Linear Precoder Design for Doubly Correlated Partially Coherent Fading MIMO Channels

We consider the single-user multiple-input multiple-output (MIMO) precoder design problem for the doubly spatially correlated partially coherent Rayleigh fading channels with discrete inputs. The objective is to design a linear precoder to adapt to the degradation caused by the imperfect channel estimation at the receiver and the transmit-receive antenna correlation. The system is partially coherent so that the MIMO channel coefficients are estimated at the receiver and its error covariance matrix is fed back to the transmitter. We utilized the cutoff rate (CR) expression, an alternative to the mutual information (MI), and propose to use it as a design criterion to design the linear precoders. A linear precoder is obtained by numerically maximizing the CR with respect to the precoder matrix with a given average power constraint. Furthermore, the precoder matrix is decomposed using singular value decomposition (SVD) into the input shaping matrix, power loading matrix, and beamforming matrix. The beamforming matrix is found to coincide with the eigenvectors of the transmit correlation matrix. The power loading and input shaping matrices are solved numerically using the difference of convex (d.c.) functions programming algorithm and optimization under the unitary constraint, respectively. A 2-block alternating optimization (AO) algorithm is proposed to solve the input shaping matrix and power loading matrix iteratively. Precoders are designed to be used in conjunction with two MIMO transmission schemes: the spatial multiplexing (SM) and space-time (ST) block transmission modes. The frame error rate (FER) and average MI are used as the performance metrics to validate the performance of the newly designed CR-precoders in comparison with the conventional no-precoding case and cutoff rate optimized partially coherent constellations (PCCs). Numerical examples show that the performance gains of the designed precoders are significant compared to the CR-PCCs and conventional codewords.