Spatial Multiplexing for Noncoherent Reception in MIMO Systems With Binary ASK: Optimal Precoder Design

Abstract

This paper focuses on precoder optimization of a spatially multiplexed multiple-input multiple-output (MIMO) system with noncoherent reception in a correlated Rayleigh fading environment. We consider a Kronecker product model for the channel correlation with a transmit equicorrelation matrix and a receive correlation matrix which is diagonal. The transmit symbol vector, in which the symbols are taken from two binary constellations <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\{0,1\}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\{1,-r\}$ </tex-math></inline-formula> (with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0\leq r &lt; 1$ </tex-math></inline-formula> ), is premultiplied by a diagonal precoder matrix with positive precoder parameters. As the average signal-to-noise ratio per diversity branch becomes large, the symbol vector error probability (SVEP) tends to reach saturation. We minimize this saturation value with respect to the precoder parameters and the constellation parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> . It is found from computation that the optimal precoder parameters are approximately in geometric progression for both constellations. By observing the patterns in optimal values obtained from computation, we simplify the optimization problem. This simplification reduces the computational effort required to solve the complex minimization problem without affecting the SVEP significantly. Furthermore, in the case of the constellation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\{1,-r\}$ </tex-math></inline-formula> , it is found from computation that as the number of transmit antennas increases, the optimal value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> decreases.