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The PARAFAC-MUSIC algorithm is proposed to estimate the direction-of-arrival (DOA) of the targets with Doppler frequency in a monostatic MIMO radar system in this paper. To estimate the Doppler frequency, the PARAFAC (parallel factor) algorithm is firstly utilized in the proposed algorithm, and after the compensation of Doppler frequency, MUSIC (multiple signal classification) algorithm is applied to estimate the DOA. By these two steps, the DOA of moving targets can be estimated successfully. Simulation results show that the proposed PARAFAC-MUSIC algorithm has a higher accuracy than the PARAFAC algorithm and the MUSIC algorithm in DOA estimation.

Recently, there has been a growing interest in multiple-input multiple-output radar which utilizes multiple antennas at both transmitter and receiver. According to the array configuration, MIMO radar can be classified into two main types, the first of which is called distributed MIMO radar. It is composed of widely separated transmit antennas which transmit the linearly independent signals. Based on the sufficient distribution space and linearly independent signals, the distributed MIMO radar is able to obtain rich scattering properties of the targets and to mitigate radar cross-section (RCS) fluctuations. The second type is called collocated MIMO radar, in which the transmit elements are collocated. By transmitting independent waveforms and capitalizing on the MIMO spatial signature, the collocated MIMO can estimate the parameters of interest via coherent processing.

On the other hand, an accurate estimation of signal DOA has made a great sense in radar system of military and commercial application. Many algorithms were proposed on DOA estimation in MIMO radar system as it provides waveform diversity and spatial distribution of flexibility. In [

Although these algorithms introduced above are useful for DOA estimation, they are poor when the Doppler frequency is taken into consideration. As the target always moves, DOA estimation of moving targets is extremely essential. In [

Assume that there is a monostatic MIMO radar system with

Transmit and receive antennas.

The received signal at time

As the transmit waveforms are orthogonal from each other, the output of the match filters at time

So the received signal before the match filters can be expressed by matrix as

The output at match filters can be expressed by matrix as

PARAFAC-MUSIC algorithm combines the advantages of PARAFAC algorithm and MUSIC algorithm. It exploits PARAFAC algorithm to estimate the Doppler frequency, then eliminates the effect in received signal generated from Doppler frequency, and finally utilizes MUSIC algorithm to estimate the DOA.

As known from formula (

In the same way,

When the three-way array is obtained, it is common to utilize TALS [

Construct the three-way array

Initialize all the estimated matrixes

Substitute

Substitute

Substitute

When the Doppler frequency has been estimated, it can be used to eliminate the Doppler effect to received signal

The covariance of

Then eigendecomposition is carried on for

Since the first

So the spectrum estimation formula of MUSIC is expressed as

Then the estimated DOA can be obtained according to the position of the spectral peak.

In order to state that PARAFAC-MUSIC algorithm has a better performance in DOA estimation with Doppler frequency, simulation is carried on with MATLAB software to compare PARAFAC-MUSIC algorithm with PARAFAC algorithm and MUSIC algorithm.

Assume that there are two targets in the far field and a MIMO radar system with 8 collocated transmit antennas and 8 collocated receive antennas. The frequency of the transmit signals is 4 GHz. The array structure is the same as Figure

Figures

Mean error of target 1.

Mean error of target 2.

Figures

RMSE of target 1.

RMSE of target 2.

Simulation results state that MUSIC algorithm suffers from Doppler frequency seriously and cannot provide an accurate DOA estimation to moving target. Besides, the PARAFAC-MUSIC is able to estimate the DOA with a higher accuracy than the PARAFAC algorithm to moving targets.

In this paper, some algorithms in DOA estimation are reviewed first. Then a new algorithm named PARAFAC-MUSIC is proposed to estimate the DOA with Doppler frequency in a MIMO radar system. The proposed algorithm is able to estimate DOAs of multiple targets. Finally simulation results confirm that the MUSIC algorithm is not suitable for DOA estimation with Doppler frequency while PARAFAC-MUSIC algorithm is very popular for DOA estimation with Doppler frequency and has a higher accuracy than the PARAFAC algorithm and the MUSIC algorithm.

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

The authors would like to thank the Pre-research Foundation for the support of their research (no. 9140C800202120C80279).