Optimal training and data power allocation for distributed transmit beamforming

Performing distributed transmit beamforming across multiple cooperative radios can focus energy at a receiver to significantly improve the power, rate, and range tradeoff. In frequency division duplexed systems, the transmit beamformer is estimated at the receiver from a training signal and fed back to the transmitters. A caveat is that the training signal is not focused and as transmitters are added training becomes a large fraction of the total transmit power. We determine the optimal allocation of power between training and data that minimizes the outage probability. Results depend on the target spectral efficiency, coherence time, SNR per receiver, and number of transmitters and receivers.