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Full Paper Proc. of Int. Conf. on Advances in Signal Processing and Communication 2012

Performance Analysis of a new CFAR Algorithm under Heterogeneous Environments F James Jen, Matthew Gialich, Bradley Lambrecht, Zekeriya Aliyazicioglu, H. K. Hwang California State Polytechnic University-Pomona, Electrical and Computer Engineering, Pomona, CA Email: jimmy.jen@gmail.com, { mgialish, blambrecht, zaliyazici, hkhwang}@ csupomona.edu Abstract—In many operating conditions, noise and clutter distributions may be highly heterogeneous with sudden jumps in clutter power or with the presence of multiple targets in close proximity. A good CFAR algorithm must reliably operate in these conditions without prohibitively high implementation costs. A number of CFAR algorithms is investigated by assessing their operational flexibility and cost of operation. As balance of performance and implementation cost, two algorithms stood out as desirable: Variability Index (VI) CFAR— a procedure that allowed for dynamically selection between the leading, lagging, or whole of the reference windows— and Switching (S) CFAR— a test cell technique that allowed for the selection of representative subsets of the reference cell as compared to the cell under test. A new algorithm, Switching Variability Index (SVI) CFAR, is introduced that combines the advantages of both VI and S CFAR.

Figure 1. CFAR Window

In the multiple target case, in addition to a target in the CUT, there is one or more targets in the reference cell. In the clutter wall environment, the mean noise or clutter power undergoes an abrupt increase. Different CFAR algorithms have employed varying strategies. Cell Averaging CFAR (CA-CFAR), the arithmetically average the power of each reference scale and before scaling it with an appropriate constant multiplier. Ordered Statistics CFAR, (OS-CFAR), another standard approach, ranks the reference cells from smallest to largest and takes the kth largest cell. Using ordered statistics, for each CUT, OS-CFAR[3]. In this paper, the performances of some existing CFAR algorithms are evaluated in homogenous, multiple targets, and clutter wall environments. Variability Index CFAR (VICFAR), and Switching CFAR (S-CFAR) are studied and compared for the algorithm of interest. Finally, the Switching Variability Index CFAR (SVI-CFAR) presented as a hybrid approach between VI-CFAR and S-CFAR.

Index Terms— CFAR Detection, Variability Index CFAR, Switching CFAR

I. INTRODUCTION Constant False Alarm Rate (CFAR) algorithms allow radar systems to adaptively set detection thresholds in target detection in noisy environment [1,2]. Radar returns whose power falls above the threshold are recognized as targets of interests and those that fall below are rejected as noise or clutter. The aim of the CFAR algorithms is to maximize the probability of detection (PD) while maintaining the desired the probability of false alarm (PFA). CFAR algorithms estimate the background noise or clutter through the use of a moving window (Fig.1). The noise or clutter of the cell under test (CUT) is estimated from the statistics of the reference cells in the leading and lagging windows. To achieve consistent detection performance with a constant false alarm rate, the actual interference power must be estimated from the data in real time so that the detection threshold can be adjusted to maintain the desired PFA. Each data sample is tested for presence or absence of a target. The cell being tested is called CUT [2]. It is compared with a threshold determined by the interference power. If the value of CUT exceeds the threshold, the processor declares a target at the appropriate range and Doppler bin. To be effective, CFAR algorithms must maximize PD and maintain PFA through a variety of signaling environments: homogeneous, multiple targets, and clutter wall. In homogeneous environments, the mean noise or clutter power is constant across all range bins. © 2012 ACEEE DOI: 02.SPC.2012.01.4

II. VARIABILITY-INDEX-CFAR ALGORITHM VI-CFAR dynamically switches between CA-CFAR, Smallest Of Cell Averaging CFAR (SOCA-CFAR), and Greatest Of Cell Averaging CFAR (GOCA-CFAR) depending on the mean and the distribution of cells in the leading and the lagging windows [4,5]. This approach captures particular advantages of each of the three CFAR approaches while avoiding their respective weaknesses. For each of the leading window and the lagging window, the mean and the variability index are computed. VI-CFAR is a second-order statistics that is closely related to an estimate of the shape parameter. The greater the variability index, the greater the variability in relatives magnitudes of the reference cells. When, for instance, a leading window contains the high powers of targets, the variability would differentially weigh the target power over that of the lower powers of the noise and magnitude, resulting in a larger variability index. 107

