A General Criterion for Analog Tx-Rx Beamforming Under OFDM Transmissions
In this paper, we study beamforming schemes for a novel MIMO transceiver, which performs adaptive signal combining in the radio-frequency (RF) domain. Assuming perfect channel knowledge at the receiver side, we consider the problem of designing the transmit and receive RF beamformers under orthogonal frequency division multiplexing (OFDM) transmissions. In particular, a general beamforming criterion is proposed, which depends on a single parameter ¿. This parameter establishes a tradeoff between the energy of the equivalent SISO channel (after Tx-Rx beamforming) and its spectral flatness. The proposed cost function embraces most reasonable criteria for designing analog Tx-Rx beamformers. Hence, for particular values of ¿ the proposed criterion reduces to the minimization of the mean square error (MSE), the maximization of the system capacity, or the maximization of the received signal-to-noise ratio (SNR). In general, the proposed criterion results in a nonconvex optimization problem. However, we show that the problem can be rewritten as a convex cost function subject to a couple of rank-one constraints, and hence it can be approximately solved by semidefinite relaxation (SDR) techniques. Since the computational cost of SDR for this problem is rather high, and building on the observation that the minima of the original problem must be solutions of a pair of coupled eigenvalue problems, we propose yet another simple and efficient gradient search algorithm which, in practice, provides satisfactory solutions with a moderate computational cost. Finally, several numerical examples show the good performance of the proposed technique for both uncoded and 802.11a-coded transmissions.