We proposed a transmit/receive spatial smoothing with improved effective aperture approach for angle and mutual coupling estimation in bistatic MIMO radar. Firstly, the noise in each channel is restrained, by exploiting its independency, in both the spatial domain and temporal domain. Then the augmented transmit and receive spatial smoothing matrices with improved effective aperture are obtained, by exploiting the Vandermonde structure of steering vector with uniform linear array. The DOD and DOA can be estimated by utilizing the unitary ESPRIT algorithm. Finally, the mutual coupling coefficients of both the transmitter and the receiver can be figured out with the estimated angles of DOD and DOA. Numerical examples are presented to verify the effectiveness of the proposed method.
A novel array radar named as multiple-input multiple-output (MIMO) radar has improved the progress of array signal processing [
The direction of departure (DOD) and direction of arrival (DOA) estimation are one of the most important aspects in bistatic MIMO radar with collocated antennas. And a lot of algorithms have been presented for this issue. In [
In recent years, although many institutes and researchers have been studying this novel radar, only a few of institutes have built up physical systems (e.g., the ONERA in France). In [
In this paper, we proposed a transmit/receive spatial smoothing with improved effective aperture (TRSSIA) method for joint DOD and DOA estimation in bistatic MIMO radar with unknown mutual coupling. Firstly, the white Gaussian noise is restrained using its dependency in both the spatial and temporal domains. Then the TRSSIA is used to construct the transmit spatial smoothing matrix and the receive spatial smoothing matrix. Due to the Vandermonde structure of steering vector with uniform linear arrays (ULA), the transmit and receive augmented spatial smoothing matrices are constructed, and these two matrices can improve the effective aperture two times larger than conventional ones. Thirdly, by using the centro-Hermitian structure of augmented matrices, the real-valued subspace methods (e.g., unitary ESPRIT) can be used to estimate DOD and DOA. Finally, an additional DOD and DOA pairing technique is proposed and the mutual coupling coefficients are estimated. The proposed approach restrains white Gaussian noise and takes full advantage of the received data, so it provides better angle estimation performance. And it can deal with more than two coherent targets.
The remainder of the paper is organized as follows. In Section
Consider a bistatic MIMO radar system equipped with
It assumes that the noise is i.i.d. complex white Gaussian noise, and we can obtain the equation written as
According to (
Factually, we can only get limited snapshots, so we obtain the asymptotic correlation coefficients:
According to (
Consider the effect of mutual coupling in both the transmitter and receiver; we construct two selection matrices:
Then we restrain the noise of selected data, based on (
After restraining the noise, we obtain the new received data vector
Firstly, we define a
For
Then we obtain an augmented matrix:
We note that
The real-valued signal subspace can be obtained by making SVD on
A class of least squares (LS) approaches [
In the same way, we estimate the angles of DOA. Firstly, for
Because the proposed TRSSIA approach tries to make full use of the received data, the angles of DOD and DOA are figured out from transmit augmented matrix and receive augmented matrix, respectively. By exploiting the relationship between the steering vectors
In order to calibrate the antennas with unknown mutual coupling, the mutual coupling coefficients need to be estimated.
For any
By Lemma
The mutual coupling coefficients in receiver also can be figured out in the same way. By exploiting the relationship between steering matrix and signal subspace
In the following simulations, we assume that both the transmit and receive arrays are ULAs with
In the first simulation, we investigate the angle estimation performances of MUSIC-Like, ESPRIT-Like, and tensor-based real-valued subspace (in this paper, we call it HOSVD) methods and our proposed TRSSIA method. There are two cases:
RMSE of angle estimation versus SNR: (a)
The second simulation is carried out to show the RMSE of angle estimation versus number of pulses with SN
(a) RMSE of angle estimation versus number of pulses. (b) The ratio of signal power to noise power versus number of pulses (
In the third simulation, it compares the angle estimation performance of the TRSSIA method with the performance of the HOSVD methods in the scenario of coherent targets. There are three cases:
RMSE of angle estimation versus SNR with coherent targets (
As we know, the forward-backward (FB) smoothing is a preferable technique to cope with coherent signals [
(a) RMSE of angle estimation versus number of pulses with coherent targets. (b) Runtime of both TRDS and TRSSIA algorithms versus number of pulses (
The performance of mutual coupling estimation is demonstrated in the fourth simulation. The RMSEs of the real part and the imaginary part of mutual coupling are adapted to measure the performance. In [
RMSE of mutual coupling estimation versus SNR (
This paper has proposed an algorithm for angle estimation with unknown mutual coupling in both the transmitter and receiver. The preliminary work is to restrain the white Gaussian noise of each channel by computing the correlation coefficients, because the noise is independent in both the spatial and temporal domains. In order to use more information of the received data, we do spatial smoothing in both the transmit array and the receive array and construct the augmented steering matrices with improved aperture. The TRSSIA algorithm adopts more elements from the transmitter and the receiver to estimate angles. So more information improves the angle estimation. For restraining noise, improving aperture and the spatial smoothing technique, the TRSSIA method proves better angle estimation than MUSIC-Like, ESPRIT-Like, and tensor-based real-valued approaches at small number of pulses and low SNR cases, and its angle estimation performance does not descend even for more than two coherent targets. Based on the more accurately estimated angles and computing the mean of every mutual coupling efficient, the mutual coupling estimation is more accurate than the other methods. The simulation results verify the advantage of the proposed method.
Firstly, we do SVD on
The authors declare that there is no conflict of interests regarding the publication of this paper.