Minimum Euclidean Distance-Based Precoding for Three-Dimensional Multiple Input Multiple Output Spatial Multiplexing Systems

Through a feedback link, the channel state information acquired at the receiver is known at the transmitter and MIMO precoding techniques can be applied according to various criteria. In this paper, an efficient linear precoder based on the maximization of the minimum Euclidean distance between two received data vectors for three data-stream MIMO spatial multiplexing systems is proposed. By using a singular value decomposition, the precoding matrix can be parameterized as the product of a power allocation matrix and an input shaper matrix. According to this representation, the optimal precoders are proposed for the case of three independent data-streams. Simulation results over Rayleigh fading channels show considerable bit-error-rate improvement with the proposed solution in comparison with other precoding strategies.