# A General Criterion for Analog Tx-Rx Beamforming under OFDM Transmissions

Summary: In this talk we will present a brief overview of the MIMAX project, whose goal is to develop a compact and low-power consuming RF-MIMO transceiver, which performs adaptive signal combining in the radio-frequency (RF) domain. Assuming perfect channel knowledge, we will consider in detail the problem of designing the transmit and receive RF beamformers under orthogonal frequency division multiplexing (OFDM) transmissions. We will present a new general beamforming criterion, which depends on a single parameter that 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 parameter, 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 non-convex optimization problem. However, we will 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 will finally propose another simple and efficient gradient search algorithm which, in practice, provides satisfactorysolutions with a moderate computational cost. The good performance of the proposed technique for both uncoded and 802.11a coded transmissions will be shown by computer simulations.

Bio: Ignacio Santamaria received his Ph. D. on Telecommunications from the Polytechnic University of Madrid in 1995. Since 2007 he is a Professor in the University of Cantabria, Spain, where he heads the Signal Processing Group. His main research interest are statistical signal processing, MIMO communications systems, information theory, and machine learning techniques. More info: http://www.gtas.dicom.unican.es/en/members/nacho