Full Paper Proc. of Int. Conf. on Advances in Signal Processing and Communication 2012

 N  PFA



TABLE I. TYPE SIZES

1 N

1

FOR

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CAMERA-R EADY PAPERS

Figure 2. Variability-Index CFAR

The variability index may be calculated by this equation: n

 X 

Case I: Same Means and Both Nonvaraible When both the leading and lagging windows are nonvaraible, they aren’t likely to contain targets; and when both windows have similar means, then the reference window probably doesn’t straddle a clutter edge. The cell under test, then, is most likely in a homogeneous environment. VI-CFAR, thus, uses CA-CFAR. The threshold is set by summing all reference cells and using the CA-CFAR threshold multiplier for length N and given as (7)

VI  n

i 1

 n  .   Xi   i 1 

(1)

where, Xi is the power of reference cell i. The summation is taken over all cells Xi of either the leading or the lagging window. Once the VI is computed, the algorithm then makes a determination of whether the leading and/or the lagging windows are variable: VI  KVI  Not Variable VI  KVI  Variable

Case II: Leading Window Variable and Lagging Window not Variable

(2)

A variable leading window is indicative of high spikes of power, and with a reasonable signal to noise ratio, these spikes are most likely the result of targets. The average power, then, of the leading window wouldn’t be indicative of the noise/ clutter contained. In this case, VI-CFAR switches to using CA-CFAR with the lagging window alone. As the lagging window is nonvaraible, it is likely to contain noise/clutter only. To set the threshold, all cells in the lagging window is summed and multiplied to the threshold multiplier for window length N/2 and given as (6).

where KVI is selected threshold [4]. The Mean Ratio (MR) is a measure of how different the leading (A) and lagging (B) window means are. It is computed as a ratio of the summations of the reference cells of each window: MR 

Xi XA   iA . X B  Xi

(3)

iB

If the MR falls within bounds defined by the mean ratio constant, KMR, then the leading and lagging window means are declared the same: K MR 1  MR  K MR  Same Mean .

Case III: Lagging Window Variable and Leading Variable Nonvariable Case III is the converse situation of Case II. When only the lagging window is variable and not the leading, the lagging window is likely to contain targets and the leading noise/ clutter only. In this case, the threshold is set by summing only the reference cells of the leading window and multiplied to a CACFAR threshold multiplier for window length N/2 and given as (6).

(4)

If not, then they are declared as different means: MR  K MR 1 or MR  K MR  Different Mean . (5) Once the variability and mean determinations had been made, then, according to the logic of Table.1 CFAR is performed with either both the leading and lagging windows, one of them, the smaller of the two, or the larger of the two. If only a half-window is chosen— either only the leading or lagging window— then the threshold multiplier becomes

 N /2  PFA



1 N /2

1

Case IV: Both Windows Variable When both the leading and lagging windows are variable, then both windows very likely contains targets. Whichever window used is likely to result in target masking. VI-CFAR, then, seeks to minimize the masking by taking the smaller of the sums of the leading and the lagging windows. The threshold is set by multiplying this smaller sum to a CA-

(6)

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Full Paper Proc. of Int. Conf. on Advances in Signal Processing and Communication 2012 CFAR threshold multiplier for window length N/2 and given as (6).

IV. SIMULATION RESULTS Simulations were performed for cell-averaging (CA), ordered statistics (OS), VI, S, and SVI-CFAR. CA and OSCFAR are standard algorithms and simulated as a basis of comparison. A reference window size of 32 and a desired PFA of 10-4 are chosen for the simulation. In the homogeneous environment, we see that all five CFAR algorithms are comparable in their PD (Fig.3). As expected by theory, CA-CFAR performs the best but the other four algorithms don’t lag far behind. The SVI-CFAR graph essentially overlaps with that of VI-CFAR. Simulated with two Rayleigh I/II targets, one in the CUT and one interfering, shows that CA-CFAR suffers a drastic decrease in PD. In this case, S and OS-CFAR both slightly outperform VI and SVI-CFAR (Fig.4.a). Where VI-CFAR experiences huge drops in PD is when interfering targets are present in both the leading and lagging windows (Fig.4.b). In this case, with three total targets, S and OS-CFAR both suffer little effects. Although SVI-CFAR performs slightly worse than the two, it is still a noticeable improvement over the original VI-CFAR approach. These difference are even more pronounced when there are four interfering targets—two in each the leading and lagging windows.

