Ahmad Bazzi

Detection of the number of superimposed signals using modified MDL criterion: A random matrix approach

The problem of estimating the number of superimposed signals using noisy observations from N antennas is addressed. In particular, we are interested in the case where a low number of snapshots L = O(N) is available. We focus on the Minimum Description Length (MDL) estimator, which is revised herein. Furthermore, we propose a modified MDL estimator, with the help of random matrix tools, which improves the estimation of the number of sources. Simulation results demonstrate the potential of the modified MDL estimator over the traditional one, in the case where L = O(N).

On the effect of random snapshot timing jitter on the covariance matrix for JADE estimation

In this paper, we focus on joint multipath angle and delay estimation (JADE) in an OFDM communication setting. We analyse the effect of Gaussian random snapshot (OFDM symbol) timing jitter on the spatio-frequency sample covariance matrix containing delay and direction information. This sample covariance matrix is an input to the JADE and many other algorithms for signal parameter estimation. The analysis suggests a simple way to compensate for the jitter in the sample covariance matrix. We also present two simple methods for estimating the jitter variance, allowing its compensation. These techniques attempt to restore the low rank nature or other structure in the signal contribution. We then finally present some simulations for the resulting estimation quality of the multipath delays (ToAs) and angles (AoAs) of the incoming signals.

Online angle of arrival estimation in the presence of mutual coupling

A novel algorithm for estimating the Angles of Arrival (AoA) of multiple sources in the presence of mutual coupling is derived. We first formulate an “Equality Constrained Quadratic Optimisation” problem, then derive a suitable MUSIC-like algorithm to solve the aforementioned problem, and thus obtain good estimates of the AoA parameters. Identifiability conditions of the proposed algorithm are also derived. Finally, simulation results demonstrate the Root-Mean-Square Error (RMSE) performance of the algorithm as a function of Signal-to-Noise Ratio (SNR) and number of snapshots, with comparison to an existing method.

Single snapshot joint estimation of angles and times of arrival: A 2D Matrix Pencil approach

Two algorithms for the problem of joint angles and delays of arrival (JADE) of multiple paths are presented. The algorithms are based on a generalisation of the Matrix Pencil algorithm to the two dimensional case, i.e. 2D Matrix Pencils. Matrix pencil algorithms offer estimation of signal parameters, i.e. angles of arrival (AoA) or times of arrival (ToA), of multiple sources using a single snapshot. We focus on a scenario, where the OFDM symbol is transmitted in a rich multipath channel, which is the case of an indoor environment, and received through multiple antennas. The first algorithm seems more interesting than the second one, since its motivated from an idea that most Wi-Fi systems use a large number of subcarriers compared to the number of antennas. Simulation results demonstrate the potential of the first algorithm and its performance as a function of Signal-to-Noise ratio (SNR).

A comparative study of sparse recovery and compressed sensing algorithms with application to AoA estimation

We investigate the performance of some sparse recovery and compressed sensing algorithms when applied to the Angle-of-Arrival (AoA) estimation problem. In particular, we review three different approaches in compressed sensing, namely Pursuit-type, Thresholding-type, and Bayesian-based algorithms. The compressed sensing algorithms reviewed herein are of vast interest when applied to AoA estimation problems because of their ability to resolve sources with a single snapshot and without prior knowledge of the number of sources. We compare the performance of these algorithms in terms of Mean-Square Error (MSE) through simulations.

Sparse recovery using an iterative Variational Bayes algorithm and application to AoA estimation

This paper presents an iterative Variational Bayes (VB) algorithm that allows sparse recovery of the desired transmitted vector. The VB algorithm is derived based on the latent variables introduced in the Bayesian model in hand. The proposed algorithm is applied to the Angle-of-Arrival (AoA) estimation problem and simulations demonstrate the potential of the proposed VB algorithm when compared to existing sparse recovery and compressed sensing algorithms, especially in the case of closely spaced sources. Furthermore, the proposed algorithm does not require prior knowledge of the number of sources and operates with only one snapshot.

