Stochastic approximation and directive antennas in wireless networks

As the interest in “smart” antennas for space-division-multiple-access (SDMA) increases it is desirable to assess whether the exploration of the “space” by these antennas can lead to fundamental improvement in the performance of the multiple access systems. Sayrafian-Pour and Ephremides (1997) revisited the problem of determination of the largest achievable stable throughput on the collision channel employing a directive antenna. We proved that the generalization of existing time partitioning methods by adding space selectivity will not improve the resulting stable throughput and, hence, the collision channel model can only benefit from the presence of multiple directive antennas (i.e. simultaneous space diversity). However it is not clear how to achieve the maximum achievable throughput with such a multibeam directive antenna in case of unknown user distribution. The thesis of this paper, motivated by the emergence of multibeam directive antennas as important tools in wireless networking, is to solve the problem of finding the optimal beamwidths for such an antenna. We propose a multi-dimensional extension of the Robbins and Monroe (1951) stochastic approximation algorithm to control the beamwidth. Convergence of the algorithm is proved and a simulation result is provided to demonstrate the behavior of the algorithm