Multi-Agent Coordination for Distributed Transmit Beamforming

Abstract

This paper presents the formulation and analysis of a two time-scale optimization algorithm for multiagent coordination for the purpose of distributed beamforming. Each agent is assumed to be randomly positioned with respect to each other with random phase offsets and amplitudes. Agents are tasked with coordinate among themselves to position themselves and adjust their phase offset and amplitude such that they can construct a desired directed beam. Here we propose a two time-scale optimization algorithm that consists of a fast time-scale algorithm to solve for the amplitude and phase while a slow time-scale algorithm to solve for the control required to re-position the agents. The numerical results given here indicate that the proposed two time-scale approach is able to reconstruct a desired beam pattern. I. INTRODUCTIONDistributed beamforming is concerned with the problem of cooperative communication where randomly located independent nodes coordinate among themselves to form a virtual antenna array. Although numerous studies on distributed beamforming have been carried out for over a decade, it was initially considered impractical due to the high complexity involved in modeling the generated beam pattern and the hardly achievable requirements on positioning and synchronization. Recent research results demonstrating the efficacy of distributed beamforming as a suitable solution for 5G communication systems such as mm-wave communication and machine to machine communications has further ignited the interest in this research field. The concept of distributed beamforming was conceived in early 2000s by two independent pieces of research under the names collaborative beamforming [1] and distributed beamforming [2].While initial research on collaborative beamforming focused on the beampattern analysis and the random Jemin George and Anjaly Parayil are with the