Performance of PN Code Acquisition in a DS/CDMA Overlay Environment with Imperfect Power Control

Transcription

1 Performance of PN Code Acquisition in a DS/CDMA Overlay Environment with Imperfect Power Control Jin Young Kim and Jae Hong Lee School of Electrical Engineering, Seoul National University, Shillim-dong, Gwanak-gu, Seoul , Korea. AbstTact- In this paper, performance of PN code acquisition is analyzed for a DS/CDMA overlay system with imperfect power control. Acquisition performance is evaluated in terms of mean acquisition time using state transition diagram for acquisition process. To apply for a DS/CDMA cellular environments, the MA1 and imperfection of power control are taken into account in the analysis of acquisition performance. The imperfect power control is considered by modelling the power of each user to be lognormally distributed about nominal received power. A narrowband user is modelled as a narrowband interference located at the fraction of a CDMA user s bandwidth. The analysis in this paper can be applied to the practical situations for a DS/CDMA overlay environment. I. INTRODUCTION A critical aspect of a receiver in a direct-sequence/codedivision-multiple-access (DS/CDMA) system is synchronization of the incoming PN sequence and the locally generated PN sequence. PN synchronization is usually done in two stages: PN acquisition stage where the phase of incoming PN sequence is coarsely aligned with that of locally generated PN sequence within a chip, followed by PN tracking stage where the coarse alignment is maintained throughout demodulation [l]. The acquisition stage mainly determines the code synchronization time, so it should be as fast as possible for rapid initial link setup and smooth handoffs in a mobile environment [2,3]. Because communication cannot take place before acquisition has been achieved, the quick and effective acquisition scheme is required. Various kinds of acquisition schemes have been proposed and analyzed in the literatures. Matched filtering is commonly used to synchronize the phase of a local PN sequence with that of a received PN sequence. A serial matched filter (MF) scheme has been proposed and analyzed [4]. To reduce mean acquisition time, a parallel MF scheme has been proposed and employed. A serial MF scheme with reference filter (RF) has been proposed in which a RF is used to estimate the variance of interference [5]. A parallel MF-RF scheme has been analyzed for a packet radio system [6]. In the previous researches, the effect of imperfect power control on acquisition performance has rarely been evaluated. To enhance spectrum efficiency, the CDMA overlay system has been proposed. In a DS/CDMA overlay system, a set of mobile DS/CDMA users communicate with a base station, while other narrowband users simultaneously transmit in the same frequency band. The basic principle of a DS/CDMA overlay is that because DS/CDMA power is diffused over a much wider bandwidth than that of narrowband users, this leaves only a fraction of the CDMA power in any given subband occupied by a given narrowband user [7,8]. Since the DS/CDMA signal spreads their power over a large bandwidth, the effect of such a transmission on a narrowband receiver is often just an imperceptible rise in its noise level [9,10]. Hence, it may possible to overlay a DS/CDMA system on an existing set of narrowband users without severely affecting either. Moreover, because of the broadband noise-like characteristics of DS/CDMA signals, it is possible to use signal processing technique to reduce narrowband interference. The reverse link of CDMA system is typically designed to be asynchronous, and an asynchronous CDMA system is vulnerable to the near-far problem in which very strong undesired signal at a receiver swamp out the effect of weaker, desired signal. A solution to the near-far problem is the use of power control, which attempts to ensure that all signals from the mobiles within a given cell arrive at the base station of that cell with equal power. The primary use of power control is to maximize the total user capacity, and an additional benefit is to minimize consumption of transmitted power of a portable unit. The performance of power control system depends on the power control algorithm, speed of adaptive power control system, transmitter dynamic range, spatial distribution of users, and fading and shadowing. All these factors influence the probability density function (p.d. f.) of the received power. In this paper, the PN acquisition performance is analyzed for a DS/CDMA overlay system with imperfect power control. To reduce the effect of narrowband users, the interference suppression filter is placed prior to the acquisition search stage. The taps of interference suppression filter is updated based on MMSE (minimum-mean-square- error) criterion [ll]. Acquisition performance is evaluated in terms of mean acquisition time which is derived using state transition diagram for acquisition process. To apply for mobile cellular environments, the effect of multiple access interference (MAI) and imperfect power control are considered in the performance analysis. For a large number of users, the p.d.f. of MA1 is usually /97 $ IEEE 2108

