak location for the
autocorrelation function is easily determined. At the zero-crossing point
on this doublet-like tracking function, maximum correlation occurs between
the incoming signal and the local replica signal. The zero-crossing point
represents the best estimate of time shift .tau. for signal
synchronization. The internal clock time corresponding to the zero
crossing point is a good estimate for time of arrival of an incoming
signal at the receiver.
Superposition of an equivalent autocorrelation function for the multipath
signal (reduced in magnitude and delayed in time) onto the autocorrelation
function AC(.tau.) for the desired satellite code signal is a useful model
for analyzing the effects of presence of multipath signals, as noted in
the Fenton et al patent and in the Lennen patent, op. cit. Superposition
of any additional signal onto the desired incoming signal, during the time
period when signal correlation occurs, will distort the desired
autocorrelation function AC(.tau.;direct) and produce an altered
autocorrelation function AC(.tau.;composite) for the composite signal
(direct plus multipath). An autocorrelation function for an uncorrupted or
"pure" direct signal is shown along with a representative, attenuated and
time delayed, multipath autocorrelation function with positive relative
polarity, compared to the direct signal, in FIG. 2A. The autocorrelation
for the composite, corrupted incoming signal is obtained by summing the
two autocorrelation functions and is compared with the uncorrupted
autocorrelation function in FIG. 2B. FIGS. 2C and 2D are similar graphs,
showing the autocorrelation function for a multipath signal with negative
relative polarity, compared to the direct signal. Any such distortion
produces errors in the indicated zero-crossing point on the
early-minus-late correlation tracking function. These errors in indicated
punctual time shift produce errors in the pseudorange measurements, and
will in turn produce an error in the final computed estimate of location
coordinates for the receiver.
Another useful and equivalent model for analyzing the effects of presence
of a multipath signal computes the autocorrelation functions
AC(.tau.;x;direct) and AC(.tau.;x;multipath) (x=E, L) for the pure direct
signal and the pure multipath signal, forms the differences
.DELTA.AC(.tau.;direct) and .DELTA.AC(.tau.;multipath) and adds these two
difference functions to obtain the autocorrelation difference function
.DELTA.AC(.tau.;composite) for the composite signal.
Representative autocorrelation difference functions for a direct incoming
signal and a composite incoming signal are shown in FIGS. 3B and 3D for
positive relative multipath polarity and negative relative multipath
polarity, respectively, compared to the direct signal. The tracking error
due to presence of the multipath signal, obtained from the difference in
zero crossing points for the direct signal and for the composite signal,
is easily seen from these figures.
Previous work in the area of multipath amelioration has focussed on two
approaches: 1) estimating the effects and compensating for
multipath-induced errors, and 2) attempting to limit the effects of the
estimated multipath errors. In the Lennen patents, op. cit., both
approaches are described. The estimation methods seek to model the
distortions to the instantaneous autocorrelation function and to create a
correction term to subtract from the indicated punctual time. Estimation
methods are worthwhile but can never obtain perfection, wherein all
multipath effects are removed, because the multipath signals are
constantly varying and corrections can only be done after the fact.
A multipath limitation method, such as described in the Lennen patent, op.
cit., operates the early-minus-late correlation tracking loop with a
shorter delay between the early signal and late signal correlators than
previous methods had employed. This limitation method reduces the effects
of the presence of multipath substantially. In FIGS. 1B and 1C, the
autocorrelation function AC(.tau.) and the corresponding tracking function
.DELTA.AC(.tau.) are shown for the case where the early-minus-late time
delay is approximately 0.15 times the width .DELTA..tau..sub.chip of a
digital signal bit or chip.
Several workers have analyzed correlation functions and/or have used
pseudorandom signal sequences in attempting to estimate or suppress the
effects of the presence of multipath signals. Examples of these are
Winters in U.S. Pat. No. 4,007,330, Tomlinson in U.S. Pat. No. 4,168,529,
Bowles et al in U.S. Pat. Nos. 4,203,070 and 4,203,071, Guignon et al in
U.S. Pat. No. 4,550,414, Dickey et al in U.S. Pat. No. 4,608,569,
Liebowitz in U.S. Pat. No. 4,660,164, Borth et al in U.S. Pat. No.
4,829,543, McIntosh in U.S. Pat. No. 4,862,478, Wales in U.S. Pat. No.
5,091,918, Fenton et al in U.S. Pat. Nos. 5,101,416, 5,390,207, 5,414,729
and 5,495,499, Cai et al in U.S. Pat. No. 5,164,959, Scott et al in U.S.
Pat. No. 5,282,228, Meehan in U.S. Pat. No. 5,347,536, Lennen in U.S. Pat.
Nos. 5,402,450 and 5,493,588, Johnson et al in U.S. Pat. No. 5,444,451,
Kuhn et al in U.S. Pat. No. 5,481,503, and Fox et al in U.S. Pat. No.
5,488,662.
In previous methods for multipath amelioration, samples are taken of the
incoming direct (desired) signal plus the incoming multipath signal(s)
over the entire width of the chip, using a uniform sampling rate and
without assigning any variable weighting to the samples. Further, little
or no account is taken of the effect of bit value transitions for
consecutive bits for the incoming digital signal. What is needed here is
an approach that obtains correlation information from portions of a chip
width where the effects of presence of multipath signals are suppressed,
by examining bit value transitions for consecutive bits for the incoming
digital signal and by use of this information to choose a (non-uniform)
weighting function for formation of a modified autocorrelation function
for the incoming digital signal. Preferably, the approach should be
adaptable to allow suppression of a controllable amount of multipath
signal contributions to the autocorrelation function and should continue
to provide tracking indicators that indicate the direction of time shift
required to achieve signal synchronization as the unit operates.
SUMMARY OF THE INVENTION
These needs are met by the invention, which provides a method that
dynamically changes the shape of a non-uniform weighting function w(t;q),
used to form an autocorrelation function for an incoming digital signal,
based on the relative values, b.sub.n-2, b.sub.n-1 and b.sub.n, of two or
three consecutive bits in a replica S.sub.d (t) of a digital bit sequence
representing the incoming digital direct signal, with multipath and noise
absent. Here q represents one or more parameters used to define the
weighting function w(t;q). A weighting function is chosen from among a
population of two or more such weighting functions to suppress or
de-emphasize the contributions of a multipath signal to an
early-minus-late autocorrelation difference function
.DELTA.AC(.tau.;q)=AC(.tau.;E;q)-AC(.tau.;L;q) in a selected region of the
time shift variable .tau.. In a first embodiment, the weighting function
chosen to form the autocorrelation functions AC(.tau.;x;q) (x=E, L) and
the difference function .DELTA.AC(.tau.;q) will vary with the relationship
between two consecutive bit values b.sub.n-1 and b.sub.n. If a bit value
transition occurs so that b.sub.n-1 .noteq.b.sub.n, a first weighting
function is used to form the autocorrelation difference function. If no
bit value transition occurs so that b.sub.n-1 =b.sub.n, a second weighting
function is used that suppresses the corresponding contribution of this
region of the time domain to the autocorrelation difference function
.DELTA.AC(.tau.;q). Using this approach, the noise contribution is
suppressed relative to the signal contribution so that the signal-to-noise
ratio (SNR) is enhanced.
In a second embodiment, the relationship between three consecutive bit
values b.sub.n-2, b.sub.n-1 and b.sub.n is examined. If b.sub.n-2
=b.sub.n-1 .noteq.b.sub.n, a first weighting function is used that
enhances the contribution of the direct signal and/or reduces the
contribution of a multipath signal that may be present in the composite
signal; and if b.sub.n-2 .noteq.b.sub.n-1, or if b.sub.n-1 =b.sub.n, or if
both of these conditions occur, a second weighting function is chosen that
suppresses the contribution of this portion of the time domain to the
autocorrelation difference function .DELTA.AC(.tau.;q). With this
approach, the contribution of a multipath signal to the autocorrelation
difference function is suppressed. The choice of weighting function thus
varies dynamically as the bit values of two consecutive bit values, or
three consecutive bit values, change.
In a third embodiment, if a bit value transition occurs so that b.sub.n-1
.noteq.b.sub.n, a first weighting function is used to form the
autocorrelation difference function; and if no bit value transition occurs
so that b.sub.n-1 =b.sub.n, a second weighting function, related to the
first weighting function but with changed periodicity, is used to form the
autocorrelation difference function.
In a fourth embodiment, if b.sub.n-2 =b.sub.n-1 .noteq.b.sub.n, a first
weighting function is used to form the autocorrelation difference
function; and if b.sub.n-2 .noteq.b.sub.n-1 and/or b.sub.n-1 =b.sub.n, a
second weighting function, related to the first weighting function but
with changed periodicity, is used to form the autocorrelation difference
function.
The invention begins with the realization, utilized in a companion patent
application, U.S. Ser. No. 08/650,331, by the title "Suppression of
Multipath Signal Effects", filed May 20, 1996 and assigned to the same
assignee, that the useful information to be obtained from the incoming
digital composite signal is available primarily in digital signal bit
value transition regions, where the bit value for the incoming digital
direct signal S.sub.d (t) changes state. Contributions from samples that
contain no useful information, but that do contain multipath signal
effects that produce erroneous distortions in the corresponding
autocorrelation function and in the resulting correlation tracking
function, are ignored or suppressed. By ignoring or suppressing the
contribution of samples taken in regions where no transition in a signal
bit value can occur, the receiver can suppress the effects of multipath
signals. The portion of a chip width where the autocorrelation difference
function .DELTA.AC(.tau.;q) is substantially zero is much larger than in
any of the previous methods for ameliorating the presence of multipath
signals. Previous methods produced wider regions of non-zero
.DELTA.AC(.tau.;q) for the desired signal. The invention, which may be
characterized as non-uniform weighting of the sampling function used to
create AC(.tau.;x;q), provides a method for substantially eliminating the
possibility for experiencing multipath effects in correlation tracking.
