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Adaptive Multichannel Detection of Frequency -Hopping Signals
1504 IEEE TRANSACTIONS ON COMMUNICATIONS. VOL, 40, NO. 9, SEPTEMBER 1992 the time index A), but they are assumed to occur infrequently momentary increase. The next level of processing is designed relative to the observation period T=NITI to excise any persistent hop false alarms due to the latter Furthermore, each spectral height is assumed to randomly transition from further processing take 1 of M possible values denoted by N,/2 I=0, . M- Under hypothesis H1, the observation consists of signal plus I with probability iP(0); l=0,., M-1. This creates a oise in 1 channel and noise alone in the other N-1. The common M-level staircase representation for the environment integrator output for the signal channel is a noncentral gamma in each channel. This assumption is only made to simplify the random variable [8 with mean and variance presentation of analytical and numerical results in this paper The above model reduces to stationary awgn of constant Ai. k= Ni.kIwi+es and uniform spectral height No/ 2 by selecting p(0)=I and o2k=(Ni)2T W1+2ES N; k p()=o,for=1,…,M-1. where Es is the received signal energy per hop If the current C Ideal performance analysis hop threshold is assumed (momentarily) to consist of noise only observations, the probability of detection per hop is Hop Decision Analysis: The rule for generating hop deci sions can be expressed as √TW1(1+入,k-KA1) DH/i, k Nik 2入1k+F2A2 o if Yik < O 1ifY,k≥0 where A1 and A2 are defined in(7) and Ai, k is the where the hap decision statistic is Y; k =Ei k -a k. If we signal-to-noise ratio (SNr)per hop given by apply the central limit theorem(CLT) for independent random ariaDIcs 7 the statistic Yi k, appropriately normalized, is AI, k- NikT1Wi asymptotically Gaussian. The mean and variance of Yik is quation(9)represents an upper bound on the hop detection WL robability since a channel revisit time of more than wHop ,.k=1,一K ∑ ajli, k- periods was assumed for the FH signal. However, the analysis in Appendix a shows that each integrator output by itself will WL have a minimal impact on future thresholds. Thus, the presence ah=0k+2∑03k- (4) of an FH signal during one integration interval will have a negligible impact on the succeeding WL hop thresholds and where Hi. k and o2k are the mean and variance of the integrator decisions. Consequently, (9) is a tight upper bound and is taken outputs Ei, k, respectively to be an equality in this analysis. Furthermore, since each noise Cnder hypothesis Ho, the observation consists of noise ctral height is assumed to randomly take 1 of M values, alone in all N channels. Hence, each integrator output is a (9)can be rewritten as gamma random variable [8] with mean and variance bi k= Ni.kIwi +2x+k2A2) 02k=(N:k)2TW1 o)where PDH/-gVT1WI(1+ At-KA1 Assuming an environment transition has not recently occurred XI= NIT,W the probability of false alarm per hop can be expressed as The dependence on the channel index i and the time index 1,k k are now implicit in the noise index l. when an infrequent PFan=O Ti xi=d vLiW(1-KAi)s (6) environment transition occurs, the hop dctection probability +K2A2 converges to PDH/! after W hop periods, when the adaptive where threshold fully adjusts to the new noise state. The next level of processing is designed to excise any persistent hop false A (7) alarms resulting from such transitions and may inadvertently excise legitimate hop detections Channel Decision Analysis: Each channel sums a block of and l*y is the cumulative distribution function of a zero- N, hop decisions to form the channel decision statistic, viz mean. unit-variance Gaussian random variable Here, the receiver maintains a constant hop false alarm probability independent of the environment. When an infrequent envi- ∑a ronment transition occurs, the probability of false alarm pcr hop abruptly deviates from pe ay in(6), but returns to this The resultant channel decisions are generated according to the value after WL hop periods, when the adaptive threshold fully rule djusts to the new noise state. a transition to a lower noise 0 if s state creates a momentary decrease in the hop false alarm D:=1if1≤S≤B (11) probability, while a transition to a higher noise state creates a 0iβ<S;≤N1 NEMSICK AND GERANIOTIS: MULTICHANNEL DETECTION OF FH SIGNALS 1505 where B NI. The second threshold B is used to recognize The resultant block decision is generated according to the rule the intermittent hop activity of an FH signal from any persis tent activity of a misleading environment transition. Given thi U(Ho) if S<L feature and that transitions are assumed to occur infrequently 1(H1)ifS≥L the transient contributions to the channel decision performance are taken as negligible in this analysis Under hypothesis Ho, the statistic s is a binomial random The adaptive threshold in(2) renders each hop decision variable, resulting in a probability of false alarm(per block) dependent on its immediate WL predecessors, resulting in of a channel decision statistic which is the sum of dependent N Bernoulli random