Adaptive PN code acquisition using instantaneous ... - Semantic Scholar

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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 8, AUGUST 2002

Adaptive PN Code Acquisition Using Instantaneous Power-Scaled Detection Threshold Under Rayleigh Fading and Pulsed Gaussian Noise Jamming Kwonhue Choi, Associate Member, IEEE, Kyungwhoon Cheun, Member, IEEE, and Taejin Jung

Abstract—An adaptive serial search pseudonoise (PN) code acquisition scheme is proposed, in which the detection threshold is scaled by the instantaneous received power measured prior to PN code correlation. We observe that the proposed scheme achieves significantly improved mean acquisition times compared to the conventional nonadaptive schemes under Rayleigh fading and pulsed Gaussian noise jamming. Furthermore, the proposed scheme is shown to be optimum under pulsed Gaussian noise jamming in the sense that it forces the worst case jamming fraction to unity. Index Terms—Adaptive system, fading channels, jamming, pseudonoise coded communication, synchronization.

I. INTRODUCTION

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N MOBILE communication systems or systems experiencing hostile jamming, where the instantaneous received signal and interference power levels are likely to be unknown and/or time varying, fixed detection threshold acquisition schemes may result in unacceptable performance, and some form of adaptive threshold setting scheme is required. In [1]–[5] and [14], several methods for adaptively selecting the detection threshold have been proposed. The long-term observation of the matched filter/correlator outputs required for these schemes inhibit their application to fast-varying channels, where the rate of change of the received signal or interference power may be comparable to the pseudonoise (PN) correlation rate, such as with intentional pulsed jamming. In this paper, we propose a new adaptive serial search acquisition scheme, in which the detection threshold is adaptively scaled by the instantaneous received power to adapt to fast-varying channels. The instantaneous received power is estimated for each correlation interval prior to PN correlation, and is used to scale a fixed reference-detection threshold. This is equivalent to a fixed-detection threshold scheme with a fast open-loop automatic gain control (AGC), which normalizes the received signal power for each correlation interval. A similar approach was taken in [6] in the context of preamble detection for narrowband packet data systems under additive white Gaussian noise (AWGN) channels. Unlike other adaptive Paper approved by M. Brandt-Pearce, the Editor for Modulation and Signal Design of the IEEE Communications Society. Manuscript received May 14, 2001; revised October 19, 2001. This work was supported in part by the Ministry of Education (MOE) of Korea through the BK21 program and the Agency for Defence Development (ADD), Korea. This paper was presented in part at CDMA International Conference (CIC), Seoul, Korea, September 1999. K. Choi is with the Electronics and Telecommunications Research Institute, Daejeon 305-600, Korea (e-mail: [email protected]). K. Cheun and T. Jung are with the Division of Electronic and Computer Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea (e-mail: [email protected].; [email protected]). Publisher Item Identifier 10.1109/TCOMM.2002.801494.

Fig. 1. Proposed acquisition system.

schemes, the detection threshold at each correlation interval is scaled by the instantaneous estimated received power of the corresponding correlation interval only, allowing agile adaptation in pulsed jamming environments. II. PROPOSED ACQUISITION SYSTEM MODEL AND ALGORITHM In order to ease the presentation of the analytical development, we first consider the case without jamming, and then extend the results to the case with pulsed Gaussian jamming. The proposed acquisition system shown in Fig. 1 consists of a conventional noncoherent correlator and a received power estimator. The complex baseband signal is filtered with a chip ( : pulse-matched filter and is sampled at the chip rate , chip duration) to form the input samples is the complex PN code assumed to be an indewhere pendent identically distributed (i.i.d.) sequence with real and and imaginary parts taking on values of with equal probability. is a complex Gaussian random due to AWGN, is variable with zero mean and variance a Rayleigh random variable with probability density function , where is the average (pdf) received chip energy, and is a uniformly distributed random . variable on The system model can easily be extended to the multiuser case by applying an appropriate Gaussian approximation to the multiple access interference term. The noncoherent correlator output and the received power estimator output are given and by , where denotes the number of chip samare the chip samples within a correlation period and ples multiplied by the complex conjugate of the local PN code of magnitude 1. We assume that and are approximately

0090-6778/02$17.00 © 2002 IEEE


constant during a correlation interval, and are approximately independent between correlation intervals [8], [9]. We denote the case when the received PN code and the local , PN code are aligned with the same phase as hypothesis . The and the case when they are out of phase as hypothesis hypothesis testing is performed by comparing the correlation where is a fixed value to the power-scaled threshold reference-detection threshold. When is greater than is declared and vice versa. The probability of being greater is given as follows: than (1) To ease the derivation of the false alarm and the detection probabilities in the following section, we rewrite (1) using new decision variables and as with and , where and denote the sample mean and variance of given as and [13]. , the probability gives the Under hypothesis and under hypothesis , it gives the detection probability false alarm probability , i.e., . In order to avoid trivial cases, we assume that , since for , and are both equal to 1, and are both equal to 0. and for III. PERFORMANCE ANALYSIS A. Detection and False Alarm Probabilities , we have , Under hypothesis is a zero mean complex Gaussian where the signal term random variable with variance , and the noise term are zero mean independent complex Gaussian variables with . Hence, the decision variables and are given variance and , where as and are the sample mean and variance of . With , the decision variable follows the exponential distribution and the chi-squared distribution, with degrees of freedom with pdfs given by [13] (2) (3) and . Unwith , and are statistically independent, since like and and are independent, due to the fact that sample mean and sample variance are statistically independent when sampled from a Gaussian distribution [13]. Using this fact, the detection probability may be derived to be

