Precoding for multiple-input multiple-output systems with space–time block coding over correlated rician fading channels

Based on the asymptotic analysis in spatially correlated Rician fading channel, the precoders for space-time block-coded multiple-input multiple-output system at high and low signal-to-noise ratios (SNRs) are, respectively, designed to minimise the system bit error rate (BER). The precoding for high SNR provides closed-form positive power allocation by using the Langrage optimisation method, and has the BER performance close to that of the optimal scheme, especially at high SNR. The Langrage multiplier does exist and is unique, and practical Newton´s method is proposed to find its optimal value. Moreover, it has a closed-form solution for some special cases. Thus, it avoids the iterative calculation of some existing precoding schemes. The precoding for low SNR has a closed-form solution similar to onedirectional (1-D) beamforming, and can obtain the performance very close to that of the optimal scheme at low SNR. By combining the above two schemes, a simple and effective suboptimal precoding scheme can be achieved for different SNRs. Simulation results show that the proposed scheme derived from the integration of high and low SNR can provide BER lower than the equal power precoding, and obtain the BER performance close to that of the existing optimal scheme with low complexity.