Modeling

The primary goal of this thesis is to provide a detailed model for the channel capacity of a PAN channel. This analysis will provide no indication as to what encoding scheme will best achieve the predicted maximum capacity. The experimental work described briefly in section #introhistory#47> addresses some of this, but it seems likely that there are encoding schemes which will be able to more effectively approach the theoretical limit. In order to evaluate the channel capacity of the body (which is taken to be a Gaussian channel), it is necessary to evaluate:

#equation48#

In this equation, C is the channel capacity, #tex2html_wrap_inline1270# is the bandwidth (and the sampling period is #tex2html_wrap_inline1272#), S is the signal power, N is the noise power, and #tex2html_wrap_inline1278# is the noise power spectral density.

In order to calculate S, it is necessary to calculate the signal strength at the receiver. This will be highly dependent on geometry and transmission strength. In order to calculate N, a noise estimate must be made, which will be dependent on geometry but is expected to be dominated by amplification noise in the receiver.

The signal calculation will be accomplished by an electrostatic model of the body or bodies with the transmitter, receiver and ground, and a circuit model of the interconnected capacitances. The noise calculation will be done from first principles for the noise in the body and empirical noise estimates for the receiver amplification.

Finally, given these values it will be possible to obtain a reasonable estimate for the channel capacity of the body given practical amplification, as well as an estimate for the absolute upper bound, given ideal amplification.