Cognitive transmit beamforming from binary link quality feedback for point to point MISO channels

Transmit beamforming is an effective way to enhance transmission range and quality of service while limiting interference to other co-channel systems, thus facilitating easier coexistence. Transmit beamforming requires channel state information to be acquired at the receiver and fed back to the transmitter. This in turn requires a relatively complex receiver, agreement on a training protocol, and a cold-start training period during which no payload is sent to the receiver. This article explores how the transmitter can learn to beam-form on-the-fly from very low-rate channel quality indicator bits fed back from the receiver, while transmitting payload at the same time. The setup is tuned to low-latency scenarios where the receiver has limited capabilities, and is paired up opportunistically with the transmitter. Leveraging the Analytic Center Cutting Plane Method (ACCPM), an online channel correlation matrix learning method is developed, based on one-bit Signal to Noise Ratio (SNR) feedback from the receiver. The method is shown to asymptotically achieve the maximum possible SNR at the receiver (attained with perfect knowledge of the correlation matrix), starting from no channel state information. A Maximum Likelihood (ML) formulation is also developed for the case when there are feedback errors, and conditions for its asymptotic convergence are derived.