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This paper presents a joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in a multiple-input multiple-output (MIMO) radar utilizing ultra wideband (UWB) signals in detecting targets with fluctuating radar cross sections (RCS). The UWB MIMO radar utilized a combination of two-way MUSIC and majority decision based on angle histograms of estimated DODs and DOAs at each frequency of the UWB signal. The proposed angle estimation scheme was demonstrated to be effective in detecting targets with fluctuating RCS, compared to conventional spectra averaging method used in subband angle estimations. It was found that a wider bandwidth resulted in improved estimation performance. Numerical simulations along with experimental evaluations in a radio anechoic chamber are presented.

The introduction of multiple-input multiple-output (MIMO) radar enables numerous improvements on the conventional single input single output radar system. The MIMO radar is typically defined as a radar system utilizing multiple transmitting and receiving antennas that are either widely distributed or colocated [

Target localization in radar has been intensively studied in literatures since the early years of radar. In general, radar systems estimate the target position by means of trilateration or triangulation. Trilateration can be implemented by using a minimum of two stations; however, the localization resolution is limited by the signal bandwidth, and usage of multiple stations is required to avoid ambiguities (ghost targets). On the contrary, triangulation is based on the angles of targets observed from the radar stations, and hence it does not suffer from the bandwidth constraint. In MIMO radar, it is possible to jointly estimate the direction-of-departure (DOD) and direction-of-arrival (DOA) by implementing array processing at both of the transmitting and receiving arrays, as depicted in Figure

Overview of angle estimation in MIMO radar.

Numerous works on DOD and DOA estimation have been reported [

The present authors proposed a joint DOD and DOA estimation in a UWB MIMO radar using the combination of a two-way MUSIC and angle histograms [

In this paper, we evaluate the performance of the proposed algorithm in detecting targets with fluctuating RCS. Here, it will be shown that combining the estimation at different frequencies through majority decisions will overcome the problem of poor estimation when detecting fluctuating targets. A comparison between the proposed technique and the conventional spectrum averaging is also presented. Numerical simulations and experimental results are presented.

It is important to mention here that the RCS fluctuation problem has been continuously studied in the radar community. Until recently, special attention has been given to the subject in the case of MIMO radar, since the usage of MIMO configuration offers further degrees of freedom in the forms of spatial, frequency, and also waveform diversity. For example, the works in [

The remainder of this paper is organized as follows. The next section discusses the proposed algorithm. Section

Consider a MIMO radar with_{t} and_{r} are the transmit and receive steering vectors, respectively, ^{(k)}(^{H} represents the conjugate transpose operation. Here, singular value decomposition (SVD) of the covariance matrix gives
^{(k)} is a diagonal matrix whose diagonal elements contain the signal and noise eigenvalues for the^{(k)} is the corresponding eigenvectors of the signal and noise components. The two-dimensional spatial MUSIC spectrum at the_{N}_{N}^{H} is the noise eigenvectors obtained from the eigendecomposition of the receive signal covariance matrix in (^{(i)} is the number of occurrences of the angle

The proposed UWB signal for MIMO radar angle estimation.

Formulation of angle histograms from two-way MUSIC spectra at each frequency component.

The majority decision is obtained by searching the peak of the histogram. As a benchmark, the performance of the proposed scheme will be compared with the conventional spectrum averaging method [

Then the wideband DOD and DOA are estimated from the

Block diagrams: (a) proposed and (b) conventional schemes.

The main advantage of a MIMO radar system is that the degrees of freedom can be enhanced by using the concept of virtual array [

The virtual array can be characterized by convolution of the transmitting and receiving antenna positions [

A full

However, as shown in Figure

Example of spurious peaks in a simulated MUSIC spectrum (

In this study, we employed a nonuniform array configuration as shown in Figure

Nonuniform array configuration used in the study (

Example of a MUSIC spectrum using the nonuniform array configuration (

This subsection presents the analysis of the computational complexity of the proposed scheme. The computational burden of a conventional 2D-MUSIC has been reported in literatures, such as in [

Considering the dimensions of the covariance matrix ^{2} and^{2}, respectively. This is the same for both the proposed and the spectrum averaging schemes. In terms of peak search operation, the proposed scheme performs two-dimensional peak search on the MUSIC spectrum, which costs

The computational complexity against

Computational complexity of the proposed scheme against

The proposed algorithm was simulated according to the parameters listed in Table

Simulation parameters.

