We introduce an iterative least squares method (ILS) for estimating the 2D-DOA and frequency based on L-shaped array. The ILS iteratively finds direction matrix and delay matrix, then 2D-DOA and frequency can be obtained by the least squares method. Without spectral peak searching and pairing, this algorithm works well and pairs the parameters automatically. Moreover, our algorithm has better performance than conventional ESPRIT algorithm and propagator method. The useful behavior of the proposed algorithm is verified by simulations.
Antenna arrays have been used in many fields such as radar, sonar, and mobile communications, and so forth, [
The ML method is often applicable but might be computationally prohibitive. ESPRIT and MUSIC algorithms are based on signal subspace and have better parameter estimation performance. The main advantages of MUSIC/ESPRIT are the high-resolution estimates of direction of arrivals (DOAs) and frequencies, while the computational effort compared to ML method is significantly reduced. MUSIC requires multiple dimensional spectral peak searching, and it is the search that is still computationally expensive. The primary computational advantage of ESPRIT is that it eliminates the search procedure inherent. ESPRIT method requires eigenvalue decomposition (EVD) to the cross spectral matrix or singular value decomposition (SVD) to the received data. Reference [
The remainder of this paper is structured as follows. Section
We denote by
We consider an L-shaped array with sensors at
The structure of L-shaped array.
The received signal of
The received signal of
The received signal of the L-shaped array antennas can be denoted as
We assume that channel state information is constant for
Define the delay matrix as
It can be seen from (
The cost function can be constructed via the least squares criterion and given by
Firstly, fix
Let the initial values
Calculate
Calculate
Calculate
The basic idea of the iterative least square algorithm is to minimize the cost function
Performance of algorithmic convergence.
We obtain the estimated matrices
We use iterative least squares method to attain the direction matrix
In contrast to ESPRIT algorithms in [
According to [
The advantages of the proposed algorithm can be summarized as follows. (1) The 2D-DOA and frequency can be paired automatically. (2) The proposed algorithm has better angle and frequency estimation performance than ESPRIT algorithm and PM algorithm.
We present Monte Carlo simulations that are to assess joint 2D-DOA and frequency estimation performance of the proposed algorithm. The number of Monte Carlo trials is 500. There are three signals impinging on L-shaped array at (
Define the root mean squared error: (RMSE) of frequency
We first investigate the convergence performance of the proposed algorithm. Define
The performance of our proposed algorithm is investigated.
Elevation angle and azimuth angle scatter.
Elevation angle and frequency scatter.
We compare our proposed algorithm with ESPRIT algorithm, MUSIC algorithm, propagator method and CRB. The simulation parameters are retained as Simulation
Angle estimation performance comparison.
Frequency estimation performance comparison.
Our proposed algorithm performance with
Angle estimation with different antennas.
Frequency estimation with different antennas.
The performance of our proposed algorithm with
Frequency estimation with different sources.
Frequency estimation with different sources.
In this paper, we develop a novel method for joint 2D-DOA and frequency estimation based on L-shaped array using iterative least squares technique. Without spectral peak searching and pairing, this algorithm works well. Furthermore, our algorithm has much better 2D-DOA and frequency estimation performance than conventional ESPRIT algorithm and PM algorithm, and it has a very close 2D-DOA and frequency estimation performance to MUSIC algorithm. The useful behavior of the proposed algorithm is verified by simulations.
This work is supported by National Nature Science Foundation of China (nos. 61179006, 60801052), Jiangsu Planned Projects for Postdoctoral Research Funds (no. 1201039C), Open project of key laboratory of underwater acoustic communication and marine information technology (Xiamen University) and Nanjing University of Aeronautics and Astronautics Research Funding (nos. NP2011036, NZ2012010, kfjj120115, kfjj20110215). The authors wish to thank the anonymous reviewers for their valuable suggestions on improving this paper.