ADAPTIVE CHANNEL EQUALIZATION IN WCDMA DOWNLINK IN SOFT HANDOVER Kari Hooli, Markku Juntti University of Oulu, Centre for Wireless Communications P.O. Box 4500 FIN-90014 University of Oulu, Finland,
[email protected] Abstract— Receivers based on channel equalization have proven to be one of the most promising candidates for terminal receivers in wideband code-division multiple-access (WCDMA) downlink. The channel equalizers provide multiple access interference (MAI) suppression, and thus ensure adequate receiver performance even with a high number of active users. However, the suitability of the equalizers to soft handover has been unclear. In this paper, adaptive equalizer structures for soft handover are introduced, and their performance is numerically evaluated. The results show a significant performance gain over the conventional Rake receiver. Keywords—WCDMA downlink, multiple access interference, equalization, soft handover
I. I NTRODUCTION The air interface of the Universal Terrestrial Radio Access (UTRA), the most important 3rd generation cellular mobile communications standard, is based on wideband code-division multiple-access (WCDMA). In the 3rd generation cellular networks, the downlink capacity is expected to be more crucial than the capacity of the uplink due to the asymmetric capacity requirements, i.e., the downlink direction should offer higher capacity than the uplink [1]. Therefore, the use of efficient downlink receivers is important. To avoid performance degradation due to multiple access interference (MAI), nearfar resistant (or multiuser) receivers [2] can be used. However, the multiuser receivers suitable for terminals typically rely on cyclostationarity of MAI, and, thus, require periodic spreading sequences with a very short period. Hence, they can not be applied in the frequency division duplex (FDD) mode of WCDMA downlink, which uses spreading sequences with one radio frame (10 ms) period. In a synchronously transmitted downlink employing orthogonal spreading codes, multipath propagation is a significant source of MAI. Due to the non-zero cross-correlations between the spreading sequences with arbitrary time shifts, there is interference between propagation paths causing MAI. If the received chip waveform, distorted by the channel, is equalized, the signal effectively experiences a single-path propagation. With orthogonal spreading sequences the equalization retains, to some extent, the orthogonality of users lost due to the multipath propagation, thus suppressing MAI. Since the equalization does not resort to the cyclostationarity of MAI, it can also be applied in systems using long spreading sequences. The channel equalizer has proven to be a viable option for the terminal receivers in WCDMA downlink. Thus, it has inspired numerous publications in the recent years. The equalization at chip-level has been treated, e.g., in [3]-[6]. Also a large variety of adaptive equalizers suitable for WCDMA The research was funded by Academy of Finland, Nokia, and Texas Instruments, which is gratefully acknowledged.
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downlink have been presented, and for in-depth discussion the reader is instructed to [7],[8] and references therein. The equalization is performed prior to the spreading sequence matched filtering in the aforementioned references, but the equalization can also be done at symbol level [9]. In soft handover, the terminal is connected to multiple base stations or to multiple sectors of a base station. Thus, the terminal receives signals from multiple base stations (sectors) at comparable power levels. In handover, there is significant interference between the signals coming from the different base stations, making the suppression of inter-cell interference desirable. The signals from the different base stations are separated with long scrambling codes and thus there is no orthogonality between them. The fundamental idea of the equalizer based receivers, namely, the restoration of the orthogonality of the user signals, is not valid in handover. Therefore the study of equalizers in handover is interesting and timely. In [10], Krauss and Zoltowski extended the approach in [6] and presented chip-level equalizers in soft handover. The considered equalizers were ideal linear equalizers, thus providing performance bounds for adaptive equalizers. In this paper, two adaptive equalizers are studied in soft handover, and their performance is evaluated in a Rayleigh fading multipath channel. II. S YSTEM M ODEL In the signal model, it is assumed that signals from J base stations are received. The signals from the other, more distant, base stations are included in the white Gaussian noise process. Since the downlink is considered, synchronous transmission of signals from a base station through the same multipath channel is assumed. The received signal r after down-conversion, lowpass filtering, and sampling can be written as r=
Kj J X X
Dj Cj Sk,j Ak,j bk,j + n ∈ CNc Ns ,
(1)
j=1 k=1
where Kj is the number of users on jth base station, Ns is the number of samples per chip, Nc is the number of chips and Mk,j is the number of symbols for the kth user in the observation window1 . The samples from multiple receive antennas are interleaved into a single vector r. Thus, Ns is the product of the number of antennas Na , and samples per chip on each of ¯ j ⊗ INa , where ⊗ is Krothe antenna branches. In (1), Dj = D (1) (Nc ) ¯ necker product, Dj = [d1,j , . . . , dLj ,j ] ∈ IRNc Ns /Na ×Lj Nc 1N = G c k,j Mk,j , where Gk,j is the spreading factor for kth user assigned to jth base station. Product Gk,j Mk,j is constant for all users.
