IN SYNCHRONOUS code division multiple access

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1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY Rapi Slot Synchronization in the Presence of Large Frequency Offset an Doppler Sprea in WCDMA Systems June Moon, Stuent Member, IEEE, an Yong-Hwan Lee, Member, IEEE Abstract Slot synchronization is the most challenging step for rapi cell search in intercell asynchronous coe ivision multiple access systems such as wie-ban coe ivision multiple access (WCDMA. For rapi cell search, it is esirable to esign the receiver robust to initial frequency offset an Doppler sprea. In this letter, we consier combining schemes for rapi slot synchronization of WCDMA signals in such channel impairments. We propose an inner-slot ifferential combining scheme that exploits partial correlation of slot synchronization coe, making the receiver tolerable to a large amount of initial frequency offset an Doppler sprea. Unlike conventional ifferential combining schemes, the propose scheme is also applicable to the use of transmit antenna iversity. The etection performance of the propose combining scheme is analyze with the use of transmit antenna iversity. Finally, the analytic results are verifie by computer simulation. Inex Terms Cell search, ifferential etection, slot synchronization, time-switche transmit iversity (TSTD, wie-ban coe ivision multiple access (WCDMA. I. INTRODUCTION IN SYNCHRONOUS coe ivision multiple access (CDMA systems such as IS-95 an cma000, the mobile station only nees to search the coe timing for initial coe acquisition. When each base station uses its own scrambling coe in an intercell asynchronous ownlink system like wie-ban CDMA (WCDMA, the mobile station nees to resolve both the timing an coe uncertainty for initial coe synchronization 1. The use of 51 complex Gol coes in the WCDMA ownlink makes it impractical to exhaustively search all the possible coes for the coe timing. This problem can be alleviate using a three-step cell-search scheme in the WCDMA system. A three-step operation for initial cell search in the WCDMA system can be processe using two synchronization channels (SCHs, i.e., the primary SCH (P-SCH an seconary SCH (S-SCH, an common pilot channel in the ownlink physical channel 3, 4. The P-SCH provies information on the slot timing (560-chip timing caniates an the S-SCH provies information on the coe group an frame bounary ( caniates. Finally, the cell searcher selects one caniate among eight scrambling coes in a coe group. Among these operations, the first step is the most elaborating process since it shoul resolve the largest amount of uncertainty. Manuscript receive June 19, 003; revise November 6, 003; accepte June 17, 004. The eitor coorinating the review of this paper an approving it for publication is J. Evans. The authors are with the School of Electrical Engineering an INMC, Seoul National University, Seoul , Korea ( myjun@trans.snu.ac.kr; ylee@snu.ac.kr. Digital Object Ientifier /TWC In the first step of the three-step cell search, the receiver searches for the slot timing by correlating the receive signal with the P-SCH coe using a matche filter (MF. Since the signal-to-noise power ratio of the transmitte P-SCH coe is very low, it is require to combine the correlation values over multiple slots to properly acquire the slot timing. A number of techniques have been propose for the combining, incluing coherent combining, noncoherent combining, an ifferential combining, 5, 6. Coherent combining schemes can provie the optimum performance in an aitive white Gaussian noise channel environment, but it may not be applie to a real environment where channel istortion an RF impairment exist. Noncoherent combining schemes have wiely been use ue to its practical aspects. It was shown that ifferential coherent combining schemes can outperform noncoherent combining schemes uner a mil channel conition 6. However, they cannot be applie to the use of time-switche transmit iversity (TSTD 3, since the ifferential prouct is extracte from the two consecutive slots. Note that the phase of the receive signals between the ajacent slots is usually inepenent in the TSTD moe. Moreover, it is necessary to employ a slot-timing etector that can operate inepenently of the use of transmit iversity, which may not be known to the receiver uring the initial cell search stage. When there exists a large amount of initial frequency offset, full correlation of the slot synchronization coe may result in a large amount of incoherence loss. This problem can be alleviate using a partial correlation scheme 5. The partial correlation values are often noncoherently combine for simplicity of implementation. However, ifferential etection is possible with the use of partial correlation values since the phase variation between the two consecutive partial correlation values heavily epens on the amount of frequency offset, which can be assume stationary uring the combining interval. In this letter, we propose an inner-slot ifferential combining scheme that exploits partial correlation of the synchronization coe, which is also applicable to the transmit antenna iversity moe. Since the propose scheme uses two consecutive partial correlation values to extract the ifferential prouct, it can be more robust to a large amount of Doppler sprea than the ifferential etection scheme propose in 6. Following this Introuction, the system moel is escribe in Section II. In Section III, the propose scheme is escribe. The performance is analyze when the transmit antenna iversity is employe in the presence of frequency offset an Doppler sprea. The analytic results are verifie by computer simulation in Section IV. Finally, conclusions are summarize in Section V /$ IEEE

