The direction of arrival (DOA) estimation is an important area of research in array signal processing. Currently, there are many DOA estimation algorithms with good performance, such as the multiple signal classification (MUSIC) algorithm, the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm,

etc. Most of these traditional DOA estimation algorithms require the source number as

a priori information and a large number of snapshots to guarantee the estimation precision. In recent years, the DOA estimation that utilizes the idea of sparse representation has become many scholars’ research hotspot [

1,

2]. The target signals can be regarded to be sparse in a spatial domain, and their DOAs can be estimated according to the array received data and a redundant dictionary. The DOA estimation algorithm by utilizing the idea of sparse representation mainly divides into two kinds [

3,

4]. One is the sparse model based on the array received data, and the other one is the sparse model based on the array covariance matrix. The singular value decomposition (SVD) of the array received data is used to propose a L

_{1}-SVD algorithm for DOA estimation [

5]. Literature [

6] introduces the idea of a sparse representation of array covariance vectors (SRACV) to propose a method called the L

_{1}-SRACV algorithm for estimating sparse signals’ DOAs. Compared to L

_{1}-SVD, the L

_{1}-SRACV algorithm does not need to determine the regularization parameter and has a higher stability. However, the L

_{1}-SRACV algorithm needs to estimate the noise power. In [

7,

8], L

_{1}-SRACV is improved such that the noise power is unnecessary and the algorithm’s robustness is enhanced. However, the above algorithms are all the resolution problems of the multiple measurement vectors (MMV) model and refer to complex operations and thus a heavy calculation burden. In this paper, the sparse model based on the array covariance matrix is transformed to a real-valued sparse model via a unitary transformation so that the amount of calculation is reduced by at least four times. Then, the real-valued sparse model is vectorized, and the MMV model is transformed to a single measurement vector (SMV) one whose calculation complexity is lower. Recently, the Khatri-Rao (KR) approach for DOA estimation increases rapidly. It can extend the array aperture effectively, increase the degree of freedom, and deal with the underdetermined DOA estimation in cases where the number of array elements is less than the source number in some conditions [

9,

10,

11]. According to the property of the KR product and the real-valued overcomplete dictionary achieved by a unitary transformation, this paper constructs a new real-valued dictionary and uses the idea of a SRACV to estimate the target signals’ DOAs. The simulations demonstrate that the proposed algorithm has a good estimation performance and a low amount of calculation.

In this paper, the italic letters, the bold italic capital letters, and the bold italic lower-case letters denote variables, matrices, and vectors, respectively. The remainder of this paper is organized as follows. The sparse DOA estimation model based on the array covariance matrix is introduced in

Section 2. The proposed algorithm and the detailed formula derivation of the proposed algorithm is given in

Section 3. The simulation results and conclusions are given in

Section 4 and

Section 5, respectively.