variable. Applying a Clt for dependent ∑()(Pc)y(1-PrAc) random variables [9], the statistic Si, appropriately normalized, y≈L(y is asymptotically Gaussian. Under hypothesis Ho, the steady- independent of the environment. Equations(6),(14), and(20 state mean of s now characterize the false alarm performance of the proposed 店;=N1FF1H receiver Analogously for hypothesis H1, the statistic s is a binomial which is also the mean for the sum of independent random random variable, resulting in a probability of detection(per variables. It is shown in Appendix a that a tight upper bound block)of on the steady-state variance of Si is ≤N1PAH(1-FpAH) P which is also the variance for the sum of independent random y=L variables. Thus, Si can be accurately approximated as the sum Equations(9),(15)-(17), and (21) now characterize N1 independent and identically distributed (ii d. Bernoulli ceiver's detection performance as a function of received Snr random variables and hence is a binomial random variable hop The probability of false alarm per channel is Average Detection Time Analysis. If an FH signal first n the initial hop of the Ith ob 2U)(PEAH)(1-PFAH)-(14)the first detection will be recorded after the / th interval with which is independent of the environment in every channel P(J)=PD(1-Pn)-J=I,+1 Under hypothesis Hi, the fh signal will be present in a given channel with probability 1/N. The average probability Consequently, the average signal detection time, mcasured in of detection per hop for a channel in noise state Nu/2 is seconds. is ()7+(4-2)rum (15) TD- Pp The statistic Si can also be accurately approximated under hypothesis H: as the sum of Ni i.i.d. Bernoulli random variables and. hence. is a binomial random variable. The II. ADAPTIVE BLOCK-SEQUENTIAL DETECTION cnvironment-dependent channel detection probability is A. Receiver Model ∑()(Pn)(1-PpHn N (16) A diagram of the receiver under consideration is shown in Fig. 2. It is a refinement of the adaptive block detection =0:…·,M-1 receiver in Fig. I which is designed to offer greatly reduced The avcragc probability of detection pcr channel is average signal detection times. Both receivers employ similar logic at the hop, channel, and overall decision levels, except that the receiver of Fig. 2 attempts successive channel and P PpchP(l) (17) overall decisions after each hop period using activity fro L=0 the most recent NI hop periods of T= NiTI seconds. That where the first term is given by(16) and the second is the is, after each hop period, a new set of parallel hop decisions respective noise state occupancy probability. The assumption is generated, the oldest set of parallel hop decisions in the of a common M-level staircase representation for the environ-T-second window is discarded, and new channel and overall ment in each channel leaves this probability a constant Ppc decisions are made. This data collection scheme results in independent of the channel successive decisions with all but two sets of pa hop Overall Decision Analysis: The parallel channel decisions decisions in common are summed to form the overall decision statistic. viz As shown in Fig. 3, the operation of the block-sequential window can be viewed as an N1-bit shift register and a ∑D (18) summing device [6]. After each hop period, the register is shifted left by one bit and the new hop decision is inserted into 1506 IEEE TRANSACTIONS ON COMMUNICATIONS. VOL 40. NO. 9. SEPTEMBER 1992 r (1) PF WI 2=-M1 ≤≤B Threshold Channel ig. 2. Adaptive multichannel radiometer employing block-sequential detection N1 Stage Registar The resultant channel decision are generated according to the ru 0进S2k=0 1if1≤S,k≤B 0ifβ<S、k≤N1 where B N1. Consistent with the channel decision analysis of Section II-C, the contributions of abrupt environment tran sitions to receiver performance are taken as negligible here The following analysis is an extension of [6 to the case Fig 3. Block-scqucntial window for the ith channel of multichannel detection of hop-by-hop random signals of unknown length Letting the contents of the register in Fig. 3 denote the the rightmost(low-order)bit. The resulting channel decision binary number Ri, k, the statistic Si, k is simply the num statistic is simply the number of binary ones in the register. ber of ones in Rik. Equations describing the channel dec]- sion performance can now be developed by recognizing that B. Environment Model LRi, k; k=1,2,. is a Markov process with finite state space 2 6], meaning that R i The model for the backgl ground environment is the same the previous state Ri k-l and on the current hop decision d i k model described in Section II. 2 for adaptive block detection The left shift of an N1-bit register is cquivalent to multipli cation by two, modulo 2. If the previous state is li.k-1=U, C ldeal performance analysis then the current state is e Hop Decision Analysis The block-sequential receiver of Ri k (2u)mod(2 if dik=0 Fig. 2 operates identically to the block receiver of Fig. 1 at (20)mo(2N)+1ifd,k=1(26) the hop decision level. As a result, the hop decision analysis of Section II-C is equally applicable here Letting pi, k denote the probability that di, k is 1, the state Channel Decision Analysis: Each channel sums a block of transition probabilities are [6] the most recent Ni hops decisions to form the channel decision P,k(v)=P{R,k=叫B1,-1=} statistic,VLz… 1-Pi, k if u=(2v)mod(2 k if 1.