An Improved VI-CFAR Detector Based on GOS

. In combination with the advantages of CA-CFAR, GO-CFAR and SO-CFAR algorithm, the VI-CFAR has strong adaptability both in homogeneous and non-homogeneous environment. However, if the interfering targets are present in both the halves of the reference sliding windows, the use of the window with the smallest mean is affected by them and therefore results in a performance degradation. In order to overcome the shortcoming, an improved VI-CFAR detector based on GOS (IVI-CFAR) is proposed in this paper. We introduce the IVI-CFAR detector and make performance simulation and analysis in homogenous and non-homogenous environment. In the homogeneous environment, the IVI-CFAR detector has some CFAR loss relative to the CA-CFAR detector. In the clutter edge environment, the IVI-CFAR detector keeps the good performance of the VI-CFAR detector. In multiple interfering targets environment, the IVI-CFAR detector performs robustly, which is similar to the OS-CFAR detector. In addition, the IVI-CFAR detector shortens the sample sorting time of the OS-CFARR detector.


Introduction
In radar and sonar signal detection, in order to get a constant false alarm (CFA R) performance, the actual average power of interfering background will be estimated by the reference cells near the test cell to adaptively set the detection threshold. For the diffe rent method of background power estimation, the method of CFA R is also different. Conventional CFAR detectors include average cell CFA R (CA-CFA R [1] ) detector and order statistics CFAR (OS-CFA R [2] ) detector. Under the homogeneous background, the CA-CFA R detector can get close to the optimal detection performance, but in the non-homogeneous environment, the detection performance of CA-CFAR seriously declines. When the actual number of the interfering targets is less than the predetermined nu mber, the OS-CFAR detector has good detection performance, and in the homogeneous environment the CFAR loss can also be acceptable. However, in the clutter edge environment, the OS-CFA R detector has a high false alarm peak, then the false alarm control ability is poor. In order to overcome the disadvantages of the CFA R detectors, the VI-CFA R detector was proposed by Smith and Varshney [3,4] . In this detector, the data in the reference slid ing window is used to compute two statistics VI and MR. Based on these statistics, two tests are performed in order to select the algorith ms (CA-CFA R, GO-CFA R [5] and SO-CFA R [6] ) to be used for the estimation of the clutter power in the test cell [7] . So the detector co mbines the advantages of the CA-CFAR, GO-CFA R and SO-CFAR algorithms. Under the homogeneous background, the VI-CFA R detector has a small CFA R loss relative to the CA-CFA R detector. Under the non-homogeneous background, the VI-CFAR detector also has strong robustness. However, when the interfering targets appear in both the leading and lagging sliding window, the possibility of the VI-CFA R detector selecting the SO-CFAR algorith m increases, this will lead to the serious deterioration of the performance of the VI-CFAR detector. Based on the OS-CA CFA R algorith m [8,9] , an imp roved VI-CFAR (IVI-CFA R) detector is introduced .Through the Monte-Carlo simu lation trials, this paper simulates the IVI-CFA R detectors detection and analyses the detection performance.
This paper is organized as follows. Section 2 introduces the principle of the VI-CFA R detector. In Section 3, an IVI-CFAR detector is proposed and the principle of the IVI-CFAR detector is introduced in detail. Simu lation results and discussions are given in Section 4. And we make conclusions in Section 5. This article assumes that the signal is independent, identically distributed (IID), zero mean, Gaussian random process. Consequently, the envelope amplitude at the output of the square-law detector is an exponentially distributed random variable. The samp les in the reference sliding window are independent of each other and of the sample in the test cell. When a target is present in the test cell, the use of guard cells (not shown in Figure 1) between the test cell and the reference sliding window prevents target energy from corrupting the reference sliding window.

The Principle VI-CFAR Detector
The VI-CFA R detector utilizes the VI as well as the MR to select the subset of reference cells used for background clutter estimat ion. The test statistics are defined by formula (1) and (2) respectively. In order to reduce the computational, VI can be simplified as VI*, of which the defined formu la is shown by formula (3). In V is the estimated population variance, and P is the estimated population mean. i X is the samples of the leading or lagging half of the reference sliding window. X is the arithmet ic mean of i X in a half reference sliding window, and n equals N/2, N is the size of the whole reference sliding window.
By the following two hypothesis tests formula (4) and formula (5) K VI and K MR are VI and MR decision thresholds respectively. The selections of them have relation to predetermined false-alarm probability and confidence levels. The corresponding error probability is shown in equation (6) and equation (7) respectively. 0 Homogeneous background By the above equations (6)- (7), the imp rovement of threshold K VI and K MR can reduce the error p robability respectively. But at the same time, the judgment sensitivity of non-homogeneous background also can be reduced.  According to the Figure 2, the OS-CA CFAR detector block d iagram can be seen. The co mmon characteristic of the OS-CA CFA R detector is: the leading reference sliding window makes local estimat ion in OS method, the lagging reference sliding window makes local estimate in CA method. At the same time, stop shift control logic constitutes the automatic screening technology with a reference cell shift register. When a target is declared in the test cell D, the lagging reference slid ing window stops shift to eliminate the sample in the test cell.