2 ~ assumed to approximate Gaussian process with a variance equal to the sum of variances of individual interfering users. To increase the capacity of cellular system, a microcellular system is considered. Microcells operate at lower power consumption of handsets and have antennas at streetlamp elevation. The fading channel in a microcellular system is modeled as a multipath Rician fading channel rather than a multipath Rayleigh fading channel. The effect of imperfect power control is taken into account by modeling power of each user to be lognormally distributed about nominal received power. For perfect power control, the logarithmic standard deviation of power control error is 0 db. Since the imperfect power control affects PN acquisition performance, its effect is considered in the analysis of acquisition performance. In Section 11, a system model of a noncoherent parallel MF-RF with interference filter and a narrowband interference model are described. In Section 111, a DS/CDMA system is modeled, and the mean acquisition time is derived. Numerical examples are presented in Section IV, and conclusions are drawn in Section V. A. Acquisition Model 11. SYSTEM MODEL A noncoherent parallel MF-RF acquisition scheme with interference suppression filter is shown in Fig. l(a). It consists of an interference suppression filter and a parallel MF-RF. A parallel MF-RF is composed of a bank of N noncoherent parallel I-& MF s with a reference filter. The parallel scheme was employed to provide faster acquisition than serial scheme. The received signal is first filtered at interference suppression filter and down-converted to inphase and quadrature components. The reference I-& MF is used to provide a reference level for the synchronization decision. When the output of parallel detecting MF s exceeds the reference MF output multiplied by a gain factor, a start signal is sent to the receiver code generator. The parallel detecting I-& MF s are loaded with transmitted PN codes and reference I-& MF is loaded with a PN code orthogonal to the transmitted PN codes. Each of transmitted PN codes consists of M = TITc chips where T and T, are data bit and chip durations, respectively. The number of taps in a detecting (or reference) I-& MF is MIA where A is a phase adjustment parameter (or phase updating step size). A running average of the output of a reference I-& MF is multiplied by a gain factor. The result is used as a decision threshold. A I-& MF shown in Fig. l(b) is loaded by one of the N transmitted PN codes. The acquisition scheme in the analysis has two modes of operation: a search mode and a verification mode (or coincidence detection). In the search mode, a tentative decision is made on the delay of the received signal. In the verification mode, a more accurate decision is achieved to avoid false alarms. The following algorithm in the verification mode is employed: acquisition is declared if B out of A tests exceed the threshold of verification mode. B. Narrowband Interference Model The narrowband user is modelled as a non-faded BPSK narrowband interference located at the fraction of the desired CDMA user s bandwidth (BW). The interference signal is given by li(t) = JIiLi(t)~o~[j(2~(fo + Af)t + 01, (1) where A f is frequency offset from fo, carrier frequency of the CDMA signal, I is interference power, 0 is phase of interference signal, and &(t) is data sequence of interference signal. The interference BW is be approximated as Bi = 2/Ti where Ti is data bit duration of interference signal. The narrowband interference is characterized by the following two parameters which are narrowband BW ratio p and frequency offset ratio q, and are given by Bi - Tc p =--- B, Ti where T, and B, are chip duration and spreading BW of a CDMA user. I I I. P E RF 0 RM A N C E AN A LY S IS To apply for a mobile cellular environment, the followings are assumed in the analysis: 1) cell pattern is hexagonal which is typically employed in performance evaluation of a mobile cellular system, 2) adjacent cell interference comes from only adjacent cells of first-tier and second-tier, that is, the number of adjacent cells is 18 in a cluster of 19 cells. 