A Lattice-Theoretic Analysis of Vector Perturbation for Multi-User MIMO Systems

This paper considers the use of multiple transmit antennas to deliver independent data streams to multiple users. In particular, we examine a multi-user technique known as vector perturbation. We provide a new lattice-theoretic approach to analyze its performance in the presence of Rayleigh fading. Vector perturbation is based on performing a channel inversion, with the additional step of perturbing the data signal prior to linear preceding to significantly reduce the required transmit power. To analyze such systems it is necessary to calculate the resulting average energy of the sphere-encoded signal vector, as this determines the signal-to-noise ratio (SNR) at the output of the demodulator. Previous results presented in the literature were partially analytic, requiring further numerical evaluation. Here, we derive a concise approximation to the output SNR. We also provide tight upper and lower bounds on the bit error rate for the reception of QAM symbols using the required modulo demodulator, as a function of the average energy of the sphere- encoded signal vector.