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is a path delay and chip waveform matrix where column vec(n) tor dl,j contains samples from appropriately delayed waveform for the lth path of nth chip from jth base station, C j ∈ CNa Lj Nc ×Nc is a block diagonal channel matrix with column vectors containing the time-variant coefficients for the Lj paths of Na antennas. Term Dj Cj models the combination of chip waveform and multipath channel, and is common for all users N ×M on the same base station. S k,j ∈ Ξc c k,j , where Ξc is the chip alphabet, is a block diagonal matrix where column vectors contain the spreading sequences for the jth base station’s kth user. The spreading sequence contains the sector specific scrambling sequence and the user specific channelization sequence, and the sequences are normalized so that S H k,j Sk,j = I. The average received amplitude for the kth user on jth base station is contained in a diagonal matrix Ak,j = Ak,j IMk,j , M vector bk,j ∈ Ξb k,j , Ξb is the symbol alphabet, contains the symbols of kth user on jth base station, assumed to be i.i.d. with unit variance. However, for the arbitrarily selected user 1 in soft handover to J base stations b1,j , denoted as b1 in the sequel, contains the same symbols for all j. The noise vector n ∈ CNc Ns contains samples from the white complex Gaussian noise process with covariance σn2 INc Ns .
In this section, the receivers are briefly presented. The conventional Rake receiver is defined first, followed by a description of the considered equalizers, namely channel-response minimum-output-energy (CR-MOE) equalizer and prefilterRake equalizer [7]. Then the linear minimum mean squared error (LMMSE) equalizer is described for the soft handover, and based on the result, the chip-level equalizer structures are defined for the soft handover. The decision variable of the Rake receiver for user 1 is J X
H H SH 1,j Cj Dj r,
x(n + 1) = (1 − µα)x(n) − µz ∗ (n)(¯r(n) − zp (n)˜ p),
(3)
where z(n) = wH¯r is the equalizer output at nth chip interval, ¯r(n) contains the output samples from the chip waveform matched filter within the equalizer, and zp (n) = ˜ pH¯r(n)/(˜ pH ˜ p). A small positive constant α introduces tap leakage, to circumvent the suppression of the desired signal component due to channel estimation errors [2]. The orthogonality between x and the channel response estimate ˜ p is lost when ˜ p is updated. Thus periodic re-orthogonalization of x is required, given by x⊥p˜ = x −
˜ pH x ˜ p. ˜ p pH ˜
(4)
It is straightforward to extend the CR-MOE equalizer for multiple receive antennas by interleaving the samples from the antennas into one vector ¯r. To limit the overall complexity of the equalizer, the output of chip waveform filter is sampled at chip rate with two receive antennas, whereas two samples per chip are used with one receive antenna. Otherwise the equalization remains unchanged. B. Prefilter-Rake Equalizer
III. R ECEIVER A LGORITHMS
y=
can be written as
(2)
j=1
i.e., the received signal is filtered by the chip waveform, appropriately time-aligned and weighted with channel coefficients in the Rake fingers, combined and finally despread. The decision variables based on the signals from different base stations are coherently combined, resulting in final decision variable y. A. CR-MOE Equalizer In both adaptive equalizers, the received signal is filtered by the chip waveform, equalized and correlated with the spreading sequence. In the CR-MOE equalizer [7], the equalizer is decomposed into non-adaptive and adaptive components, i.e., w = ˜ p + x. The channel response matched filter ˜ p, i.e., the cross-correlation vector between the received signal and the desired response, is used as the non-adaptive part. The filter x is adapted to minimize the energy at the equalizer’s output, while being constrained onto subspace orthogonal to ˜ p to avoid the suppression of the desired signal. The adaptation algorithm
