Impact of Backward Crosstalk in 2x2 MIMO Transmitters on NMSE and Spectral Efficiency

Crosstalk between the transceiver branches appears in practical multi-antenna transmitters. This paper analyzes the backward crosstalk in 2x2 transmitters, which is caused by crosstalk from the outputs to inputs or by the combination of output crosstalk and impedance mismatch. We consider arbitrarily correlated input signals, while feedback networks and third-order memoryless polynomials are used to model the backward crosstalk and power amplifier, respectively. By utilizing the Bussgang decomposition, the transmitted signals are expressed as a linear transformation of the input signals plus uncorrelated distortion. First, the normalized mean-square errors (NMSEs) in the transmitted signals are derived analytically and used to obtain a closed-form expression for the power back-off that minimizes the worst NMSE of the two branches. Then, an achievable spectral efficiency (SE) is found for communication to a single-antenna receiver. The SE-maximizing precoder is derived by exploiting the hardware characteristics. Furthermore, the optimum power back-off is analyzed for two sub-optimum precoders, which either do not exploit any hardware knowledge or only partial knowledge. The simulation results show that the performances of these two sub-optimum precoders are in general close to the optimum SE. Furthermore, the power back-offs that minimize the NMSE and maximize SE are not the same.