A tracking point or zero-crossing point .tau.=t.sub.P associated with the
difference .DELTA.AC(.tau.) of the autocorrelation functions AC(.tau.;E)
and AC(.tau.;L) is determinable as before, but with reduced contributions
from the direct signal and from the multipath signal in a selected central
region that does not include the tracking point .tau.=t.sub.P. This
central region does not include any time shift values t for which the
instantaneous value of a reference or local replica digital direct signal
S.sub.d (t+.tau.) can make a signal bit value transition (from 0 to 1, or
from 1 to 0) relative to the instantaneous value of an incoming digital
composite signal s(t). Thus, little or no qualitative information is lost
by de-emphasizing the contribution of this central region to a
corresponding autocorrelation function. However, much of the important
information arising from presence of the multipath signal is also present
in this central region, and this multipath information is suppressed or
de-emphasized by suppressing the contribution of this central region to
the autocorrelation function. Location of the "true" tracking point for
the direct signal (absent multipath) is unchanged or is changed only
minimally by this approach; the contribution of the multipath signal in
the selected central region is reduced to substantially zero.
The invention in the related patent application, 08/650,331, suppresses the
contribution of a central region to the computed autocorrelation function
AC(.tau.;x;qx) (x=E, P or L) for the composite signal by imposing a
non-uniform weighting function w(t;q) in the integral or sum of the
digital signal product s(t)S.sub.d (t+.tau.) over a chosen time interval
t1.ltoreq.t.ltoreq.t2, to produce an adjusted or modified autocorrelation
function. In one embodiment, the weighting function w(t;q) is positive (or
negative) in signal bit value transition regions (t.apprxeq.t1 and
t.apprxeq.t2=t1+.DELTA..tau..sub.chip) and tends monotonically toward zero
as .tau. approaches an intermediate time t3 (t1<t3<t2) from either side;
this type of non-uniform weighting function is referred to as a "notch"
function. The chip half-width .DELTA..tau..sub.chip /2=(t2-t1)/2 might be
chosen to be the inverse of twice the carrier frequency, (2
f.sub.carrier).sup.-1, associated with the reference digital signal
S.sub.d (t). The contributions of different portions of the "contribution
interval", t1<t<t2, are weighted non-uniformly to reduce the effects of a
multipath signal in a central region surrounding a tracking point, as
discussed above. In another embodiment, the weighting function w(t;q) is
chosen to be an "anti-notch" function, which is defined as a constant
minus a notch function. In another embodiment, the weighting function
w(t;q) is unrestricted and may have positive, zero and negative values
anywhere in the interval t1<t<t2.
One embodiment of the invention disclosed and claimed in this patent
application improves the analysis of the autocorrelation functions
AC(.tau.;x;qx) (x=E, P or L) and of the autocorrelation difference
function .DELTA.AC(.tau.;q) by providing at least two distinct weighting
functions W1(t;q) and W1#(t;q), at least one of which is non-uniform, and
by selecting which weighting function will be used at a given time to
compute AC(.tau.;x;qx) and .DELTA.AC(.tau.;q) based upon characteristics
of two, three or more consecutive incoming digital signal bit values,
b.sub.n-2, b.sub.n-1 and b.sub.n. In a first embodiment, if no bit
transition occurs between bit value b.sub.n-1 and bit value b.sub.n, the
contribution to the autocorrelation function AC(.tau.;x;qx) of the time
interval t.apprxeq.t.sub.n (corresponding to the bit region where
b.sub.n-1 changes to b.sub.n) is ignored or drastically suppressed, by use
of a different weighting function than the weighting function used if
b.sub.n-1 .noteq.b.sub.n. In a second embodiment, if (1) no bit value
transition occurred between bit value b.sub.n-2 and bit value b.sub.n-1
(b.sub.n-2 =b.sub.n-1) and (2) a bit value transition occurs between bit
value b.sub.n-1 and bit value b.sub.n (b.sub.n-1 .noteq.b.sub.n), a first
weighting function w1(t;q) is used to compute the autocorrelation
functions AC(.tau.;x;qx) (x=E, L) and the autocorrelation difference
function .DELTA.AC(.tau.). If either or both of these two conditions is
not both met, a second weighting function w1 (t;q) (which may be
identically zero) is used to compute the autocorrelation functions
AC(.tau.;x;qx) and the autocorrelation difference function
.DELTA.AC(.tau.;q). One result of this approach is that the contribution
of any multipath signal that may be present in a composite signal (direct
plus multipath) is further suppressed.
Another embodiment of the invention provides a method for decoding a signal
to reduce signal distortion, using the steps of: (1) receiving a signal
having at least two consecutive bits, with each bit having a value that is
represented in the received signal over a time interval; (2) generating a
reference signal having at least two consecutive bits, for matching the
received signal; (3) generating a weighting signal, having an amplitude
that varies over time, that conforms to (a) a first sequence of weighting
values when each bit of a consecutive bit sequence of the reference signal
is part of a predetermined bit sequence and (b) a second sequence of
weighting values when at least one bit of a consecutive bit sequence of
the reference signal is not part of a predetermined bit sequence; and (4)
mixing the received signal, the reference signal and the weighting signal
to determine a timing relationship between the received signal and the
reference signal.
In addition, the first and second sequences of weighting values can be
represented in the weighting signal over a selected time interval having a
length that is less than the length of the time interval (one chip) for
representing one of the bit values, and the selected time interval can be
begun a selected time increment before the beginning of a respective time
interval for each reference signal bit.
In one version, a reference signal bit sequence having two consecutive bits
is examined. The first sequence of weighting values is used when the two
consecutive bits have different bit values, and the second sequence of
weighting values is used when the two consecutive bits have the same bit
value.
In another version, a reference signal bit sequence having three
consecutive bits is examined. The first sequence of weighting values is
used when (i) the first and second consecutive bits of a three-bit
sequence have the same bit value and (ii) the third consecutive bit in the
three-bit sequence has a different bit value. The second sequence of
weighting values is used when at least one of the conditions (i) and (ii)
for use of the first sequence of weighting values is not satisfied.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A and 1B are graphical views of a representative autocorrelation
function AC(.tau.;x) (x=P, E, L).
FIG. 1C is a graphical view of an early-minus-late autocorrelation function
difference signal .DELTA.AC(.tau.)=AC(.tau.;E)-AC(.tau.;L) formed from the
autocorrelation functions shown in FIG. 1B. In all early-minus-late
autocorrelation difference functions shown herein, unless otherwise
stated, the early-minus-late spacing .DELTA.t.sub.L-E =t.sub.L -t.sub.E is
15 percent of the chip width .DELTA..tau..sub.chip for definiteness. Other
values for .DELTA.t.sub.L-E can be used here.
FIGS. 2A and 2B compare an autocorrelation function AC(.tau.;direct),
formed using only a direct signal, with an autocorrelation function
AC(.tau.;multipath) and AC(.tau.;composite), respectively, where the
multipath signal included in the composite signal has positive polarity
relative to the direct signal.
FIGS. 2C and 2D compare an autocorrelation function AC(.tau.;direct),
formed using only a direct signal, with an autocorrelation function
AC(.tau.;multipath) and AC(.tau.;composite), respectively, where the
multipath signal included in the composite signal has negative polarity
relative to the direct signal.
FIGS. 3A and 3B compare an autocorrelation difference function
.DELTA.AC(.tau.;direct), formed using only a direct signal, with an
autocorrelation difference function .DELTA.AC(.tau.;multipath) and
.DELTA.AC(.tau.;composite), respectively, where the multipath signal in
the composite signal has positive polarity relative to the direct signal.
FIGS. 3C and 3D compare an autocorrelation difference function
.DELTA.AC(.tau.;direct), formed using only a direct signal, with an
autocorrelation difference function .DELTA.AC(.tau.;multipath) and
.DELTA.AC(.tau.;composite), respectively, where the multipath signal in
the composite signal has negative polarity relative to the direct signal.
FIGS. 4B and 4C are graphical views of punctual (P), early (E) and late (L)
autocorrelation functions AC0(.tau.;x) and of an early-late
autocorrelation difference function .DELTA.AC0(.tau.), computed
conventionally. FIG. 4A illustrates a uniform weighting function w0=1.
FIGS. 5B and 5C are graphical views comparing an autocorrelation function
AC1(.tau.;x;qx) (x=E, P or L) and an early-late autocorrelation difference
function .DELTA.AC1(.tau.;q), computed using a non-uniform weighting
function (two-value step function) w1 shown in FIG. 5A, with AC0(.tau.;x)
and .DELTA.AC0(.tau.;x). FIG. 5D illustrates a multi-interval weighting
function.
FIGS. 6-16 illustrate other non-uniform weighting functions that can be
used with the invention to suppress or to emphasize multipath effects.
FIGS. 17A and 17B show representative autocorrelation difference functions,
before and after application of the invention, respectively.
FIGS. 18A, 18B, 18C, 18D and 18E illustrate a weighting function for noise
reduction according to the invention.
FIG. 19 is a flow chart of one embodiment of a suitable procedure according
to the invention.
FIG. 20 is a flow chart of a second embodiment of a suitable procedure
according to the invention.
FIGS. 21 and 23 are schematic views of approaches suitable for implementing
the two-consecutive-bit and the three-consecutive-bit procedures,
respectively.
FIGS. 22A-22E and 24A-24L are timing diagrams for signals produced by the
apparati in FIGS. 21 and 23, respectively.
FIG. 25 is a schematic view of other apparatus for practising the
invention.
FIG. 26 illustrates an apparatus suitable for implementing a
two-consecutive-bit procedure according to the invention, using readily
available digital signal processor chips.
FIG. 27A is a graphical view of early and late replicas of a direct digital
signal.
FIG. 27B is a graphical view of early and late replicas of a direct digital
signal, time delayed relative to the signals shown in FIG. 27A.
FIG. 27C is a graphical view of early and late replicas of a direct digital
signal, time advanced relative to the signals shown in FIG. 27A.
FIGS. 27D and 27E are graphical views of early and late weighting functions
obtained from combining uniformly weighted correlators.
