Embedded space–time codes for multiple-input–multiple-output systems in Rayleigh fading

In this study, novel designs of embedded space-time multiplexing codes are presented. The space-time codes are constructed initially based on the decomposition of normal matrices that produce diagonal structures. The eigenvalue decomposition of circulant matrices, a type of normal matrices, can generate these codes. A key constraint in the design is that only the diagonal matrices are function of data. Since the components of the diagonal matrix are linear combinations of the data, the codes are called embedded. These codes provide an embedded diversity, full rate and enable multi-user applications with reduced interference. Later constructions in Galois fields are used to reduce the constellations expansion introduced by the dependency of the eigenvalues of the diagonal matrix to the data. The pairwise error probability for the codes is derived. Performance of the codes based on simulation and theoretical analysis, are compared with the conventional spatial-multiplexing codes and other complex orthogonal designs. Simulation results demonstrate the advantage of the proposed codes. Simulation has been done for Rayleigh-fading channels with known channel-state information.