(4) where

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Under hypothesis is given by , are i.i.d. random variables taking on values where , with equal probability. Since of are complex zero mean Gaussian random , and are zero mean variables with pdf identical to . complex Gaussian random variables with variance are uncorrelated but not independent. In Note that form an order to ease the analysis, we assume that independent sequence rendering s independent. Then, the and follow the exponential and the decision variables chi-squared distributions, respectively. Specifically, and are identical to (2) and (3) with and reand . placed with The assumption that s are independent also assures statistical can easily computed to independence of and and thus, be (5) Note that the false alarm probability is a function of and only and does not depend on nor . Thus, the proposed scheme achieves constant false alarm rate (CFAR.) B. Nonadaptive Acquisition Scheme In conventional nonadaptive serial search acquisition schemes, hypothesis testing is performed by comparing the correlator outputs to a fixed detection threshold . Since follows the exponential the noncoherent correlator output under hypothesis distribution with mean [8], is given as (6) are assumed to be independent to simUnder hypothesis plify the analysis as in Section II-A. Then, follows the expogiving nential distribution with mean (7) Numerical results in Section IV show that (7) very accurately approximates the simulation results. We observe that unlike (5), is a function of . We also note that as the signal increases, as well as increases for a given energy threshold due to self noise [10], [11]. C. Pulsed Gaussian Noise Jamming Under pulsed Gaussian noise jamming, the total received power during a correlation interval is time varying, depending on the state of the jammer. Here, for simplicity, we assume that each correlation interval is jammed independently and that the jammer is either on or off during a correlation period. Denoting and the jammer-off state as the jammer-on state as and are given as (8) (9)

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where is the jamming fraction denoting the probability that the and jammer is on during a correlation interval, and are the detection and the false alarm probabilities conditioned on . For simplicity, under pulsed the jammer state jamming, we assume that the jammer dominates the AWGN and neglect the effect of AWGN in the following. 1) Nonadaptive Acquisition Scheme: When the pulsed jammer is on during a correlation period, the despreader output and , is given as denotes the jammer contribution modeled as a comwhere plex i.i.d. Gaussian random sequence [7], [12] with variance where denotes the total jamming power. Using (6) and and for the case of the nonadaptive acquisition (7), scheme are given as (10) (11) (12) (13) For sufficiently large , which is usually the case, it is possible and . to choose a proper , such that is larger than from (10) and (12), is Since also approximately unity. Hence, neglecting thermal noise, and in (8) and (9) are approximately given as (14) (15) also results in maximum mean acThus, that maximizes quisition time. Differentiating (15) with respect to and setting the result to zero gives the worst case jamming fraction as for and 1 for , where . Note decreases with decreasing . This implies that as the that total jammer power decreases, the jammer should decrease in order to increase the instantaneous jammer power to maximally degrade the performance of the nonadaptive acquisition scheme. 2) Proposed Adaptive Acquisition Scheme: Let us define for the case the equivalent signal-to-noise ratio (SNR), when the pulse jammer is on during a correlation period as , where is the received signal power. The detection probability when the jammer is on, , is then given by (4) with replaced with which can be written as (16) and the false alarm probability is identical to (5) irrespective of the jammer state, since the false alarm probability does not depend on the SNR. Since the false alarm probability is not a function of , the value of that minimizes the detection probin ability maximizes the mean acquisition time. Setting

Fig. 2. Detection and false alarm probabilities, N = 64;

(4) gives into (8) gives lows:

;o

: simulations.

, and substitution of this result and (16) under the pulsed jamming environment as fol-

(17) is negative for , It can be shown that , and , which implies that is minimized for . In other words, the pulsing operation of the jammer degrades the jammer performance, irrespective of the total jammer power for the proposed scheme, and thus, the proposed scheme forces the pulsed jammer to the full-time jammer. IV. NUMERICAL RESULTS In Fig. 2, we first show the analytical results for and as a function of for the nonadaptive and the proposed adaptive schemes, without jamming (Rayleigh fading only), for several values of along with the simulation results for . We note that the analytical results quite accurately fit the


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an antijamming system can hope for. In Fig. 3, we also show versus for worst case jamming fractions, which indicate that significant savings in minimum mean acquisition times can be achieved by the proposed adaptive acquisition scheme over traditional fixed-threshold schemes. V. CONCLUSION

