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In the paper, joint angle and range estimation issue for monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) is proposed, and a tensor-based framework is addressed to solve it. The proposed method exploits the multidimensional structure of matched filters in FDA-MIMO radar. Firstly, stack the received data to form a third-order tensor so that the multidimensional structure information of the received data can be acquired. Then, the steering matrices contain the angle and rang information are estimated by using the parallel factor (PARAFAC) decomposition. Finally, the angle and range are achieved by utilizing the phase characteristic of the steering matrices. Due to exploiting the multidimensional structure of the received data to further suppress the effect of noise, the proposed method performs better in angle and range estimation than the existing algorithms based on ESPRIT, simulation results can prove the proposed method’s effectiveness.

Multiple-input multiple-output (MIMO) radar was first proposed in [

FDA radar can get the distance information of the target [

In [

The advantages of FDA are developed based on the characteristics of the multidimensional structure of the signal. The abovementioned traditional matrix processing method cannot make good use of the multidimensional characteristics, which limits their performance [

The proposed method compares the achievement with traditional estimation of signal parameters via rotational invariance techniques (ESPRIT) method [

Notation:

The paper is based on a narrowband monostatic FDA-MIMO radar. It is composed by

Monostatic FDA-MIMO radar.

After the matched filter, the receiving data can be rearranged as

Under the interference of noise, the signal model is updated as

Schematic diagram of trilinear decomposition.

Under the definition of PARAFAC decomposition, equation (

We apply the tensor signal model and parallel factor decomposition to the monostatic FDA-MIMO radar and derive the PARAFAC-based angle and range estimation method. In the following section, we will derive the method in more detail.

In this section, according to the trilinear alternating least square (TALS) method, we can estimate the transmitting direction matrix and the receiving direction matrix. The TALS method can be explored for data analysis in trilinear models.

According to [

According to equations (

For the received noise signals, according to the trilinear decomposition, we can get the estimated parameter matrices:

From the trilinear decomposition in the previous section, we can get estimates of the direction matrices

It can be seen from the signal model that the steer vector of

In the paper, the receive array can be preset as half-wavelengths spaced uniform linear arrays (ULA), so the receive steering vector of

Let

After the receiving steering vector is well calibrated, it is represented as

The receive angle

For the tensor-based data model, the range and transmit angle of the uncorrelated target are both included in the transmit steering vector. So, the transmit steering vector can be expressed as

The transmit array is preset as half-wavelengths spaced ULA, so the transmitting steer vector of

In the previous section, the direction of arrival (DOA)

In the previous section, we have obtained the estimated receive vector

The range

So far, we already get the angle and range of the uncorrelated target in the monostatic FDA-MIMO radar. We can recap the key processes of the proposed method as follows:

Step 1: according to equation (

Step 2: apply the trilinear decomposition principle; we can obtain the transmitting direction matrix

Step 3: take the phase

Step 4: the phase

Step 5: similarly, we can obtain

The input signal spectrum is defined as

When

In this section, the effectiveness and advantages of our proposed method can be proved by some numerical simulations. The ESPRIT method and Unitary-ESPRIT method can be utilized to contrast with our proposed method. We default the monostatic FDA-MIMO radar with

Unless otherwise specified, it is supposed that there are

In addition, the probability of successful detection is another metric used to appraise the achievement of our method, which is defined by

We preset

The range and angle estimation performance of the proposed method with

And then,

RMSE of angle estimation versus SNR.

RMSE of range estimation versus SNR.

From the following, we explore the relationship between RMSE and snapshots of range estimation and angle estimation in the third simulation, and the results are shown in Figures

RMSE of angle estimation versus the total amount of snapshots.

RMSE of range estimation versus the total amount of snapshots.

In the fourth simulation, the relationship between probability and SNR of angle and range probability successful detection is obtained. The number of snapshots is preset to

Probability of angle successful detection versus SNR.

Probability of range successful detection versus SNR.

In the paper, we proposed a tensor-based range and angle estimation method in monostatic FDA-MIMO radar. The proposed method uses the trilinear model to obtain the direction matrices through PARAFAC decomposition and extracts the phase from the direction matrix to estimate the distance and angle. This method uses the multidimensional information of the received data. Compared with the subspace methods such as ESPRIT and Unitary-ESPRIT methods, the proposed method has the best performance. The superiority of the proposed method can be verified by simulation.

No data were used to support this study.

The authors declare that they have no conflicts of interest.

This work was supported by the Hainan Provincial Natural Science Foundation of China (no. 2018CXTD336) and National Natural Science Foundation of China (no. 61864002).