期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 54, 期 6, 页码 2239-2251出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2006.872578
关键词
broadcasting; convex optimization; downlink beamforming; minimization of total radiation power; multicasting; semidefinite programming; semidefinite relaxation (SDR); very-high-bit-rate Digital Subscriber line (VDSL) precoding
This paper considers the problem of downlink transmit beamforming for wireless transmission and downstream precoding for digital subscriber wireline transmission, in the context of common information broadcasting or multicasting applications wherein channel state information (CSI) is available at the transmitter. Unlike the usual blind isotropic broadcasting scenario, the availability of CSI allows transmit optimization. A minimum transmission power criterion is adopted, subject to prescribed minimum received signal-to-noise ratios (SNRs) at each of the intended receivers. A related max-min SNR fair problem formulation is also considered subject to a transmitted power constraint. It is proven that both problems are NP-hard; however, suitable reformulation allows the successful application of semidefinite relaxation (SDR) techniques. SDR yields an approximate solution plus a bound on the optimum value of the associated cost/reward. SDR is motivated from a Lagrangian duality perspective, and its performance is assessed via pertinent simulations for the case of Rayleigh fading wireless channels. We find that SDR typically yields solutions that are within 3-4 dB of the optimum, which is often good enough in practice. In several scenarios, SDR generates exact solutions that meet the associated bound on the optimum value. This is illustrated using measured very-high-bit-rate Digital Subscriber line (VDSL) channel data, and far-field beamforming for a uniform linear transmit antenna array.
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