Serial PN Acquisition Using Smart Antenna and Censored Mean Level CFAR Adaptive Thresholding for a DS/CDMA Mobile Communication

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1 01 IEEE 14th International Conferene on High Performane Computing and Communiations Serial PN Aquisition Using Smart Antenna and Censored Mean Level CFAR Adaptive Thresholding for a DS/CDMA Mobile Communiation Nour Alhariqi, Mourad Barkat, Fellow IEEE, and Aghus Sofwan Department of Computer Engineering King Saud University Riyadh, Kingdom of Saudi Arabia noor.ksu@gmail.om, mbarkat58@gmail.om, and aghus.sofwan@gmail.om Abstrat In [1], a novel approah using smart antenna with adaptive thresholding onstant false alarm rate (CFAR) in pseudo-noise (PN) ode aquisition for diret sequene ode division multiple aess (DS/CDMA) ommuniation systems in Rayleigh slowly fading multipath hannel was proposed. In this paper, we onsider the use of the ensored mean level detetor onstant false alarm rate (CMLD-CFAR) algorithm as an adaptive threshold proessor for DS/CDMA in multiuser signals situations. Under mobile ommuniation environments, multipath signals and other users' signals affet the performane of the PN ode aquisition. Fixed threshold tehniques are unable to adapt to these varying environments. Aordingly, a high false alarm rate and/or a low detetion probability may result, and thus, adaptive thresholding tehniques are essential. A smart antenna is an array of antenna elements that an modify the array pattern adaptively to minimize the effet of noise, multiple aess interferene (MAI) of other users, and multipath. The proposed system still onsiders PN ode serial aquisition by using the smart antenna, but an adaptive threshold value based on a referene window of CMLD-CFAR proessing. We derive an exat expression for the probability of false alarm for the proposed system, while the detetion performane of the system is studied in terms of omputer simulations under various parameters. The simulation results show that the system proposed is robust in a MAI environment. Keywords: Code Aquisition; CDMA; Adaptive CFAR; CMLD; Smart Antenna I. INTRODUCTION The pseudo-noise (PN) odes synhronization between the reeived ode and the loally generated one is an essential step for the reeiver to be able to demodulate properly the reeived signal in the diret sequene ode division multiple aess (DS/CDMA) ommuniation system. The goal of this proess is to align the loally generated dispreading PN ode sequene with the inoming spreading PN ode sequene. This proess is performed in two stages; the PN aquisition stage, whih oarsely aligns the two PN ode sequenes within a fration of the hip duration, and then the PN traking stage, whih is a finer alignment that aims to reduing synhronization errors to an aeptable limit. In the aquisition stage, the reeiver searhes in an unertainty region of phases. Aording to the searh mehanism, the aquisition stage an be lassified as: the serial searh aquisition in whih a one unertainty ode phase is tested at a time [,3], the parallel searh aquisition in whih all possible ode phases are tested simultaneously [4,5], and the hybrid searh aquisition whih ombine the serial searh with the parallel searh [6,7]. In searhing for synhronization, the orrelation between the inoming and the loally generated PN odes is omputed and ompared to a threshold value to make the synhronization deision. In the mobile ommuniations, the reeived signal levels are unknown and loation varying [8]. Therefore, using a fixed threshold may ause too many false alarms and/or low detetion probability aording to the seleted threshold value [9]. If the threshold value is too low, the false alarm probability will be inrease seriously. On the other hand, if it is too high the probability of miss is inreased. To overome these problems, the threshold value should be set adaptively aording to the surrounding environment. Using onstant false alarm rate (CFAR) proessing, whih is well developed in automati and adaptive radar signal detetion [10], to set an adaptive threshold for the PN aquisition has been used in literature [8-11]. The main idea is to use the orrelator outputs to estimate the bakground noise variane, whih is not known, to set the threshold adaptively. In the last few years there was a fous on utilizing a smart antenna to improve the PN ode aquisition proess [1, 1-14]. The smart antenna is a ombination of an antenna array and a digital signal proessing (DSP) unit. In [1], a novel approah for the PN ode aquisition has been provided that ombined the smart antenna with the adaptive /1 $ IEEE DOI /HPCC

