A low complexity monostatic cross multiplein multipleout (MIMO) radar scheme is proposed in this paper. The minimumredundancy linear array (MRLA) is introduced in the cross radar to improve the efficiency of the array elements. The twodimensional directionofarrival (DOA) estimation problem links to the trilinear model, which automatically pairs the estimated twodimensional angles, requiring neither eigenvalue decomposition of received signal covariance matrix nor spectral peak searching. The proposed scheme performs better than the uniform linear arrays (ULA) configuration under the same conditions, and the proposed algorithm has less computational complexity than that of multiple signal classification (MUSIC) algorithm. Simulation results show the effectiveness of our scheme.
Multiplein multipleout (MIMO) radar is a relative new concept in radar system that received considerable attention [
Classical angle estimation algorithms such as multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) require eigenvalue decomposition (EVD) or singular value decomposition (SVD) of received signal covariance matrix. In addition, MUSIC algorithm requires spectral peak searching, which would cause computation disaster in the situation of 2D angle estimation. ESPRIT algorithm is sensitive to the manifold of the arrays, making it unsuitable for MRA manifolds. Another problem that how to pair the estimated parameters arises within the ESPRIT algorithm, which requires the extra computational load, and usually fails to work in lower SNR. Furthermore, the subspace based methods suppose that the number of the sources is known, which is contrary to actual applications.
Trilinear decomposition (also called PARAFAC analysis) can be thought of as a generalization of ESPRIT and joint approximate diagonalization ideas [
In this paper, the minimumredundancy linear array (MRLA) configured monostatic cross MIMO radar is proposed for twodimensional (2D) directionofarrival (DOA) estimation, which turned out to be effective than the ULA configuration for a given number of antennas. The improved trilinear model based blind angle estimation algorithm is developed for the proposed radar scheme. The DOA estimation problem links to the trilinear model. In order to eliminate the phase ambiguity, the estimated phase is adaptively compensated according to the array manifold. With this improvement, the proposed algorithm could be extended for arbitrarily array manifolds. We also analyse the complexity and error characteristics of the algorithm. Simulation results show the effectiveness of the proposed scheme.
The rest of the paper is organized as follows. In Section
Consider a monostatic cross MIMO radar model, as shown in Figure
Monostatic cross MIMO radar.
The received signal
Define
Due to the matched filters in every receiver antenna, the transmitted waveforms can be separated from each other. The virtual elements were formed through the channel of the
Virtual elements of cross MIMO radar.
However, the referenced uniform linear array is redundant, which cannot utilize the elements of the array in the most efficient way. In the conventional methods, the minimumredundancy linear array geometries together with appropriate matrix augmentation techniques have proven to provide better performances than the simple uniform linear array configuration in terms of ability to detect and resolve a greater number of sources [
Some MRLA configurations.
Antenna number  The relative locations of antennas 

3 

4 

5 

6 

7 

8 

9 

10 

The data in (
Trilinear slice model.
The data matrix
Trilinear alternating least square (TALS) algorithm is the common data detection method for trilinear model [
According to (
Similarly, the LS fitting of
Finally, the LS fitting of
Although TALS algorithm is easy to implement and guarantee to converge, it also suffers from slow convergence. In [
Just as singular value decomposition (SVD) is a decomposition of twoway arrays into rank one twoway components, trilinear decomposition is a decomposition of threeway arrays into rank one threeway components. The fundamental difference is that the trilinear decomposition is unique under certain rank conditions, whereas bilinear decompositions into rank one components are not unique without imposing additional constraints. According to [
When the matrix
Once trilinear decomposition is accomplished, the estimated direction matrices
Similarity, define
The azimuth angle and elevation angle can be paired automatically through the following formula:
Traditional Capon and MUSIC algorithm requires 2D peak searching, which brings very heavy complexity. Others are effective only in condition that transmit and receive are uniform arrays. However, the proposed trilinear decompositionbased algorithm is effective for manifold of the ULA and MRLA. Compared with ESPRIT, which process the complexity of
According to [
To assess the angle estimation performance of the proposed algorithm, 1000 Monte Carlo simulations are presented. The root mean squared error (RMSE) of 2DDOD is defined as follows:
Figures
Angle estimation results with
Angle estimation results with
We compare the proposed algorithm and 2D MUSIC algorithm with
Average programme time comparison.
Algorithm SNR  −5 dB  0 dB  5 dB  10 dB 

2D MUSIC  6.476 s  6.479 s  6.529 s  6.482 s 
Proposed algorithm  0.236 s  0.228 s  0.227 s  0.226 s 
 
Algorithm SNR  15 dB  20 dB  25 dB  30 dB 
 
2D MUSIC  6.498 s  6.559 s  6.578 s  6.508 s 
Proposed algorithm  0.224 s  0.224 s  0.226 s  0.224 s 
RMSE comparison with 2D MUSIC.
Figure
RMSE comparison with ULA.
The performance of the proposed scheme under different pulse number
RMSE comparison with different
We also compared the RMSE performance of the cross radar with MRLA and ULA configuration, as shown in Figure
RMSE comparison with different
In this paper, we proposed the MRLA scheme for monostatic cross MIMO radar, and the trilinear decomposition algorithm is developed for twodimensional angle estimation. Without eigenvalue decomposition of received signal covariance matrix and peak searching, the proposed algorithm can achieve automatic pairing twodimensional angles and works well. Furthermore, our scheme has better performance than the ULA based scheme and has a very close performance to 2D MUSIC algorithm, which has heavier computational complexity than the proposed algorithm. Simulation results proved that the proposed scheme would achieve super performance in radar parameter estimation.
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 Contract nos. 61071163, 61071164, 61271327, and 61201367 and partly funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PADA).