[Paper Review] Power Allocation and Parameter Estimation for Multipath-based 5G Positioning

Anastasios Kakkavas, Henk Wymeersch+4 more|arXiv (Cornell University)|Dec 2, 2020

Network Time Synchronization Technologies57 references30 citations

TL;DR

This paper designs power allocation strategies for fixed Tx beams to minimize the expected Cramer-Rao lower bound for single-anchor 5G positioning in multipath channels. It also proposes a gridless compressed sensing-based position estimator that leverages clock offset information from NLOS paths.

ABSTRACT

We consider a single-anchor multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) 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 the reference signals based on a set of fixed beams. In this work, we develop strategies for the power allocation among the beams aiming to minimize the expected Cram\\'er-Rao lower bound (CRLB) for Rx positioning. Additional constraints on the design are included to ensure that the line-of-sight (LOS) path is detected with high probability. Furthermore, the effect of clock asynchronism on the resulting allocation strategies is also studied. We also propose a gridless compressed sensing-based position estimation algorithm, which exploits the information on the clock offset provided by non-line-of-sight paths, and show that it is asymptotically efficient.

Motivation & Objective

• Motivate high-accuracy single-anchor positioning in 5G with mm-Wave and large antenna arrays.
• Develop beam power allocation strategies to minimize the expected SPEB under prior geometry knowledge.
• Incorporate clock asynchronism effects and ensure LOS path detection with high probability.
• Propose a two-stage position estimation algorithm that uses gridless channel parameter estimation and mapping to position parameters.

Proposed method

• Model a single-anchor MIMO-OFDM system with fixed Tx beam codebook and imperfect Tx-Rx clock synchronization.
• Formulate the hybrid Fisher information-based SPEB and optimize the beam power allocation to minimize its expectation over priors.
• Use cubature rules to approximate ESPEB and derive a semidefinite program for optimal power allocation.
• Introduce a low-complexity surrogate via per-path optimization and weighted combination to reduce dimensionality.
• Present a gridless parameter estimation method for multipath parameters, followed by a mapping to position and clock offset.

Experimental results

Research questions

• RQ1 How should transmit power be allocated across a fixed beam codebook to minimize expected positioning error in a multipath 5G channel?
• RQ2 What is the impact of clock asynchronism on power allocation and LOS detection reliability?
• RQ3 Can a gridless compressed sensing-based estimator accurately recover multipath parameters and clock offset for position estimation?
• RQ4 How can recovered channel parameters be mapped to a 2D position and orientation under uncertain prior geometry?

Key findings

• A LOS-detection-aware power allocation strategy is formulated to minimize the ESPEB.
• A semidefinite program is derived to solve the power allocation under positivity and total-power constraints.
• A low-complexity approach uses per-path optimization and weighting to approximate the ESPEB with reduced complexity.
• A gridless parameter estimation algorithm recovers TOAs, AODs, AOAs, and gains, enabling a two-stage position mapping.
• The estimator exploits clock-offset information from NLOS paths to improve localization accuracy.