Gridless Two-dimensional DOA Estimation With L-shaped Array Based on the Cross-covariance Matrix

The atomic norm minimization (ANM) has been successfully incorporated into the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for super-resolution. However, its computational workload might be unaffordable when the number of snapshots is large. In this paper, we propose two gridless methods for 2-D DOA estimation with L-shaped array based on the atomic norm to improve the computational efficiency. Firstly, by exploiting the cross-covariance matrix an ANM-based model has been proposed. We then prove that this model can be efficiently solved as a semi-definite programming (SDP). Secondly, a modified model has been presented to improve the estimation accuracy. It is shown that our proposed methods can be applied to both uniform and sparse L-shaped arrays and do not require any knowledge of the number of sources. Furthermore, since our methods greatly reduce the model size as compared to the conventional ANM method, and thus are much more efficient. Simulations results are provided to demonstrate the advantage of our methods

2-D DOA Estimation for L-Shaped Array With Array Aperture and Snapshots Extension Techniques

A two-dimensional (2-D) direction of arrival estimation method for L-shaped array with automatic pairing is proposed. It exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and the number of virtual snapshots simultaneously, and then applies the principle of MUSIC to construct an angle cost function and transforms the conventional 2-D search into 1-D via a Rayleigh quotient, which can greatly reduce the computation complexity. Finally, the azimuth and elevation angles are estimated without pair matching. Simulation results show that the proposed method has a better performance and can resolve more sources than some existing computationally efficient methods

Parallel Factor-Based Model for Two-Dimensional Direction Estimation

Two-dimensional (2D) Direction-of-Arrivals (DOA) estimation for elevation and azimuth angles assuming noncoherent, mixture of coherent and noncoherent, and coherent sources using extended three parallel uniform linear arrays (ULAs) is proposed. Most of the existing schemes have drawbacks in estimating 2D DOA for multiple narrowband incident sources as follows: use of large number of snapshots, estimation failure problem for elevation and azimuth angles in the range of typical mobile communication, and estimation of coherent sources. Moreover, the DOA estimation for multiple sources requires complex pair-matching methods. The algorithm proposed in this paper is based on first-order data matrix to overcome these problems. The main contributions of the proposed method are as follows: (1) it avoids estimation failure problem using a new antenna configuration and estimates elevation and azimuth angles for coherent sources; (2) it reduces the estimation complexity by constructing Toeplitz data matrices, which are based on a single or few snapshots; (3) it derives parallel factor (PARAFAC) model to avoid pair-matching problems between multiple sources. Simulation results demonstrate the effectiveness of the proposed algorithm

2-D angle of arrival estimation using a one-dimensional antenna array

In this paper, a two-dimensional (2-D) angle of arrival (AOA) estimator is presented for vertically polarised waves in which a one-dimensional (1-D) antenna array is used. Many 2-D AOA estimators were previously developed to estimate elevation and azimuth angles. These estimators require a 2-D antenna array setup such as the L-shaped or parallel antenna 1-D arrays. In this paper a 2-D AOA estimator is presented which requires only a 1-D antenna array. This presented method is named Estimation of 2-D Angle of arrival using Reduced antenna array dimension (EAR). The EAR estimator utilises the antenna radiation pattern factor to reduce the required antenna array dimensionality. Thus, 2-D AOA estimation is possible using antenna arrays of reduced size and with a minimum of two elements only, which is very beneficial in applications with size and space limitations. Simulation results are presented to show the performance of the presented method

Two-Dimensional AOA Estimation Based on a Constant Modulus Algorithm

We propose a two-dimensional (2D) angle of arrival (AOA) estimator using the algebraic constant modulus algorithm (ACMA). This algorithm was originally introduced to estimate the one-dimensional (1D) AOA. An extension to estimate and automatically pair the elevation and azimuth angles for different sources is derived and proved in this paper. The ACMA method factorises a matrix into two different matrices; one is of constant modulus and contains the azimuth AOA information; however the second was previously ignored. In this paper we will prove that this second matrix contains the elevation AOA information. Thus, 2D AOA estimation is proved possible using the ACMA method. Simulation results are presented to illustrate the proposed method’s performances under different conditions

Direction finding and mutual coupling estimation for uniform rectangular arrays

A novel two-dimensional (2-D) direct-of-arrival (DOA) and mutual coupling coefficients estimation algorithm for uniform rectangular arrays (URAs) is proposed. A general mutual coupling model is first built based on banded symmetric Toeplitz matrices, and then it is proved that the steering vector of a URA in the presence of mutual coupling has a similar form to that of a uniform linear array (ULA). The 2-D DOA estimation problem can be solved using the rank-reduction method. With the obtained DOA information, we can further estimate the mutual coupling coefficients. A better performance is achieved by our proposed algorithm than those auxiliary sensor-based ones, as verified by simulation results