=(2)mod2~)+1(28) d for all 7,m∈{0,1 NEMSICK AND GERANIOTIS: MULTICHANNEL DETECTION OF FH SIGNALS Let the variables &i k i denote the probability that Ri, k where h'is the number of hop periods the FH signal has been assumes the values j=0, 1, .. 21-1. The channel decision present. The first part of (32)represents the transition from N1 D k will take the value 1 with a probability given by the noise only observations to Nr-signal plus noise observations, summation of all &i;, k, where the number of ones in the binary while the second part represents the equilibrium achieved representation of j is betwcen 1 and B, inclusive. Since Ri k+1 when the window is filled with signal plus noise samples is independent of the leftmost bit of Ri k, the variables &i, k+1., The difficulty in composing succinct expressions for the exact are given by the recursive relations [6] hannel detection probability during the transition phase has motivated the above approximation 6k+12=[6,k+65,k12N21](1-P,k) The average probability of detection per channel is 6k+12y+1=6k,+6:k,+2N-12 M一1 rj=0,1, DCA ∑Pocn.kp(l) (33) t=0 Under hypothesis Ho, the probability Pi k in(28 )and(29)is givcn by PFAH in(6). It is assumed that a channel decision is where the first term is given by(32)and the second is not made until the block-sequential window is initially filled. the respective noise state occupancy probability. Again, the However, [6] shows that after the first N, hop decisions, the assumption of a common M-level staircase representation rocess R i k has reached equilibrium, meaning that &i, k,;=6, for the environment in each channel leaves this probability for R= N1, N1 +1 independent of the channel index i Once equilibrium has been N1), both data collection schemes 8,=(PFAH)(1-PFAH) (30 offe al channel detection performance(per block Overall Decision Analysis: The parallel channel decisions and S, is thc number of oncs in the binary representation are summed to form the overall decision statistic, viz of j. These equilibrium probabilities are independent of the an channel index i and the time index h. The process Ri, h remains in equilibrium until either an FH signal appears or an environment transition occurs The probability of false alarm per channel is given by the The resultant block-sequential decision is generated according summation of all & such that S,E [L,., 6]. This can be to the rule expre essed as D 0(Ho) if Sk <L 1(H1)ifSk≥L ∑()nm) Under hy pothesis Ho, the statistic Sk is a binomial random variable, resulting in a probability of false alarm(per block independent of the environment in every channel. Equation of (31) is valid for each channel decision, although successive decisions share a common hop activity [6- Equations(14 and (31)reveal that both data collection schemes offer identical PA=∑(PAc)(1-Pc)(0 =(y channel false alarm performance(per block). Under hypothesis Hi, the probability Pi, k in(28)and(29 )is given by PDH/ in independent of the environment. Equations(20)and(36 (15). The FH signal is assumed to first appear on hop period reveal that both data collection schemes offer identical false K+ l, with th ss Ri k having reached (per block) at the overall decision level g K hop periods re given Analogously, for hypothesis Hi, the statistic Sk is a bino by the equilibrium probabilities of (30), with the variables mial random variable, resulting in a probability of detection Di, K+k, then being given by the recursive relations of ( 29)(per block) of for pi k = P 飞向OB/, The proce2 k returns to equilibrium the first appearance of the FH signal. The ∑ (PpC/k)(1- PDC/)s(37) equilibr probabilities are then given by(30)with PDH/ d for Pr The probability of detection per channel can be accurately Equations(9,(15),(32),(33),and(37) approximated as 1-i, K+*, o or one minus the probability of snr per hop. Once equilibrium has been reached, both data more than B legitimate hop detections, within a window of NI collection schemes offer identical detection performance(per hop periods negligible. Thus, the channel detection probability lock) at the overall decision level Average detection Time Analysis: If an FH signal first for noise state N1/2 is appears on hop period K t l, the probability that the first PcLk= detection is recorded on hop period K+h is 1-(1-PhAH)-(1-PD/)1≤K≤N P)=P/kI(1-Pk)k=1,2 P DH/ IEEE TRANSACTIONS ON COMMUNICATIONS, VOL 40. NO. 9. SEPTEMBER 1992 where PDjo=0. Consequently, the average signal detection TABLE I lime. measured in seconds. is RECEIVER CHARACTERISTICS FOR NUMERICAL EXAMPLES Receiver channels T∑kP(K) Channel bandwidth WI 500H Integration Time 2 ms Time-Bandwidth product Unfortunately, a simple closed-form solution to this equation Prob, of Detection(per block) t P does not exist, thus requiring numerical evaluation using Proh. of False Alarm(per black )t F. computer assets Observation Interval l Hops pcr Block