On the multiplexing gain of MIMO microwave backhaul links affected by phase noise

We consider a multiple-input multiple-output (MIMO) AWGN channel affected by phase noise. Focusing on the 2 × 2 case, we show that no MIMO multiplexing gain is to be expected when the phase-noise processes at each antenna are independent, memoryless in time, and with uniform marginal distribution over [0, 2π] (strong phase noise), and when the transmit signal is isotropically distributed on the real plane. The scenario of independent phase-noise processes across antennas is relevant for microwave backhaul links operating in the 20-40 GHz range.