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Analysis of Vector Precoding at High SNR: Rate Bounds and Ergodic Results

Besides the optimal but impractically complex dirty paper coding (DPC), linear precoding and vector precoding (VP) have been proposed for the vector broadcast channel (BC). Linear precoding is simple, as only a linear transform is applied to the data signals, whereas VP necessitates a closest-point search in a lattice to find the perturbation signal which reduces the necessary transmit power. In this paper, we analyze the high signal-to-noise ratio (SNR) performance of VP assuming optimal decoding. As the perturbation process hinders the analytical assessment of the VP performance, lower and upper bounds on the expected data rate of VP systems are reviewed and proposed. Based on these bounds, VP is compared to linear precoding w.r.t. the weighted sum rate, the power resulting from a quality of service (QoS) formulation, and the performance when balancing the rates.