Threshold Window Length 环L IV. NONIDEAL PERFORMANCE ANALYSIS Weighting Coefficients 1/wL Hop Threshold t A. la Time Synchronization Channel Thresholds B Overall Decsion Threshold] L The assumption of perfect time synchronization means that an interceptor has exact know ledge of when a message performance objective optimum value transmission begins and of the epochs of the individual hop pulses. This leads to the calculation of received signal strengths whcrc f" is the frcqucncy misalignment bctween the hop and that are too low for a given detection performance since signal channel center frequencies and Th is the inverse baud rate of energy is distributed in adjacent integration intervals he fh signal The ratio T1/Tb denotes the number of symbols Referring to the receivers in Figs. 1 and 2, the fraction per hop. Analogously, the fractional energy passed by the ith of input hop pulse energy falling in the current integration adjacent channel is [4] interval is f-(-1/2)/Tb e=1-T/-/2≤T≤T/2(40) SIn TfTb df(44) where T is the time misalignment between the epoch of the f-(2+1/2)Ib hop pulse and the intcgration interval. For positive valucs of for i = +1.+2 T, the fractional energy in the next interval is Neglecting the "spillover"components in(44), the average e1=T/T 1) fraction of received hop pulse energy is found by averaging (43)over the range space of f. Assuming the misalignment while, for negative values of T", the fractional energy in the is uniformly distributed over[-1 216: 1/2161 previous interval is verage is ho = 0.6452 [4]. Hence, all received signal T/TI (42) strengths calculated via the analyses in Sections II and Ill must be increased by the multiplicative factor 1/ho= 1.55, or the additive factor 1.90 dB, to achieve the desired performance. Neglecting the spillover'components in (41)and (42 ) Combining this frequency penalty with the timc penalty of the average fraction of received hop pulse energy is found Section IV-A results in a total signal level increase of the by averaging eo over the range space of T. Assuming the multiplicative factor 2.07, or the additive factor 3. 15 dB misalignment is uniformly distributed over [T1/2, T1/2, the resultant average is e0 =0.75. Consequently, all received V. NUMERICAL RESULTS signal strenghts calculated via the analyses in Sections II and The performance of the receivers in Figs. 1 and 2 is now II must be increased by the multiplicative factor 1/eo illustrated with numerical examples. The two metrics of par 1.33, or the additive factor 1.25 dB, to achieve the desired ticular interest are the receivers'probability of detection(per performance block and average signal detection time, both as a function of the input SNR. B Lack of Frequency Synchronization Detection Scenario: Consider a fast FH signal operating The assumption of perfect frequency synchronization means at 500 hops/s over an sS bandwidth of 1.024 MHz.The that an interceptor has knowledge of the hop center frequencies receivers require 2048 channels, all of bandwidth 500 Hz and and has each channel appropriately tuned. This also lcads to integration time 2 ms, for each optimum detection of this sig- the calculation of received signal strengths that are too low nal. These features, along with the remaining features defining for a given detection performance since signal energy will be the receivers, are summarized in Table l. The last three entries distributed in several channels simultaneously represent optimum values, in the sense of being the thresholds Assuming an ideal rectangular filter characteristic for each rhich at snr to achieve the citcd bandpass filter, the fraction of input hop pulse energy passed performance objectives. The resultant minimum input SNR is by the signal channel is (41 1.25 dB for operation in stationary AWGN The background environment is taken as a random bilevel ho(f)= T/nx厂b at fa f 43 spectral height in each channel. The heights No/2 and N1/2 can bc viewed as noisc and noisc plus interference states f-1/2T with occupancy probabilities P(O)and p(1)=1-p(0) NEMSICK AND GERANIOTIS: MULTICHANNEL DETECTION OF FH SIGNALS 1509 10 ()=0,p(=l 28苏65岩 BL△ CK-SECUENTA parx。N P=10 N2=2(N△/2 Pr 3-2-10 NPUT SNR PER HOP(o INPUT SNR PER HOP(dB Fig. 4. Detection performance for 3 dB intcrfercncc Fig. 6. Average signal detection time for alternative PFA requirements detection performance cited above. The receiver maintains (ideally) a constant false alarm probability(per block)of 10 independent of the environment These figures show that the adaptive block receiver can detect FH signals at low input SNR's cvcn in the presence 己 of interference. As the likelihood of each channel being in an interference state increases, the minimum input SNr for maintaining a given detection performance also increases, but A-Ip(o)m*y3 p(0-2/39 only by one or two dB for modest values of p(1). This is because every channel contributes to the decision process p0-/3(-/ whether or not it is in an interference state and. for modest 10 in a noise-only state This logic also suggests that, for modest values of p(1), the required SNR increases will be relatively 8 insensitive