Multiple Antenna Constellation Design for Partially Coherent Rayleigh Fading Channels

Space-time (ST) constellations for multiple-input multiple-output (MIMO) systems have usually been designed assuming either perfect or no channel state information (CSI) at the receiver. Practical systems are often partially coherent, i.e., have imperfect receiver CSI. In this paper, we consider the partially coherent ST code and constellation design for MIMO systems in Rayleigh fading channels. We assume that receiver acquires an imperfect CSI estimate, which is Gaussian random variable with zero mean and a non-zero variance, while the transmitter has perfect knowledge of the CSI estimation variance available via feedback. We propose to use the cutoff rate (CR) with respect to signal points as the design criterion. The CR expression is first derived. The CR maximization problem is formulated and numerical optimization algorithms are proposed. Numerical examples show that the designed constellations outperform earlier ones with respect to the peak-to-average power ratio (PAPR), mutual information between the channel input and output as well as symbol error rate (SER) especially at low or medium signal-to-noise ratio (SNR) regime.