Scaling wideband distributed transmit beamforming via aggregate feedback

Abstract

We investigate distributed beamforming from a cluster of N cooperating transmitters to a distant destination over a wideband dispersive channel. Feedback from the destination is critical for enabling this. In order to develop protocols that scale to arbitrarily large numbers of cooperating nodes, we restrict attention to aggregate feedback broadcast from the destination to the entire transmit cluster, rather than per-transmitter channel feedback as in conventional feedback-based MIMO systems. We first show that naive application of a one-bit feedback algorithm developed for narrowband channels to each subcarrier in an OFDM system does achieve beamforming gain on each subcarrier, but results in an effective channel at the destination with severe phase discontinuities across frequency, which is not amenable to standard receive channel estimation algorithms. We then show that it is possible to enforce smoothness of phase across frequency by augmenting the feedback to 2 bits per subcarrier, which enables modeling and estimation of the effective channel as sparse in the time domain. Our preliminary results show that, even when the SNR per node is well below the threshold for reliable demodulation, it is possible to bootstrap using the N-fold power pooling gain obtained from incoherent combining of the signals from multiple transmitters, and to attain a significant fraction of the N2-fold beamforming gain using the proposed algorithm. We also discuss a number of open issues, recognizing that this is only a first step in developing scalable, wideband, distributed MIMO systems.