Usman et al. RESEARCH Sparse-based Reconstruction for DOA Estimation using non-Exhaustive Search Koredianto Usman 1,2* , Hendra Gunawan 3 and Andriyan B. Suksmono 1 Abstract A sparse-based direction-of-arrival (DOA) estimation recently gains a lot of attention due to its capability to reduce the number of samples significantly. However, this capability has to be paid by a heavy computation at the reconstruction side. Previous researches have addressed this problem, for example, by utilizing the unitary transform to change a complex-valued reconstruction problem to a real-valued one. In this paper, we proposed a simpler but effective approach using a non-exhaustive search to speed up the reconstruction process. This technique reduces scanning direction into a limited range, which reduces reconstruction complexity. Combined with convex optimization for sparse reconstruction, however, non-exhaustive search does not immediately produce a desirable result, because limiting the searching range causes spurious spikes that make actual DOAs difficult to identify. This problem is mitigated by additional side-scan. Three side-scan schemes are proposed : uniform, random, and progressive. Computer simulations show that the proposed schemes has a closed performance to the exhaustive scheme, especially the progressive side-scan. In terms of complexity, the proposed schemes reduce sensing matrix down to five times smaller. Keywords: Direction-of-arrival; sparse reconstruction; compressive sensing; l 1 -norm; convex optimization; non-exhaustive search 1 Introduction The problem of DOA estimation has been investigated for decades. DOA estimation is used in many engineer- * Correspondence: koredianto.usman@telkomuniversity.ac.id 1 School of Electrical and Informatics, Institut Teknologi Bandung, Jl.Ganesha 10, Bandung, Indonesia Full list of author information is available at the end of the article ing applications, such as radar, sonar, positioning, and sensing. Among the DOA estimation techniques, con- ventional subspace-based methods, such as MUSIC [1] and ESPRIT [2], gain popularity due to their high res- olution performance. Subspace techniques and other conventional DOA estimation algorithms, however, rely on the statisti- cal property of acquired samples. Therefore, a large number of samples is needed for an accurate DOA es- timate [3]. This requirement creates a traffic problem when the conventional DOA techniques are applied for distributed monitoring system such as Radar Sensor Network (RSN). A small traffic is necessary for such a system [4, 5]. One of the methods to reduce number of samples is by utilizing sparse reconstruction. This technique is now widely known as Compressive Sensing or Com- pressive Sampling (CS). This theory states that if a signal x of length N is K-sparse in a particular basis (Ψ), then it is possible reconstruct it back perfectly us- ing small amount of measurement (K · log(N )) [6, 7, 8]. Due to the universality of sparse signal, CS has been applied in a wide range of applications, from Astron- omy [9] to GPRs [10] and MRI imaging [11]. In Elec- trical Engineering, Hayasi et al. [12] has given a com- prehensive report on the application of CS, especially in Communication System including the DOA. There are many approach to utilize sparse-based re- construction for DOA estimation. Early research, for example, was done by Gorotnisky and Rao using iter- ative method called FOCUSS. They succeed in DOA estimation using single signal snapshot [13]. Another method, for example, is based on dimensional reduc- tion using SVD and l 1 minimization[14]. Combination of compressive sensing and classical algorithm such as MVDR and MUSIC also have been under research re- cently [15, 16]. Some successful simulations and ex- periments using CS in radar and sonar related appli- cations, for examples, are shallow ocean beamforming [17], sonar localization [18], speed and location estima- tion [19]. All of the sparse reconstruction methods, especially those which are based on l 0 or l 1 minimization, usually suffered from a heavy computational load. This is be- cause these algorithms compute the optimal solution