It is commonly known that an adaptive equalizer can be implemented in two parts, the first part containing the received signal’s covariance matrix inverse R−1 (R = E(rrH )), and the second part containing the cross-correlation vector between the received signal and desired response. In [11], the approach was suggested for the chip-level equalizers, as well as the use of Rake receiver as the cross-correlation vector estimate. The equalizer was refined in [7] by replacing the matrix multiplication with the inverse estimate by prefiltering. In the prefilter-Rake, a filter matched to the chip waveform is preceding the prefilter, and its output is sampled at the chip rate. The filtering with prefilter approximates the multiplication with R−1 , and is based on the asymptotic Toeplitz structure of R−1 . The output of the prefilter is fed to Rake receiver performing despreading and maximal ratio combining. The prefilter coefficients can be adapted by using the Levinson algorithm [8],[12], or appropriate parts of (inverse) QR-RLS algorithm [13, Chap. 14], or as in this paper, appropriate parts of Householder RLS (HRLS) algorithm [7],[14]. All algorithms provide roughly equal performance, but the use of the Levinson algorithm results in the lowest complexity. The prefilter-Rake equalizer is inherently sensitive for an illconditioned covariance matrix R. To avoid the problem, two separate prefilters are used with two receive antennas. The solution does not allow equalization in spatial domain, as the CR-MOE equalizer does. C. Adaptive Equalizers in Soft/Softer Handover The LMMSE equalizer is defined for user 1 in soft handover by L = arg min E |LH r − b1 |2 [15], and it is rather straightL forward to show that the LMMSE equalizer for soft handover
TABLE I C HANNEL PROFILES .
Channel estimator for BS 1
Rake for BS 1 Chip matched filter
path # 1 path # 2 path # 3 path # 4
Prefilter Rake for BS 2
Channel estimator for BS 2
Fig. 1. Prefilter-Rake structure in handover.
can be simplified to L = R−1
J X
Dj Cj S1,j A1,j
(5)
R−1 Dj Cj S1,j A1,j .
(6)
j=1
=
J X j=1
Based on the connection between LMMSE receiver and chip-level channel equalizers presented in [8] (i.e., how chiplevel equalizers approximate LMMSE receiver), we can conclude from (6) that the decision variable in handover is obtained by summing the decision variables of the chip-level equalizer based receivers, assigned to base stations from # 1 to # J.2 From (5) one can notice that the prefilter-Rake equalizer may use one common prefilter followed by Rake receivers, assigned to base stations from # 1 to # J. The structure of the prefilter-Rake is illustrated in Fig. 1. IV. S IMULATION M ODELS AND R ESULTS In this section, the performance of the equalizers is numerically evaluated in a Rayleigh fading channel, and compared to that of the conventional Rake receiver. Both one and two receive antenna cases are considered. With two antennas, the CR-MOE equalizer performs space-time equalization, whereas the prefilter-Rake equalizer operates only in the temporal domain. However, it naturally benefits from the antenna diversity. Thus, the selection of the receivers allows also comparisons between the antenna diversity, space-time equalization and plain time domain equalization. In the simulations, QPSK modulation, Walsh channelization codes, base station sector specific random scrambling codes, and root raised cosine waveform with roll-off factor 0.22 were used, but no channel coding was employed. Terminal velocity was set to 60 km/h. Signals from two base stations were modeled, while the more distant base stations were modeled as a part of Gaussian noise process. Both base stations transmitted signals for 4 users with spreading factor 8, desired user with spreading factor 64, and common pilot channel (CPICH) with spreading factor 64. The transmission power of the CPICH 2 To ensure proper combination of signals, one should be aware of any scaling differences between the equalizers, due to e.g. scaling of the reference signal (whether it is pilot signal or channel estimate).
