List Encoding of Vector Perturbation Precoding

Abstract

In this letter, we propose a new nonlinear precoding algorithm, List encoding of Vector Perturbation precoding (LVP) for Multiple Input Multiple Output (MIMO) system. Different from the traditional VP based on sphere search strategy to minimize the Frobeniuas norm of the precoded signal with a exponential search complexity, LVP adopts multiple encoders design, a list of encoder perform only one dimensional integer optimization through several iterations in parallel. During each iteration each encoder searches through several perturbation results and retain one of them to the next iteration. When the iterations ends, the historical optimal perturbation result with the least Frobenius norm is output as the precoding result. The search complexity of LVP is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(M)$</tex-math></inline-formula> which increases linearly with the antenna number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> . This complexity is much smaller than sphere search based strategy. Compared with other low dimensional search algorithm represented by D2VP, the search complexity drops from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(M^{2})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(M)$</tex-math></inline-formula> , with a significant BER gain thanks to the multiple encoder design. To the best of our knowledge, with similar BER performance the LVP algorithm has the lowest complexity.