FIG. 28 illustrates another apparatus suitable for implementing a
two-consecutive-bit procedure according to the invention.
DESCRIPTION OF BEST MODES OF THE INVENTION
In a conventional approach, no variable weighting is used in computing the
autocorrelation function. Equivalently, the weighting function applied to
the integrand or summand is constant: w0(t)=g (constant)>0, with g=1
preferred, across the contribution interval, for example, t.sub.P
-.DELTA..tau..sub.chip /2.ltoreq.t.ltoreq.t.sub.P +.DELTA.96 .sub.chip /2,
as illustrated in FIG. 4A. The quantity .DELTA..tau..sub.chip is the
temporal length of one bit in the incoming digital signal of interest. An
autocorrelation function .DELTA.C0(.tau.), computed without a variable
weighting function, has small or vanishing values outside the interval
t.sub.P -.DELTA..tau..sub.chip .ltoreq.t.ltoreq.t.sub.P
+.DELTA..tau..sub.chip, due to the properties of pseudorandom sequences
that are used for the direct signal. As the autocorrelation displacement
variable .tau. increases from .tau.=t.sub.P -.DELTA..tau..sub.chip to
.tau.=t.sub.P +.DELTA..tau..sub.chip, the autocorrelation function
increases approximately linearly to a maximum value at a tracking point
.tau..apprxeq.t.sub.P, then decreases approximately linearly beyond the
tracking point (FIG. 1A). This conventional approach is equivalent to
using the uniform weighting function w0(t), shown in FIG. 4A, in computing
a conventional autocorrelation function AC0(.tau.;x) (x=E, P or L), shown
in FIG. 4B, and in computing a conventional early-minus-late
autocorrelation difference function .DELTA.AC0(.tau.), illustrated in FIG.
4C. The time shift values .tau.=t.sub.E and .tau. =t.sub.L chosen for the
approximate peak values of the replica autocorrelation functions
AC0(.tau.;x) (x=E or L) satisfy the constraints t.sub.P
-.DELTA..tau..sub.chip <t.sub.E <t.sub.P <t.sub.L <t.sub.P
+.DELTA..tau..sub.chip, where .tau.=t.sub.P is the time shift value for
the actual peak in the measured autocorrelation function. The time shift
values .tau.=t.sub.E and .tau.=t.sub.L may be, but need not be, chosen
symmetrically about time shift value .tau.=t.sub.P.
Assume that a multipath signal S.sub.m (t;.DELTA.t.sub.m) is present, with
a time delay .DELTA.t.sub.m and reduced in magnitude relative to the
direct signal S.sub.d (t), in the incoming digital composite signal
s(t)=S.sub.d (t)+S.sub.m (t;.DELTA.t.sub.m). The time-delayed and
reduced-amplitude multipath signal S.sub.m
(t;.DELTA.t.sub.m).apprxeq..chi.S.sub.d (t-t.sub.P -.DELTA.t.sub.m)
(.vertline..chi..vertline.<1) is also summed across the contribution time
interval in formation of the autocorrelation signal AC(.tau.;x) (x=E, P or
L). Because of linear superposition, the multipath signal S.sub.m
(t;.DELTA.t.sub.m) contributes a proportional amount (reduced in amplitude
and delayed in time as indicated) to the early and late autocorrelation
functions AC(.tau.;E) and AC(.tau.;L) and to the difference function
.DELTA.AC(.tau.)=AC(.tau.;E)-AC(.tau.;L) for the incoming digital
composite signal s(t). Typical multipath signal contributions to
AC(.tau.;x) (x=E, L) are illustrated in FIGS. 2A, 2B, 2C and 2D.
The polarity of a multipath signal S.sub.m (t.DELTA.t.sub.m) that is part
of an incoming digital composite signal may be positive or negative
relative to the desired digital direct signal S.sub.d (t). A multipath
signal with positive relative polarity will add to the direct signal
contribution to the autocorrelation function for a composite signal. FIGS.
2A and 2C compare the autocorrelation function AC(.tau.;x;direct) with the
multipath-only functions AC(.tau.;x;multipath;positive) and
AC(.tau.;x;multipath;negative) for a "bare" multipath signal having
positive and negative multipath relative polarity, respectively. A
multipath signal with positive (negative) multipath relative polarity will
add to (subtract from) the direct signal contribution in the
autocorrelation function AC(.tau.;x;composite). FIGS. 2B and 2D compare
the autocorrelation function .DELTA.AC(.tau.;x;direct) with the respective
composite signal functions AC(.tau.;x;composite;positive) and
.DELTA.AC(.tau.;x;composite;negative).
Because the effects of presence of a multipath signal are additive, one can
analyze the autocorrelation difference functions by using the sum
.DELTA.AC(.tau.;direct)+.DELTA.AC(.tau.;multipath) or by forming the sum
composite signal=direct signal+multipath signal before the autocorrelation
difference function .DELTA.AC(.tau.;composite) is computed.
FIGS. 3A and 3C graphically illustrate the autocorrelation difference
functions .DELTA.AC(.tau.;direct) (solid curve) and
.DELTA.AC(.tau.;multipath) (broken line curve) for two representative
situations, using the constant weighting function w0(t)=1 in FIG. 4A,
where the multipath signal has positive and negative relative polarity,
respectively. FIGS. 3B and 3D graphically compare .DELTA.AC(.tau.;direct)
and .DELTA.AC(.tau.;composite) for positive and negative relative
multipath polarity, respectively. Note that the apparent tracking or zero
crossing point, where .DELTA.AC(.tau.;composite) for the composite signal
is shifted to the right (t.sub.P+) or to the left (t.sub.P-) relative to
the desired tracking point .tau.=t.sub.P for the direct signal, depending
in part on the relative multipath polarity.
In one embodiment of the invention, illustrated in FIGS. 5A, 5B and 5C, a
non-uniform weighting function w1(t;g1;t1';t2') is used that may be
continuous or discontinuous and is not necessarily symmetric. The
endpoints t1 and t2 of the time interval used for definition of the
weighting function, such as w1(t;g1;t1';t2'), satisfy the constraints
t1.apprxeq.t.sub.P, (2A)
t2=t1+.DELTA..tau..sub.chip, (2B)
For notational convenience herein, a set of weighting function parameters,
such as g1, t1' and t2' for a non-uniform weighting function, such as w1,
will often be denoted by a symbol "q". With this notation adopted, this
weighting function becomes w1(t;q). In FIG. 5A, the weighting function
w1(t;q) is a two-value step function that is non-zero only in regions near
t=t.sub.P, and near t =t.sub.P +.DELTA..tau..sub.chip. In a center region,
away from the tracking points .tau.=t.sub.P and .tau.=t.sub.P
+.DELTA..tau..sub.chip, where no signal bit transition can occur, little
or no new qualitative information is presented, and use of a non-uniform
weighting function w1(t;q) suppresses or de-emphasizes this largely
redundant information, as discussed above.
A weighting function, such as w1(t;q), is preferably extended periodically,
using a prescription such as
w1(t;q)=w1(t+n .DELTA..tau..sub.chip ;q) (n=0,.+-.1,.+-.2, . . . ).(3)
Where non-uniform weighting is used, an autocorrelation function is formed
according to one of the prescriptions
##EQU2##
depending upon whether integration or summation of sampled values over a
suitable contribution time interval is used to compute the composite
autocorrelation function. The length T of the time interval used to
compute the weighted autocorrelation function in Eq. (4A) or (4B) is often
chosen to be N times the chip length .DELTA..tau..sub.chip, where N is a
large positive integer.
FIG. 5B compares the approximate forms of the conventional punctual
autocorrelation function AC0(.tau.;P), which uses a constant weighting
function (w0(t)=1), with an adjusted punctual autocorrelation function
AC1(.tau.;x;q) (x=P), which uses the non-uniform weighting function
w1(t;q). The early and late autocorrelation functions AC1(.tau.;E;q) and
AC1(.tau.;L;q) are formed in a similar manner and have the same shape as
the punctual autocorrelation function AC1(.tau.;P;q).
FIG. 5C illustrates the approximate form of the autocorrelation difference
function .DELTA.AC1(.tau.;q)=AC1(.tau.;E;q)-AC1(.tau.;L;q), which should
be compared with the corresponding autocorrelation function difference
.DELTA.AC0(.tau.), shown in FIG. 4C and repeated as a dashed line curve in
FIG. 5C, that uses a uniform weighting function w0(t)=1. The spacing
intervals .DELTA.t.sub.P-E =t.sub.P -t.sub.E and .DELTA.t.sub.L-P =t.sub.L
-t.sub.P are selected to be equal in each of FIGS. 4C and 5C. If the time
shift variable .tau. for the autocorrelation difference function
.DELTA.AC1(.tau.;q) lies a small amount to the left (to the right) of the
peak correlation location .tau.=t.sub.P or zero crossing value, the
tracking system uses the presence of positive (negative) values of
.DELTA.AC1(.tau.;q) near this peak correlation location to increase
(decrease) the value of the shift variable .tau. and drive the
autocorrelation function AC1(.tau.;x;q) toward its peak correlation value,
where .DELTA.AC1(.tau.;q)=0.
More generally, a non-uniform weighting function w1'(t;g1;t1';t2';t2"; . .
. ; tn';tn";t(n+1)') that has a sequence of steps of equal amplitude (=g1)
in the time intervals t1<t<t1', tk'<t<tk" (k=3, . . . , Q; Q.gtoreq.3) and
t2'<t<t2, illustrated in FIG. 5D, can be used here.
Where the non-zero amplitudes of the steps are equal, as in FIG. 5A or 5D,
use of a non-uniform weighting function, such as w1(t;q) or w1'(t;q), is
equivalent to use of non-uniform sampling density in forming the
autocorrelation function AC(.tau.;q) in Eq. (4A) or (4B). In this
non-uniform sampling approach, samples of incoming digital signal values
in the regions t1 <t<t1', tk'<t<tk" and t2'<t<t2 are given a uniform,
non-zero weight g, and samples in all other regions are assigned a weight
of zero. Alternatively, non-uniform weighting and non-uniform sampling may
be combined to compute an autocorrelation function.
