Graph signal smoothness for direction-of-arrival estimation of source targets using non-uniform line arrays

Abstract

Performing direction-of-arrival (DOA) estimation of a detected source target using data collected from an array of sensors is a long-studied problem in signal processing. The emerging framework of signal processing on graphs (SPG) offers the opportunity to look at this problem from a different point of view by adding the concept of a graph underlying the measured data as an extra layer of information that can be incorporated in to the data processing system. While a recent presentation [J. Acoust. Soc. Am. 143, 1852 (2018)] showed how to use the Graph Fourier Transform to estimate DOA on a uniform line array, the purpose of this talk is to show how we can use the smoothness of a graph signal across vertices for the more involved case of a non-uniform line array. The scope of the problem was narrowed to DOA estimation of a single, far-field, and narrowband source signal. An iterative approach was developed that demonstrates the utility of SPG, and the approach was verified and tested through simulation under different signal-to-noise ratios. We also compared the results to conventional delay-and-sum beamforming to gain insight on what differentiates SPG over existing methods.

Direction-of-Arrival Estimation Using Signal Processing on Graphs

“…Our early contributions to the area demonstrated how SPG can be applied to the problem of DOA estimation. In [22,23], we addressed how ULA measured data, characterized as a far-field plane wave, can be modeled on a one-dimensional graph with undirected edges. In addition, we attempted to develop a new DOA estimation method by applying two existing operators in SPG: the the Graph Fourier Transform (GFT) and graph signal smoothness.…”

Narrowband Angle of Arrival Estimation Exploiting Graph Topology and Graph Signals

“…In the following, akin to [11], [12], we operate with a single source, I = 1 (for brevity, let Ω 1 = Ω), and investigate how GSP could assist us with the AoA estimation problem.…”

“…For the temporal component A t of the adjacency matrix, based on (11) and analogously to (13), we have that…”

“…Graph signal processing (GSP) and graph spectral analysis allow the characterisation and efficient analysis of data that has been obtained on an irregularly sampled grid [10], and therefore provide an interesting fit to an array whose elements may be arbitrarily arranged in space. To date, two papers have attempted to harness GSP for array signal processing and AoA estimation in particular: [11] experimentally established a coarse correspondence of the graph Fourier transform (GFT) coefficients to the AoA for a single source in a ULA; also for a ULA, [12] have chosen the graph topology, and hence the GFT, such that a MUSIC-like subspace projection can be exploited to estimate the AoA of a source. Specifically, the graph is constructed so that the steering vector for the source signal is an eigenvector (with unit eigenvalue) of the graph's adjacency matrix.…”

“…The ULA in [11], [12] defines a simple and straightforward adjacency between sensor elements, and derives a cyclic spatial graph structure by connecting each sensor node with its two nearest neighbours using unweighted [11] or weighted edges [12]. In [12], temporal samples acquired by each sensor are also modelled by a cyclic graph.…”