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Capacity improvement for finite-input constellation using unitary precoding for two user channels

In [1], it was shown that introduction of a relative phase shift between the transmitted constellations of both the users in a two user Gaussian Multiple Access Channel (GMAC) improves the capacity region when finite input constellation is used for both the users. This idea was also shown to improve the capacity region of the two user Gaussian Interference Channel (GIC) under the strong interference assumption, with finite constellation [2]. In the current work, we extend the idea of introducing the phase shift to the two symbol case. We show that for both, GMAC and GIC with strong interference, if one user precodes the signal with a 2×2 unitary matrix, then the capacity improves when compared to [1] and [2]. In particular, it is shown that the entries of the unitary precoder have to be complex in order to improve the capacity region. Using simulations, the entries of the unitary precoder for certain ranges of SNR are computed.