IEEE SIGNAL PROCESSING LETTERS, VOL. 23, NO. 12, DECEMBER 2016 1697 Improved Wideband DOA Estimation Using Modified TOPS (mTOPS) Algorithm Arnab K. Shaw, Member, IEEE Abstract—Test of orthogonality of projected subspaces (TOPS) estimates directions of arrival of wideband sources by exploiting or- thogonality between signal and noise subspaces in spectral domain. TOPS performs well at mid signal-to-noise ratio (SNR) range, but fares poorly at high SNR and noise-free cases. The TOPS pseu- dospectrum often exhibits spurious peaks at all SNR levels. This paper attempts to explain the cause of poor performance, and pro- poses suitable modifications to extend the effectiveness of TOPS from low SNR to noise-free case. The proposed modified-TOPS (mTOPS) achieves reduction in spurious peaks by incorporating signal-subspace projection instead of null-space projection used in TOPS. It also uses trace as performance metric, instead of loss of rank used in TOPS. The effectiveness of mTOPS has been studied via simulations. Index Terms—Array signal processing, direction of arrival (DOA) estimation, DOA, high resolution, test of orthogonality of projected subspaces (TOPS), wideband sources. I. INTRODUCTION E XISTING wideband direction of arrival (DOA) estimation algorithms utilize signal and noise subspaces at source frequencies by coherent [3]–[8] or incoherent combination [9]. Except for the work reported in [8], the coherent meth- ods require prior DOA estimates or beam steering to focus the array at potential source directions, and well-separated source DOAs need to be estimated iteratively [3]. Important DOA estimation algorithms have been covered in two recent collections [12], [13]. The TOPS algorithm [1], [2] is a novel concept that aligns source frequency components to a reference frequency to con- duct tests of orthogonality of projected subspaces. Unlike many existing wideband DOA estimation algorithms, among the key advantages of TOPS are that it does not require preliminary DOA estimates for focusing [3]–[6] or beamforming [10], [11]. Furthermore, closely spaced and well-separated DOAs are estimated in a single step without iterations. The core concept of TOPS is based on loss of rank of a matrix formed with dot products between noise subspace and frequency-aligned signal-subspaces at hypothesized DOAs, [1], [2]. In practice, however, null-space-based DOA estimation per- forms poorly. Further improvement in TOPS is attained by pro- jecting the frequency-aligned signal subspaces onto the null space of the hypothesized source spectral manifold [1]. With the projection operation TOPS performs well, but primarily in the mid signal-to-noise ratio (SNR) ranges as noted in the Ab- Manuscript received May 17, 2016; revised September 22, 2016; accepted September 25, 2016. Date of publication September 28, 2016; date of current version October 19, 2016. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Peter K. Willett. The author is with the Electrical Engineering Department, Wright State Uni- versity Dayton, Dayton, OH 45435 USA (e-mail: arnab.shaw@wright.edu). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LSP.2016.2614310 stract of [1], “this new technique performs better than others in mid-SNR ranges.” It has been shown in this letter that perfor- mance of TOPS may suffer at all SNR levels due to spurious peaks in the TOPS pseudospectrum. This letter proposes two key modifications to TOPS that ef- fectively reduce the spurious peaks exhibited by TOPS. First, it is observed that the original TOPS algorithm projects the noise subspaces onto the signal null space. It is argued here that signal null space and noise subspace span the same subspace, and their dot-product tends to compound the overall effect of noise, causing the spurious peaks in the TOPS pseudospec- trum. Therefore, this letter proposes that the signal subspace be projected onto the source spectral manifold at hypothesized DOAs. The rationale is that the projection of signal subspaces onto the signal subspace would reinforce the signal subspace instead of the noise-compounding effect in original TOPS. Sec- ond, trace[D H (φ)D(φ)] is used as performance metric to mea- sure the strength of the projected vector dot-product spaces to determine when nulling occurs. It is demonstrated that the combined effect of two mod- ifications steps, i.e., signal-subspace projection and trace metric substantially reduces spurious peaks in the mTOPS pseudospectrum—eliminating it completely with no noise. Sim- ulation studies show mTOPS is effective from low-SNR to no- noise case, overcoming known limitations of original TOPS. II. PROBLEM FORMULATION The observed signal is assumed to be composed of P plane waves having known overlapping bandwidths B ∈ [ω L ,ω H ]. P is assumed to be known [1], [2]. The received signal is sampled simultaneously at the output of a uniform linear array (ULA) of M (>P ) equally spaced sensors. The signal received at the mth sensor at kth time instant is x m (n)= P  p =1 s p (n − m d c sinθ p )+ z m (n) 0 ≤ n ≤ N − 1, 0 ≤ m ≤ M − 1 (1) where s p (·) is the signal radiated by the pth source, d is the separation between the sensors, c is the propagation velocity, and θ p is the unknown boresight DOA of the pth wavefront with the line of array. z m (·) is the additive noise at mth sensor, which is assumed to be spatially and temporally uncorrelated with the source signals. In Fourier domain X m (ω l )= P  p =1 e −jω l m d c sinθ p S p (ω l )+ Z m (ω l ) (2) with ω l =2πf l ∈ B, l = l 1 ,...,l 1 + L, where, ω l 1 = ω L and ω l 1 +L = ω H . In matrix notation x(ω l )  A l (θ)s(ω l )+ z(ω l ) (3) 1070-9908 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.