Since the normally assumed white Gaussian interference is the most destructive in terms of minimizing channel capacity, substantial improvement can usually be obtained if the real-world interference environment (non-Gaussian) is properly taken into account. In this paper, the performance of the locally optimum Bayes detector (LOBD) is compared to the performance of various ad hoc nonlinear detection schemes. The known results are reviewed, and then it is demonstrated that these theoretical results may be misleading due to the assumptions that are required in order to derive them analytically. For a particular type of broad-band impulsive noise, the critical assumptions of "sufficiently" small signal level and large number of samples (large time-bandwidth product so that the central limit theorem applies) are removed; the first analytically, and the second by computer simulation. The thus-derived performance characteristics are then compared, especially as the signal level increases. One result is that there are situations where the bandpass limiter outperforms the LOBD as the signal level increases; that is, the locally optimum detector may not remain "near optimum" in actual operational situations.

This paper investigates the optimum detection of a weak signal, where this signal is dominated by broad-band impulsive noise. It has been suggested that by using a form of space diversity reception (many receiving sites), it would be possible to "look between the large noise pulses" and thereby detect a signal well buried in the noise. In this paper we obtain and determine the performance of the locally optimum (or threshold) detector for any form of interference and apply these results to an example case of atmospheric noise for the single receiver case and for the diversity case of many receivers. Substantial improvement or processing gain can be obtained with one receiver with substantial, but less, additional improvement obtainable by then going to many additional receivers.

Because communications systems are seldom significantly interfered with by classical white Gaussian noise, it is necessary to consider other, appropriate (and tractable) interference models, if realistic estimates of system performance are to be obtained for the general spectral-use environment. For this purpose, Middleton's recently developed canonical statistical-physical model of "impulsive" interference is applied to real-world communication channels. The principal features of this model are first summarized, including the statistical relations required for the solution of signal detection problems. [Excellent agreement of these model statistics with correspondingly measured statistics is also noted.] The model for narrow-band impulsive interference (Class A noise, a subset of the overall model) is next specifically applied to an important class of coherent signal detection problems. Algorithms for error probabilities in optimum detection are then obtained, along with performance bounds, for the same error probabilities. Since it is known that in order to gain significant improvement over current receivers, the number of (essentially) independent samples of the received interference waveform must be enlarged (i.e., large "processing gains"), the performance results here are given parametrically in the number of samples, or equivalently, in the time-bandwidth product. Performance of current suboptimum receivers is then obtained and compared to the optimum performance. It is shown that very substantial savings in signal power and/or spectrum space can usually be achieved by using the indicated optimal algorithms. Since physical realization of the completely optimum detection algorithms cannot, in general, be economically realized, the somewhat more conservative, corresponding locally optimum Bayes detection (LOBD) receivers are derived. In general, these LOBD structures require adaptive, highly non-linear filters, preceding the conventional correlation detector elements characteristic of optimum receivers for Gaussian interference. Performance for these non-linear, optimum threshold systems is then determined, specifically in Part I for coherent reception.

In Part I, the relevant statistical properties of the recently developed statistical-physical model of generalized impulsive interference have been briefly reviewed (for sub Class A noise) and then applied specifically to optimum coherent detection. It is shown that by using optimum and (locally optimum) detection algorithms (canonically and explicitly derived), substantial savings in signal power and/or spectrum space can be achieved for operation in these highly nonGaussian interference environments. This paper (Part II) extends the preceding analysis to cover various important cases of incoherent reception. The same general model for narrow-band (Class A) impulsive interference and interference examples used in Part I are again employed here. In addition to providing both canonical LOBD structures and expressions for performance, this permits explicit quantitative comparisons between coherent and incoherent reception for common classes of specific digital signal waveforms.