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For a multiuser data communications system operating over a mutually cross-coupled linear channel with additive noise sources, we determine the following: (1) a linear cross-coupled receiver processor (filter) that yields the least-mean-squared error between the desired outputs and the actual outputs, and (2) a cross-coupled transmitting filter that optimally distributes the total available power among the different users, as well as the total available frequency spectrum. The structure of the optimizing filters is similar to the known 2 x 2 case encountered in problems associated with digital transmission over dually polarized radio channels. I. INTRODUCTIONA variety of communication channels can be modeled as multiinput, multi-output, mutually cross-coupled linear networks with ad ditive noise sources. A few examples of communications systems operating over such channels are dually polarized radio systems, frequency/time-division multiplexing with crosstalk, cordless PBXs, spread-spectrum multiuser systems, and multisensor radar/sonar sys tems. In many applications it is beneficial to design cross-coupled transmitters and receivers that take advantage of the inherent mutual interferences. The chief purpose of this paper is to explore these issues from a theoretical point of view.The general problem we address follows. We consider an iV" input-* AT&T Bell Laboratories.

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A major contribution to system outage in a terrestrial digital radio channel is deep fading of the frequency transfer characteristic, which in addition to causing a precipitous drop in received signal‐to‐noise ratio (s/n) also causes signal dis persion that can result in severe intersymbol interference. Because the temporal variation of the channel is slow compared to the signaling rate, the information theoretic channel capacity and the “Efficiency Index” in bits/cycle—a figure‐of‐merit we use for the communication techniques considered—can be viewed as random processes. Starting from an established mathematical model characterizing fading channels (derived from extensive measurements), we estimate the probability distribution of channel capacity and the distributions of efficiency indices for different communications techniques. The repertoire of communication methods considered involves quadrature amplitude modulation with adaptive linear and decision feedback equalization, and maximum likelihood sequence estimation. For specific outage objectives the maximum number of bits per cycle achievable by each technique is estimated. The sensitivity of the distributions to bit‐error‐rate objective and unfaded s/n is assessed. For certain desired operating points the efficacy of adaptive equalization is demonstrated. There are some operating points where adaptive equalization alone is not adequate and therefore space diversity should be considered. An estimate of the effect of frequency diversity is also included.