Fig. 3. Minimum mean acquisition time versus J=S for various values of ; N = 64.

simulation results, and that for the nonadaptive scheme for a . given value of increases significantly with increasing This is due to the dominance of the self-noise term as increases [10]. On the other hand, remains constant for the proposed adaptive scheme as was shown in Section II-A. In order to compare the performance of the nonadaptive and the proposed adaptive schemes under pulsed Gaussian noise jamming, we evaluate the mean acquisition times normalized by the temporal length of the uncertainty region. The asymptotic formula for the normalized mean acquisifor a single dwell search system1 is given by tion time , where is the false alarm penalty factor set to 1000 for all the following numerical results [14]. Fig. 3 shows the minimum mean acquisition times with optimized detection thresholds for each for . Note the strong dependence various values of , when on . For example, for the nonadaptive scheme at of dB, there is more than an order-of-magnitude differfor the worst case pulse jammer and the ence between . For the proposed adaptive scheme, full-time jammer increases monotonically with irrespective of . In accordance with the analysis given in the previous section, we minimizing observe that the worst case jamming fraction decreases as decreases for the nonadaptive scheme, above which the and that there exists a certain level of is the worst case jammer. On the full-time jammer is always unity, irrespective of for the other hand, proposed scheme. Hence, using the proposed adaptive acquisition scheme, we have forced the Gaussian pulsed jammer back to the full-time Gaussian jammer, which is generally the best 1The advantages gained by using the proposed adaptive scheme are not dependent on the specific search scheme used. Here, we adopt the simplest single dwell search strategy in order to clearly bring out the differences between the adaptive and the nonadaptive schemes without having to tweak with extra system parameters.

We proposed a new adaptive PN code serial search scheme achieving constant false alarm probability, and analyzed its performance over Rayleigh fading channels with and without pulsed Gaussian noise jamming, and the accuracy of the analytical results were confirmed via computer simulations. Under the pulsed Gaussian noise jamming environment, significant improvements were observed compared to conventional fixed-threshold schemes. Furthermore, the worst case jamming fraction was shown to be unity for the proposed adaptive scheme and the pulsed jammer is forced back to a full-time jammer. REFERENCES [1] B. B. Ibrahim and A. H. Aghvami, “Direct sequence spread spectrum matched filter acquisition on frequency selective Rayleigh fading channels,” IEEE J. Select. Areas Commun., vol. 12, pp. 885–890, June 1994. [2] P. W. Baier, J. Meyer, and H. Waibel, “Power level adaptive synchronization circuit for spread-spectrum-BOK-receivers in burst transmission systems,” in Proc. MILCOM’82, vol. 2, Boston, MA, pp. 27.1.1–27.1.6. [3] S. G. Glisic, “Automatic decision threshold level control in direct sequence spread spectrum systems,” IEEE Trans. Commun., vol. 39, pp. 187–192, Feb. 1991. [4] S. Chung, “A new serial search acquisition approach with automatic decision threshold control,” in Proc. VTC, vol. 2, Chicago, IL, July 25–28, 1995, pp. 530–536. [5] C. Kim, H. Lee, and H. Lee, “Adaptive acquisition of PN sequences for DSSS communications,” IEEE Trans. Commun., vol. 46, pp. 993–996, Aug. 1998. [6] M. R. Soleymani and H. Girad, “The effect of the frequency offset on the probability of miss in a packet modem using CFAR detection method,” IEEE Trans. Commun., vol. 40, pp. 1205–1211, July 1992. [7] E. W. Siess and C. L. Weber, “Acquisition of direct sequence signals with modulation and jamming,” IEEE J. Select. Areas Commun., vol. SAC-4, pp. 254–272, Mar. 1986. [8] A. J. Viterbi, CDMA Principles of Spread Spectrum Communication. Reading, MA: Addison-Wesley, 1995. [9] S. Tantaratana, A. W. Lam, and P. J. Vincent, “Noncoherent sequential acquisition of PN sequences for DS/SS communications with/without channel fading,” IEEE Trans. Commun., vol. 43, pp. 1738–1745, Feb.-Apr. 1995. [10] V. M. Jovanovic´ and E. S. Sousa, “Analysis of noncoherent correlation in DS/BPSK spread spectrum acquisition,” IEEE Trans. Commun., vol. 43, pp. 565–573, Feb.-Apr. 1995. [11] A. Polydoros and C. L. Weber, “A unified approach to serial search spread-spectrum code acquisition—Part II: A matched-filter receiver,” IEEE Trans. Commun., vol. 32, pp. 550–560, May 1984. [12] K. Cheun, Introduction to Spread Spectrum Communications. Pohang, Korea: POSTECH Press, 1995. [13] R. E. Walpole and R. H. Myers, Probability and Statistics for Engineers and Scientists. Reading, MA: Addison-Wesley, 1986. [14] J. K. Holmes, Coherent Spread Spectrum Systems. New York: Wiley, 1981.