2 thresholding trimmed-mean (TM) CFAR proessing. In this paper, we onsider the system proposed in [1] where adaptive thresholding CFAR proessing is adopted and is based on the ensored mean level detetor (CMLD) CFAR in a Rayleigh slowly fading multipath ommuniation hannels. In mobile ommuniations it is known that the reeiver reeives multiple opies of the transmitted signal from several paths with different attenuations and time delays, furthermore multiple aess interferene (MAI) signals are ommon in DS/CDMA systems. All these interfering signals have serious effets on the PN ode aquisition performane. Hene, one way to irumvent those problems is the use of smart antenna sine smart antenna has a good ability in ombating MAI signals, traking mobile signals, reduing multipath fading, and improving signal power gain. The main idea is to reeive the signals by all elements of the smart antenna that use the least mean square (LMS) adaptive algorithm to adjust its weight vetor, then the adaptive threshold value is omputed and used to make the synhronization deision. Under the presenes of multipath and MAI signals, setting the adaptive threshold based on the ell averaging (CA) CFAR algorithm is not effetive [1]. In the CMLD-CFAR, the outputs from the referene ells are rank- ordered aording to their magnitude and the highest ells whih orrespond to multipath replias and interferenes from the other users are ensored before to estimate the bakground noise power level and use it as a threshold value, as will be explained in the next setion. The CMLD proved to be robust under an environment with multiple interfering signals [15, 16]. This paper is organized as follows. In Setion, we desribe the proposed aquisition system and derive a losed form expression for the probability of false alarm. The simulated detetion performane of the proposed system and disussions are presented in Setion 3. The onlusion is given in Setion 4. II. DESCRIPTION AND ANALYSIS OF THE PROPOSED ACQUISITION SYSTEM The blok diagram of the proposed PN aquisition system is shown in Fig. 1. The system onsists of a smart antenna with M antenna elements, eah antenna element followed by a orrelator that orrelates the reeived PN ode sequene with the loally generated PN ode sequene. The outputs of the M orrelators serve as inputs to the LMS beamformer to adjust the smart antenna's weight vetor. After getting the optimum beamforming weight vetor, the spatial orrelation outputs from the LMS are fed into the CMLD-CFAR proessor, whih is a tapped delay line, to set the threshold adaptively in order to make a final deision about whether there is aquisition or not. In this ommuniation system onsidered we assume that there are D users from simultaneous transmitters. The first user is the initial synhronization user, while the other D 1users may be onsidered as interferers to the first user. A. The reeived signal model The ommuniation hannel model onsidered onsists of L tapped delay lines that orrespond to the number of Figure 1. Blok diagram of the proposed system resolvable multipath with a Rayleigh distributed amplitude α il and a phase ζ il, i = 1,..., D and l = 0,..., L 1. Taking into aount the effet of hannel fading, the reeived signal onsists of the signal from the first user, multiple aess interferenes from the others, and an AWGN n (t). Thus, the reeived signal at the mth antenna element of the array is [17]: L = 1 rm ( t) Ps 1l 1( t 1 lt ) exp ( j( φ1l ( m 1)sin) ) + l= 0 D L 1 PI ili ( t i lt ) exp( j( φil ( m 1)sin) ) + n( t) (1) i= l= 0 where i, i = 1,..., D is the spreading sequene, P s is the reeived signal power of the first user during initial synhronization, PI is the average reeived power of the interfering signal, i is the relative time delay assoiated with the asynhronous ommuniation hannel model, φ il, l = 0,...,L 1, are the phases in the demodulator of the reeiver, whih are independent and identially distributed random variables and uniformly distributed on the interval [0,], and T is the hip duration. B. The Correlator The reeived signal is first down-onverted into in-phase (I) and quadrature phase (Q) omponents. These omponents are then multiplied by the loally generated PN ode ( t jt / ), j = 0,1,..., N ( N represent the referene window size), and integrated over dwell time interval τ D = RT seonds, where R is the orrelation length integer, to yield respetively the I and Q branh omponents Y i and Y si, whih are squared to give the orrelator output Y, Y = Y i + Ysi. In ase the reeived signal is aligned with the loal PN ode ( H1 hypothesis), the output Y will result in a high orrelation value. Otherwise, it will be a negligible value due to the nonalignment ase ( H0 hypothesis). The probability density funtion (pdf) of the output Y under the aligned hypothesis is given by [18]:

3 f y 1 ( ) exp y y H1 =, y 0 σ0 (1 + v) 0 (1 ) σ + v () where v = 9σ f /(3 / σ 0 ). σ f is the Rayleigh fading hannel power while the variane σ 0 is given by [3]: ( L 1) ψ L( D 1) βψ 1 σ 0 = + + 3R 3R RS β represents the average reeived power of the interfering signal to the signal power of the first user ratio and is defined as = P I / PS, while S represents the SNR / hip and is given by S = T Ps / N0, and = f. Under the nonaligned hypothesis, the onditional pdf under the null hypothesis f Y ( y H0) is obtained by replaing 0 (1 + ) with 0 in (). C. Smart Antenna As mentioned in the previous setion, the reeiving antenna array onsists of M idential elements for signal reeption and PN ode aquisition. The spae d between two antenna elements is equal to half the wavelength of the arrier transmitted signal λ ( i. e. d = 0.5λ ). In our ase, the smart antenna performs adaptive beamforming using the LMS algorithm for direting the main array pattern towards the first user signal and reating nulls in the diretions of the interfering signals. We hose the LMS algorithm beause of its simpliity, ease of implementation, and relatively good onvergene properties. The outputs Y m, m = 1,,..., M from the M branhes of the orrelator are inputs to the LMS proessor as shown in Fig. 1. The LMS algorithm omputes iteratively the optimum beamforming weight vetor based on the minimum squares error (MSE) riterion between the desired signal value and the LMS proessor output. One the minimum MSE is attained, the weight vetor is then used to generate a spatial orrelation output Z. If the output Y m of the onsidered orrelator is under the aligned hypothesis, we assume the DOA of the desired signal an be loated optimally by the smart antenna. The pdf of the deision variable Z orresponding to the aligned hypothesis is then given by [1]: 1 ( ) exp z f 1, 0 (4) 0 ( ) 0 ( ) Z z H = z σ M + M v σ M + M v When the output Y m of the orrelator is under a nonaligned hypothesis onsideration, it is assumed that the smart antenna traks in a different angle than the desired signal. Therefore, the pdf of the non-aligned hypothesis f Z ( z H 0 ) is obtained by replaing 0 ( M + M ) = σ 0 M in (4). (3) D. CMLD-CFAR Proessor The outputs of the LMS beamformer are serially fed into a shift register of length N + 1 as shown in Fig.. The first register, denoted as Z 0, stores the urrent output of the LMS beamformer. The following N registers, denoted by Z, = 1,,..., N are alled the referene ells. The ontents of these referene ells are sorted in asending order aording to their magnitude to form the ordered samples Z( j), j = 1,,..., N. Then k ells are ensored from the upper end (where k is number of the assumed interfering ells = ( L 1) + ( D 1)L ), and the remaining ones are ombined to get an estimate of the bakground noise level U : U = N k j= 1 Z ( j) (5) The adaptive threshold value U is saled by the threshold multiplier T to ahieve the design false alarm probability. If Z 0 is larger than the threshold TU, a PN ode aquisition is delared, and the traking loop is triggered. Otherwise, the aquisition sheme shifts the loally generated PN ode phase and the searh ontinue until a orret PN ode phase is found. Next, we will derive an expression for the probability of false alarm for the proposed system. The probability of false alarm is the probability that a orrelation of a non-alignment tested phase is greater than the threshold value. It is given by: T T Pfa = EU { P( Z0 > TU H0 )} = MU M, a 0M (6) = U = σ σ 0M a where MU is the moment generation funtion (MGF) of the estimate U. As in [19], we will define independent random variables W i = ( N k i +1) Z' i, i = 1,..., N k, where Z' i = Z( i) Z( i 1), Z(0) = 0. Then the estimate U an be written as: U = N k i= 1 W Figure. CMLD-CFAR proessor i (7)

4 The MGF of U is simply the produt of the individual MGF of thew 's. Therefore, the probability of false alarm is: where and The i g i s, M M W1 Wi P fa T = a N k = M i= 1 ( N k) T gi = a T + g i Wi T a N N T + N k, i =,..., N k i =,..., N k are given by: N i + 1 gi = N k i + 1 (8) (9) (10) (11) after ensoring beomes lower whih yields a better detetion probability. As we see, that all CMLDs ( k = 1,, 3and 4 ) have muh better performane than the CA-CFAR ( k = 0 ). From Fig. 4, we observe that as the number of antenna elements in also inreased, the probability of detetion also inreases. Three interfering signals are assumed present and ensored before the omputation of the adaptive threshold. The number of antenna elements is M =1,,3,4, 5 and 6. We also note that the detetion performane improves signifiantly and this is due to the nature of smart antenna whih has the apability of improving signal power gain, ombating MAI signals, and reduing multipath fading. As the number of antenna is more than M = 4, we observe that we start reahing saturation. III. RESULTS AND DISCUSSION In this setion, the detetion performane of the proposed system is evaluated in terms of the different parameters of the system of ommuniation onsidered. The performane is studied using MATLAB simulations for a Rayleigh fading hannel with the power normalized to one ( σ f = 1). The design probability of false alarm is P = 10 3 fa, the number of referene ells is N = 4, and the orrelation length integer of the dwell time interval is set at value of R = 18. The threshold multiplier value T is readily obtained from the expression of the false alarm probability given in (8). It has been shown in [1] that the performane of the proposed system using CA-CFAR proessing to set the adaptive threshold with N = 4 is omparable to the performane of the system proposed in [1] by Wang and Kwon. In Fig.3, we show again as in [1] that the detetion performane of the system using CA-CFAR proessing, where the adaptive threshold is the arithmeti mean