to the interference level. This is seen by comparing p(0)=0,p(1)= the detection curves in Fig. 4 to their counterparts in Fig. 5 Given that some rf bands may contain interference levels tens of dBs above the noise floor, this robust detection capability becomes very important NPUT SNR PER HOP(dB) The receivers in Figs. 1 and 2 were shown to offer identical Fig. 5. Detection performance for 6 dB inter ference detection performance (per block) once the latter has reached equilibrium. As a result, Figs. 4 and 5 also plot the equilib rium detection performance of the adaptive block-scquential respectively. This results in an environment of AWgn plus receiver random interference, where each channel experiences interfer- Average Signal Detection Time: Fig. 6 plots the average sig ence with probability p(1). When expressing input SNRS, the nal detection time associated with each receiver as a function noise component corresponds to noise state No /2 of input SNR for operation in AWGN. For receivers having Probability of Detection: Figs. 4 and 5 plot the adaptive an identical probability of false alarm(per block) of 10 block receiver's probability of detection (per block) for in- the block-sequential scheme is shown to offer greatly reduced terference levels of 3 dB and 6 db above the noise floor detection times. This superior performance results from mak in each channel, respectively. The curves parameterized ing overall decisions after each hop period T1, instead of only {p(O)=1,p(1)=0}and{r(0)=0,p(1)=1} correspon ch observation period NIT1. The block scheme AWGN of uniform spectral height No/2 and N1/2, respec- has a minimum detection time of T seconds, which is evident tively, and establish the bounds on receiver sensitivity for these in Fig. 6 where T= 1.0 s was assumed. Conversely, the cxamples. The cross-hatched point corresponds to the optimum block-sequential scheme has a minimum detection time of 510 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL 40, NO 9, SEPTEMBER 1992 Ti seconds. This could be shown in Fig. 6 by extending the The first term represents the variance for the sum of inde vertical axis downward to cover T1=2.0 ms. pendent random variables, while the second accounts for their Given the increased rate at which the block-sequential dependency. Each covariance term in(45)can be expressed scheme attempts overall decisions the above comparison as under common PFA requirements may seem unfair. However Fig. 6 also plots the avcrage signal detection time of the block- Ck=P{Y;,1+k≥01Y,≥0}FEAH-(PFAH)(46) sequential scheme for several increasingly stringent false alarm where Yi, k is the statistic resulting in hop decision di, k. USing requirements. This family of curves further illustrates the superior performance of the block-sequential scheme, even (2), the conditional probability in (46)is given by when operating under a PFA requirement three-orders of WL magnitude smaller than the block scheme PA=P{E1+2K∑1E+- L VI. CONCLUSIONS E2k∑aE1-(.(47 a possible approach to the detection of FH signals in complex signal environments has been investigated. This is accomplished through the use of a parallel bank of narrowband rork∈ WL, an upper bound for Plk is found radiometers, where each channel updates its hop decision from(47) to be threshold to reflect the current environment and excises any WL persistent hop activity inconsistent with an FH signal from Pi k sPEi, 1+k-K aE,1+k-1 further processing. The two data collection schemes considered l=1,4≠k for the receiver are block and block-sequential dctection WL Block detection attempts successive overall decisions using k K∑aB,1-m0 (48) nonoverlapping blocks of data spanning T seconds each r=1 Block-sequential detection also uses blocks of data spanning =P{Zk≥0}.(49) new datum is collected. Equations describing the falsc alarm Invoking the CLT for independent random variables [71. and detection performance of both schemes are developed the statistic /i, k, appropriately normalized, is asymptotically in terms of input SNR, all for an environment modeled as Gaussian The mean and variance of Zi,] is Gaussian noise with a random spectral height in each channel WL WL This analysis serves as a tool for determining optimum receiver ,k=H1+-K∑aH41+=1-akK∑a,- configurations and for quantifying thcir general performance E=1,≠k a significant feature of both data collection schemes are the small input SNR increases needed to maintain a given ai k =Oi, 1-k+& WL WL a detection performance in environments other than AWGN ,1+k-(+k2 l=1,≠k The examples presented here suggest a degradation of only (50) one or two db for modest interference conditions. whilc maintaining(ideally) a constant false alarm performance. This where Ai, k and of, k are the mean and variance of the integrator obust detection capability can be important as many RF bands outputs Fi, k, respectively. Consequently, Pi.h is upper and ome increasingly crowded with other users, whose added lower bounded by transmissions can overwhelm conventional (nonadaptivere ceivers 0≤Pk≤P={k,ohk} The block-sequential scheme is designed to offer greatly reduced average detection