SIGNAL DESIGN FOR THE NONCOHERENT GAUSSIAN CHANNEL.
Interim technical rept.,
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF ELECTRICAL ENGINEERING
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A fundamental problem in communication theory is the design of M-ary communication systems. Our concern here is with the signal design portion of the problem for the noncoherent additive white Gaussian noise channel. The signalling waveforms under consideration will consist of M equiprobable, equipowered narrow-band waveforms of equal time duration. We begin by presenting the mathematical model for the noncoherent communication system and then show how the probability of error varies with signal-to-noise ratio and the signal waveform inner product matrix. We then derive a high signal-to-noise ratios approximation to the error probability. Using the aforementioned expression, we show that the noncoherent orthogonal signal structure globally minimizes the probability of error at large signal-to-noise ratios when the dimensionality of the signal set is unrestricted. We then consider the dimensionality constrained signal design problem. The problem of finding optimal signal sets of given dimension is formulated as a variational one. This leads to a necessary condition that must be satisfied so as to locally extremize the error probability. Author