Power control scheme for multiple antenna systems with space-time coding in Rayleigh fading channels

Two optimal power control (PC) schemes under the power constraint for space-time coded multiple input multiple output systems over the flat Rayleigh fading channel with the imperfect channel state information (CSI) are presented. One is based on the minimization of a bit error rate (BER), and the other is based on the maximization of a fuzzy signal-to-noise ratio. In these schemes, different powers are allocated to individual transmit antennas rather than equal power in the conventional one. For the first scheme, the optimal PC procedure is developed. It is shown that the Lagrange multiplier for the constrained optimization in the power control does exist and is unique. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. In the second scheme, some existing schemes are included, and a suboptimal PC procedure is developed by means of the asymptotic performance analysis. With this suboptimal scheme, a simple PC calculation formula is provided, and thus the calculation of the PC will be straightforward. Moreover, the suboptimal scheme has the BER performance close to the optimal scheme. Simulation results show that the two PC schemes can provide BER lower than the equal PC and antenna selection scheme under the imperfect CSI.