# Rao and Wald Tests for Moving Target Detection in Forward Scatter Radar
## 1 Introduction  
A radar system in which the receiver is located separately from the transmitter is known as a bistatic radar [1; 2; 3; 4]. When the bistatic angle, which represents an angle between the line of sight of the receiver antenna and the target and the line of sight of the transmitter antenna and the target, exceeds \(135^{\circ}\), the receiver works in the forward scatter region of the target. In the forward scatter region of the target, the radar cross-section of the target increases with the bistatic angle and reaches its maximum when the bistatic angle becomes \(180^{\circ}\). The forward scatter radar (FSR) is a bistatic radar with a bistatic angle close to \(180^{\circ}\)[5; 6; 7; 8]. The forward scattering makes the FSR system have an enhanced radar cross-section compared with monostatic radar system. Moreover, the forward scattering cross-section is independent of the material of the target. Therefore, FSR geometry has received extensive attention in the fields of target motion parameter estimation, passive FSR, target localization, target classification, and target detection in recent years [9; 10; 11]. For target motion parameter estimation, the method to estimate the target velocity, target position, and crossing time is discussed in [12; 13] in a global navigation satellite system-based FSR network. Based on single-baseline and dual-baseline FSR configurations, closed-form expressions of Cramer-Rao bounds of the target motion parameters are given in [11]. For passive FSR, the matched filter and linear canonical transformation are used to realize aerial target passive sensing with satellite-based FSR in [14]. The ability of a digital video broadcasting terrestrial-based passive FSR to detect targets is discussed in [15; 16]. For target localization, the maximum likelihood estimation (MLE) method for locating a moving target in FSR is discussed in [17]. For target classification, a neural network classifier was designed to classify ground targets using FSR in [18]. Target detection is one of the most important applications of FSR [11]. In Ref. [19], a stationary and slow-moving target detection scheme is proposed for a novel FSR system in which the transmitter is rotated. By using this novel FSR system and the proposed target detection scheme, stationary and crawling human intruders can be detected. In Ref. [20], matched filtering theory is utilized to maximize signal-to-noise ratio for ground target detection through forward scatter micro radars. In Ref. [21], the theoretical performance of a crystal video detector (CVD) scheme which consists of the squared modulus operation, a narrow high-pass filter, and a matched filter is derived. The comparison of the CVD with the ideal detector shows that the CVD undergoes detection performance losses under the condition that the target approaches the near field. To improve the detection performance, adaptive detectors for FSR were designed by utilizing the generalized likelihood ratio test (GLRT) when the parameters of direct signal, target signal, and noise are partly known and completely unknown in [22]. The new detectors can achieve more than 3 dB detection performance improvement than the CVD. The GLRT is one of the most widely used design criteria for the adaptive detector, which is designed by jointly utilizing the primary data and the secondary data and is compared with a detection threshold set according to a pre-assigned probability of false alarm to decide whether the target exists [23; 24; 25; 26]. However, the GLRT does not generally have optimality properties in the finite-sample case. Apart from GLRT, the Rao test and Wald test are alternative design criteria that are asymptotically equal to the GLRT. The adaptive detectors designed according to the Rao test and Wald test may achieve better detection performance than the GLRT in the finite-sample case [27; 28; 29; 30; 31]. Therefore, it is of interest to investigate the behavior of the adaptive detectors derived according to the Rao and Wald tests.