Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding distance between channels in terms of their ML-decoders which is meaningful from the decoding point of view, in the sense that the closer two channels are, the larger is the probability of them sharing the same ML-decoder. We give explicit formulas for these probabilities.
Mismatched decoding has an extensive literature ( @cite_7 has many relevant references on the subject). The approach, however, is essentially information theoretical, guided by the fundamental question of determining . This means that most of the work in the area aims to understand what is achievable asymptotically, for example, what are the achievable rates for families of channels with the input-output sets' size going to infinity. Those are very difficult questions and hence a significant part of the effort is directed to find bounds for those rates (and other significant invariants).
@cite_7
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Channel reciprocity in time-division duplexing (TDD) massive multiple-input multiple-output (MIMO) systems can be exploited to reduce the overhead required for the acquisition of channel state information (CSI). However, perfect reciprocity is unrealistic in practical systems due to random radio-frequency (RF) circuit mismatches in uplink and downlink channels. This can result in a significant degradation in the performance of linear precoding schemes, which are sensitive to the accuracy of the CSI. In this paper, we model and analyse the impact of RF mismatches on the performance of linear precoding in a TDD multi-user massive MIMO system, by taking the channel estimation error into considerations. We use the truncated Gaussian distribution to model the RF mismatch, and derive closed-form expressions of the output signal-to-interference-plus-noise ratio for maximum ratio transmission and zero forcing precoders. We further investigate the asymptotic performance of the derived expressions, to provide valuable insights into the practical system designs, including useful guidelines for the selection of the effective precoding schemes. Simulation results are presented to demonstrate the validity and accuracy of the proposed analytical results.