Collaborative one-shot beamforming under localization errors: A discrete optimization approach
Authors : Yagiz Savas, Erfaun Noorani, Alec Koppel, John Baras, Ufuk Topcu, and Brian M. Sadler
Journal : Signal Processing pp. 1-10, Volume 200, November 2022, 108647
We consider a mobile multi-agent network in which the agents locate themselves in an environment through imperfect measurements and aim to transmit a message signal to a far-field base station via col- laborative beamforming. The agents imperfect measurements yield localization errors that degrade the quality of service at the base station due to unknown phase offsets in the channels. Assuming that the localization errors follow Gaussian distributions, we study the design of a one-shot (non-iterative) beam- forming strategy that ensures reliable communication between the agents and the base station despite the localization errors. We formulate a risk-sensitive discrete optimization problem to choose an agent subset for transmission so that the desired signal-to-interference-plus-noise ratio (SINR) at the base sta- tion is attained with minimum variance. We show that, when the localization errors have small variances characterized in terms of the carrier frequency, greedy algorithms globally minimize the variance of the received SINR. Moreover, when the localization errors have large variances, we show that the variance of the received SINR can be locally minimized by exploiting the supermodularity of the mean and vari- ance of the received SINR. Simulations demonstrate that the proposed algorithms synthesize beamform- ers orders of magnitude faster than convex optimization-based approaches while achieving comparable performance with fewer agents.
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