times as compared to the block Combining(45),(46), and(51)results in the follow ing scheme. This significant feature is also supported by the bounds for a examples presented here. This reduction in detection time can be important when attempting to intercept low-duty cyclc FH (52) waveforms APPENDIX A az=N1 PFAH(1-(2WL+1)PFAH (53) VARIANCE oF TIIE CIIANNLL DECISION STATISTIC Under hypothesis Ho, the steady-state variance of the chan =a+2N1 1 PAH (5 nel decision statistic s, is A morc rclaxcd uppcr bound can be found by recognizing that WL ed by PAh in(6) under a2=NPFA(1-PPAH)+2N>Cov(di, 1, d, 1 +k]. steady - state conditions. Thus, an alternative bound is (45) air,= nipah(1- peah>gi (55) NEMSICK AND GERANIOTIS: MULTICHANNEL DETECIION OF FH SIGNALS 1511 which, as noted earlier. is the variance for the sum of ind Larry W. Nemsick(M'8S)was born in Baltimore pendent random variables MD, on September 22, 1962. He received the B Es The percentage difference in the upper and lower bounds of degree(with honors) in clectrical cnginccring from The Johns Hopkins University, Baltimore, MD, in (55)and(53) can be expressed as 1984, and the m.s. degree in electrical engineering from the University of Maryland, College Park, in PD=(-a2)/,÷2WLAH.(56) In 1984 he joined the staff of The Johns Hopk University Applied Physics Laboratory where he has Numerically evaluating (56) for a variety of receiver config nce performed various studies and experiments urations shows PD to be significantly less than 0.01 for all communications and signal proccssing practical designs. In fact, the receivers used in the examples R pics have included the interception and exploitation of spread spec- trun signals, the modeling and performance evaluation of HF communications of Chapter 5 achieve PD=0.0006. These small differences networks, and the application of adaptive interference cancellation to ELF result from a receiver s hop threshold adaptation scheme communications having to achieve a Pf AH pcrformance several orders of as Vice chairman of the baltimore chapter of the ieee comm unications magnitude smaller than its overall PFA requirement. Given Society PFA requirements nominally ranging from 10-3 to 10-5 and threshold window lengths on the order of hundreds of hop periods, PD in(56) is seen to be quite small The significance of the above result is that o, in(45 can be accurately approximated by thc uppcr bound in(55) ling )and(55) reveals that the channel decision fe otis(S’76-M82-SM88) statistic S, can be accurately approximated (under steady ceived Diploma (with highest honors) in state conditions) as the sum of i.i. d. random variables. This electrical engineering from the National Technical University of Athens. Athens, Greece, in 1978 conclusion also holds under hypothesis Hi and the M.s.and Ph.D. degrces in electrical ngineering from the University of llinois at Urbana-Champaign, in 1980 and 1983, respectively. bcr 1982 to august 1985 hc was [1 w.w. Peterson, T.G. Birdsall, and W.C. Fox, "The theory of signal an Assistant Professor of Electrical and Computer TRE Trans. Inform. Theory, vol. PGIT-4, Sept. 1954 E It the University of massachusetts [2] D.G. Woodring, ""Performance of optimum and suboptimum detectors Amherst. Since September 1985 he has been with for spread spectrum waveforms, "Naval Res. Lab, Washington, DC, of Electrical Enginccring and a joint faculty mcmbct of the Systems Rep.8432,De.1980. their hybrids in low-probability-of-intercept communications, "Naval Res. theory and their applications with emphas is on spread-spectrum n ation [3] J.D. Edel, " wideband, noncoherent, frequency-hopped waveforms and Research cente. His research has been in communications theory, inform b, Washington, DC, Rep 802 Ⅳ.1976 jam communications; multi-user communications for mobile, satellite, and [4] M. K. Simon, Spread Spectrum Communications, Volume ll. rockville optical networks; interception and classitication of signals; radar detection MD: Computer S and discrimination; and multi- sensor correlation and data fusion he is the author of over 100 technical papers in journals and conference proceedings. [5] R.A. Dillard, "Detection of covert signals, "Naval Electron. Lab. Cent., He serves regularly as a consultant for governmental and industrial clients San Diego, CA, Rep. 2722, June 1974 [6]GM. Dillard, "Binary detection of randomly accurring signals, "Naval Dr. Geraniotis has received sevcral awards including a first National Prize Electron. Lab Cent., San Diego, CA, Rep 1741, Nov. 1970 RoSS, A First Course in Probability. New York: MacMillian, 1976. Research Laboratory Publication Award in 1990. In the past three years he [8]w. w. Chapman and R D Short, "An adaptively configured channelized has served as officer of the Washington DC/Northern Virginia Chapter of receiver for frequency hopped signal detection and tracking IEEE Int. the Information Theory Society and was its Chairman from 1989 to 1990 Conf. Commun, Chicago, IL, 1985. Since February 1989 he has been Editor for Spread-Spectrum of the IEEE [9 P. Billingsley, Probability and Measure. New York: Wiley, 1979 TRANSACTIONS ON COMMUNICATIONS

