Distributed transmit beamforming with one bit feedback revisited: How noise limits scaling

Distributed transmit beamforming with N cooperating nodes, each with fixed transmit power, provides a received power scaling with N2, corresponding to a “power pooling” gain of N and a beamforming gain of N. Prior work has shown that the optimal beamforming solution can be attained using a decentralized, iterative algorithm based on one bit (per iteration) feedback broadcast from the receiver to the transmitters. The algorithm is provably convergent in a noiseless setting, and is the basis for several successful prototypes. In this paper, we develop a framework for providing analytical insight into the effect of receiver noise, with the following key question in mind: can we bootstrap the algorithm from the incoherent power-pooled solution to operate in a regime in which the received SNR per node can be made arbitrarily small as we scale up the number of nodes N? Our analytical computations, validated by simulations, yield a somewhat negative answer: while the power-pooling gain guarantees a linear increase in received power with N, the per-node SNR cannot be scaled down with N if we wish to attain a quadratic increase in received power. Specifically, the fraction of the ideal beamforming gain attained using the one-bit algorithm is asymptotically independent of N, and depends only on the per-node SNR. However, the one-bit algorithm provides significant performance gains in practical regimes with a moderate number of cooperating nodes: the per-node SNR required for attaining a substantial fraction of the beamforming gain is low enough (e.g., - 5dB for 65% of the beamforming gain) to provide significant extension in operation regimes, while providing aggregate SNRs which permit reliable communication at high spectral efficiency: for example, starting from -5 dB per-node SNR, we obtain about 11 dB aggregate SNR with 10 cooperating nodes, and 17 dB SNR with 20 cooperating nodes.

Gencel, M. F., Rasekh, M. E. and Madhow, U.
Proceedings of the 2015 IEEE International Symposium on Information Theory
Pages: 2041-2045
State: Hong Kong
Country: China
Date: June, 2015
ICB Affiliated Authors: Upamanyu Madhow