We analyze a millimeter wave network, deployed along the streets of a city, in terms of positioning and downlink data-rate performance, respectively. First, we present a transmission scheme where the base stations provide jointly positioning and data-communication functionalities. Accordingly, we study the trade- off between the localization and the data rate performance based on theoretical bounds. Then, we obtain an upper bound on the probability of beam misalignment based on the derived localization error bound. Finally, we prescribe the network operator a scheme to select the beamwidth and the power splitting factor between the localization and communication functions to address different quality of service requirements, while limiting cellular outage.

Positioning Data-Rate Trade-Off in mm-Wave Small Cells and Service Differentiation for 5G Networks

We consider a single-anchor multiple-input multiple-output orthogonal frequency-division multiplexing system with imperfectly synchronized transmitter (Tx) and receiver (Rx) clocks, where the Rx estimates its position based on the received reference signals. The Tx, having (imperfect) prior knowledge about the Rx location and the surrounding geometry, transmits reference signals based on a set of fixed beams. We develop strategies for the power allocation among the beams aiming to minimize the expected Cramer-Rao lower bound for Rx positioning. Additional constraints on the design are included to make the optimized power allocation robust to uncertainty on the line-of-sight (LOS) path direction. Furthermore, the effect of clock asynchronism on the proposed allocation strategies is studied. Our evaluation results show that, for non-negligible synchronization error, it is optimal to allocate a large fraction of the available power for the illumination of the non-LOS (NLOS) paths, which help resolve the clock offset. In addition, the complexity reduction achieved by our proposed suboptimal approach incurs only a small performance degradation. We also propose an off-grid compressed sensing-based position estimation algorithm, which exploits the information on the clock offset provided by NLOS paths, and show that it is asymptotically efficient.

Power Allocation and Parameter Estimation for Multipath-Based 5G Positioning

In this work, we study optimal transmit strategies for minimizing the positioning error bound in a line-of-sight scenario, under different levels of prior knowledge of the channel parameters. For the case of perfect prior knowledge, we prove that two beams are optimal, and determine their beam directions and optimal power allocation. For the imperfect prior knowledge case, we compute the optimal power allocation among the beams of a codebook for two different robustness-related objectives, namely average or maximum squared position error bound minimization. Our numerical results show that our low-complexity approach can outperform existing methods that entail higher signaling and computational overhead.

5G Downlink Multi-Beam Signal Design for LOS Positioning

In this paper, we propose various localization error optimal beamforming strategies and subsequently study the trade-off between data and localization services while budgeting time and frequency resources in a multi-user millimeter-wave framework. Allocating more resources for the data service phase instead of localization would imply higher data rate but, concurrently, also a higher position and orientation estimation error. In order to characterize this trade-off, we firstly derive a flexible application-dependent localization error cost function combining the Cramer-Rao lower bounds of delay, angle of departure and/or angle of arrival estimates at a mobile receiver over the downlink. Consequently we devise different fairness criteria based localization error optimal beamforming strategies in a multi-user context. Finally, we show the advantage of the latter beamforming strategies and assess the communication-localization trade-off with respect to various time-frequency resource division schemes.

https://hal-univ-rennes1.archives-ouvertes.fr/hal-02498131/document

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

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.

/pdf/localization-optimal-multi-user-beamforming-with-multi-1szvbylx5t.pdf

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

In this paper we study optimal beamforming policy to minimize the Cramer Rao Lower Bound (CRLB) of joint angle of arrival (AoA) and time delay estimation for a multicarrier millimeter wave (mmWave) system. Considering one single base station (BS) with rough a priori knowledge of channel coefficients and location information of the mobile station (MS), we show that it is possible to improve the accuracy of AoA and time delay estimation, and hence of mobile station (MS) positioning, by means of optimized beamforming. Mathematical formulation of the CRLB is first introduced and the related optimization problem is solved for a each single subcarrier independently. Then we propose a solution optimizing the beamformer jointly for the multicarrier system. A few examples are provided to illustrate the benefits from bound-based beamforming optimization.

Davide Dardard

Papers

Localization bound based beamforming optimization for multicarrier mmWave MIMO