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简要介绍了Ad Hoc和移动IP的工作原理,探讨了一种基于Ad Hoc和移动IP集成的无线移动网络体系结构,并分析了其工作过程和服务性能。

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ADAPTIVE CONTROL

自适应控制理论,适合控制人员学习和使用,了解自适应知识。

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adaptive importance sampling

adaptive importance sampling

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Adaptive Multichannel Detection

Adaptive Multichannel Detection of Frequency -Hopping Signals

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Adaptive Filter Theory

The primary aim of this book is to develop the mathematical theory of various realizations of linear adaptive filters. Adaptation is accomplished by adjusting the free para meters (coefficients) of a filter in accordance with the input data, which, in reality, makes the adaptive filter nonlinear

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Adaptive Software Systems

LNCS 2009-6 Architectures for Adaptive Software Systems

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Adaptive Backstepping Control

Adaptive Backstepping Control of a Nonlinear Electromechanical System with Unknown Parameters

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Adaptive Digital Filters

Adaptive Digital Filters Second Edition, Revised and Expanded Maurice G. Bellanger

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Adaptive Business Intelligence

In the modern information era, managers must recognize the competitive opportunities represented by decision-support tools. Adaptive business intelligence systems combine prediction and optimization techniques to assist decision makers in complex, rapidly changing environments. These systems address

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Adaptive Signal Processing

Wiley Series in Adaptive and Learning Systems for Signal Processing, Communication, and Contro

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adaptive image process

ADAPTIVE IMAGE PROCESSING A Computational Intelligence Perspective Stuart William Perry Hau-San Wong Ling Guan

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ModbusTCP/RTU网关设计

基于UIP协议栈,实现MODBUS联网,可参考本文档资料,有MODBUS协议介绍

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html+css+js制作的一个动态的新年贺卡

该代码是http://blog.csdn.net/qq_29656961/article/details/78155792博客里面的代码,代码里面有要用到的图片资源和音乐资源。

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