A Graph Signal Processing Approach to Direction of Arrival Estimation

Narrowband Angle of Arrival Estimation Exploiting Graph Topology and Graph Signals

“…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. Modelling the ULA by a cyclic graph leads to a sparse graph adjacency matrix [18] that contains only two non-zero elements in each row.…”

“…In this paper, we further develop the approach in [12] and particularly consider the case of non-uniform sampling, i.e. the case where arrays may be arbitrarily distributed in three dimensional space [9].…”

“…the case where arrays may be arbitrarily distributed in three dimensional space [9]. Since for an arbitrary array, spatial adjacency of sensors is not clearly defined, and sparsity of a graph's adjacency matrix has no implications on the sparsity of the GFT, we replace the adjacency matrix used in [12] for a fully connected graph in both spatial and temporal domains. The resulting algorithm has a similar philosophy to that in [12] but differs in detail.…”

“…Since for an arbitrary array, spatial adjacency of sensors is not clearly defined, and sparsity of a graph's adjacency matrix has no implications on the sparsity of the GFT, we replace the adjacency matrix used in [12] for a fully connected graph in both spatial and temporal domains. The resulting algorithm has a similar philosophy to that in [12] but differs in detail. We further develop a low complexity scheme, and highlight the performance difference between the GSP and MUSIC approaches.…”