On vector perturbation precoding for the MIMO Gaussian broadcast channel

Precoding schemes in the framework of vector perturbation (VP) for the multiple-input multiple-output (MIMO) Gaussian broadcast channel (GBC) are investigated. The VP scheme, originally a one-shot technique, is generalized to encompass processing over multiple time instances. Using lattice-based extended alphabets (perturbations), and considering the infinite time-span extension limit, a lower bound on the achievable sum-rate using the generalized VP scheme is analytically obtained, by which it is shown to achieve the optimum sum-rate in the high signal-to-noise ratio (SNR) regime (both in terms of degrees-of-freedom and power offset). The above lower bound is constructively obtained by means of an efficient practically oriented suboptimum transmit energy minimization algorithm, which has merits of its own, and it demonstrates the significant performance enhancement that can be obtained by preprocessing over multiple symbol instances, potentially eliminating the gap to the ultimate performance at high SNRs. For the 2 × 2 MIMO GBC, the VP scheme is generalized further, and an inner bound for the entire achievable rate region is obtained, by which an interesting correspondence is identified to the ultimate capacity region, as obtained by dirty paper coding (DPC).