Optimal minimum distance-based precoder for MIMO spatial multiplexing systems

We describe a new precoder based on optimization of the minimum Euclidean distance d_min between signal points at the receiver side and for use in multiple-input multiple-output (MIMO) spatial multiplexing systems. Assuming that channel state information (CSI) can be made available at the transmitter, the three steps ( noise whitening, channel diagonalization and dimension reduction), which are currently used in investigations on MIMO systems, are performed. Thanks to this representation, an optimal d_min precoder is derived in the case of two different transmitted data streams. For quadrature phase-shift keying (QPSK) modulation, a numerical approach shows that the precoder design depends on the channel characteristics. Comparisons with maximum signal-to-noise ratio (SNR) strategy and other precoders based on criteria, such as water-filling (WF), minimum mean square error (MMSE), and maximization of the minimum singular value of the global channel matrix, are performed to illustrate the significant bit-error-rate (BER) improvement of the proposed precoder.