Estimation of the direction of arrival of unknown number of sources using compressive MMV and sparse array geometry
Asghar, Sayed Zeeshan
Date of Issue2017-08-16
School of Electrical and Electronic Engineering
Array Signal Processing has multitude of applications. With the advent of new applications like self-driving cars and 5G mobile communications, this field has seen a renewal in interest from researchers. Compressive sensing, on the other hand is a comparatively new field of research and has generated tremendous interest in the past decade, since its conception. In this thesis, we explore integration of Compressive Sensing (CS) algorithms with the problem of Direction of Arrival (DOA) estimation through an array of antennas/sensors. Compressive Sensing has gained popularity in multitude of fields due to its ability of successful recovery of sub-Nyquist sampled signals, which was previously thought of as unlikely, if not all out impossible. The main goal of this thesis is to achieve efficiency and reduction of resources (e.g. number of array elements) through the use of CS algorithms to the problem of DOA estimation using antenna arrays. Antenna arrays used in compressive sensing based algorithms are generated randomly to minimize mutual coherence, a property of sensing matrix (which is also referred to as ''array manifold matrix'' in array processing jargon). Random sampling of aperture, although useful for compressive sensing, suffers from practical limitations. For an antenna array that is sufficiently random, some elements of the array would almost always fall very close to each other, which is infeasible to implement in a practical scenario. Rectangular arrays, although very uniform, suffer from a very high mutual coherence, which in turn degrades the performance of CS algorithms. Aperiodic arrays are a compromise solution. We demonstrate, in this thesis, that it is possible to design aperiodic arrays that perform much better than rectangular arrays by using a simple disturbance optimization scheme, which can be applied to other aperiodic geometries as well. We use Danzer tiling as a base geometry and device an optimization scheme, which uses very few parameters to generate an aperiodic geometry. We extend this framework to design aperiodic array geometries for broadband DOA estimation scenario and apply this technique to array geometries formed based on Penrose and Danzer aperiodic tiling. Furthermore, we study the problem of estimating DOA when we have multiple measurement vectors (MMV). The classical approach to address this problem is to use the MUSIC algorithm. But to use this algorithm, we must have complete knowledge of the number of sources. This drawback was eliminated by a MUSIC-like algorithm that does not presuppose the knowledge of the number of sources. This algorithm, computes the covariance matrix from MMV (or snapshots of data.) The covariance matrix has to be full rank for the algorithm to work properly. We, in thesis, devise a recursive MUCIC-like algorithm based on a generalized MUSIC criterion, which is capable of estimating DOA even when the covariance matrix is rank deficient. This algorithm is based on the principle of greed, which treats local maximum at every step as a global maximum. We compare this algorithm with other greedy algorithms like Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm and show that its performance is better than SOMP. Lastly, we address the problem of estimating DOA for broadband sources using Compressive Sensing algorithms. The recursive algorithm, discussed previously, is extended by using Taylor series expansion and focusing matrices approach to estimate the broadband sources. We also extend well known MMV algorithm, SOMP, to estimate DOA of broadband sources.