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Rank-Based Detection of Random Signals in a Weakly Dependent Noise Model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kim, Kwang S. Jung, Hye Jung Kim, Sun Yong Song, Iickho Lee, Jeong Hoon |
| Copyright Year | 1999 |
| Abstract | In this paper, we consider nonparametric signal detection problems under the presence of additive noise exhibiting weak dependence. We derive the test statistic of the locally optimum rank detector under a weakly dependent noise model for random signals. The performance characteristics of the locally optimum rank detector are analyzed in terms of asymptotic relative efficiency. I. I NTRODUCTION Locally optimum (LO) detectors [1]-[5] have been of much interest in signal detection theory and applications because of their capability and effectiveness for detecting weak signals. A subclass of the LO detectors, the locally optimum rank (LOR) detector, has been investigated because an LOR detector requires only simple arithmetic operations, has lower sensitivity to small deviations of the noise pdf, and has nonparametric nature [6]-[8]. It has been commonly assumed that the additive noise samples are statistically independent. In practice, however, this assumption is often violated. Thus, investigations on signal detections in dependent noise are desirable. Among the typical investigations on signal detection problems under various dependent noise models are those in [9]-[12]. In this paper, we will investigate the LOR detector for random signals under a weakly dependent noise model. The weakly dependent noise will be modeled as the first order moving average (MA) of an independent and identically distributed (i.i.d.) random process. The test statistic of the LOR detector will be derived and then the asymptotic performance characteristics of the LOR detector will be investigated. II. THE OBSERVATION MODEL Let H0 andH1 be the null and alternative hypotheses, respectively. Then, the observation model can be written as H0: Xi = Wi; i = 1; 2; ; n; H1: Xi = si +Wi; i = 1; 2; ; n; (1) wherefXig are the observations, fWig are the weakly dependent noise components, is a signal strength parameter, and fsig are the signal components. The weakly dependent noise fWig can generally be modeled by the Volterra expansion [13], which is, however, almost intractable to handle because of the infinitely many terms of the expansion. In this paper, we will assume that the weakly dependent noise Wi, i = 1; 2; ; n, are the MA of i.i.d. random variables as Wi = ei + ei 1ui 2; (2) whereei, i = 1; 2; ; n, are i.i.d. random variables with common pdffe. The pdffe is even symmetric with bounded continuous derivatives and satisfies the regularity conditions [6]. In (2), is called the dependence parameter determining the correlation coefficient of Wi, andui is the unit step sequence defined byui = 1 wheni 0 andui = 0 wheni < 0. Let X , W , e, and s be then-tuple vectors representing (X1; X2; ; Xn), (W1;W2; ;Wn), (e1; e2; ; en), and (s1; s2; ; sn), respectively, andfW (W ), fe(e) = Qn i=1 fe(ei), andfs(s) be the pdfs of W , e, ands, respectively. Then, we have fW (W ) = fe(W1)fe(W2 W1) fe(Wn Wn 1 + + ( ) W1) = fe(X1 s1)fe(X2 s2 (X1 s1)) fe(Xn Xn 1 + + ( ) X1 (sn sn 1 + + ( ) s1) = n Y i=1 fe(Yi ci) = fe(Y c); (3) whereYi = Pi 1 k=0( )Xi k, ci = Pi 1 k=0( )si k, Y = (Y1; Y2; ; Yn), andc = (c1; c2; cn). 0-7803-5538-5/99/$10.00 (c) 1999 IEEE III. T HE LOCALLY OPTIMUM RANK DETECTOR Let us define the sign vector Z = (Z1; Z2; ; Zn) and the magnitude rank vector Q = (Q1; Q2; ; Qn), where Zi = sgn(Yi) andQi is the rank ofjYij in the setjY j = fjY1j; jY2j; ; jYnjg. We will also usejY j[i] to denote theith smallest member of jY j. Let the random signal components fsig form a random process with mean zero and covariance function rs(i; j). Then, the joint pmf of(Q;Z) is p(q; zj ) = PrfQ = q; Z = zj ) = Z |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://bungae.kaist.ac.kr/pub/paper/ic094.pdf |
| Alternate Webpage(s) | http://sejong.kaist.ac.kr/~ssp/paper/IC094.pdf |
| Alternate Webpage(s) | http://www.argreenhouse.com/society/TacCom/papers99/07_6.pdf |
| Alternate Webpage(s) | http://dcl.yonsei.ac.kr/papers/IC_16.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Additive white Gaussian noise Arabic numeral 0 Assumed Binary prefix Carrier-to-noise ratio Coefficient Detection theory Detectors Estradiol Exhibits as Topic HL7PublishingSubSection |
| Content Type | Text |
| Resource Type | Article |
