Localization Optimal Multi-user Beamforming with multi-carrier mmWave MIMO

Abstract

In this paper, we propose optimal beamforming strategies for a millimeter wave (mmWave) system consisting of multiple users based on the localization performance bounds. We consider a single base station (BS) with prior coarse knowledge of the users' positions and formulate the optimal beamforming problem in order to minimize the localization error consisting of Cramer Rao Lower Bounds (CRLBs) of delay, angle of departure (AoD) and angle of arrival (AoA) estimation at the mobile users. We first formulate the simplified CRLB of estimation parameters, taking advantage of multiple sub-carriers, and then formulate the localization error for optimization of the beamformer. Finally, we evaluate the resulting position and orientation error bounds after optimization for several fairness strategies through Monte Carlo simulations.

Localization and Throughput Trade-Off in a Multi-User Multi-Carrier mm-Wave System

“…Since we solved the optimization problems in equations (19) and (20) without the rank constraints to maintain convexity of the problem, we perform the rank-1 approximation of matrix F * n as for the single-user case in equation (17). We can see that objective function for min max fairness scheme in equation (19a) is a linear maximization problem with N 2 t N + 3 variables whereas that for the proportional fairness scheme is a non linear optimization problem in equation (20a) with N 2 t N + 3 U optimization variables.…”

“…This SPEB is shown to be equivalent to a linear combination of the CRLB terms associated with delay and AoD estimates. Furthermore, [19] studies different fairness policies for localization error optimal beamforming in a multi-user multi-carrier system.…”

“…Similarly, in [22], the authors investigate different beam training strategies and the corresponding trade-offs between communication and positioning. Likewise, the authors study optimal beamwidth selection with energy [19] and power [23] budgeting schemes between localization and communication services in a single-user scenario.…”

Large Intelligent Surface for Positioning in Millimeter Wave MIMO Systems

“…It was shown that even a single BS can achieve promising positioning accuracy. Extensions to multiple-carrier and multiuser scenarios were studied in [7].…”

“…Practical positioning algorithms for the single-anchor mmWave MIMO system can be classified into two major categories, i.e., direct positioning [6] and two-stage positioning [4], [5], [7], [8]. The direct positioning aims at estimating the coordinates of the MS from the received signal directly, while the two-stage positioning first estimates the instantaneous channel realization: the channel gains, the angle of departure (AoD), the angle of arrival (AoA), and the time of arrival (ToA).…”