Other suitable non-uniform weighting functions w(t;q), each having one or
more parameters q to define the function, are illustrated in FIGS. 6-16.
Each of the weighting functions w2(t;q) and w3(t;q) in FIGS. 6 and 7 is a
three-step weighting function, with amplitudes g1, g2 and g3, with one of
these amplitudes being zero in FIG. 6. FIG. 8 illustrates a five-step
weighting function w4(t;q). FIGS. 9 and 10 illustrate a triangular
weighting function w5(t;q) and a power law weighting function w6(t;q),
respectively. FIGS. 11 and 12 illustrate a first situation in which the
weighting functions w7(t;E;q) and w7(t;L;q), used to form the
autocorrelation functions AC(.tau.;E) and AC(.tau.;L), are chosen
independently. FIGS. 5-12 illustrate non-uniform weighting functions
wm(t;q) (m=1, 2, . . . , 7) that are "notch" functions. A "notch" function
has positive values w(t1;q) and w(t2;q) at the two ends of the defining
interval t1.ltoreq.t.ltoreq.t2 and decreases monotonically toward zero as
the time variable t approaches some intermediate value t3
(t1.ltoreq.t3.ltoreq.t2) from either direction within the defining time
interval.
Each of FIGS. 13 and 14 illustrates a non-uniform weighting function,
w8(t;q) and w9(t;q), that is an "anti-notch" function, having the form
w(t;q)=g0 -w(t;q;notch), where g0 is a constant and w(t;q;notch) is a
notch function. An anti-notch function can be used to emphasize, rather
than suppress, multipath effects in some situations.
FIG. 15 illustrates another suitable non-uniform weighting function
w10(t;q) that is neither a notch function nor an anti-notch function. The
non-uniform weighting function w(t;q) need not be non-negative everywhere
on the defining interval t1.ltoreq.t.ltoreq.t2. FIG. 16 illustrates a
suitable non-uniform weighting function w11(t;q) that is positive in some
regions and negative in some other regions of the defining interval.
In the preceding analysis, the correlator spacings .DELTA.t.sub.P-E
=t.sub.P -t.sub.E and .DELTA.t.sub.L-P =t.sub.L -t.sub.P have been chosen
to be equal, for definiteness, but this is not required. It is generally
required here that 0<.DELTA.t.sub.L-E =.DELTA.t.sub.P-E +.DELTA.t.sub.L-P
<2.DELTA..tau..sub.chip.
A multipath signal S.sub.m (t;.DELTA.t.sub.m), if it is present in an
incoming digital composite signal s(t), usually arrives "late," that is,
after the direct signal S.sub.d (t) has begun to arrive. FIG. 17A shows an
autocorrelation difference function .DELTA.AC(.tau.;q), using the
weighting function w1(t;q) shown in FIG. 5A, before application of the
invention. Ideally, after application of the invention .DELTA.AC(.tau.;q)
appears as in FIG. 17B, where the "early spike" ES has been removed, and
only the "late spike" LS (which is irrelevant and thus ignored) and the
"central spike" CS remain. This is accomplished in the invention by
dynamically changing the weighting function used to compute the
autocorrelation functions AC(.tau.;x;qx), depending upon the
characteristics of a portion of the incoming digital signal that is
presently arriving.
Comparison of consecutive incoming digital signal bit values is useful in
reducing the noise associated with computation of the autocorrelation
function and the autocorrelation difference function. Where two
consecutive incoming digital signal bit values, such as b.sub.n-1 and
b.sub.n, differ from each other, a bit value transition has occurred, and
useful information is present that is needed to maintain tracking of the
incoming digital signal: the signal bit values near t=t.sub.P for both
bits should be sampled. Where two consecutive signal bit values coincide,
no transition has occurred and no additional useful information is
present. Sampling the bit signal values near t=t.sub.P for both bits in
this situation will merely introduce additional noise into the
computations. A digital direct signal S.sub.d (t), such as the one shown
in FIG. 18A, represents the baseband incoming digital direct signal. In
FIG. 18A, a bit value transition for S.sub.d (t) occurs near t=t1 but does
not occur near t=t2. The non-zero step, of amplitude g1, for the
non-uniform weighting function w1(t;q) is two clock pulses wide and
overlaps the time interval endpoints t=t1 and t=t2=t1+.DELTA.t.sub.chip,
as shown in FIG. 18B. A sequence of clock pulses with pulse-to-pulse
separation .DELTA.t(clock) (usually<.DELTA..tau..sub.chip) is shown in
FIG. 18C. The weighting function w1(t;q) is superimposed on each of an
early replica and a late replica of the digital direct signal S.sub.d
(t+.tau.) in FIGS. 18D and 18E, where the correlator spacings satisfy
.DELTA.t.sub.P-E=.DELTA.t.sub.L-P .ltoreq..DELTA.t(clock)/2. The weighting
function w1(t;q) overlaps the early replica signal domain in the time
intervals A1 and B1 and overlaps the late replica signal domain in the
time intervals B1 and C1, where a bit value transition occurs in the bit
sequence for the incoming digital direct signal S.sub.d (t). The periodic
extension of the weighting function w1(t;q) overlaps the early replica
signal domain in the time intervals A2 and B2 and overlaps the late
replica signal domain in the time intervals B2 and C2, where no bit value
transition occurs in the bit sequence for the incoming digital direct
signal S.sub.d (t). Let EA and EB (A=A1, A2; B=B1, B2) denote the sampled
value of the early replica signal S.sub.d (t+.tau.-t.sub.E) in the time
intervals A and B, and let LB and LC (B=B1, B2; C=C1, C2) denote the
sampled value of the late replica signal S.sub.d (t+.tau.-t.sub.L) in the
time intervals B and C. Let IA, IB and IC denote the bit values of the
incoming digital direct signal S.sub.d (t) in the time intervals A, B and
C, respectively.
The contributions to the autocorrelation difference function
.DELTA.AC1(.tau.;q) of the early and late replica signals in the regions
A1, B1 and C1 are
.DELTA.s=g1 EA1 IA1+g1 EB1 IB1-g1 LB1 IB1-g1 LC1 IC1. (5)
If noise is absent, the value of .DELTA.s is zero if the system is tracking
perfectly. However, if the system is not tracking perfectly, the value of
.DELTA.s will be positive or negative. The net result from the difference
function formed in Eq. (5) is a positive or negative contribution to
.DELTA.AC1(.tau.;q) from the time intervals A1, B1 and C1 and will
indicate whether the value of the tracking variable .tau. should be
increased or decreased to drive the value .DELTA.s=.DELTA.s(.tau.) toward
zero.
The contributions to the autocorrelation difference function
.DELTA.AC1(.tau.;q) of the early and late replica signals in the regions
A2, B2 and C2 are
.DELTA.s=g1 EA2 IA2+g1 EB2 IB2-g1 LB2 IB2-g1 LC2 IC2=0, (6)
because no bit value transition occurs in the incoming digital direct
signal S.sub.d (t), and thus in the early and late replica signals, in any
of the time intervals A2, B2 and C2. The net result from the difference
.DELTA.s formed in Eq. (6) is zero contribution to .DELTA.AC1(.tau.;q)
from the time intervals A2, B2 and C2. However, noise will contribute to
each of the differences formed in Eqs. (5) and (6). For these reasons, if
tracking is not perfect, the non-zero contribution of the difference in
Eq. (5) to .DELTA.AC1(.tau.;q), where a bit value transition occurs in the
incoming digital direct signal S.sub.d (t), should be included in the
computation, but the net zero contribution of the difference in Eq. (6)
should not be included. Thus, for narrow correlator spacings, if the
contribution of noise to a modified autocorrelation difference function
.DELTA.AC1#(.tau.;q) is to be minimized, the signal product difference
.DELTA.s.sub.E-L (t)=w1(t+.tau.-t.sub.E ;q)s(t)S.sub.d
(t+.tau.-t.sub.E)-w1(t+.tau.-t.sub.L ;q)s(t)S.sub.d (t+.tau.-t.sub.L),(7)
which contributes to the integral or sum used to compute the
autocorrelation difference function .DELTA.AC1#(.tau.;q), should be
included near a possible signal bit value transition point t.apprxeq.t1 or
t.apprxeq.t2 only if the bit value transition for the incoming digital
direct signal S.sub.d (t) satisfies
.DELTA.b.sub.n =1, (8)
for the incoming digital signal at or near that time point, where the bit
value change function .DELTA.b.sub.n is defined by
##EQU3##
One method of insuring that the contribution of the signal product
difference .DELTA.s.sub.E-L to the autocorrelation difference function
.DELTA.AC1#(.tau.;q) is included only from regions where an incoming
digital direct signal bit value transition occurs, is to use the weighting
function
w(t.sub.n ;q)=w1(t.sub.n ;q) if .DELTA.b.sub.n =1, (10A)
w(t.sub.n ;q)=w1 (t.sub.n ;q) if .DELTA.b.sub.n =0, (10B)
where w1 (t;q) is a selected weighting function that is different from
w1(t;q) and that suppresses the contribution of the signal product
difference .DELTA.s.sub.E-L in the time interval t.sub.n
-.DELTA..tau..sub.chip /2.ltoreq.t<t.sub.n +.DELTA..tau..sub.chip /2. One
suitable choice is w1 (t;q)=0. This approach will minimize the noise
contribution from any region that does not affect location of the zero
crossing or tracking point for the autocorrelation difference function
.DELTA.AC1(.tau.;q).
FIG. 19 is a flow chart illustrating suitable procedural steps that can be
taken for analysis of an incoming digital signal according to one
embodiment of the invention. In step 140, the incoming digital composite
signal s(t) is received. In step 141, a replica of the expected bit
sequence for the incoming digital direct signal S.sub.d (t) is generated.