2 136 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY 005 Fig. 1. Transmission of synchronization coe. (a No transmit antenna iversity. (b Two transmit antenna iversity. II. SYSTEM MODEL The slot timing is acquire using a P-SCH coe in the first step of the three-step cell search operation. The base station repeately transmits the P-SCH coe of length M uring the first symbol of each slot comprising N chips. As shown in Fig. 1, one P-SCH coe is alternately transmitte using a single antenna for each slot in the transmit iversity moe. A complex baseban-equivalent receive signal at the kth slot can be represente as { Ec α r k i k e jπf oit c +θ c p i+n k i, i 0,M 1 n k i, i M,N 1 (1 where E c is the chip energy, f o is initial frequency offset ue to the oscillator instability, T c is the chip uration, θ is the phase offset, which can be assume zero without the loss of generality, c p i enotes the P-SCH coe of length M with c p ic pi 1, n k i enotes all the interference terms, having one-sie power spectral ensity N 0, an α k enotes the Rayleigh faing channel gain. It is assume that the channel faing is static uring M-chip interval an the signal unergoes flat faing. The power of the receive signal is constant uring each slot interval since the SCH signal is time multiplexe with the primary common control channel 3. Thus, we can assume that the power of n k i is constant because the power of the P-SCH coe is sufficiently low compare to that of the receive signal. In the initial coe acquisition stage, there can be a large amount of frequency offset ue to inherent oscillator instability. It was shown that the use of a partial correlation scheme coul provie etection performance robust to the initial frequency offset 5. The correlation interval is ivie into L subintervals an LM s -tap MFs are employe to obtain the partial correlation values, where M LM s. The partial correlation value of the lth subinterval at the kth slot can be represente as a kl i 1 lm s 1 M s m(l 1M s r k i + mc pm, k 1,N s ; l 1,L. ( The timing etection can be moele as a simple hypothesis problem. Let H 1 an H 0 be the hypothesis that the two coes are aligne an not, respectively. Then the partial correlation value a kl i can be moele as a kl i { skl + η kl, H 1 η kl, H 0 (3 where s kl α k Ec sin(m s επ/m s sin(επexp(jπεm s l exp jπε(m s + 1, ε f o T c, an η kl enotes the interference term approximate as a zero-mean complex Gaussian ranom variable (RV with E{ η kl } N 0 /M s. The selfnoise term can be ignore when M s is not too small since E c /N 0 is very low in a nominal operating environment. III. PROPOSED COMBINING SCHEME A. Combining Scheme A conventional etection scheme noncoherently combines the partial correlation value over N s slots for reliable etection as 5 z n i N s L a kl i. (4 The slot timing can be obtaine using a maximum likelihoo metho, i.e., by fining i such that i n arg max (z n i. (5 i 0,N 1 In the presence of initial frequency offset, the phase variation between the two consecutive partial correlation values significantly epens on the amount of initial frequency offset. Assuming that the amount of frequency offset oes not change uring the combining interval (i.e., N s slots, the inner-slot partial correlation values can be combine ifferentially for

3 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY Fig.. Propose combining scheme. peak etection as shown in Fig.. Using the ifferentially combine output z i over N s slots N s z i a klia k(l+1 i (6 the slot timing can be obtaine by fining the chip inex i maximizing z i z i. The initial frequency offset can also be estimate using the phase information of z i since the amount of phase variation between the two consecutive partial correlation values is closely relate to the initial frequency offset. The initial frequency offset can be estimate as ˆf o (1/πM s T c arg{ z i }.This frequency offset estimator can facilitate the initial operation of automatic frequency control, proviing rapi initial stabilization of the receiver. B. Performance Analysis The propose scheme is evaluate in terms of the etection probability as a performance measure. The etection probability of the first step can be obtaine by P 0 f H1 (zf N 1 H 0 (zz (7 where f H1 (z enotes the probability ensity function (pf of z uner hypothesis H 1 an F H0 (z enotes the cumulative istribution function (cf of z uner hypothesis H 0.Forsimplicity of mathematical escription, we will omit the chip inex i because there are only two simple hypotheses. To obtain f H1 (z in the presence of Doppler sprea, the faing channel gain shoul be characterize. Accoring to Jake s moel, α k is a complex Gaussian ranom process whose autocorrelation is given by 10 E { α k α k+m} J0 (πf mnt c (8 where J 0 ( is the zeroth orer Bessel function of the first kin, E{X} enotes the expectation of X, an f enotes the maximum Doppler frequency. Let α α 1 α α Ns T be the channel vector representing the channel gain uring the combining interval. Taking the transmit antenna iversity into consieration, the (k, lth element R kl of the channel covariance matrix R can be obtaine by R kl E {α k αl } { J0 (πf NT c k l, mo( k l,k0 0, otherwise where K is the number of transmit antennas an mo(a, b enotes the remainer of a/b. It is assume that there is no correlation between the antennas. To characterize the combine correlation value uring multiple slots, let us efine γ by (9 N s γ α H α α i. (10 i1 The characteristic function of γ can be obtain as 6 Φ γ (w E{jwα H α} N s 1 1 jwλ k (11 where λ k is the eigenvalue of R. Note that all the eigenvalues are nonzero since R is a Toeplitz matrix. When all the eigenvalues are istinct, Φ γ (w can be expresse in a summation form of Φ γ (w N s g k/(1 jwλ k where g k Π N s,l k (λ k/λ k λ l. Then, the pf of γ can be obtaine by f γ (γ N s g k γ e λ k. (1 λ k When all the eigenvalues are not istinct, f γ (γ can easily be erive using a partial fraction ecomposition metho.