Base station # 1 Power Delay 0 dB 0 ns -1 dB 309 ns -9 dB 716 ns -10 dB 1090 ns
Base station # 2 Power Delay 0 dB 98 ns 0 dB 505 ns -6 dB 895 ns -
was 10% from the whole base station transmission power. Only the desired user was modeled to be in handover. The fading channel profiles employed are defined in Table I. The channels profiles were the same for both receive antennas, but the fading processes were independent between the antennas. One should notice that the channel for the base station # 1 is a truncated version of ITU Vehicular A channel. In the sequel, PT,j and Pd,j are used to denote the total received power and the power of the desired user from the jth base station on one receive antenna branch, respectively. For simplicity, ratio Pd,i /PT,i was the same in the both base stations involved in handover. Eb is defined as the average bit energy over all receive antenna branches, and I is the equivalent power spectral density of interference, corresponding to N0 . Interference includes intra-cell and inter-cell interference. To obtain reasonable values for ratio PT /σn2 , defining indirectly Eb /N0 , it was assumed that the noise is to a large extent composed of interference originating from more distant base stations. It was also assumed that the base stations are transmitting at the same total power, i.e., the load is evenly distributed in the network, and that the average signal power is proportional to d−3 . . . d−4 , where d is the distance. Based on these assumptions, PT /σn2 was selected to be 3 dB when the terminal is at the cell border (i.e., the attenuation is equal for both base stations.). Similarly, PT /σn2 was selected to be 9 dB for the handover between base station sectors. The difference in PT /σn2 is due to the different relative distances to the more distant base stations, modeled as noise. In the first case, the terminal was ’located’ between two cells/sectors so that the average signal attenuation for the both base stations was the same, and the performance of the receivers was studied as the average power for the desired user was varied. The obtained bit error rates (BER) are presented against Pd /PT in Fig. 2 for handover between cells and in Fig. 3 for handover between sectors. From the results one can immediately see that the second receive antenna provides roughly a 3 dB gain for the Rake receiver. The equalizers provide performance gain of 1 dB or less in the cases of 1-antenna equalizers, or 2-antenna prefilter-Rake with time-domain restricted equalization. On the other hand, CR-MOE with spacetime equalization provides a gain of 2 dB to over 3 dB compared to the Rake receiver with 2 antennas. One can also notice that the gains provided by the equalizers are larger for the handover between sectors than for the handover between cells. The difference is due to PT /σn2 ratio. The equalization is designed for the whole base station signal, and also the adaptation algorithms utilize the whole base station signal. Thus, a more
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Fig. 4. BER for the 1-antenna receivers moving from sector # 1 to sector # 2. BERs for receivers in handover are presented with solid lines, and for receivers not in handover with dashed lines. Pd /PT = −15 dB.
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Fig. 3. BER vs. Pd /PT for 1-antenna (solid lines) and 2-antenna (dashed 2 = 9 dB). Terminal lines) receivers in handover between sectors (PT /σn is located on sector boundary, i.e., PT ,1 = PT ,2 .
Fig. 5. BER for the 2-antenna receivers moving from sector # 1 to sector # 2. BERs for receivers in handover are presented with solid lines, and for receivers not in handover with dashed lines.