3) the desired user is located at the cell-of-interest surrounded by 18 adjacent cells. In-cell users are the users who are located at the same cell as the desired user. Outof-cell users are the users who are located at the 18 adjacent cells, 4) MA1 signals are not chip and phase synchronous with the desired signal, and 5) code uncertainty region is a full code length. It is also assumed that the multipath delay spread is much less than one data symbol period, so that intersymbol interference can be ignored. Each of cells in the first and second tiers is assumed to have the same distribution within a cell. A. DS/CDMA Modeling For a DS/CDMA system with K users for each cell, the kth user s transmitted signal is given by where Pk is signal power, ak(t) is data sequence, Ck(t) spreading sequence, WO is carrier frequency, and +k is carrier phase. The data and spreading sequences are assumed to have rectangular pulse of 1 or -1. The received signal of the reference user (user 1) is given by 21 09

3 ~ where dli is distance from the ith mobile to base station of interest, dji is distance from the ith mobile to the jth base station (2 5 j 5 19), y is path loss exponent which describes how the received power falls off with distance, C is the number of cells in the system, rkl is propagation delay of kth user's lth path, Ck is the cell number (ck = 1,2,.~~,C), Akl and,bkl are specular and diffuse components' power, and n(t) is AWGN with two-sided power spectral density No/2. The propagation delays { r~} are uniformly distributed in [0, TI, and the carrier phases {+kl} are uniformly distributed in [0, 27~1. All delays and phases are assumed independent of one another and independent of the data. The interference suppression filter is employed at the receiver front end to suppress narrowband user's signal [12]. If the power of narrowband user is too large, the PN code acquisition cannot be achieved [13]. The use of interference suppression filter is necessary in a DS/CDMA overlay system to reduce the effect of narrowband user on a de- where is detection probability in search mode at sired CDMA user. The output of double-sided interference suppression filter is given by subcell i of HI, PD2,i is detection probability in verification mode at subcell i of HI, PF 1 is false alarm probability in search mode, PF~,; is false alarm probability in verification 0 m=-q where fm is filter coefficient and Q is the one-sided tap number. The interference suppression filter is double-sided so that fo = 1 and fm = f-m. The decision statistic of the reference user (user 1) is given by Z = D, +Ma +Mu +I, + N,, (7) where D, is the desired component of reference user, and Ma is multiple access interference (MAI), Mu is the multipath, I, is narrowband interference, and Ng is AWGN components with variances U;,, o;", U;" and o;,, respectively. From the Gaussian approximation of MAI, multipath interference and narrowband interference components, the total interference power is given by mode, HM (2) is miss detection probability, x is the number of HI subcell. When the penalty time due to false alarm is Jd, Hp (2) is given by Using straight-line approach for uniformly-distributed starting code phase offset over code uncertainty region, mean acquisition time is obtained by B. Acquisition Performance Thc acquisition proccss is modeled using statc transition diagram shown in Fig. 2. The HI hypothesis is the case where acquisition occurs and Ho hypothesis is the case where false alarm occurs. It is assumed that the code tracking loop can track PN code if initial phase offset between the local PN code and the transmitted PN code is at most 0.5 chip. In Fig. 2, the transfer functions of each state are given as follows: i=2 2 1,=I J HD (2)12=1 (1-2 where v - 1 is the number of cells of Ho. IV. NUMERICAL RESULTS The mean acquisition time normalized by chip duration is computed for a noncoherent parallel MF-RF with interference suppression filter. The thresholds of search arid verification modes are selected numerically to minimize mean acquisition time for each SNR/chip. For numerical example, the following parameters are assumed: 1) penalty time due to a false alarm in the verification mode J= lo6 (chips), 2) A = 4, B = 2, 3) phase updating parameter A = 0.5, 4) path loss exponent y =3, and 5) the number of each outof-cell user is 30. In the power control scheme, 1) assuming 21 10

