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Collaborative Beamforming Under Localization Errors A Discrete Optimization Approach

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Document pages: 14 pages

Abstract: We consider a network of agents that locate themselves in an environmentthrough sensor measurements and aim to transmit a message signal to a basestation via collaborative beamforming. The agents sensor measurements resultin localization errors, which degrade the quality of service at the basestation due to unknown phase offsets that arise in the agents communicationchannels. Assuming that each agent s localization error follows a Gaussiandistribution, we study the problem of forming a reliable communication linkbetween the agents and the base station despite the localization errors. Inparticular, we formulate a discrete optimization problem to choose only asubset of agents to transmit the message signal so that the variance of thesignal-to-noise ratio (SNR) received by the base station is minimized while theexpected SNR exceeds a desired threshold. When the variances of thelocalization errors are below a certain threshold characterized in terms of thecarrier frequency, we show that greedy algorithms can be used to globallyminimize the variance of the received SNR. On the other hand, when some agentshave localization errors with large variances, we show that the variance of thereceived SNR can be locally minimized by exploiting the supermodularity of themean and variance of the received SNR. In numerical simulations, we demonstratethat the proposed algorithms have the potential to synthesize beamformersorders of magnitude faster than convex optimization-based approaches whileachieving comparable performances using less number of agents.

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