Based on TLS-ESPRIT algorithm, this paper proposes a weighted spatial smoothing DOA estimation algorithm to address the problem that the conventional TLS-ESPRIT algorithm will be disabled to estimate the direction of arrival (DOA) in the scenario of coherent sources. The proposed method divides the received signal array into several subarrays with special structural feature. Then, utilizing these subarrays, this paper constructs the new weighted covariance matrix to estimate the DOA based on TLS-ESPRIT. The auto-correlation and cross-correlation information of subarrays in the proposed algorithm is extracted sufficiently, improving the orthogonality between the signal subspace and the noise subspace so that the DOA of coherent sources could be estimated accurately. The simulations show that the proposed algorithm is superior to the conventional spatial smoothing algorithms under different signal to noise ratio (SNR) and snapshot numbers with coherent sources.

Recently, Gan and Luo have proposed a direction-of-arrival estimation method for uncorrelated and coherent signals in the presence of multipath propagation [3]. In their method, uncorrelated and coherent signals are distinguished by rotational invariance techniques and the property of the moduli of eigenvalues. However, due to the limitation of finite number of sensors, the pseudo-inverse matrix derived in this method is an approximate one. When the number of sensors is small, the approximation error is large, which adversely affects the property of the moduli of eigenvalues. Consequently, the method in [3] performs poorly in identifying uncorrelated signals under such circumstance. Moreover, in cases of small number of snapshots and low signal to noise ratio, the performance of their method is poor as well. Therefore, in this letter we first study the approximation in [3] and then propose an improved method that performs better in distinguishing between uncorrelated signals and coherent signals and in the aforementioned two cases. The simulation results demonstrate the effectiveness and efficiency of the proposed method.

A new direction of arrival (DOA) estimation method is introduced with arbitrary array geometry when uncorrelated and coherent signals coexist. The DOAs of uncorrelated signals are first estimated via subspace-based high resolution DOA estimation technique. Then a matrix that only contains the information of coherent signals can be formulated by eliminating the contribution of uncorrelated signals. Finally a subspace block sparse reconstruction approach is taken for DOA estimations of the coherent signals.

This paper addresses the issue of Unconditional or Stochastic Maximum likelihood (SML) estimation of directions-of-arrival (DOA) finding using sensors with arbitrary array configuration. The conventional SML estimation is formulated without an important condition that the covariance matrix of signal components must be non-negative definite. An likelihood function can not be evaluated exactly for all possible sets of directions. First, this paper reveals that the conventional SML has three problems due to the lack of the condition. 1) Solutions in the noise-free case are not unique. 2) Global solution in the noisy case becomes ambiguous occasionally. 3) There exist situations that any local solution does not satisfy the condition of the non-negative definiteness. We propose an exact formulation of the SML estimation of DOA to evaluate an likelihood function exactly for any possible set of directions. The proposed formulation can be utilized without any theoretical difficulty. The three problems of the conventional SML are solved by the proposed exact SML estimation. Furthermore we show a local search technique in the conventional SML has a good chance to find an optimal or suboptimal DOA although the suboptimal solutions violate the condition of the non-negative definiteness. Finally some simulation results are shown to demonstrate good estimation properties of the exact SML estimation.

Estimating the number of signals (NIS) is an important goal in array signal processing, such as direction-of-arrival (DOA) estimation. A common approach for solving this problem is to use an eigenvalue of the array covariance matrix and information criterion, such as the Akaike information criterion (AIC) and minimum description length (MDL). However they suffer serious degradation, when the incoming signals are coherent. To estimate the NIS of the coherent signals impinging on a uniform linear array (ULA), a method for estimating the number of signals without eigendecomposition (MENSE) is proposed. The accuracy of the NIS estimation performance of MENSE is superior to the other algorithms equipped with preprocessing such as the spatial smoothing preprocessing (SSP) and forward/backward spatial smoothing techniques (FBSS) to decorrelate the coherency of signals. Instead of using SSP or FBSS preprocessing, MENSE uses the Hankel correlation matrices. The Hankel correlation matrices can not only decorrelate the coherency of signals but also suppress the influence of noise. However, in severe conditions like low signal-to-noise ratio (SNR) or a closely spaced signals impinging on a ULA, the NIS estimation metric of MENSE has some bias which causes estimation error. In this paper, we pay attention to the multiplicity defined by the ratio of the geometric mean to the arithmetic mean. Accordingly, we propose a new estimation metric that has less bias than that in MENSE. The Computer simulation results show that the proposed method is superior to MENSE in the above severe conditions.

To handle coherent signals with unknown arrival angles, an adaptive beamforming method is proposed which can be applied to an arbitrary array. The proposed method efficiently solves a generalized eigenvalue problem to estimate the arrival angles of the desired coherent signal group, by exploiting the Brent method in conjunction with alternating maximization. We discuss the condition for the correct direction estimation without erroneously taking interference direction estimates for the desired ones. Simulation results show that the performance of the proposed beamformer is very similar to that of the beamformer with the exact composite steering vector (CSV).

A uniform circular array (UCA) is a well-known array configuration which can accomplish estimation of 360 field of view with identical accuracy. However, a UCA cannot estimate coherent signals because we cannot apply the SSP owing to the structure of UCA. Although a variety of studies on UCA in coherent multipath environments have been done, it is impossible to estimate the DOA of coherent signals with different incident polar angles. Then, we have proposed Root-MUSIC algorithm with a cylindrical array. However, the estimation performance is degraded when incident signals arrive with close polar angles. To solve this problem, in the letter, we propose to use SAGE algorithm with a cylindrical array. Here, we adopt a CLA Root-MUSIC for the initial estimation and decompose two-dimensional search to double one-dimensional search to reduce the calculation load. The results show that the proposal achieves high resolution with low complexity.

Mainly, a uniform linear array (ULA) has been used for DOA estimation of coherent signals because we can apply the spatial smoothing preprocessing (SSP) technique. However, estimation by a ULA has ambiguity due to the symmetry, and the estimation accuracy depends on the DOA. Although these problems can be solved by using a uniform circular array (UCA), we cannot estimate the DOA of coherent signals because the SSP technique cannot be applied directly to the UCA. In this paper, we propose to estimate 2-dimensional DOA (polar angles and azimuth angles) estimation of coherent signals using a cylindrical array which is composed of stacked UCAs.

A robust adaptive beamforming method is proposed to cancel coherent, as well as incoherent, interference using an array of arbitrary geometry. In this method, coherent interferences are suppressed by a transformation of received data with the estimates of their arrival angles and then, to reject incoherent interferences, the array output power is minimized subject to the look direction constraint in the transformed signal-plus-interference (TSI) subspace. This TSI subspace-based beamforming results in robustness to errors in the angle estimations. Its performance is theoretically examined. The theoretic results conform to simulation results. It is straightforward to apply the theoretic results to the performance analysis of subspace-based adaptive beamfomers only for incoherent interference cancellation.