Blind on board wideband antenna RF calibration for multi-antenna satellites

The problem of joint Angle-of-Arrival (AoA) and calibration parameters in a wideband scenario is addressed. The system consists of multiple sources transmitting from different directions and in certain subcarriers. Sources in the same beam are regarded as transmitted from the same AoA and their signals are allocated to different subcarriers while users in different beams may transmit on the same subcarrier, i.e. the signals are multiplexed in space and frequency. Then, signals from a given beam not necessarily occupy the full bandwidth but only specific subcarriers. In addition, due to the wideband of the signal, each RF chain introduces frequency dependent gain and phase shift that need to be calibrated to perform a subsequent demultiplexing in a digital beamforming matrix. We propose a novel blind algorithm that (i) estimates the AoAs of all present sources in the bandwidth of interest and (ii) estimates the different gains/phases at each antenna per frequency up to an unknown impairment at a reference antenna. We provide identifiability conditions that ensure a successful parameter estimation. Finally, the potential of the proposed algorithm compared to the case of known calibration parameters is assessed by simulations.

On mutual coupling for ULAs: Estimating AoAs in the presence of more coupling parameters

The problem of Angle-of-Arrival estimation of multiple sources in the presence of mutual coupling is addressed. The presence of unknown mutual coupling between antenna array elements is known to degrade the performance of direction-finding algorithms. We first present a result explaining why some traditional methods, that estimate Angles-of-Arrival (AoAs) of multiple sources in the presence of mutual coupling, suffer from an identifiability issue, when the number of coupling parameters exceeds a certain level. Then, we present a first method that estimates AoAs of sources when more coupling parameters are present, namely when the number of coupling parameters exceeds that certain level. Finally, we propose a refinement of the proposed algorithm, which could further enhance the AoA estimates. Simulation results have demonstrated the potential of the proposed method and its refined version, for different scenarios, as it enjoys better performance than existing methods. A better description of the paper could be found in the Conclusions section.

Performance analysis of an AoA estimator in the presence of more mutual coupling parameters

The problem of Angle-of-Arrival estimation of multiple sources in the presence of mutual coupling is addressed. In this paper, we derive a Mean-Squared-Error (MSE) expression of a recently proposed algorithm that could estimate the Angles-of-Arrival of multiple sources in the presence of more mutual coupling parameters, compared to traditional methods. The MSE expression is compared with the MSE of MUSIC with known mutual coupling parameters and to the Cramer-Rao bound (CRB) of any unbiased estimator that estimates the Angles-of-Arrival in the presence of mutual coupling. It is shown that the proposed method is asymptotically unbiased. In addition, it is also shown that the method attains CRB for large number of antennas with fixed coupling parameters and uncorrelated sources. For high SNR, the CRB is not necessarily attained, however, we study the gap between the derived MSE and the CRB.

JADED-RIP: Joint Angle and Delay Estimator and Detector via Rotational Invariance Properties

A novel approach entitled “Joint Angle and Delay Estimator and Detector”, or simply JADED, is presented. This approach allows simultaneous estimation of number of coherent/non-coherent sources and joint estimation of the angles and times of arrival of each source. The system is composed of a Uniform Linear Array (ULA) receiving known OFDM symbols from a user in an indoor environment, which is rich in multipath. Therefore, the objective is to apply the JADED approach to this scenario, which allows extraction of the Line-of-Sight component based on the first arriving path. The first method, called JADED-RIP, makes use of the Rotational Invariance Properties (RIP) of ULAs and OFDM symbols, detects the number of multipath components, and estimates the angles and times of arrival of each path by performing a 2D search. The second method is a Computationally Efficient Single Snapshot (CESS) version of the JADED-RIP, i.e. it requires a 1D search followed by a least squares fit, and can only be used when a single OFDM symbol is available. Future insights are given in the Conclusions section.