In step 142, two consecutive signal bits, with signal bit values b.sub.n-1
and b.sub.n, are received and examined for the digital direct signal
S.sub.d (t). In step 143, the bit value change function .DELTA.b.sub.n is
computed. In step 145, the system determines whether .DELTA.b.sub.n =1. If
.DELTA.b.sub.n =1, a first non-uniform weighting function W1(t;q) is used
to compute a contribution to the autocorrelation function AC1#(.tau.;x;qx)
(x=E, P or L) and to an autocorrelation difference function
.DELTA.AC1#(.tau.;q), in step 147, by integration or summation of the
quantities W1(t+.tau.-t.sub.E ;q)s(t)S.sub.d (t+.tau.-t.sub.E) and
W1(t+.tau.-t.sub.L ;q)s(t)S.sub.d (t+.tau.-t.sub.L) over a time interval
I.sub.n, of length .DELTA..tau..sub.chip and defined by
I.sub.n ={t.vertline.t.sub.n-1 +.DELTA.<t.ltoreq.t.sub.n +.DELTA.},(11)
where .DELTA. is a selected time value satisfying
0.ltoreq..DELTA.<.DELTA..tau..sub.chip. If .DELTA.b.sub.n =0, a second
weighting function W1 (t;q) (not necessarily non-uniform) is used to form
a contribution to the autocorrelation function AC1#(.tau.;x;qx) (x=E, P or
L) and the autocorrelation difference function .DELTA.AC1#(.tau.;q), in
step 149, by integration or summation of the quantities W1
(t+.tau.-t.sub.E ;q)s(t)S.sub.d (t+.tau.-t.sub.E) and W1 (t+.tau.-t.sub.L
;q)s(t)S.sub.d (t+.tau.-t.sub.L) over the time interval I.sub.n.
Comparison of consecutive incoming digital direct signal bit values is also
useful in suppressing the multipath signal contribution in computation of
the autocorrelation function and the autocorrelation difference function.
Where three consecutive incoming digital direct signal bit values,
b.sub.n-2, b.sub.n-1 and b.sub.n, satisfy the conditions b.sub.n-2
=b.sub.n-1 .noteq.b.sub.n, a bit value transition (b.sub.n-1
.fwdarw.b.sub.n) has occurred, and useful information is present that is
needed to maintain tracking of the incoming digital signal: signal bit
values for both bits should be sampled. Where b.sub.n-1 =b.sub.n, no
transition has occurred and no additional useful information is present.
Sampling the bit signal values for both bits in this situation will merely
introduce additional noise into the computations. Where b.sub.n-2
.noteq.b.sub.n-1, a bit value transition in the multipath signal, delayed
in time by approximately .DELTA..tau..sub.chip relative to a bit value
transition in the corresponding digital direct signal, will appear near
the bit value transition point t=t.sub.n. Sampling the bit signal values
for both bits in this situation will introduce additional multipath noise
into the computations. The analysis is similar to the analysis associated
with FIGS. 18A-18E. Table 1 indicates the eight possibilities for three
consecutive bit values, b.sub.n-2, b.sub.n-1 and b.sub.n, for an incoming
digital direct signal, where b.sub.n is the present bit value and the two
consecutive preceding bits (having values b.sub.n-2 and b.sub.n-1) have
already arrived at the signal receiver.
TABLE 1
______________________________________
Bit Value Transitions
(n-2)-to-(n-1) bit
(n-1)-to-n bit
Weighting
b.sub.n-2
b.sub.n-1
b.sub.n
transition occurs
transition occurs
used
______________________________________
0 0 0 No No w1
0 0 1 No Yes w1
0 1 0 Yes Yes w1
0 1 1 Yes No w1
1 0 0 Yes No w1
1 0 1 Yes Yes w1
1 1 0 No Yes w1
1 1 1 No No w1
______________________________________
Here, w1(t;g1;t1';t2') is the weighting function shown in FIG. 5A, or some
other suitable non-uniform weighting function, and w1 A(t;q) is an
alternative weighting function (e.g., w1 (t;q)=0). Other choices of the
weighting function w1 (t;q) can be used.
One motivation for this approach is as follows. If a multipath signal
S.sub.m (t;.DELTA.t.sub.m), with corresponding time delay .DELTA.t.sub.m,
is present in the incoming digital composite signal s(t), this multipath
signal will contribute significantly to computation of an autocorrelation
difference function .DELTA.AC#(.tau.;q) only if the multipath signal delay
time satisfies .vertline..DELTA.t.sub.m
.vertline..ltoreq..DELTA..tau..sub.chip +.DELTA.t.sub.L-E /2, where
.DELTA.t.sub.L-E =.DELTA.t.sub.P-E +.DELTA.t.sub.L-P. If
.vertline..DELTA.t.sub.m .vertline.>.DELTA..tau..sub.chip
+.DELTA.t.sub.L-E /2, this multipath signal contributes nothing to
computation of an autocorrelation difference function .DELTA.AC#(.tau.;q),
because of the nature of pseudorandom sequences.
If a bit value transition has not occurred at an immediately preceding bit
value transition time (i.e., b.sub.n-2 =b.sub.n-1, or .DELTA.b.sub.n-1 =0)
and a bit value transition occurs at the present bit value transition time
(i.e., b.sub.n-1 .noteq.b.sub.n, b.sub.n , or .DELTA.b.sub.n =1), the
contribution of this time interval I.sub.n is emphasized by using the
weighting function w1(t;q) to compute the autocorrelation function
AC#(.tau.;x;qx). If a bit value transition has occurred at the immediately
preceding bit value transition time (t=t.sub.n-1, where .DELTA.b.sub.n-1
=1), a multipath signal S.sub.m (t;.DELTA.t.sub.m) with an associated time
delay .DELTA.t.sub.m .apprxeq..DELTA..tau..sub.chip will arrive near the
current bit value transition interval (t.apprxeq.t.sub.n). In this
situation, the contribution of this current bit value transition interval
I.sub.n to the autocorrelation function AC#(.tau.;x;qx) should be
de-emphasized to de-emphasize the signal information arising from the
multipath signal bit value transition (with the associated time delay
.DELTA.t.sub.m .apprxeq..DELTA.t.sub.chip). Here, de-emphasis is achieved
by using the weighting function w1 (t;q)=0. However, any other weighting
function w1 (t;q) that substantially reduces the contribution of the
associated time interval I.sub.n to AC#(.tau.;x;qx) (x=E, L) and/or to
.DELTA.AC#(.tau.;q) can be used in place of the weighting function w1
(t;q)=0. Representative autocorrelation difference functions,
.DELTA.AC(.tau.;q) and .DELTA.AC#(.tau.;q), which would be obtained before
and after application of this process, are shown in FIGS. 17A and 17B,
respectively.
A formally equivalent approach for identifying the bit value transitions of
interest in Table 1 uses the bit value change function .DELTA.b.sub.n
defined in Eq. (9), for the incoming digital signal. The weighting
function used for computation of the autocorrelation function
AC#(.tau.;x;qx) is selected to be w1(t;q) if
B.sub.n =(.DELTA.b.sub.n-1)*.multidot..DELTA.b.sub.n =1, (12A)
and is selected to be w1 (t) if
B.sub.n =(.DELTA.b.sub.n-1)*.multidot..DELTA.b.sub.n =0, (12B)
where b* is the Boolean complement for the binary value b (=0 or 1).
The weighting function w1(t;g1;t1',t2') shown in FIG. 5A can be replaced by
any other suitable non-uniform weighting function W1(t;q), such as
w2(t;q), w3(t;q), w4(t;q), w5(t;q), w6(t;q), w7(t;q), w8(t;q), w9(t;q),
w10(t;q), and w11(t;q) shown in FIGS. 6, 7, 8, 9, 10, 11/12, 13, 14, 15
and 16, respectively. The weighting function w1 (t;q) can be replaced by
any other weighting function W1 (t;q) that de-emphasizes the corresponding
contribution to the autocorrelation function.
FIG. 20 is a flow chart illustrating suitable procedural steps that can be
taken for analysis of an incoming digital signal according to one
embodiment of the invention. In step 120, the incoming digital composite
signal s(t) is received. In step 121, a replica of the incoming digital
direct signal S.sub.d (t) is generated. In step 122, three consecutive
signal bits, with signal bit values b.sub.n-2, b.sub.n-1 and b.sub.n, are
received for the digital direct signal S.sub.d (t). In step 123, the value
of the Boolean function B.sub.n
=(.DELTA.b.sub.n-1)*.multidot..DELTA.b.sub.n is determined. In step 125,
the system determines whether B.sub.n =1. If B.sub.n =1, a first
non-uniform weighting function W1(t;q) is used to form a contribution to
the autocorrelation function AC1#(.tau.;x;q) (x=E, P or L) and to the
autocorrelation difference function .DELTA.AC1#(.tau.;q), in step 127, by
integration or summation of the quantities W1(t+.tau.-t.sub.E
;q)s(t)S.sub.d (t+.tau.-t.sub.E) and W1(t+.tau.-t.sub.L ;q)s(t)S.sub.d
(t+.tau.-t.sub.L) over the time interval I.sub.n. If B.sub.n =0, a second
weighting function W1 (t;q) (uniform or non-uniform) is used to form a
contribution to the autocorrelation function AC1#(.tau.;x;q) (x=E, P or L)
and the autocorrelation difference function .DELTA.AC1#(.tau.;q), in step
129, by integration or summation of the quantities W1 (t+.tau.-t.sub.E
;q)s(t)S.sub.d (t+.tau.-t.sub.E) and W1 (t+.tau.-t.sub.E ;q)s(t)S.sub.d
(t+.tau.-t.sub.L) over the time interval I.sub.n.
As a third embodiment, an alternative or adjunct to dynamically changing
the weighting function w(t;q) according to the relative bit values
b.sub.k-2, b.sub.k-1 and b.sub.k (or b.sub.k-1 and b.sub.k) of the
incoming digital signal, the periodicity M.sub.k of the weighting function
W1(t;q) can be changed dynamically. This alternative is implemented as
follows. For any particular time t.apprxeq.t.sub.k, the periodicity of the
weighting function W1(t;q) is defined by
W1(t;q)=W1(t+n M.sub.k .DELTA..tau..sub.chip ;q) (n=0,.+-.1,.+-.2, . . .
