Noncircular Sources-Based Sparse Representation Algorithm for Direction of Arrival Estimation in MIMO Radar with Mutual Coupling

Abstract

In this paper, a reweighted sparse representation algorithm based on noncircular sources is proposed, and the problem of the direction of arrival (DOA) estimation for multiple-input multiple-output (MIMO) radar with mutual coupling is addressed. Making full use of the special structure of banded symmetric Toeplitz mutual coupling matrices (MCM), the proposed algorithm firstly eliminates the effect of mutual coupling by linear transformation. Then, a reduced dimensional transformation is exploited to reduce the computational complexity of the proposed algorithm. Furthermore, by utilizing the noncircular feature of signals, the new extended received data matrix is formulated to enlarge the array aperture. Finally, based on the new received data, a reweighted matrix is constructed, and the proposed method further designs the joint reweighted sparse representation scheme to achieve the DOA estimation by solving the l 1-norm constraint minimization problem. The proposed method enlarges the array aperture due to the application of signal noncircularity, and in the presence of mutual coupling, the proposed algorithm provides higher resolution and better angle estimation performance than ESPRIT-like, l 1-SVD and l 1-SRDML (sparse representation deterministic maximum likelihood) algorithms. Numerical experiment results verify the effectiveness and advantages of the proposed method.

Joint Smoothed l0-Norm DOA Estimation Algorithm for Multiple Measurement Vectors in MIMO Radar

“…Then, by matched filtering operation, the $N\times 1$ dimensional complex envelop of the output of the m th carrier matched filter is expressed as [14,27] $\begin{array}{c}\hfill {\mathrm{boldx}}_m\left(t\right)=\sum _{p=1}^P{\mathbf{a}}_r\left({\theta }_p\right){\mathbf{a}}_{tm}^{\mathtt{T}}\left({\theta }_p\right)s_p\left(t\right)+{\mathrm{boldn}}_m\left(t\right),\end{array}$ where ${\mathbf{a}}_r\left({\theta }_p\right)={\left[1,e^{j\pi sin\left({\theta }_p\right)},e^{j\pi 2sin\left({\theta }_p\right)},\dots ,e^{j\pi (N-1)sin\left({\theta }_p\right)}\right]}^{\mathtt{T}}$ is the receive steering vector, ${\mathrm{bolda}}_{tm}$ is the m th element of the transmit steering vector ${\mathbf{a}}_t\left({\theta }_p\right)={\left[1,e^{j\pi sin\left({\theta }_p\right)},e^{j\pi 2sin\left({\theta }_p\right)},\dots ,e^{j\pi (M-1)sin\left({\theta }_p\right)}\right]}^{\mathtt{T}}$, $s_p\left(t\right)$ contains the target reflection coefficient and the transmitted baseband signal such as non-circular signal, and ${\mathbf{n}}_m\left(t\right)$ is the noise vector after the m th matched filter. After all the matched filters, the received data vector, i.e., the vector composed of the outputs of the M matched filters, is given by [2,25,28] …”

“…Note that, for the dimension reduction in Equation (11), the reduced-dimensional matrix $\mathit{R}$ satisfies $\mathrm{bold-italicR}{\mathrm{bold-italicR}}^{{H}}={\mathit{I}}_{M+N-1}$. Hence, if the noise vector $\tilde{\mathit{n}}\left(t\right)$ is white Gaussian with covariance matrix ${\rho }^2{\mathit{I}}_{MN}$, it remains white Gaussian with covariance matrix $\mathrm{bold-italicR}{\rho }^2{\mathit{I}}_{MN}{\mathrm{bold-italicR}}^{{H}}={\rho }^2{\mathit{I}}_{M+N-1}$ after the transformation [2,25]. On the other hand, if the noise vector $\mathrm{bold-italicn}\left(t\right)$ is colored Gaussian with covariance matrix ${\mathrm{bold-italicV}}_a$, its covariance matrix turns into $\mathrm{bold-italicR}{\mathit{V}}_a{\mathrm{bold-italicR}}^{{H}}$ after the dimensional reduction.…”

“…Then, by matched filtering operation, the dimensional complex envelop of the output of the m th carrier matched filter is expressed as [ 14 , 27 ] where is the receive steering vector, is the m th element of the transmit steering vector , contains the target reflection coefficient and the transmitted baseband signal such as non-circular signal, and is the noise vector after the m th matched filter. After all the matched filters, the received data vector, i.e., the vector composed of the outputs of the M matched filters, is given by [ 2 , 25 , 28 ] where and is the zero-mean Gaussian white or colored noise vector. is the reflected signal vector after the M carrier matched filters, and it is assumed to be statistically independent and non-Gaussian with zero-mean.…”

“…Colocated multiple-input multiple-output (MIMO) radar has attracted a growing interest recently because it can achieve higher resolution and better parameter identification compared with conventional phased-array radar [ 1 ]. As one type of colocated MIMO radar, the monostatic MIMO radar is equipped with closely-located transmit and receive arrays, which result in the same angle for direction-of-departure (DOD) and direction-of-arrival (DOA) [ 2 ]. Aiming at DOA estimation, a large quantity of methods have been proposed, most of them are based on the signal and noise subspaces [ 3 , 4 , 5 , 6 ], such as the representative MUSIC (multiple signal classification) algorithm [ 3 ] and ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm [ 4 ].…”

Design and Analysis of Multiple-Input Multiple-Output Radar System Based on RF Single-Link Technology

“…However, the genetic algorithm has limitations: it easily falls into the local extremum and cannot find the optimal solution. The DOA estimation for MIMO radar with mutual coupling is also addressed in [15,16]. The reweighted sparse representation algorithm based on noncircular sources was suggested to provide higher resolution and better angle estimation performance than ESPRIT algorithm.…”