Nonparametric rank detectors on quantized radar video signals

Permutation tests for nonparametric detection

“…Other way of computing ranks is as follows [22,23] n r = (r!,r 2 ,...,r"); r t = ^ u(x;-x,<), i=l,2,...,n k = l 1 <fj <n.…”

“…According to our previous works on parametric and nonparametric (rank and permutation) detectors [22][23][24]32] under IID clutter samples, the optimum statistic for parametric and permutation detectors is the clipping statistic [32] under spiky K-distributed clutter (v=0.5) and the linear (or quadratic) statistic under Rayleigh clutter (v = co). For rank detectors [22,24], the linear rank statistic is quasi-optimum under spiky clutter (v=0.5) and suboptimum under Rayleigh clutter (v = co).…”

“…It is supposed that tied samples (i.e., x,=x,, i^j) are solved by uniform randomization [23]. Partition (15) is well defined by the rank vector r=(ri,r 2 r") where r is a permutation of (1, 2 n), and can be computed from sample vector x=(x!, x 2 x") after ordering (sorting) its components, i.e., x fl <x J2 < • • • <x in , so we have r ik = k, fe = l,2,...,n. Note that each value of the rank vector r defines a unique region D, -, i=l, 2 n!, shown in (15); for example, r=(l, 2 n) corresponds to the region Xi <x 2 < ... <x", and r=(2,1 n) corresponds to x 2 < Xi < ... < x", etc.…”

“…Interesting classical tutorial papers about nonparametric detection are due to Carlyle and Thomas [18] and Thomas [19]. Applications of rank tests to radar detection can be found in [20][21][22][23][24] and references therein. Other rank applications to (wireless) communications are, for example, in [25][26][27][28][29] and references therein.…”

“…Other rank applications to (wireless) communications are, for example, in [25][26][27][28][29] and references therein. Finally, although rank tests have been applied to detection [16][17][18][19][20][21][22][23][24][25][26][27][28][29], the more general family of permutation tests has seldom been applied to radar detection [30][31][32][33][34][35], at least, as far as the authors know. Now, some comments on the methodology of test optimization are required.…”