A Joint Gauss-Seidel and Neumann Series Precoding Scheme for a Downlink Massive MIMO System

In the downlink (DL) of a Time Division Duplex (TDD) massive MIMO system, the effect of multi-user interference is ameliorated efficiently by Zero Forcing (ZF) linear precoding, which may achieve an almost optimal sum-rate performance. However, ZF suffers from a high implementation complexity of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(K^{3})$</tex> owing to the inversion of a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K\times K$</tex> channel correlation matrix due to its direct inversion method. To lessen this complexity, approximate matrix inversion by the Gauss-Seidel (GS) or Neumann series (NS) methods has been explored extensively. In this paper, the authors propose a joint Gauss-Seidel Neumann series (JGSNS) algorithm that approximates square matrix inversion with faster convergence speed and fewer FLOPs than the Neumann series. The performance of the precoding scheme is evaluated in a DL, TDD massive MIMO system as a function of antenna array size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> and number of simultaneous users K.