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A theory of linear least-mean-squares equalization in digital data communications operating over two coupled linear dispersive channels, with particular application to dually polarized terrestrial radio systems is presented. We jointly optimize transmitter and receiver matrix filters when the inputs are two independent quadrature-amplitude-modulated data signals of fixed total average power. Formulas for minimum total mean-square error, upper bounds on probability of error, matched filter bounds, and the Shannon limit are provided. Using this theory in conjunction with a proposed propagation model for the dually polarized radio channel, we provide estimates of probability distributions of the data rates that can be supported by the optimum receiver structures as well as the jointly optimized transmitter-receiver. The distribution of data rates predicted from the Shannon limit as well as from the matched filter bounds are also given. For the dually polarized radio channel, we find that linear equalization structures can practically eliminate the effects of cross-polarization interference contributed by the antennas and their feeds. At very low outage probabilities, the combined-channels data rate achieved with the jointly optimized structures is about 4 b/s/Hz less than predicted from their matched filter bounds. Also, the combined data rate associated with the Shannon limit is about 3 b/s/Hz higher than predicted by the matched filter bound at very low outage probabilities. Sensitivity analyses reveal that about 1 b/s/Hz can be gained for each 3-dB increase in carrier-to-noise ratio. For each order-of-magnitude decrease in the required error rate, about 0.3 b/s/Hz is given up.
Amitay et al. (Sat,) studied this question.