4 138 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY Conventional Combining: Uner hypothesis H 0, z n in (4 can be moele as a central χ -istribute RV with LN s egrees of freeom. The cf of z n uner hypothesis H 0 can be expresse as 11 F H0 (z 1 e z σ a LN s 1 m0 ( m 1 z m! σa (13 where σa N 0 /M s. Uner hypothesis H 1 an given γ, z n can be moele as a noncentral χ -istribute RV with LN s egrees of freeom 11 f H1 (z γ 1 ( LNs 1 z σa s γ e (s γ+z ( σ s a I LNs 1 γz σa (14 where I n ( is the nth orer moifie Bessel function of the first kin an s E c L sin(m s επ/(m s sin επ. Averaging f H1 (z γ with respect to γ, using (1 an (14, it can be shown that f H1 (z 0 N s f H1 (z γf γ (γγ β k 1 ( Γ LN s 1, s λ k z s λ k σ a+4σ 4 a Γ(LN s 1 e z (s λ k +σ a (15 where Γ(x is the gamma function, Γ(x, y enotes the incomplete gamma function efine by Γ(x, y y tx 1 e t t, an β k is a constant term expresse as β k ( g k λ σ LNs a k s λ k +1 s (s λ k +σa. (16 The Propose Combining: Uner hypothesis H 0, z can be expresse as N s z ηklη k(l+1. (17 Since η kl is a zero-mean complex Gaussian RV, the pf of the multiplication of two η kl s can be expresse as a form that inclues the moifie Hankel function 8. Since z is the sum of (L 1N s RVs, it can be approximate as a zero-mean complex Gaussian RV with E{ z } (N s N0 /Ms from the central limit theorem. Thus, we can moel z as a central χ -istribute RV with two egrees of freeom. The cf of z is represente as M s z F H0 (z 1 e (NsN 0. (18 Uner hypothesis H 1,wehave z (k a kla k(l+1 (s kl + ηkl ( s k(l+1 + η k(l+1 L ( s kls k(l+1 + s klη k(l+1 + s k(l+ ηk(l+1 ( + s k ηk1 + s k( η kl ηklη k(l+1. (19 + Here, the first term is the signal component expresse as s kls k(l+1 ( α k e jπm sε sin (M s επ Ms sin (επ E c (0 an the secon term is the noise term ue to successive ifferential summation, represente as L ( s klη k(l+1 + s k(l+ ηk(l+1 L ( s klη k(l+1 +e j4πmsε s kl ηk(l+1 L e jπm sε Re e jπmsε s kl ηk(l+1 e jπm sε α k ς k (1 where ς k is a zero-mean real Gaussian RV with variance σς (L N 0 E c sin (M s επ/ms 3 sin (επ. The thir term can be moele as α k κ k, where κ k is a zero-mean complex Gaussian RV with real an imaginary parts having the same variance σκ N 0 E c sin (M s επ/ms 3 sin (επ. Ignoring the last noise term of (19, the inner-slot combine correlation value z (k can be approximate as z (k e jπm sε ( α k sin (M s επ Ms sin (επ E c+ α k ς k +α k κ k. ( Thus, we have N s N z z (k s e jπm sε z (k (L 1γ sin (M s επ Ms sin (επ E N s c + α k ς k N s + e jπmsε α k κ k (3

5 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY TABLE I SYSTEM PARAMETERS where the last summation term is a complex RV representing the correlation between the signal an noise. Since the power of this term is negligible compare to the others, z can further be approximate as z (L 1γ sin (M s επ Ms sin (επ E N s c + α k ς k +Re Ns e jπmsε α k κ k (µγ + ν (4 where µ (L 1(sin (M s επ/m s sin (επe c an ν enotes a zero-mean Gaussian RV with variance σ ν γ(σ ς + σ κ. The conitional pf of z can be expresse as a noncentral χ istribute pf with one egree of freeom 1 f H1 (z γ πzγ ( σς + σκ σς + σκ. (5 (z+µ γ e γ(σ zµ ς cosh( +σ κ Averaging f H1 (z γ with respect to γ, wehave f H1 (z N s g k exp } 1 {( λ k + µ z σς +σκ σς +σκ {λk ( σ ς + σκ + λ k µ } z ( zµ cosh σς + σκ. (6 Substituting (18 an (6 into (7, we can obtain the etection probability of the propose scheme. The performance analysis of the propose scheme can be extene into a multipath environment using a metho similar to 9. IV. NUMERICAL RESULTS To verify the synchronization performance of the propose scheme, the etection probability is compare as a function of E c /N 0 with the use of single an two antennas. The parameters for performance evaluation are summarize in Table I 7. Fig. 3 epicts the etection probability in the flat Rayleigh faing channel with f 10Hzwhen f o is 10 an 0 khz, an N s 15. It can be seen that the analytic results agree well with Fig. 3. Detection probability of the propose scheme. (a K 1.