Two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals has received much attention in many applications, such as radar, wireless communication and sonar in the multipath environment.

There are several high resolution techniques proposed to solve the rank deficiency of spatial covariance matrix caused by the presence of coherent signals. The conventional solution to this problem is the spatial smoothing method, which partitions the original array into a series of overlapping sub-arrays.

In order to reduce the computational complexity, an efficient method is performed by another researcher. This method, called the matrix enhancement and matrix pencil (MEMP) algorithm, exploits the structure inherent in an enhanced matrix from the original data. However, the pairing result is not always correct when there are repeated parameters.

Fortunately, a modified MEMP (MMEMP) method is proposed to successfully solve the pairing problem. In order to decorrelate the coherent signals thoroughly, recently, other researchers proposed an estimation of signal parameters via rotational invariance techniques (ESPRIT)-like algorithm for coherent DOA estimation. By reconstructing a Toeplitz matrix from the covariance matrix, this approach can decorrelate the impinging waves thoroughly. More recently, it is extended to the 2-D situation, namely the 2-D ESPRIT-like method, in conjunction with the MMEMP method. Although there is no peak searching existing in this algorithm, the computational burden is still heavy, due to the complex eigenvalue decomposition (EVD) and singular value decomposition (SVD) involved.

REN Shiwei, MA Xiaochuan, YAN Shefeng and HOU Chaohuan (CAS Member) from the State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences considered an application of unitary transformation to 2-D DOA estimation of coherent sources.

In this research, a 2-D unitary ESPRIT-like (2-D UESPRIT-like) algorithm is presented to reduce the computation complexity. It can transform the complex computations into real-valued ones and provide significant computational savings. The following DOA extractions are achieved simply by the one-dimensional (1-D) unitary ESPRIT, avoiding the computations of 2-D matrices.

Simulation results show that the real computations required for our new algorithm are much less than that of the 2-D ESPRIT-like method. It becomes especially obvious when the dimensionality of the Hankel matrix tends to be large. Additionally, the variance of the estimates from the proposed method is close to the Cramer-Rao bound. Also, the resolution ability is superior to the others for the forward-backward average processing.

This research result was published online:
http://www.mdpi.com/search?q=&journal=sensors&volume=&authors=shiwei+ren&section=10&issue=&article_type=&special_issue=&page=&search=Search and on the recently issued Sensors (2013, 13, 4272-4288; doi:10.3390/s130404272).