An Improved VI-CFAR Detector Based on GOS
According to the outcomes of the VI hypothesis test and MR hypothesis test, the IVI-CFA R detector adaptively chooses corresponding CFAR detection algorith m. When the clutter edge is present, the IVI-CFA R detector adopts the OSCA GO-CFAR and the order value k 1 of the OSCA GO-CFAR is set to a large value. When the interfering targets exist in the lead ing reference slid ing window or the lagging reference slid ing window, the IVI-CFA R detector also uses the OSCA GO-CFA R, but the order value k 2 of the OSCA GO-CFA R is set to a small value. When the interfering targets exist in both the halves of the reference sliding window The specific adaptive threshold production rules and the corresponding CFAR algorith m selections of the IVI-CFA R detector are shown in Table 1. C N , C OSCAGO and C OSCASO are the threshold multip lier factors, which correspond to different CFA R method. AB 6 , A 6 and B 6 are the sums of the whole and the half reference sliding respectively. X A (k 1 ), X A (k 2 ) and X A (k 3 ) are the 02002-p.2 local estimation of the lead ing reference sliding window in OS method respectively. X B (k 2 ) is the local estimat ion of the lagging reference sliding window in OS method.

OSCASO
Under the homogeneous background, the threshold mu ltip lier factor C N is determined based on CA-CFA R with N cells as shown in formula (8) [10] : When the interfering targets are present in a single half o f the reference slid ing window o r the clutter edge is around the test cell, the calculation of C OSCAGO is based on OSCAGO-CFA R as shown in formula (9): In the presence of interfering targets in both the halves of the reference sliding window, the value of C OSCAGO is based on OSCASO-CFAR and obtained by formula (10):

Simulation results and discussions
To illustrate the detection performance of the IVI-CFA R detector in homogeneous and non-homogeneous environments characterized by the p resence of interfering targets and the presence of clutter edge, we adopt 100000 Monte-Carlo simu lation trials. The whole reference sliding window size N is 36, the P fa is fixed to 10 -4 , and the main target(in test cell) and interfering targets are both Swerlling . The confidence level of VI hypothesis test α0 is fixed to 3.3×10 -4 , the confidence level of MR hypothesis test β0 is set as 0.08 and corresponding K VI and K MR are equal to 4.76 and 1.806 respectively [11] . single half of the reference sliding window. In addition, the order value of the OSCASO-CFAR is 10 when the interfering targets are present in both halves of the reference slid ing window. Fro m Figure 3,we can see that the IVI-CFAR detector has a little CFA R loss relative to the CA-CFA R and outperforms the GO-CFAR and VI-CFA R detectors. When P d =0.5, the CFAR loss of the IVI-CFA R relative to the CA-CFAR is about 0.1 d B. The CFA R loss for the VI-CFA R relative to the IVI-CFAR is about 0.15dB.

Performance in Multi-target Environment
It is assumed that interfering-to-noise ratio (INR) is equal to the signal-to-noise ratio (SNR) in the mu lti-target environment in this paper [12] . In order to analyse the different effect of interfering targets location in the reference sliding window on the detection performance of the VI and IVI-CFAR, this paper analyses in two different conditions [12] , i.e. the interfering targets only appear in the lead ing reference sliding window A and the interfering targets exist in the both halves of reference sliding window at the same time.    Figure 5 show the P d of the CA-CFA R, GO-CFA R, SO-CFA R, OS-CFAR, VI-CFA R and IVI-CFA R in the case of two interfering targets in the lead ing reference sliding window and four interfering targets in the lagging reference sliding window respectively. As can be seen, the IVI-CFA R exh ib its a lo w CFAR loss relative to the SO-CFA R and outperforms the VI-CFAR and VI-CFA R. With the increase of the value of SNR, the P d of IVI-CFA R and VI-CFA R approach that of OS-CFAR. In Figure 4,when P d =0.5, the CFAR loss of the IVI-CFA R relative to the SO-CFA R is about 0.15 d B. The CFA R loss of the VI-CFA R relative to the IVI-CFAR is about 0.3dB. Figure 6 shows the P d of the CA-CFA R, GO-CFA R, SO-CFAR, OS-CFA R, VI-CFA R and IVI-CFAR in the case of two interfering targets in both the halves of the reference slid ing window. It can be seen fro m Figure 6 that the thresholds of both the VI-CFA R and SO-CFA R are overestimated, so the detection performance degerade quickly wh ile the OS-CFA R and IVI-CFA R perform well.

Performance in Clutter Edge Environment
It is assumed that clutter envelope obeys Rayleigh distribution, and clutter-to-noise ratio is CNR. In Monte-Carle simu lation trails, the clutter edge progressed from 02002-p.4

ICMM 2016
left to right(window A to window B). The P fa of the CA,GO,SO,OS,VI and IVI-CFA R in clutter edge environment is shown in Figure 7 where the CNR is equal to 10dB. In this case, it can be seen that the falsealarm regulation properties of the IVI-CFAR and VI-CFA R are almost consistent. The false-alarm regulat ion properties of the CA-CFAR and OS-CFA R are poor relatively and that of SO-CFAR is the worst.

Conclusions
In this paper, we have presented an improved version of VI-CFAR, called IVI-CFA R detector and have analyzed the performance of the proposed IVI-CFAR detector in a homogeneous and non -ho mogeneous environ ments. In th e ho mog ene ous env ir on men t, t he d ete ct io n performance of the IVI-CFAR detector has some CFA R loss relative to the CA-CFA R detector and outperforms the GO-CFAR and VI-CFAR detectors. In the mult iple targets situations, the IVI-CFA R detection is more robust than the VI-CFAR detector when the interfering targets are present in both the halves of the reference slid ing window. In clutter edge environment, the performance of the IVI-CFAR detector is almost consistent with that of the VI-CFA R. In addition, the false-alarm regualt ion property of the IVI-CFA R is even better than that of the GO-CFAR.