Sum Rate of p-Sphere Encoding for MIMO Broadcast Channels with Reduced Peak Power

Vector perturbation is a sum-capacity approaching non-linear precoding technique. Vector perturbation uses sphere encoding to perturb data such that the unscaled sum power is minimized. Unfortunately, this minimization does not guarantee that the peak to average power ratio (PAPR) remains in the acceptable range for the transmitter. A p-sphere encoder was proposed in literature to reduce the PAPR by using p-norm minimization instead of the 2-norm one used typically in vector perturbation and its performance was analyzed in terms of bit error rate (BER). In this paper we focus on the spectral efficiency of the p-sphere encoding and investigate its sum rate for multiple-input multiple-output broadcast channel (MIMO-BC) with multiple-antenna users and uniformly distributed input. The results show that for p=5, the PAPR is reduced by 25%, while the sum rate is just slightly less than that of vector perturbation employing 2-norm sphere encoding (only 1% reduced sum rate).