Maximum likelihood joint angle and delay estimation from multipath and multicarrier transmissions with application to indoor localization over IEEE 802.11ac Radio

In this paper, we tackle the problem of joint angle and delays estimation (JADE) of multiple reflections of a known signal impinging on multiple receiving antennae. Based on the importance sampling (IS) concept, we propose a new non-iterative maximum likelihood (ML) estimator that enjoys guaranteed global optimality and enhanced high-resolution capabilities for both single- and multi-carrier models. The new ML approach succeeds in transforming the original multi-dimensional optimization problem into multiple two-dimensional ones thereby resulting in huge computational savings. Moreover, it does not suffer from the off-grid problems that are inherent to most existing JADE techniques. By exploiting the sparsity feature of a carefully designed pseudo-pdf that is intrinsic to the new estimator, we also propose a novel approach that enables the accurate detection of the unknown number of paths over a wide range of practical signal-to-noise ratios (SNRs). Computer simulations show the distinct advantage of the new ML estimator over state-of-the art JADE techniques both in the single- and multi-carrier scenarios. Most remarkably, they suggest that the proposed IS-based ML JADE is statistically efficient as it almost reaches the Camér-Rao lower bound (CRLB) even in the adverse conditions of low SNR levels. Using real-world channel measurements collected from four access points (APs) with IEEE 802.11ac standard's setup parameters in an indoor environment, we also show that the proposed ML estimator achieves a localization performance below 15 cm accuracy.