),(13)
where M.sub.k is a positive or negative integer that may vary with the time
interval (t.apprxeq.t.sub.k) within which the time variable t is found.
Where .DELTA.b.sub.k =1 (first embodiment) or B.sub.k =1 (second
embodiment), the choice M.sub.k =1 is appropriate in Eq. (13); when
.DELTA.b.sub.k =0 (first embodiment) or B.sub.k =0 (second embodiment),
the choice .vertline.M.sub.k .vertline.>1 is appropriate. In both
situations, the same weighting function, such as w1(t;q) shown in FIG. 5A,
is used, but with two or more different periodicities.
Implementation
FIG. 21 illustrates apparatus for implementation of a first embodiment,
wherein presence of a bit value transition (b.sub.n-1 .noteq.b.sub.n)
determines whether or not a time interval I.sub.n, of length
.DELTA..tau..sub.chip and including the bit value transition time
t=t.sub.n, is included in the computation for the autocorrelation function
AC1#(.tau.;x;qx). A periodic clock pulse signal is provided on a first
signal line 161, and a code signal, Code(t;.tau.)=S.sub.d (t+.tau.), is
provided on a second signal line 163. Optionally, the clock pulse signal
can be passed through a divide-by-N module 162 that issues a clock pulse
after the module 162 has received N consecutive clock pulses on the first
signal line 161.
The clock signal is received at the clock input terminal, denoted CLK, of
each of a plurality of time delay or "D" flipflops 165, 167, 169, 171, 173
and 175, with the code signal Code(t;.tau.) being received at the D input
terminal of the first flipflop 165. An output signal issues from the Q
terminal of the D fliptlops 165, 167 and 169 and is received at the D
input terminals of the D flipflops 167, 169 and 171, respectively. The
output signals from the Q output terminals of the D flipflops 167, 169 and
171 are denoted "E", "P" and "L", respectively. The code signal and the
output signal from the Q output terminal of the flip flop 171 are received
at two input terminals of an EXclusive OR ("XOR") gate 177. The output
signal Code(t;.tau.).sym.L(t) from the XOR gate 177 is received at the D
input terminal of the flipflop 173 and also serves as a gating signal,
denoted "EG." The output signal from the Q output terminal of the flip
flop 173 is received at the D input terminal of the flipflop 175, and the
output signal from the flipflop 175 serves as a second gating signal,
denoted "LG." The gating signals EG(t) and LG(t) serve as enable signals
for the early and late correlation signals, respectively. That is, if the
enable signal is low or "false," the correlator does not accumulate the
present contribution to the autocorrelation function AC1#(.tau.;q); and if
the enable signal is high or "true," the correlator does accumulate the
present contribution to the autocorrelation function AC1#(.tau.;q). The
various output signals from the flipflops and the XOR gate 177 can be
expressed mathematically by the relations
E(t)=Code(t-2.DELTA.t;.tau.), (14B)
L(t)=Code(t-4.DELTA.t;.tau.), (14C)
EG(t)=XOR(t)=Code(t;.tau.).sym.L(t), (14D)
LG(t)=XOR(t-2.DELTA.t), (14E)
where Code(t;.tau.) is the instantaneous signal that appears on the code
line 163 and .DELTA.t=.DELTA.t(clock) is the minimum period of the clock
pulse appearing on the clock line 161. Table 2 sets forth the output
signal values of the flipflops and the XOR gate for some sequences of code
signals.
TABLE 2
______________________________________
Output Signals For Two-consecutive-bit Scheme
Code(t;.tau.)
E(t) P(t) L(t) XOR(t) = EG(t)
LG(t)
______________________________________
0 0 0 0 0 0
1 0 0 0 1 0
1 0 0 0 1 0
1 1 0 0 1 1
1 1 1 0 1 1
1 1 1 1 0 1
1 1 1 1 0 1
1 1 1 1 0 0
. . .
0 1 1 1 1 0
0 1 1 1 1 0
0 0 1 1 1 1
0 0 0 1 1 1
0 0 0 0 0 1
0 0 0 0 0 1
0 0 0 0 0 0
. . .
1 0 0 0 1 0
______________________________________
The notation ". . ." indicates that the present line in Table 2 will be
identical to the preceding line, unless and until the code signal
Code(t;.tau.) changes.
Returning to FIG. 21, a digital computer C1 receives the clock pulse
signals on the signal line 161 and receives the signals E(t)=S.sub.d
(t+.tau.-t.sub.E), L(t) =S.sub.d (t+.tau.-t.sub.L), EG(t) and LG(t). A
memory for the computer C1 contains a weighting functions w(t;E;qE) and
w(t;L;qL), which may be the same or may differ from each other. The
computer C1 provides a sequence of two or more sampling times t=t.sub.k
(k=1, 2, 3, . . . ) for an incoming signal that has been frequency
converted to baseband, s(t). For a given sampling time t=t.sub.k, the
computer C1 examines the incoming signals EG(t.sub.k) and LG(t.sub.k). If
the value of EG(t.sub.k) is high, the computer computes a first signal
product w(t.sub.k +.tau.;E;qE)S.sub.d (t.sub.k +.tau.)s(t.sub.k) and adds
this to a first accumulated integral or sum that will become the early
autocorrelation function AC(.tau.;E;qE), when fully accumulated. If the
value of EG(t.sub.k) is low, the value 0 is added to the first accumulated
integral or sum for the sampling time t.sub.k. If the value of LG(t.sub.k)
is high, the computer computes a second signal product w(t.sub.k
+.tau.;L;qL)S.sub.d (t.sub.k +.tau.)s(t.sub.k) and adds this to a second
accumulated integral or sum that will become the late autocorrelation
function AC(.tau.;L;qL), when fully accumulated. If the value of
LG(t.sub.k) is low, the value 0 is added to the second accumulated
integral or sum for the sampling time t.sub.k. The computer C1 computes
the difference .DELTA.AC(.tau.;qE;qL)=AC(.tau.;L;qL)-AC(.tau.;E;qE) and
determines a value .tau.=t0 for which .DELTA.AC(t0;qE;qL) changes sign or
passes through the value 0. The computer C1 interprets the value t0 as a
time at which the desired signal S.sub.d (t), relatively free of the
presence of any accompanying multipath signals, arrived at the signal
antenna or receiver.
FIGS. 22A, 22B, 22C, 22D and 22E are contemporaneous timing diagrams
illustrating how the apparatus shown in FIG. 21 operates where a bit value
transition (0.fwdarw.1) occurs at a time t=t.sub.n (b.sub.n-1
.noteq.b.sub.n), where a second bit value transition (1.fwdarw.0) occurs
at a second time t=t.sub.n+1 (b.sub.n .noteq.b.sub.n+1), and where a bit
value transition does not occur at a third time t=t.sub.n+2 (b.sub.n+1
=b.sub.n+2). In FIG. 22A, a bit value transition in the code signal
Code(t;.tau.) occurs at time t=t.sub.n. An early replica signal E(t) and a
late replica signal L(t), corresponding to the bit value transition at
t=t.sub.n, change from 0 (or low) to 1 (or high) at times
t.apprxeq.t.sub.n +2.DELTA.t and t.apprxeq.t.sub.n +4.DELTA.t,
respectively, as shown in FIGS. 22B and 22C. The signal EG(t)=XOR(t) shown
in FIG. 22D changes from 0 to 1 at a time t.apprxeq.t.sub.n and changes
from 1 to 0 at a time t.apprxeq.t.sub.n +4.DELTA.t, when the signal L(t)
changes from 0 to 1, assuming that the code signal Code(t;.tau.) has not
changed in the time interval t.sub.n .ltoreq.t<t.sub.n +4.DELTA.t. The
early gating signal EG(t) thus acts as an enable signal for the early
signal correlation and is high (EG(t)=1) only during the time interval
t.sub.n .ltoreq.t<t.sub.n +4.DELTA.t. In a similar manner, the late gating
signal LG(t), shown in FIG. 22E, acts as an enable signal for the late
signal correlation and is high only during the time interval t.sub.n
+2.DELTA.t.ltoreq.t<t.sub.n +6.DELTA.t. For ease of illustration, it is
assumed that t.sub.n+1 -t.sub.n >4.DELTA.t here.
At a second time t=t.sub.n+1, the code signal Code(t;.tau.) changes from 1
to 0, as shown in FIG. 22A. The early replica signal E(t) and the late
replica signal L(t) change from 1 to 0 at the times t=t.sub.n+1 +2.DELTA.t
and t=t.sub.n+1 +4.DELTA.t, as shown in FIGS. 22B and 22C, respectively.
The early gating signal EG(t) and the late gating signal LG(t), shown in
FIGS. 22D and 22E, respectively, become high only during the time
intervals t.sub.n+1 <t.ltoreq.t.sub.n+1 +4.DELTA.t and t.sub.n+1
+2.DELTA.t<t.ltoreq.t.sub.n+1 +6.DELTA.t, respectively. The early gating
signal EG(t) and the late gating signal LG(t) thus serve as enable signals
for the early signal correlation and the late signal correlation, whenever
the signal Code(t;.tau.) changes from 0 to 1 or from 1 to 0.
At a third time t=t.sub.n+2 the code signal Code(t;.tau.) does not change,
as shown in FIG. 22A, over a time interval of length, say, greater than
4.DELTA.t. During this last time interval, Code(t;.tau.), E(t) and L(t)
have the same value (0 or 1) so that XOR(t)=Code(t;.tau.).sym.L(t) is 0
over this time interval, as are the gating signals EG(t) and LG(t). The
early and late enable signals remain low (0) in this situation, as should
occur where no bit value transition occurs.
