Modelling Aspects of Planar Multi-Mode Antennas for Direction-of-Arrival Estimation

Multi-mode antennas are an alternative to classical antenna arrays, and hence a promising emerging sensor technology for a vast variety of applications in the areas of array signal processing and digital communications. An unsolved problem is to describe the radiation pattern of multi-mode antennas in closed analytic form based on calibration measurements or on electromagnetic field (EMF) simulation data. As a solution, we investigate two modeling methods: One is based on the array interpolation technique (AIT), the other one on wavefield modeling (WM). Both methods are able to accurately interpolate quantized EMF data of a given multi-mode antenna, in our case a planar four-port antenna developed for the 6-8.5 GHz range. Since the modeling methods inherently depend on parameter sets, we investigate the influence of the parameter choice on the accuracy of both models. Furthermore, we evaluate the impact of modeling errors for coherent maximum-likelihood direction-of-arrival (DoA) estimation given different model parameters. Numerical results are presented for a single polarization component. Simulations reveal that the estimation bias introduced by model errors is subject to the chosen model parameters. Finally, we provide optimized sets of AIT and WM parameters for the multi-mode antenna under investigation. With these parameter sets, EMF data samples can be reproduced in interpolated form with high angular resolution

Tyler's Covariance Matrix Estimator in Elliptical Models with Convex Structure

We address structured covariance estimation in elliptical distributions by assuming that the covariance is a priori known to belong to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of Moments (GMM) optimization applied to robust Tyler's scatter M-estimator subject to these convex constraints. Unfortunately, GMM turns out to be non-convex due to the objective. Instead, we propose a new COCA estimator - a convex relaxation which can be efficiently solved. We prove that the relaxation is tight in the unconstrained case for a finite number of samples, and in the constrained case asymptotically. We then illustrate the advantages of COCA in synthetic simulations with structured compound Gaussian distributions. In these examples, COCA outperforms competing methods such as Tyler's estimator and its projection onto the structure set.Comment: arXiv admin note: text overlap with arXiv:1311.059

Time Delay Estimation from Low Rate Samples: A Union of Subspaces Approach

Time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel. Various approaches have been proposed in the literature to identify time delays introduced by multipath environments. However, these methods either operate on the analog received signal, or require high sampling rates in order to achieve reasonable time resolution. In this paper, our goal is to develop a unified approach to time delay estimation from low rate samples of the output of a multipath channel. Our methods result in perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate, even in the presence of overlapping transmitted pulses. This rate depends only on the number of multipath components and the transmission rate, but not on the bandwidth of the probing signal. In addition, our development allows for a variety of different sampling methods. By properly manipulating the low-rate samples, we show that the time delays can be recovered using the well-known ESPRIT algorithm. Combining results from sampling theory with those obtained in the context of direction of arrival estimation methods, we develop necessary and sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate. Our results can be viewed in a broader context, as a sampling theorem for analog signals defined over an infinite union of subspaces

Low-complexity three-dimensional AOA-cross geometric center localization methods via multi-UAV network

The angle of arrival (AOA) is widely used to locate a wireless signal emitter in unmanned aerial vehicle (UAV) localization. Compared with received signal strength (RSS) and time of arrival (TOA), AOA has higher accuracy and is not sensitive to the time synchronization of the distributed sensors. However, there are few works focusing on three-dimensional (3-D) scenarios. Furthermore, although the maximum likelihood estimator (MLE) has a relatively high performance, its computational complexity is ultra-high. Therefore, it is hard to employ it in practical applications. This paper proposed two center of inscribed sphere-based methods for 3-D AOA positioning via multiple UAVs. The first method could estimate the source position and angle measurement noise at the same time by seeking the center of an inscribed sphere, called the CIS. Firstly, every sensor measures two angles, the azimuth angle and the elevation angle. Based on that, two planes are constructed. Then, the estimated values of the source position and the angle noise are achieved by seeking the center and radius of the corresponding inscribed sphere. Deleting the estimation of the radius, the second algorithm, called MSD-LS, is born. It is not able to estimate angle noise but has lower computational complexity. Theoretical analysis and simulation results show that proposed methods could approach the Cramér–Rao lower bound (CRLB) and have lower complexity than the MLE

Super-resolved localisation in multipath environments

In the last few decades, the localisation problems have been studied extensively. There are still some open issues that remain unresolved. One of the key issues is the efficiency and preciseness of the localisation in presence of non-line-of-sight (NLoS) path. Nevertheless, the NLoS path has a high occurrence in multipath environments, but NLoS bias is viewed as a main factor to severely degrade the localisation performance. The NLoS bias would often result in extra propagation delay and angular bias. Numerous localisation methods have been proposed to deal with NLoS bias in various propagation environments, but they are tailored to some specif ic scenarios due to different prior knowledge requirements, accuracies, computational complexities, and assumptions. To super-resolve the location of mobile device (MD) without prior knowledge, we address the localisation problem by super-resolution technique due to its favourable features, such as working on continuous parameter space, reducing computational cost and good extensibility. Besides the NLoS bias, we consider an extra array directional error which implies the deviation in the orientation of the array placement. The proposed method is able to estimate the locations of MDs and self-calibrate the array directional errors simultaneously. To achieve joint localisation, we directly map MD locations and array directional error to received signals. Then the group sparsity based optimisation is proposed to exploit the geometric consistency that received paths are originating from common MDs. Note that the super-resolution framework cannot be directly applied to our localisation problems. Because the proposed objective function cannot be efficiently solved by semi-definite programming. Typical strategies focus on reducing adverse effect due to the NLoS bias by separating line-of-sight (LoS)/NLoS path or mitigating NLoS effect. The LoS path is well studied for localisation and multiple methods have been proposed in the literature. However, the number of LoS paths are typically limited and the effect of NLoS bias may not always be reduced completely. As a long-standing issue, the suitable solution of using NLoS path is still an open topic for research. Instead of dealing with NLoS bias, we present a novel localisation method that exploits both LoS and NLoS paths in the same manner. The unique feature is avoiding hard decisions on separating LoS and NLoS paths and hence relevant possible error. A grid-free sparse inverse problem is formulated for localisation which avoids error propagation between multiple stages, handles multipath in a unified way, and guarantees a global convergence. Extensive localisation experiments on different propagation environments and localisation systems are presented to illustrate the high performance of the proposed algorithm compared with theoretical analysis. In one of the case studies, single antenna access points (APs) can locate a single antenna MD even when all paths between them are NLoS, which according to the authors’ knowledge is the first time in the literature.Open Acces