Case V: Not Variable but Different Mean When both the leading and lagging variables are nonvariable but different in mean, then the cell under test is very likely near a clutter wall. The goal for VI-CFAR, in this case, is to set the threshold by the higher edge of the clutter wall. The threshold is set by taking the larger of the sums of the leading and lagging window and multiplied to the CACFAR threshold multiplier for window length of N/2 and given as (6). III. SWITCHING-CFAR ALGORITHM Switching CFAR (S-CFAR) is an approach designed to address the weaknesses of some CFAR algorithms in handling target masking. Unlike CA, OS, or VI-CFAR, S-CFAR utilizes test cell statistics: the value of the CUT is used in the decisionmaking and computations of the algorithm [6]. The algorithm begins by scaling the power of the CUT, z, with a pre-determined factor, α. Each reference cell, zk, is then compared with this value. Those with power less than the scaled CUT is put into set S0, and those larger is put into set S1. S

zk    z .

(8)

S 1

If the number of members in set S0 is equal to or greater than a threshold amount, NT, then only the members of S0 are used is averaged and multiplied with a pre-determined thresholdmultiplier, â, to set the threshold.

T

0 N S0

z

zk S0

(9)

Otherwise all of the reference cells are averaged and scaled by the same threshold multiplier. The threshold multiplier may be determined experimentally or through the equations provided in [6]

T

0 N  zk . N k 1

Figure 3. Homogeneous P D. Homogeneous probability of detection of various CFAR algorithms for desired P FA=10 -4

In addition to handling the heterogeneity associated with multiple targets, an efficient CFAR algorithm should maintain its desired PFA during sudden jumps in noise power or a quick clutter wall transitions (Fig.5). At the clutter wall; CA, OS, and S-CFAR all suffer in excess of a 100-fold increase right at the clutter wall. VI and SVI-CFAR, by comparison suffer less than a 10-fold increase from the desired 10-4 PFA.

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IV. SWITCHING VARIABILITY INDEX CFAR ALGORITHM To overcome the deficiencies in VI-CFAR and S-CFAR, a hybrid approach is proposed: Switching variability index CFAR (SVI-CFAR). SVI-CFAR utilizes the decision logic of VI-CFAR but replaces the SOCA-CFAR decision branch with S-CFAR— thereby improving PD when masking targets are present across both the leading and lagging windows.

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Full Paper Proc. of Int. Conf. on Advances in Signal Processing and Communication 2012

Figure 5. Clutter Wall P FA. Clutter wall probability of false alarm with a desired PFA=10 -4

CONCLUSIONS A CFAR algorithm must not only dynamically hold constant its false alarm rate, but do so in a variety of heterogeneous environment. Two standard heterogeneous test-cases are when there are multiple targets and when there is a clutter wall transition. In this paper, we furthered SVICFAR, a novel approach that improves upon VI-CFAR in its ability to handle multiple targets in both leading and lagging windows while maintaining PFA performance in the presence of clutter wall transitions. REFERENCES [1]

[2] [3]

Figure 4. (a) Probability of detection with one interfering target. (b) Probability of detection with two interfering targets– one in the leading window and one in the lagging window

[4]

[5]

[6]

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Finn, H.M., and Johnson, R.S.: ‘Adaptive detection mode with threshold control as a function of spatially sampled clutter estimates’, RCA Rev., 1968, vol.29, no.3, pp. 414–464. Richards, M.A. Fundamentals of Radar Signal Processing. New York; McGraw-Hill. 2005 P.P. Gandhi; S.A. Kassam; , “Analysis of CFAR processors in homogeneous background,”, IEEE Transactions on Aerospace and Electronic Systems, vol.24, no.4, pp.427-445, Jul 1988 Smith, M.E.; Varshney, P.K., “Intelligent CFAR processor based on data variability,” IEEE Transactions on Aerospace and Electronic Systems, vol.36, no.3, pp.837-847, Jul 2000. Hansley, G.V. Sawyer. J.H.,”Detectibilty loss due to greatestof-selection in a cell averaging CFAR,” IEEE Transactions on Aerospace and Electronic Systems, 1980-16, pp.115-118 Cao, AT.V., “Constant False-Alarm Rate algorithm based on test cell information”, IET Radar, Sonar and Navigation, vol.2, Issue:3, pp: 200 – 213, June 2008,.