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We study the generalized degrees of freedom (gDoF) of block-fadingnoncoherent multiple input multiple output (MIMO) channels with asymmetricdistributions of link strengths and a coherence time of T symbol durations. Wederive the optimal signaling structure for communication for the asymmetricMIMO channel, which is distinct from that for the MIMO channel with independentand identically distributed (i.i.d.) links. We extend the existing results forthe single input multiple output (SIMO) channel with i.i.d. links to theasymmetric case, proving that selecting the statistically best antenna isgDoF-optimal. Using the gDoF result for the SIMO channel, we prove that forT=1, the gDoF is zero for MIMO channels with arbitrary link strengths.,extending the result for MIMO with i.i.d. links We show that selecting thestatistically best antenna is gDoF-optimal for the multiple input single output(MISO) channel. We also derive the gDoF for the 2X2 MIMO channel with differentexponents in the direct and cross links. In this setting, we show that it isalways necessary to use both the antennas to achieve the gDoF, in contrast tothe results for the 2X2 MIMO channel with i.i.d. links. We show that havingweaker crosslinks, gives gDoF gain compared to the case with i.i.d. links. Forthe noncoherent MIMO channel with i.i.d. links, the traditional method oftraining each transmit antenna independently is degrees of freedom (DoF)optimal, whereas we observe that for the asymmetric 2X2 MIMO channel, thetraditional training is not gDoF-optimal. We extend this observation to alarger MX M MIMO channel by demonstrating a strategy that can achieve largergDoF than a traditional training-based method.

Generalized Degrees Freedom of Noncoherent MIMO Channels with Asymmetric Link Strengths