Optimum Codebook Design and Average SEP Loss Analysis of Spatially Independent and Correlated Feedback Based MISO Systems With Rectangular QAM Constellation

In this correspondence, we present an optimum codebook design algorithm that minimizes the loss in average symbol error probability (SEP) of a spatially correlated multiple-input single-output (MISO) system with finite-rate feedback under both perfect and imperfect channel estimate assumptions. Towards the goal of designing an optimum codebook that minimizes average SEP (ASEP) loss due to finite-rate channel quantization, we derive the distortion function as a first order approximation of the instantaneous SEP loss. Utilizing high resolution quantization theory and assuming perfect channel estimation at the receiver, we analyze the loss in ASEP for spatially independent and correlated finite-rate feedback transmit beamforming MISO systems with $M_{1} \times M_{2}$-QAM constellation. We then consider the high-SNR regime and show that the loss associated with quantizing the spatially independent channels is related to the loss associated with quantizing the spatially correlated channels by a scaling constant given by the determinant of the correlation matrix. We also present simulation results that illustrate the effectiveness of the new codebook design and validate the derived analytical expressions for ASEP loss.