Globally Optimal Joint Uplink Base Station Association and Beamforming

TL;DR

This paper proves polynomial time solvability for joint uplink base station association and beamforming problems in SISO/SIMO networks, introduces a fixed point binary search algorithm, and proposes a normalized fixed point method with empirical rapid convergence to global optima.

Contribution

It establishes polynomial time solutions for the problem, introduces a novel fixed point based binary search algorithm, and presents a new iterative method with proven geometric convergence.

Findings

The problems are polynomial time solvable in SISO and SIMO cases.

The NFP algorithm converges rapidly to the global optimum.

Empirical results show the NFP method outperforms polynomial algorithms in speed.

Abstract

The joint base station (BS) association and beamforming problem has been studied extensively in recent years, yet the computational complexity for even the simplest SISO case has not been fully characterized. In this paper, we consider the problems for an uplink SISO/SIMO cellular network under the max-min fairness criterion. We first prove that the problems for both the SISO and SIMO scenarios are polynomial time solvable. Secondly, we present a fixed point based binary search (BS-FP) algorithm for both SISO and SIMO scenarios whereby a QoS (Quality of Service) constrained subproblem is solved at each step by a fixed point method. Thirdly, we propose a normalized fixed point (NFP) iterative algorithm to directly solve the original problem and prove its geometric convergence to global optima. Although it is not known whether the NFP algorithm is a polynomial time algorithm, empirically it converges to the global optima orders of magnitude faster than the polynomial time algorithms, making it suitable for applications in huge-scale networks.