FIG. 23 illustrates apparatus for implementation of the second (three-bit
transition) embodiment, wherein the value of B.sub.n
=(.DELTA.b.sub.n-1)*.multidot..DELTA.b.sub.n determines whether or not the
interval I.sub.n is included in the computation for the autocorrelation
function AC1#(.tau.;x;qx). A periodic clock pulse signal is provided on a
first signal line 191, and a code signal, Code(t;.tau.)=S.sub.d (t+.tau.),
is provided on a second signal line 193. The clock signal is received at
the clock input terminal, denoted CLK, of each of a plurality of time
delay or "D" flipflops 195, 197, 199, 201, 203, 205 and 213 and at a JK
flipflop 211. The code signal is received at the D input terminal of the
first flipflop 195. An output signal issues from the Q terminal of the D
flipflops 195, 197 and 199 and is received at the D input terminals of the
D fliptlops 197, 199 and 201, respectively. The output signals from the Q
output terminals of the D fliptlops 197, 199 and 201 are denoted "E", "P"
and "L", respectively. Optionally, a divide-by-N module 192 is included
for the clock pulse signals.
The code signal and the output signal from the Q output terminal of the
flip flop 201 are received at two input terminals of an EXclusive OR
("XOR") gate 207. The output signal Code(t;.tau.).sym.L(t) from the XOR
gate 207 is received at the D input terminal of the flipflop 203. The
output signal from the Q output terminal of the flip flop 203 is received
at the D input terminal of the flipflop 205. The output signal from the
flipflop 203 is also received and inverted at a first input terminal of an
AND gate 209. The output signal from the flipflop 205 is received at a
second input terminal of the AND gate 209. The output signal from the AND
gate 209 is received at the "J" input terminal of a JK flipflop 211, and
the "K" input terminal receives a CCOTO signal, which is discussed below.
The output signal from the JK flipflop 211 is received at the D input
terminal of a D flipflop with enable 213 (referred to here as a D/EN
flipflop).
The output signal from the XOR gate 207 and the inverted output signal from
the flipflop 213 are received at two input terminals of an AND gate 215,
whose output signal is a first gating signal, denoted "EG." The output
signal from the flipflop 205 and the inverted output signal from the
flipflop 213 are received at two input terminals of an AND gate 217, whose
output signal is a second gating signal, denoted "LG." A table of value
assignments similar to that shown in Table 2 is easily set down for the
apparatus in FIG. 23.
FIGS. 24A-24L are contemporaneous timing diagrams illustrating how the
apparatus shown in FIG. 23 operates where a bit value transition (0
.fwdarw.1 or 1.fwdarw.0) occurs in the code signal Code(t;.tau.) at times
t=t.sub.n (b.sub.n-1 .noteq.b.sub.n), t=t.sub.n+1 (b.sub.n
.noteq.b.sub.n+1), t=t.sub.n+3 (b.sub.n+2 .noteq.b.sub.n+3) and
t=t.sub.n+4 (b.sub.n+3 .noteq.b.sub.n+4), and does not occur at times
t=t.sub.n+2 (b.sub.n+1 =b.sub.n+2) and t=t.sub.n+5 (b.sub.n+4 =b.sub.n+5),
as shown in FIG. 24A. For ease of illustration, it is assumed that
t.sub.n+1 -t.sub.n =.DELTA.t.sub.chip >6.DELTA.t. FIG. 24B illustrates the
signal CCOTO(t), which is defined by
##EQU4##
The CCOTO signal goes high one clock pulse interval before each chip
transition time occurs (at t=t.sub.r -.DELTA.t), for one clock pulse
interval, and is low at all other times. This particular choice is used
for illustrative purposes in FIGS. 23 and 24B. Other choices of the CCOTO
signal can also be used, with appropriate changes in the apparatus shown
in FIG. 23. The signals
##EQU5##
are shown in FIGS. 24C-24L, respectively. The functions F.sub.J,K (f(t),
g(t)) and F.sub.D,EN (f(t), g(t)) are determined by the output signals for
the JK flipflop 211 and for the D/EN flipflop 213, viz.
##EQU6##
The timing diagrams shown in FIGS. 24A-24L can be verified by analysis
similar to that employed for FIGS. 22A-22E. The gating signal EG(t) is
high, indicating enablement, only for times in the interval t.sub.n+3
.ltoreq.t.ltoreq.t.sub.n+3 +4.DELTA.t, which includes the only code signal
transition point (t=t.sub.r with r=n+3) for which B.sub.r
=(.DELTA.b.sub.r-1)*.multidot..DELTA.b.sub.r =1 in FIG. 24A; that is,
B.sub.n =B.sub.n+1 =B.sub.n+2 =B.sub.n+4 =B.sub.n+5 =0 in FIG. 24A.
Similarly, the gating signal LG(t) is high, indicating enablement, only
for times in the interval t.sub.n+3 +2.DELTA.t.ltoreq.t.ltoreq.t.sub.n+3
+6.DELTA.t.
Returning to FIG. 23, a computer C2 receives the clock pulse signals on the
signal line 191 and receives the signals E(t)=S.sub.d (t+.tau.-t.sub.E),
L(t)=S.sub.d (t+.tau.-t.sub.L), EG(t) and LG(t). The computer C2 provides
the weighting functions w(t;E;qE) and w(t;L;qL). forms the first and
second signal products w(t.sub.k +.tau.;E;qE)S.sub.d (t.sub.k
+.tau.)s(t.sub.k) and w(t.sub.k +.tau.;L;qL)S.sub.d (t.sub.k
+.tau.)s(t.sub.k), computes the first and second accumulations
AC(.tau.;E;qE) and AC(.tau.;L;qL), forms the accumulation difference
.DELTA.AC(.tau.;qE;qL), determines a time shift value .tau.=t0 at which
the accumulation difference changes sign, and interprets the value t0
exactly as does the computer C1 in FIG. 21.
FIG. 25 illustrates more general apparatus for implementation of the
various embodiments of the invention. An incoming composite signal is
downconverted from an intermediate frequency to a baseband signal and
converted to an incoming, digital composite signal s(t), using carrier
signal mixing in a baseband conversion module 261, in a well known manner.
The incoming digital composite signal s(t) is despread, using code phase
mixing to form an early signal product s(t)S.sub.d (t.tau.-t.sub.E) in an
early signal despread module 263, and using code phase mixing to form a
late signal product s(t)S.sub.d (t+.tau.-t.sub.L) in a late signal
despread module 265. An early weighting function w(t;E;qE) is combined
multiplicatively with the early signal product to form a weighted early
signal product w(t+.tau.-t.sub.E ;E;qE)s(t)S.sub.d (t+.tau.-t.sub.E) in an
early weighting module 267, and an early signal correlation function is
formed in an early correlator 269. A late weighting function w(t;L;qL) is
combined multiplicatively with the late signal product to form a weighted
late signal product w(t+.tau.-t.sub.L ;L;qL)s(t)S.sub.d (t+.tau.-t.sub.L)
in a late weighting module 271, and a late signal correlation function is
formed in a late correlator 273. The early and late correlation signals
are received by a computer 275 that determines the direction the time
shift variable .tau. should move to drive the system toward the zero
crossing or tracking point. The time shift adjustment information is fed
back to the early and late signal despread modules 263 and 265 and to the
early weighting and late weighting modules 267 and 271, for use in forming
an adjusted early signal product and an adjusted late signal product, and
is fed back to the baseband conversion module 261.
FIG. 26 illustrates another apparatus 280 for implementing the invention,
where the choice of weighting function is based upon the values of two
consecutive bits, b.sub.n-1 and b.sub.n, in the reference signal, using
readily available digital signal processor chips. The apparatus 280
includes a first channel 281A, a second channel 281B and a computer 283
and uses weighting functions W1(t;q) such as are shown in FIGS. 5A, 6, 27D
and 27E, with W1 (t;q)=0. The apparatus 280 uses early and late weighting
functions W(t;E;qE) and W(t;L;qL), which may be the same or may be
different, having non-zero values only near the two ends of a time
interval width t1.ltoreq.t <t2, with periodic extensions as discussed
above. The weighting functions W(t;E;qE) and W(t;L;qL) may be chosen, for
example, to be step functions as shown in FIGS. 27D and 27E, with the same
or different step function widths and the same or different step function
gains or amplitudes.
Each channel 281z (z=A, B) has a code phase NCO and generator 285z whose
output signal is received by the first of a sequence of three D flipflops
287z, 289z and 291z, each with an associated time delay .DELTA.t(clock).
An incoming signal I(t) is received by a first input terminal of a first
signal multiplier 293z. A second input terminal of the signal multiplier
293z receives a carrier signal from a carrier phase NCO 295z that is
controlled by signals received from the computer 283. The carrier signal
mixes with the incoming signal to produce a baseband signal. The output
signal from the first signal multiplier 293z is received by first input
terminals of second and third signal multipliers 297z and 299z. Second
input terminals of the signal multipliers 297z and 299z receive the output
signals from the first and third D flipflops 287z and 291z, respectively.
Output signals from the signal multipliers 297z and 299z are received by
an early signal correlator module 301z and a late signal correlator module
303z, respectively. Output signals from the early signal correlator module
301z and late signal correlator module 303 are received by the computer
283 to vary the time shift variable .tau. that is part of the reference
signal S.sub.d (t+.tau.) received from the code phase NCO and generator
285z. The code phase NCO 285z, the D flipflops 287z, 289z and 291z, the
carrier phase NCO 295z, the early signal correlator module 301z and the
late signal correlator module 303z are all driven by a master clock 305.
The D flipflop clock signals are optionally passed through a divide-by-Nz
module 307z as shown, where NA and NB are independently selectable
positive integers The carrier phase NCOs 295A and 295B are run
identically. The clock pulse width is .DELTA.t(clock).
In one preferred embodiment, the code phase NCO 285B in the second channel
281B has a selected positive time delay .DELTA.t(B-A)=.tau..sub.B
-.tau..sub.A >0 relative to the code phase NCO 285A in the first channel
281A, as indicated by a comparison of FIGS. 27A and 27B. In another
preferred embodiment, the code phase NCO 285B in the second channel 281B
has a selected negative time delay .DELTA.t(B-A)=.tau..sub.B -.tau..sub.A
<0 (that is, an advancement) relative to the code phase NCO 285A in the
first channel 281A, as indicated by a comparison of FIGS. 27A and 27C.
