Ingenieria Electronica

Progress In Electromagnetics Research, PIER 88, 135–148, 2008

CA-CFAR DETECTION PERFORMANCE OF RADAR TARGETS EMBEDDED IN “NON CENTERED CHI-2 GAMMA” CLUTTER M. A. Habib INRS-EMT, University of Quebec Montr´al, Qc., Canada e M. Barkat American University of Sharjah Sharjah, UAE B. A¨ ıssa and T. A. Denidni INRS-EMT, University of Quebec Montr´al, Qc., Canada e Abstract—This work is aboutevaluating radar performance in detection of targets embedded in a clutter following Non centered chi-2 Gamma distribution model. This model, also called NG-distribution model, is able to fit high resolution sea radar clutter. In this paper, NG model is described. The performances of CA-CFAR radar, namely probability of detection and probability of false alarm, are calculated and closed forms of theseprobabilities are achieved. In order to evaluate the obtained results, simulation and analytical results are compared. Good matching between these results is achieved.

1. INTRODUCTION In radar detection, prediction of clutter level highly affects detection performances, in terms of probability of detection and probability of false alarm. Gaussian model has been widely considered but it showedlimitations when considering high resolution radars [1–6]. Many other models have been considered such Lognormal law, Weibull model and the K-distribution [7, 8]. K-distribution is the most suitable model to fit sea clutter in high resolution radars and quantity of work [9–14]

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has been related to this area. However, a main drawback is related to this clutter model; it is notpossible, with K-distribution clutter, to achieve a closed form expression when calculating the probability of detection of the CA-CFAR radar (Cell-Averaging Constant False Alarm Radar) [15]. Shnidman has proposed a new model to describe high resolution sea radar clutter, named “Non-centered chi-2 Gamma” or more simply NG-distribution [16]. He compared this model both Weibull and Lognormal ones andalso compared it to real data in order to confirm that this model is able to fit the high resolution sea radar clutter. Hence, it is worth to evaluate performance of radar in detection of targets embedded is such kind of clutter. In this paper, we propose to study the NG-distribution. We calculate the performance of a CA-CFAR detector within the case of NG clutter. We achieve a closed formexpression for both probability of detection and probability of false alarm. Simulation results are then compared to theoretical results. 2. NG-DISTRIBUTION While illuminating the sea surface by high resolution radar, received signal can be assumed to be a non-centered gaussian random process. The received signal is assumed to be a complex variable when considering both the in phase and in quadraturephase components [16]. Hence, we have in the kth cell is rk = rki + jrkq (1)

where rk is the kth return in the kth cell. The mean of each component can be expressed by mki = mk cos θ (2) mkq = mk sin θ where θ is the relative phase between the received signal and the oscillator. It is assumed to be a uniformly distributed random variable. The quadratic detection leads to the following signal Zk =|rk |2 = (rki )2 + (rkq )2 , and the function density of Zk is given by [16] 1 zk + m2 k fZk (zk ) = 2 exp − 2σ 2σ 2
  

(3)

I0 

zk m 2 k 2σ 2

(4)

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IN (·) is the N th order modified Bessel function, Zk is a χ − 2 non centered process with 2 degrees of freedom, and (mk )2 is the noncentrality parameter. Supposing theexistence of Nc returns yields to a new variable
Nc

Z=
k=1

Zk

(5)

Let define the following parameter
Nc

κ=
k=1

m2 ; k √

(6)

the density function of Z becomes 1 fZ (z |2Nc , κ, σ ) = 2 2σ z κ
Nc −1

z+κ exp − INc −1 2σ 2

zκ 2σ 2

(7)

When considering the following notations κ z y = 2 , κn = 2 2σ 2σ then we obtain fY (y |2Nc , κn ) = y κn
Nc −1

(8)

√...