Unitary Matrix Design via Genetic Search for Differential Space-Time Modulation and Limited Feedback Precoding

Because of their orthogonality properties, unitary matrices are an important class of matrices that are used in mathematics, physics, control, communications and others. In multiple-input multiple-output (MIMO) communication systems, there are two main applications that use unitary matrices: differential space-time modulation (DUSTM) and precoding. DUSTM is used when the channel state information (CSI) is not available for both transmitter and receiver, while unitary precoding is used when complete or partial CSI is available for both sides. For DUSTM and limited feedback MIMO systems, a codebook of unitary matrices should be designed. Conventionally, design parameters are optimized based on a cost function depending on the application. This optimization is time consuming when the system dimension and/or codebook size are increased. In this paper, we propose to relax the design parameters to be real rather than integer and use a genetic algorithm to find the optimal solution based on the related cost function. This approach provides better codes than the codes extracted from exhaustive search over integer parameters. The code extraction is rapid even when the system dimensions are large