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This paper focuses on the target detection in low-grazing angle using a hybrid multiple-input multiple-output (MIMO) radar systems in compound-Gaussian clutter, where the multipath effects are very abundant. The performance of detection can be improved via utilizing the multipath echoes. First, the reflection coefficient considering the curved earth effect is derived. Then, the general signal model for MIMO radar is introduced in low-grazing angle; also, the generalized likelihood test (GLRT) and generalized likelihood ratio test-linear quadratic (GLRT-LQ) are derived with known covariance matrix. Via the numerical examples, it is shown that the derived GLRT-LQ detector outperforms the GLRT detector in low-grazing angle, and both performances can be enhanced markedly when the multipath effects are considered.

MIMO radar has gotten considerable attention in a novel class of radar system, where the term MIMO refers to the use of multiple-transmit as well as multiple-receive antennas. MIMO radar is categorized into two classes: the statistical MIMO radar and the colocated MIMO radar, depending on their antenna placement [

Much published literature has concerned the issue of MIMO radar detection. Guan and Huang [

Low-grazing angle targets are difficult to detect, which is one of the great threats propelling radar development. Otherwise, detection of low-altitude targets is of great significance to counter low-altitude air defense penetration. However, up to now, this problem has not been effectively resolved. Multipath effect plays an important role in the low-altitude target detection, by which the target echo signal is seriously polluted, even counteracted [

In this paper, we consider low-grazing angle target detection in compound-Gaussian clutter for MIMO radar. The compound-Gaussian clutter represents the heavy-tailed clutter statistics that are distinctive of several scenarios, for example, high-resolution or low-grazing angle radars in the presence of sea or foliage clutter [

A point source at a distance of

To model the received signals more accurately, the curvature of the signal path due to refraction in the troposphere, in addition to the curvature of the earth itself, must be taken into account. The multipath geometry for a curved earth is given in Figure

Multipath geometry for a curved earth.

In (

When an electromagnetic wave is incident on a round earth surface, the reflected wave diverges because of the earth’s curvature. Due to divergence, the reflected energy is defocused and radar power density is reduced. The divergence factor can be derived solely from geometrical considerations. A widely accepted approximation for the divergence factor

The surface roughness factor

Consider a narrowband MIMO radar system with

We rewrite the received signal (

In the presence of multipath, consider atmosphere refraction and the curved earth effect; the reflected signals from a point target of MIMO radar include four parts: directly-directly path, directly-reflected path, and reflected-directly path, reflected-reflected path. Assume the point target is located at

Multipath MIMO radar.

Directly-directly path

Directly-reflected path

Reflected-directly path

Reflected-reflected path

The directly-directly path echo signal is given by (

The reflected-directly path echo signal is

The reflected-reflected path echo signal is

Thus, the received signal of MIMO radar with multipath is

The problem of detecting with MIMO radar can be formulated in terms of the following binary hypotheses test:

Standard GLRT is the following decision rule:

The log-likelihood function of (

According to [

Thus, the ML estimator of

The estimator

Substituting the estimator

We rewrite the detection problem as

As the transmit-receive subarrays are widely separated, the clutter returns can be considered to be independent; hence, the low-grazing angle likelihood ratio test (LRT) detector for MIMO radar in the compound-Gaussian clutter is given by

If we assume that covariance matrix

According to [

The probability of detection

For a given signal-to-clutter ratio (SCR), denoted by

This section is devoted to the performance assessment of the GLRT and GLRT-LQ detectors in low-grazing angle for MIMO radar, when the texture component of clutter distributed as gamma distribution, leading to the wellknown

In our first example, we, respectively, analyze the GlRT-LQ detectors considering multipath effect and without considering multipath effect. Assume MIMO radar is with three transmit antennas and two receive antennas, the heights of transmit arrays are fixed at 100 m, 200 m, and 300 m, the height of receive arrays are fixed at 100 m, and 200 m, and the target’s height is fixed at 200 m. The

Figure

GLRT-LQ detector performance in low-grazing angle.

Figure

GLRT detector performance in low-grazing angle.

Figure

Comparison of GLRT-LQ detector and GLRT detector.

Figures

Detection performance of GLRT-LQ detector with different numbers.

Detection performance of GLRT detector with different numbers.

Figures

GLRT-LQ detector detection performance varies with the height of target.

GLRT detector detection performance varies with the height of target.

GLRT-LQ detector detection performance varies with the height of target.

In this paper, we have introduced the concept of reflection coefficient under considering curved earth effect and introduced general signal model for MIMO radar in low-grazing angle, firstly. Then, we have derived the GLRT-LQ and GLRT detectors, respectively. Furthermore, we have compared the performance of GLRT-LQ and GLRT detector for MIMO radar between with multipath and without multipath effects. The simulation results have shown the importance of multipath effects for target detection in low-grazing angle and demonstrated that GLRT-LQ detector outperforms the GLRT detector in low-grazing angle.

The authors wish to thank the anonymous reviewers for their efforts in providing comments that have helped to significantly enhance the quality of this paper. This work was supported in part by the National Science Foundation of China under Grant no. 61302142.