Four time regions are identified from FIGS. 27A, 27B and 27C, corresponding
to the four regions for the weighting functions shown in FIGS. 27D and
27E. A first region X, of temporal width .DELTA.t(X), spans the separation
between the early and late signals for the channel 281A. A second region
Z, of temporal width .DELTA.t(Z), spans the separation between the early
and late signals for the channel 281B. A third region YA, of temporal
width .DELTA.t(YA), spans the separation between the late signal in the
channel 281A and the early signal in the channel 281B. A fourth region YB,
of temporal width .DELTA.t(YB)=.DELTA.t(YA), spans the separation between
the early signal in the channel 281B and the late signal in the channel
281A. The temporal widths are
.DELTA.t(X)=.DELTA.t.sub.L-E,A, (18)
.DELTA.t(Z)=.DELTA.t.sub.L-E,B, (19)
.DELTA.t(YA)=.DELTA.t(YB)=(t.sub.E,B -t.sub.L,A). (20)
The weighting functions w12(t;x;qx) (x=E,L) used in the time-delayed
version or time-advanced version illustrated in FIGS. 27A, 27B and 27C are
constructed as follows. Define a square wave function by the relations
##EQU7##
where t1.ltoreq.ta<tb.ltoreq.t2. The weighting functions w12(t;x;qx)
(x=E,L) used in the time-delayed embodiment in FIGS. 27A and 27B are
defined by
w12(t;E;qE)=g1.multidot.SQ(t1;t1+.DELTA.t(YA))+g,2.multidot.SQ(t2-.DELTA.t(
X);t2), (22)
w12(t;L;qL)=g3.multidot.SQ(t1;t1+.DELTA.t(Z))+g4.multidot.SQ(t2-.DELTA.t(YB
);t2). (23)
The autocorrelation difference function .DELTA.AC(.tau.;qE;qL) is then
computed, for .tau.=.tau..sub.A or .tau..sub.B, as the integral, or sum of
sampled values, of the difference
.DELTA.s.sub.E-L (t)=w12(t+.tau.-t.sub.E ;E;qE)S.sub.d
(t+.tau.-t.sub.E)s(t) -w12(t+.tau.-t.sub.L ;L;qL)S.sub.d
(t+.tau.-t.sub.L)s(t), (24)
over a suitable time interval 0.ltoreq.t.ltoreq.T that contains the time
interval t1.ltoreq.t.ltoreq.t2, with t2-t1=.DELTA..tau..sub.chip.
The square wave functions SQ(t;ta;tb) used in Eqs. (22) and (23) are
obtained from uniform weighting correlations, such as shown in FIGS. 27A
and 27B, by the following linear combinations of correlation values.
SQ(.tau.;t1;t1+.DELTA.t(YA))={AC0(.tau..sub.A ;L)-AC0(.tau..sub.B
;E)}/2,(25)
SQ(.tau.;t2;t2-.DELTA.t(X))={AC0(.tau..sub.A ;L)-AC0(.tau..sub.A ;E)}/2,(26
)
SQ(.tau.;t1;t1+.DELTA.t(Z))={AC0(.tau..sub.B ;E)-AC0(.tau..sub.B ;L)}/2,(27
)
SQ(.tau.;t2;t2-.DELTA.t(YB))=-{AC0(.tau..sub.A ;L)-AC0(.tau..sub.B
;E)}/2(28)
Proceeding in a similar manner, the weighting functions w12(t;x;qx) (x
=E,L) used in the time-advanced embodiment in FIGS. 27A and 27C are
computed as set forth in Eqs. (22) and (23) for the time-delayed
embodiment. The square wave functions SQ(t;ta;tb) are obtained for the
time-advanced embodiment from the following linear combinations of
correlation values.
SQ(.tau.;t1;t1+.DELTA.t(YA))={AC0(.tau..sub.A ;L)+AC0(.tau..sub.B
;E)}/2,(29)
SQ(.tau.;t2;t2-.DELTA.t(X))={AC0(.tau..sub.A ;L)-AC0(.tau..sub.A ;E)}/2,(30
)
SQ(.tau.;t1;t1+.DELTA.t(Z))=-{AC0(.tau..sub.B ;E)-AC0(.tau..sub.B
;L)}/2,(31)
SQ(.tau.;t2;t2-.DELTA.t(YB))=-{AC0(.tau..sub.A ;L)+AC0(.tau..sub.B
;E)}/2.(32)
The digital reference function S.sub.d (t+T.sub.y -t.sub.x) (x=E,L; y=A,B)
used to compute the autocorrelation functions AC0(.tau..sub.y ;x) has a
fixed offset t.sub.x and a variable offset .tau..sub.y, where the
difference .DELTA.t(B-A)=.tau..sub.B -.tau..sub.A is selected initially.
For the time-delayed embodiment, or the time-advanced embodiment, the
offset .tau..sub.A and/or the offset .tau..sub.B, subject to the
constraint .DELTA.t(B-A)=.tau..sub.B -.tau..sub.A =constant, is varied to
determine the value of .tau..sub.A (or .tau..sub.B) for which the
difference .DELTA.s.sub.E-L (t), integrated over the time interval
0.ltoreq.t.ltoreq.T, is zero. The value of .tau..sub.A (or .tau..sub.B)
thus found becomes the tracking point for the incoming signal.
In the apparatus shown in FIG. 26, the dynamic, or time varying selection
of W1(t;q) and of W1 (t;q) (=0 here) is performed automatically. If two
consecutive digital signal bit values satisfy b.sub.n-1 =b.sub.n (or
.DELTA.b.sub.n =0), Eqs. (25)-(28) and Eqs. (29)-(32) become identically
zero for the time interval I.sub.n, which effectively insures that W1
(t;q)=0. If b.sub.n-1 .noteq.b.sub.n (or .DELTA.b.sub.n =1), Eqs.
(25)-(28) and Eqs. (29)-(32) are not identically zero and do provide a
non-zero weighting function W1(t;q).
FIG. 28 illustrates a single channel apparatus 310 that provide similar
weighting functions w12(t;x;qx) by combining uniformly weighted
autocorrelation function values. This apparatus includes a code phase NCO
and generator 311 whose output signal is received by the first of a
sequence of D flipflops 313-1, . . . , 313-N1, . . . , 313-N2, . . . ,
313-N3, with associated time delay .DELTA.t(clock), where the numbers N1,
N2 and N3 are chosen to satisfy
(N1-1) .DELTA.t(clock)=t.sub.L,A -t.sub.E,A, (33)
(N2-1) .DELTA.t(clock)=t.sub.E,B -t.sub.E,A, (34)
(N3-1) .DELTA.t(clock)=t.sub.L,B -t.sub.E,A, (35)
with N1>1 and N3>N2, where the subscripts A and B refer to the desired
different desired times for an equivalent "A" channel and an equivalent
"B" channel. Here, N2 may be less than, equal to or greater than N1. An
incoming signal I(t) is received by a first input terminal of a first
signal multiplier 315. A second input terminal of the first signal
multiplier 315 receives a carrier signal from a carrier phase NCO 317 that
is controlled by signals received from a computer 319. The carrier signal
mixes with the incoming signal to produce a baseband signal. The output
signal from the first signal multiplier 315 is received by first input
terminals of second, third, fourth and fifth signal multipliers 321, 323,
325 and 327. Second input terminals of the signal multipliers 321, 323,
325 and 327 receive the output signals from the D flipflops 313-1, 313-N1,
313-N2 and 313-N3, respectively. Output signals from the signal
multipliers 321, 323, 325 and 327 are received by a first early signal
correlator module 329, a first late signal correlator module 331, a second
early signal correlator module 333 and a second late signal correlator
module 335, respectively. Output signals from the four early signal and
late signal correlator modules 329, 331, 333 and 335 are received by the
computer 319 to vary the time shift variable .tau. that is part of the
reference signal S.sub.d (t+.tau.) that is produced by the code phase NCO
and generator 311. The code phase NCO 311, the D tlipflops 331-y (y=1, . .
. , N1, . . . , N2, . . . , N3), the carrier phase NCO 317, and the early
signal and late signal correlator modules 329, 331, 333 and 335 are all
driven by a master clock 337, with the D flipflop clock signals being
optionally passed through a divide-by-N module 339 as shown. The clock
pulse width is .DELTA.t(clock).
Computation of the selected reference signals S.sub.d (t+.tau..sub.y
-t.sub.x) (x=E,L; y=A,B), of the autocorrelation functions AC0(.tau..sub.y
;x), and of the tracking point for .tau..sub.A (or .tau..sub.B) proceeds
as in the earlier development for FIG. 26.
The approach developed here is applicable to analysis of any incoming
digital signal that has been transmitted using a code division multiple
access (CDMA) format, in which the underlying incoming digital signal is a
known pseudo-random code and the time of arrival of the direct signal
(with multipath signals absent) is unknown. The source of the incoming
digital signal may be satellite based or be ground based, with fixed
location or variable location relative to the observer. By variably
suppressing the contribution of a particular time interval I.sub.n to the
autocorrelation difference function .DELTA.AC#(.tau.,q), depending upon
the transitions in bit values at t=t.sub.n, at t =t.sub.n-1, and/or at
t=t.sub.n-2, the contribution of noise and/or multipath signals to a
modified autocorrelation difference function .DELTA.AC#(.tau.;q) can be
suppressed.
The phrase "autocorrelation function" is used herein to refer to a sum or
integral over a collection of time values of a digital signal product
w(t+.tau.;q)s(t)S.sub.d (t+.tau.), where the digital composite signal s(t)
includes the digital direct signal S.sub.d (t) and, possibly, one or more
multipath signals S.sub.m (t;.DELTA.t.sub.m).
* * * * *
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