On Commonalities in Signal Design for Non-Gaussian Channels
NAVAL RESEARCH LAB WASHINGTON DC
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We derive for additive non-Gaussian white noise channels signal waveforms that are simultaneously optimal with respect to the minimum probability of error, the mini-max, and the Neyman-Pearson criteria. We show that for a large class of non-Gaussian statistics, there exist only two asymptotically optimal signal waveforms one impulsive while the other is constant in amplitude. The impulsive waveform is optimal when the tails of the noise density fall off faster than the tails of the Gaussian density. We show that under each of the three optimality criteria the asymptotic performance for small signals is essentially determined by the signal energy, while for large signals the performance is determined by a non-Euclidean metric that varies with respect to the tails of the noise density function. To support these results, we offer simulations for a variety of non-Gaussian channels. In each case, the asymptotic theory holds strikingly well even for decidedly nonasymptotic regimes.
- Operations Research
- Optical Detection and Detectors