4 that both reverse and forward links suffer from identical shadowing, mobile user estimates signal strength by measuring pilot signal and controls its transmission power, 2) 1dB power control step size is used, 3) feedback power control scheme is employed with power control feedback delay (the delay from when power control command is sent to when power is adjusted). The tap coefficient is determined to satisfy the following Wiener-Hopf equation: 5 fmi[(n - m)t,] + k[nt,] = 0, (17) m =- Q,m#O where i(.) is autocorrelation function of input signal to interference suppression filter. In Fig. 3, mean acquisition time normalized by chip duration vs. the number of active users in the cell-of-interest is shown with standard deviation of power control error, op, as a parameter. The numerical results are shown for SNR/chip = -5 db, narrowband BW ratio p = 0.1, frequency offset ratio q = 0.4, and the one-sided number of taps Q = 2. For a perfect power case (U, = 0 db), the fastest acquisition is achieved. It is shown that as the power control error increases, the mean acquisition time substantially increases. It is also shown that the effect of power control error on acquisition performance becomes more significant with the number of users in the cell-of-interest. In Fig. 4, normalized mean acquisition time vs. narrowband BW ratio of narrowband interference signal with respect to a desired CDMA user with the one-sided number of taps for interference suppression filter, Q, as a parameter. The numerical results are shown for SNR/chip = -5 db, standard deviation of power control error up = 1 db, frequency offset ratio q = 0.4, and the number of users of the cell-of-interest K = 30. It is shown that the acquisition performance is improved with the use of interference suppression filter. It is also shown that acquisition performance is degraded with narrowband BW ratio of interference suppression filter because the larger interference BW means the larger power spread on a desired CDMA user s BW. It can be noted that a very slight improvement on acquisition performance is achieved for the tap number of more than 5. That is, the diminishing returns on acquisition performance are found with the number of taps of interference suppression filter. When hardware complexity is considered, the one-sided tap number of 4 or 5 for interference suppression filter is sufficient to suppress narrowband interference. In Fig. 5, normalized mean acquisition time vs. frcquency offset ratio of narrowband interference signal from the desired CDMA user is shown with the one-sided number of taps for interference suppression filter, Q, as a parameter. The numerical results are shown for SNR/chip = -5 db, standard deviation of power control error up = 1 db, narrowband BW ratio p = 0.1, and the number of users of the cell-of-interest K = 30. It is shown that acquisition performance is improved as the separation of center frequency between narrowband interference and a desired CDMA user. The diminishing returns on acquisition per- formance are also found with the number of taps of interference suppression filter. V. CONCLUSIONS The acquisition performance was evaluated for a noncoherent parallel MF-RF acquisition scheme with interference suppression filter in a DX/CDMA overlay environment. A narrowband user was modelled as a narrowband interference located at the fraction of the desired CDMA user s BW. It was shown that the mean acquisition time increases with the number of users in the system. It was also shown that for the perfect and imperfect power control, the acquisition scheme with interference suppression filter results in faster acquisition than that without interference suppression filter. The one-sided tap number of 4 or 5 for interference suppression filter is sufficient to suppress narrowband interference. The imperfect power control substantially increases mean acquisition time when the standard deviation of received power is above 1 db regardless of the presence of interference suppression filter. The power control scheme must be accurate within 1 db, and be fast enough to compensate for the near-far and the fading effects. The considerations in this paper can be applied to the design for a DS/CDMA overlay system. REFERENCES R. L. Pickholts, L. B. Milstein, and D. L. Schilling, STread spectrum for mobile communications, IEEE Trans. Veeh. Technol.. pp , May E. Sourour and S. C. 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5 interference N parallel detectmg comparator acquisltton reference I-QMF factor MF correlator square - law MF correlator square - law t detector J? sino,,t (b) Fig. 1. Block diagram of acquisition scheme. (a) Noncoherent parallel PN acquisition scheme. (b) A I-Q MF scheme of N parallel detecting I-Q MFs PcI state -e- Q=0tap + Q = 1 tap -- Q=2tap Q=3tap 0=4tap t Q = 5 tap I I 1E Narrowband BW ratio Fig 2. State transition diagram for acquisition process. Fig. 4. Normalized mean acquisition time vs. narrowband BW ratio with the number of taps as a parameter... + sigma-p = OdB -- sigma-p = 1 db sigma-p = 2 db E F -ic- Q = 0 tap --c 0 = 1 tap - -c Q = 2 tap Q=3tap Q = 4tap -2- Q = 5 tap Number of Users 1E+03J ii Frequency offset ratio Fig 3 Normalized mean acquisitlon tlme vs the number of users with power control error as a parameter Fig 5 Normalized mean acquisition time vs. frequency offset ratio with the number of filter taps as a parameter.