This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multiple-input multiple-output (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schur-concave and Schur-convex functions. Once the optimal structure of the transmit-receive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closed-form expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peak-to-average ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel water-filling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.

This paper considers an abstract multi-input multi-output (MIMO) system that may correspond to a variety of physical communication channels. An important property of MIMO channels is the multiplexing property, i.e., the fact that more than one symbol can be simultaneously transmitted establishing more than one channel substream on the MIMO channel. Transmit and receive linear processing techniques are designed to optimize the performance of the communication system according to some criterion. Previous results choose a specific objective function and design the system accordingly. We take a unifying approach and generalize the known results by obtaining the optimal transmit-receive structure for two great families of functions that embrace most reasonable criteria: Schur-concave and Schur-convex functions (these types of functions arise in majorization theory). For illustrative purposes, we then analyze in detail a specific criterion: the minimization of the maximum of the mean square error (MSE) of the channel substreams.