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For radar imaging, a target usually has only a few strong scatterers which are sparsely distributed. In this paper, we propose a compressive sensing MIMO radar
imaging algorithm based on smoothed _{0}), and Bayesian method with Laplace prior in performance of sparse signal reconstruction. Two-dimensional image quality of MIMO radar using the new method has great improvement comparing with aforementioned reconstruction algorithm.

Multiple Input Multiple Output (MIMO) radar has been widely concerned in recent years. Unlike the conventional radar system which transmits correlated signals, a MIMO radar system transmits multiple independent signals and receives the scattered signals via its antennas [

The recent developed new field, known as sparse learning, is a technique proposed recently to recovery sparse signal by optimization theory [

The targets in sky are usually sparse and can be viewed as ideal point targets for DOA estimation. The signal model in this case fits the requirement of sparse learning. Angle-Doppler estimation of targets using sparse learning of MIMO radar was studied in [

This paper is organized as follows. Section

In this section, we describe a signal model for the MIMO radar. Considering a monostatic MIMO radar imaging system with only one snapshot signal, it has a

Geometry of MIMO radar imaging.

Let

The above equation can be rewritten as a simple matrix form

Through time domain sampling, the received signal can be expressed as a matrix

For sparse learning, the optimization algorithms have been developed for real valued signals. We divide the signal into its real and imaginary parts as follows:

Because the strong scatterers are sparsely distributed for imaging,

In order to obtain an approximate

The comparison of Gauss function and the approximate hyperbolic tangent function.

Therefore sparse signal recovery algorithm based on

There are many methods to solve (

First, we compute the Newton direction of approximate hyperbolic tangent function

To meet the requirement,

Finally, the Newton direction in this paper is simplified as

initialization:

let the minimum

choose a proper decreasing sequence of

for

let

minimize the function

for

compute the revised Newton direction

use the revised Newton method and obtain

project

set

final answer is

Now let us explain the choosing of some parameters.

In practical application,

In simulation 1, we compare the proposed sparse signal recovery algorithm with OMP, SL0 method, and Bayesian method with Laplace prior. The signal model with noise is

Computation costs of different methods.

When there is no noise, the reconstruction probability for different methods with different

Correct position estimation for different

Correct position estimation for different number of measurement.

MSE for different

Correct position estimation frequencies for different

In simulation 2 and simulation 3, we consider imaging of a target in two-dimension. The center frequency

(a) Original image of the target, (b) reconstructed image of OMP, (c) reconstructed image of Bayesian method with Laplace prior, (d) reconstructed image of SL0, and (e) reconstructed image of ANSL0.

In simulation 3, some scatterers of the target are not on the grid points; then the scenario is a more realistic situation. The parameters of MIMO radar are the same as simulation 2. The target consists of 9 scatterers. The distance from the target to the radar is 200 km. The relative positions of the scatterers are (1, 1), (0.5, 5), (1.5, 7), (5.5, 4.5), (5, 6.5), (5.5, 3), (9, 1.25), (9.25, 5), and (9.25, 8.25) (m, m). The sampling distance of grid points in two dimensions is all 1 m.

Contour plot of reconstructed images using (a) OMP, (b) Bayesian method with Laplace prior, (c) SL0, and (d) ANSL0.

In the simulation 4, the parameters of MIMO radar are the same as simulation 2.

There are three target scatterers in the imaging region. The distance from the target to the radar is 150 km. Three target scatterers locate at (14, 11), (13, 14.2), (16, 11.2) (m, m).

The targets locate at close range. The complex amplitudes are 0.2, 0.5, and 0.9, respectively.

(a) Original image of the targets, (b) reconstructed image of OMP, (c) reconstructed image of Bayesian method with Laplace prior, (d) reconstructed image of SL0, and (e) reconstructed image of ANSL0.

RMSE of images versus SNR.

Sparse learning reconstruction algorithm can improve the image quality of a target including scatterers discrete distribution. We propose one new approximate hyperbolic tangent function and use revised Newton method to reconstruct MIMO radar imaging algorithm. In practical imaging, the coefficient matrix may be ill conditioned. By using the main value weighted method in this paper, the robustness of this algorithm is strengthened consumedly compared with the traditional algorithm described in [

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

This work was supported by the Chinese National Natural Science Foundation under Contracts nos. 61471191, 61201367, and 61271327 and Funding of Jiangsu Innovation Program for Graduate Education and the Fundamental Research Funds for the Central Universities (CXZZ12_0155) and partly funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PADA).

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