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A novel algorithm is proposed for two-dimensional direction of arrival (2D-DOA) estimation with uniform rectangular array using reduced-dimension propagator method (RD-PM). The proposed algorithm requires no eigenvalue decomposition of the covariance matrix of the receive data and simplifies two-dimensional global searching in two-dimensional PM (2D-PM) to one-dimensional local searching. The complexity of the proposed algorithm is much lower than that of 2D-PM. The angle estimation performance of the proposed algorithm is better than that of estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm and conventional PM algorithms, also very close to 2D-PM. The angle estimation error and Cramér-Rao bound (CRB) are derived in this paper. Furthermore, the proposed algorithm can achieve automatically paired 2D-DOA estimation. The simulation results verify the effectiveness of the algorithm.

Direction-of-arrival (DOA) estimation is a fundamental problem in array signal processing and has been widely used in many fields [

Propagator method, which is known as a low complexity method without eigenvalue decomposition (EVD) of the covariance matrix of the received data, has been proposed for DOA estimation through peak searching [

In this paper, we derive a reduced-dimension PM (RD-PM) algorithm, which reduces the high complexity for 2D-DOA estimation with uniform rectangular array compared with 2D-PM algorithm. The proposed algorithm applies the rotational invariance property of propagator matrix to get the initial angle estimation and then employs one-dimensional local searching to get more accurate angle and finally obtains the other angle via least square (LS) method and estimate azimuth and elevation angles. The proposed algorithm has the following advantages:

The remainder of this paper is structured as follows: Section

As illustrated in Figure

The structure of uniform rectangular array [

The received signal of the first subarray

Similarly, the received signal of the

For the signal model in (

In this section, we give a brief introduction of 2D-PM algorithm.

Partition the matrix

For estimating the propagator matrix

Define

Define

construct the covariance matrix

partition the

find the

compute

estimate

In this paper, we assume that the target number

The proposed algorithm gets the estimation of

The proposed algorithm requires

The proposed algorithm has much lower complexity than 2D-PM algorithm. The major complexity of the proposed algorithm is

The complexity comparison with different parameters is shown in Figures

Complexity comparison of different algorithms with different values of

Complexity comparison of different algorithms with different values of

This section aims at analyzing the theoretic estimation error of the proposed algorithm and deriving the Cramér-Rao bound (CRB).

Assume that the receive data in (

Since

The function from which we search for the minima in order to determine the estimates is

Define

That is,

According to (

According to [

We present 1000 Monte Carlo simulations to assess the angle estimation performance of the RD-PM algorithm. Define root mean square error (RMSE):

Figure

Angle estimation performance of the proposed algorithm with SNR = 20 dB.

Figures

Angle estimation performance comparison (

Angle estimation performance comparison (

Figure

Angle estimation performance with different values of

Figure

Angle estimation performance with different values of

Figures

Angle estimation performance with

Angle estimation performance with

Figure

Angle estimation performance of the proposed algorithm with the closely spaced sources.

In this paper, we have presented a novel algorithm for 2D-DOA estimation for uniform rectangular array using RD-PM algorithm. The proposed algorithm, which only requires one-dimensional local searching and avoids the EVD of the covariance matrix of the receive data, has a much lower complexity than 2D-PM algorithm. Simulation results show that the angle estimation performance of the proposed algorithm is better than that of ESPRIT algorithm and conventional PM algorithms, also very close to that of 2D-PM algorithm. Furthermore, the proposed algorithm can achieve paired 2D-DOA estimation automatically.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by China NSF Grants (61371169, 61301108,61471191,61471192, and 61271327), Jiangsu Planned Projects for Postdoctoral Research Funds (1201039C), China Postdoctoral Science Foundation (2012M521099, 2013M541661), Open Project of Key Laboratory of Modern Acoustic of Ministry of Education (Nanjing University), the Aeronautical Science Foundation of China (20120152001), Qing Lan Project, priority academic program development of Jiangsu high education institutions, and the Fundamental Research Funds for the Central Universities (NZ2012010, NS2013024, kfjj130114, kfjj130115).