Parameters | Description |
---|---|

Number of transmitting antennas, |
4 |

Number of receiving antennas, |
4 |

Number of targets, |
2 |

Signal to noise ratio, SNR | 15 dB |

Number of snapshots | 50 |

Target positions | ( |

Type of targets | Fixed point targets or Weibull targets |

Two different scenarios were simulated, where the MIMO radar was detecting either a fixed point target or a target with fluctuating RCS. The fixed point target was modeled with a constant RCS, normalized by the free space propagation loss coefficient in each frequency. The targets with fluctuating RCS were modeled by Weibull distribution, since it was shown in literatures that measured RCS of complex targets such as automobiles and small cars follows Weibull distribution [

Simulated RCS of a simulated Weibull target in comparison with a fixed point target considering propagation loss in frequency domain.

Cumulative distribution of the simulated RCS of a Weibull target in frequency domain.

Figure

Angle histograms of estimated DODs and DOAs in detecting fixed point targets using a signal bandwidth of (a) 50 and (b) 1000 MHz.

Angle histograms of estimated DODs and DOAs in detecting Weibull targets using a signal bandwidth of (a) 50 and (b) 1000 MHz.

The performance of the proposed scheme was evaluated in terms of estimation error, defined by

Estimation errors against bandwidth: (a) fixed point and (b) Weibull targets.

The performance of the proposed scheme in terms of root mean square error (RMSE) against SNR is plotted in Figure

RMSE performance of the proposed scheme: (a) DOD and (b) DOA.

We could observe that the proposed scheme marked the best performance, which was the nearest to the CRB, and produced no estimation error when the SNR exceeds 14 dB. It was also shown that the performance of Silva method depended on the frequency for the targets with fluctuating RCS.

The impact of a number of antennas on the performance of the proposed scheme was plotted in Figure

RMSE of the proposed scheme against

Experiments were conducted to verify the results of the numerical simulations. The measurements were done in a radio anechoic chamber, using a measurement setup illustrated in Figure

Measurement setup.

The setup was used to localize two targets positioned at (^{2}. The complex targets were constructed so that they yield a fluctuating RCS in the frequency domain. An example of the complex target is shown in Figure

Example of a fabricated complex target.

Measured frequency-domain data of the fabricated targets.

Measurement scenario in a radio anechoic chamber.

The estimation errors from measurement campaign were plotted in Figure

Estimation errors against bandwidth obtained from measurements: (a) spherical and (b) complex targets.

A series of experiments was conducted to evaluate the localization performance of the proposed scheme. A single complex target was positioned in several locations in the radio anechoic chamber. The positions of the target are summarized in Table

Target positions in a radio anechoic chamber.

Target positions | Actual DOD and DOA | Target distance from radar |
---|---|---|

A | ( |
1.5 m |

B | ( |
2.2 m |

C | ( |
3.0 m |

D | ( |
3.3 m |

Localization errors from measurements in a radio anechoic chamber.

The performance of a joint DOD and DOA estimation in a UWB MIMO radar detecting fluctuating targets was evaluated through numerical simulations and experimental evaluations. From the investigation, it was found that in detecting targets with fluctuating RCS (in this case Weibull distributed RCS against frequency), it is essential to use large signal bandwidth to reduce the estimation error using the proposed algorithm. When taking wider signal bandwidth, the usage of majority decisions from the angle histograms resulted in good estimation performance compared to the conventional spectrum averaging method. We concluded based on the work that the proposed scheme was a suitable candidate to implement joint angle estimation in MIMO radar using ultra wideband signal. Although the resolution of target localization based on DOD and DOA estimations, in general, does not depend on the signal bandwidth, it was demonstrated that utilization of wider bandwidth in the proposed scheme leads to improvement of estimation performance, considering that the targets have fluctuating RCS in the frequency domain. Since the proposed scheme utilizes multiple subcarriers, it is suitable to be extended to an OFDM-based radar system.

The MIMO antennas could be arranged in such a way that they produce a filled virtual array; however, the filled virtual array tends to consist of less number of unique virtual elements due to redundant elements. A few examples are depicted in Figure

Illustration of examples of virtual arrays in MIMO radars: (a) uniform linear array, (b) truncated filled array, and (c) nonuniform array.

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