Correlation of distortion noise between the branches of MIMO transmit antennas

Despite the tremendous research effort spent on MIMO systems - very few papers address the impact of hardware imperfections. In this paper we analyze the distortion noise of the transmitter branches of a MIMO transmitter. In particular we analyze the cross-correlation of the distortion noises for the case that the transmitted signals are correlated. This case arises when there is just a single stream being transmitted with beamforming or in the case of multiple streams and linear precoding. We analyze the problem in two ways: using analytical derivations and using measurements on our testbed. In the analytical case we assume a transmitter impaired by a 3rd order non-linearity. For this scenario we find that the absolute correlation coefficient of the distortion noises is given by the absolute value of the correlation coefficients of the input signals to the power of three, while the phase is the same as that of the input signal. Our measurements also show good agreement between measurements and analytical results. It seems to suggest that the distortion noises can be regarded as practically independent whenever there are two or more modulation streams being transmitted (spatial multiplexing). In a single-stream scenario, the distortion noise will tend to have the same spatial distribution as the desired signal.