(b K. the simulation results an that the propose scheme provies better performance than the conventional one particularly when E c /N 0 is low. Note that the use of two antennas may not work better than the use of a single antenna when E c /N 0 is low because the use of antenna iversity may not be appropriate in a noise-ominant environment. It can also be seen that the propose scheme is quite effective in low E c /N 0 even with the use of two antennas. Fig. 4 epicts the etection performance for ifferent values of L as a function of the initial frequency offset. It can be seen that the use of full correlation (L 1is quite impractical when the initial frequency offset is large. The etection performance becomes robust to the frequency offset as L increases since incoherent loss can be mitigate by reucing M s. Moreover, the performance gain with the use of the propose scheme over the conventional one increases as L increases. This is mainly ue to the fact that coherent combining with large LN s makes the ecision variable of the propose scheme more reliable. Fig. 5 epicts the effect of the Doppler frequency on the etection performance, when L 4, N s 15, f o 10 khz, E c /N 0 17, 0 B, an K 1 an. It can be seen

6 1330 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY 005 TSTD scheme (K. However, the performance ifference between K 1an K becomes marginal as the Doppler frequency increases since the iversity gain is sufficiently obtaine in the time omain. The combining process can obtain full time iversity gain when the slot interval is larger than the coherence time of the faing channel. As a result, the improvement of the etection performance becomes marginal for f > 750 Hz. Fig. 4. Detection probability of the single-antenna scheme in the presence of initial frequency offset. V. C ONCLUSION To improve the cell search performance in the WCDMA system, we have propose an inner-slot ifferential combining scheme that can be combine with the use of transmit antenna iversity. The performance of the propose scheme has been analyze an verifie by computer simulation when multiple antennas are use in the presence of initial frequency offset an Doppler sprea. Numerical results show that the propose scheme can provie performance robust to a large amount of initial frequency offset an Doppler sprea, outperforming conventional noncoherent combining schemes. Fig. 5. Detection probability as a function of the maximum Doppler frequency. that the etection performance is improve as the Doppler frequency increases ue to the time iversity effect obtaine from the combining process. It can also be seen that the propose scheme outperforms the conventional one an that aitional antenna iversity gain can also be obtaine with the use of a REFERENCES 1 Association of Raio Inustries an Businesses (ARIB, Japan s Proposal for Caniate Raio Transmission Technology on IMT-000: W-CDMA, Jun K. Higuchi, M. Sawahashi, an F. Aachi, Fast cell search algorithm in inter-cell asynchronous DS-CDMA mobile raio, IEICE Trans. Commun., vol. E81-B, no. 7, pp , Jul Physical Channels an Mapping of Transport Channels Onto Physical Channels, 3GPP TS 5.11, Sep Spreaing an Moulation (FDD, 3GPP TS 5.13, Jun Y.-P. E. Wang an T. Ottosson, Cell search in W-CDMA, IEEE J. Sel. Areas Commun., vol. 18, no. 8, pp , Aug Y. K. Jeong, O.-S. Shin, an K. B. Lee, Fast slot synchronization for intercell asynchronous DS/CDMA systems, IEEE Trans. Wireless Commun., vol. 1, no., pp , Apr UE Raio Transmission an Reception, 3GPP TS 5.101, Oct M. H. Zarrabizaeh an E. S. Sousa, A ifferentially coherent PN coe acquisition receiver for CDMA systems, IEEE Trans. Commun., vol. 45, no. 11, pp , Nov R. R. Rick an L. B. Milstein, Parallel acquisition in mobile DS-CDMA systems, IEEE Trans. Commun., vol. 45, no. 11, pp , Nov W. C. Y. Lee, Mobile Communication Engineering. New York: McGraw-Hill, 1998, ch J. G. Proakis, Digital Communications. New York: McGraw-Hill, 1994.