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On capacity of noncoherent MIMO with asymmetric link strengths

We study the generalized degrees of freedom (gDoF) of the block-fading noncoherent MIMO channel with asymmetric distributions of link strengths, and a coherence time of T symbol durations. We first derive the optimal signaling structure for communication over this channel, which is distinct from that for the i.i.d MIMO setting. We prove that for T = 1, the gDoF is zero for MIMO channels with arbitrary link strength distributions, extending the result for MIMO with i.i.d links. We then show that selecting the statistically best antenna is gDoF-optimal for both Multiple Input Single Output (MISO) and Single Input Multiple Output (SIMO) channels. We also derive the gDoF for the 2×2 MIMO channel with different exponents in the direct and cross links. In this setting, we show that it is always necessary to use both antennas to achieve the optimal gDoF, in contrast to the results for 2 × 2 MIMO with identical link distributions. We also show that having weaker crosslinks gives gDoF gain compared to the case with identically distriuted links.