of the referene ells, is seriously degraded in the presene of the interferenes (multipath and the MAI signals). So the exlusion of or exising the interfering signals from the referene ells before estimating the noise power level of the environment will be an effetive solution. This is in essene the CMLD-CFAR proessing as explained earlier. Fig. 3 shows the simulated detetion probability P d of the system against SNR / hip under different numbers of ensored ells. The number of antenna elements used is M = 3 and the number of interfering signals is Inter = 4, while the average reeived power of the interfering signal to the signal power of the first user ratio is β = We observe that as the number of interfering signals ensored inreases, the detetion performane improves as expeted. This is due to the fat that the adaptive threshold omputed Figure 3. Comparison of P d using CA-CFAR proessing with CMLD- CFAR system after ensoring; P fa=10-3, N =4, M=3, Inter=4, and =0.3 Figure 4. Effet of the number of antenna elements M on the detetion performane; P fa=10-3, N =4, Inter=3, and k=

5 Fig.5 shows the detetion probabilities P d of the system proposed with different number of antenna elements and for different numbers of ensored ells. The number of antenna elements in the first system is M =, while in the seond system is M = 5. The number of interfering signals is Inter = 3 with β = We observe that as the number of antenna elements inreases the probability of detetion improves as expeted. It should be noted though that the detetion performane in the presene of two interfering signals when M = 5 and k = 1, is better than the ase with M = and k = 3 ase, whih is the ase with no interfering signals, for all SNR / hip values. We also observe a apture effet on the detetion probability as it annot reah P d = 1 without ensoring and this for all interfering signals. This emphasizes the robustness of the ensoring algorithm whih allows the probability of detetion to reah asymptotially one as the SNR / hip inreases. In Fig. 6, we plot the probability of detetion P d against the SNR / hip for different number of referene ells N =16, 4, and 3 with different number of antenna elements M = 3 and 5. Three interfering signals are assumed to be present and ensored before the omputation of the adaptive threshold. As expeted, inreasing the window size N inreases the detetion probability as it gives estimate of the noise power in the ell under test. On the other hand, we observe that in the probability of detetion for the same number of referene ells is substantial inreased when the number of antenna elements is inreased from 3 to 5. This indiates that the effet of the number smart antennas elements on the reeived signal power is muh more pronouned on the probability of detetion than the number of ells used in estimating the noise power. It also justifies the idea of ombining both adaptive thresholding based on order statistis and ensoring of interfering signals, and smart antenna. Figure 5. Comparison of Pd between two systems differ in the number of antenna elements M ; P fa=10-3, N =4, and Inter=3 Figure 6. Effet of the number of referne ells N on the detetion performane; P fa=10-3, M =3 and 5, Inter=3, and k=3 IV. CONCLUSION In this paper, we onsidered the problem of PN aquisition using smart antenna and adaptive threshold in DS/CDMA ommuniations. An adaptive serial searh aquisition system that employs all elements of the smart antennas and the CMLD-CFAR proessing in a Rayleigh slowly fading multipath ommuniation hannels was proposed. An exat expression for the probability of false alarm for the proposed ommuniation system was derived while the detetion performane of the system was studied using MATLAB omputer simulation. We observe that the system using the CMLD-CFAR based on rank ordering the referene ells and ensoring the interferenes samples was really robust in presene of MAI. Further analysis of suh system will be onsidered in order to determine the mean aquisition time under different parameters, and hopefully obtain a losed form expression for the probability of detetion REFERENCES [1] A. Sofwan and M. Barkat, PN Code Aquisition Using Smart Antennas and Adaptive Thresholding Trimmed-Mean CFAR Proessing for CDMA Communiation, Spring World Congress on Engineering and Tehnology, SCET01, China, May 01, Aepted. [] A. Polydoros and C. L. Weber, '"A Unified Approah to Serial Searh Spread-Spetrum Code Aquisition--Part I: General Theory", IEEE Transations on Communiations, vol. COM-3, no. 5, pp , May [3] L. L. Yang and L. Hanzo, "Serial Aquisition of DS-CDMA Signals in Multipath Fading Mobile Channels", IEEE Transations on Vehiular Tehnology, vol. 50, no., pp , Marh 001. [4] E. A. Sourour and S.C. Gupta, "Diret-Sequene Spread-Spetrum Parallel Aquisition in a Fading Mobile Channel", IEEE Transations on Communiations, vol. 38, no. 7. pp , July [5] R. R. Rik and L. B. Milstein, "Parallel Aquisition in Mobile DS- CDMA Systems", IEEE Transations on Communiations, vol. 45, pp , November

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