Transmit beamforming for physical-layer multicasting

• Published in: IEEE transactions on signal processing Vol. 54; no. 6; pp. 2239 - 2251
• Main Authors: Sidiropoulos, N.D., Davidson, T.N., Zhi-Quan Luo
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Array signal processing; Availability; Beamforming; Broadcasting; Channel state information; Channels; convex optimization; Cost function; Detection, estimation, filtering, equalization, prediction; Digital; Downlink; downlink beamforming; Exact sciences and technology; Exact solutions; Fading; Information, signal and communications theory; Lagrangian functions; Linear antenna arrays; minimization of total radiation power; Multicasting; Optimization; Rayleigh channels; semidefinite programming; semidefinite relaxation (SDR); Signal and communications theory; Signal to noise ratio; Signal, noise; Studies; Telecommunications and information theory; Transmitters; very-high-bit-rate Digital Subscriber line (VDSL) precoding; Performance evaluation; Parameter estimation; Wireless telecommunication; Transmitter; Downlink; Data broadcast; Information dissemination; Beam forming; Optimization; Multicast; semidefinite programming; Relaxation; Subscriber; minimization of total radiation power; Channel estimation; very-high-bit-rate Digital Subscriber line (VDSL) precoding; Broadcasting; Availability; Maximin problem; Rayleigh channels; semidefinite relaxation (SDR); downlink beamforming; Digital transmission; Simulation; multicasting; Minimax method; NP hard problem; convex optimization; Approximate solution; Software radio; Signal to noise ratio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.872578

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.