efficient equalization is achieved with a higher PT /σn2 ratio. In the second case, the terminal ’moves’ in handover from sector # 1 to sector # 2. The movement was implemented by varying PT,1 /PT,2 , Pd,1 /Pd,2 and other corresponding ratios. The noise level was kept constant, and 9 dB below PT,1 on the sector boundary PT,1 = PT,2 . Based on Fig. 3, ratio Pd /PT was set to −15 dB for 1-antenna receivers, and to −18 dB for 2-antenna receivers. For the 2-antenna CR-MOE equalizer, ratio Pd /PT = −21 dB was also used. BERs are presented in Figs. 4 and 5 for one and two antenna receivers, respectively. BER is presented for receivers in handover, as well as for receivers not in handover. From Figs. 4 and 5, one can notice that the gain provided by the equalizers obtains the smallest value at the sector border (PT,2 /PT,1 = 0 dB). However, the equalizers recover significantly faster than the Rake receiver when the terminal moves away from the sector boundary. The equalizers not in handover achieve BER target values for higher PT,2 /PT,1 values than the Rake receiver, indicating that the equalizers require a narrower handover region. In turn, narrower handover region allows more efficient use of radio resources in the network. If
BER target value is set to 5%, the gain in PT,2 /PT,1 is 3 dB for one antenna equalizers, 4 dB for 2-antenna prefilter-Rake, and almost 8 dB for 2-antenna CR-MOE equalizer. The minor asymmetry in BER between base station # 1 and # 2 is due to the differences in channel profiles, presented in Table I. Based on the results, the 2-antenna CR-MOE equalizer exhibits significantly better performance than the other receivers considered. The CR-MOE is able to suppress the interference from other cell due to the space-time equalization, since spatially separated and bandwidth limited signal sources can be more efficiently suppressed in the spatial domain than in the temporal domain [16]. In Fig. 5, BER is presented for the CRMOE equalizer with 3 dB lower power (Pd /PT = −21 dB), and still the equalizer provides some gain over the Rake receiver. BER for the CR-MOE in handover with Pd /PT = −18 dB is not visible since the BER remains below 1%. The instantaneous Eb /(N0 + I) at the output of receiver was calculated from impulse responses every 256 chip interval, with the assumption that the correlation with spreading sequence provides gain equal to the spreading factor. The sample distribution functions of Eb /(N0 + I) with 2-antenna re-
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Fig. 6. Sample distribution functions of Eb /(N0 + I) for 2-antenna receivers in handover between sectors (solid lines) and not in handover (dashed lines). Ratio Pd /PT was set to -18 dB and ratio PT ,2 /PT ,1 to -6 dB. 1
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rather than to look for significant performance gains. At a cell border, the one antenna equalizers were found not only to obtain the Rake receiver performance, but also to provide performance gain over the Rake receiver. Significant performance gains were obtained with two antenna CRMOE equalizer employing space-time equalization. It was also found that the equalizers provide larger performance gains in the handover between sectors than in the handover between cells, due to a higher PT /σn2 ratio in the former case. The equalizers recover also faster from a handover than the Rake receiver, implying that the equalizers require a narrower handover region. Exceptionally narrow region was implied by the 2-antenna CR-MOE equalizer. Thus, the equalizers exhibit two advantages in soft handover over the Rake receiver, namely, a smaller signal power requirement at a cell border, and a narrower handover region requirement. These in turn benefit either the user by more reliable connection in handover, or the network by a decrease in interference and in the number of users in handover, resulting in higher system capacity. R EFERENCES
Sample distribution function
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Fig. 7. Sample distribution functions of Eb /(N0 + I) for 2-antenna receivers in handover between sectors (solid lines) and not in handover (dashed lines). Ratio Pd /PT was set to -18 dB and ratio PT ,2 /PT ,1 to 0 dB.
ceivers are presented for PT,2 /PT,1 = −6 dB in Fig. 6 and for PT,2 /PT,1 = 0 dB in Fig. 7. From the figures the effect of handover can be observed as a smaller variation in Eb /(N0 +I), or as a steeper sample distributions. In Fig. 7, one should notice the curve for the CR-MOE equalizer not in handover. Since the receiver is not in handover, it experiences a lower degree of diversity than the other receivers presented in the figure. Thus, the Eb /(N0 + I) distribution has significantly larger variance and the lower tail extends beyond the lower tail of Rake receiver’s distribution. In Figs. 6 and 7, CR-MOE equalizer provides roughly 3 dB gain in Eb /(N0 +I) over the Rake receiver. V. C ONCLUSIONS The performance of channel equalizers was studied in WCDMA downlink soft handover, and compared to that of the Rake receiver. The handover can be considered problematic for the equalizers, since the idea of the equalizers is the suppression of MAI caused by the loss of the orthogonality of user signals. In handover, a significant source of interference is the non-orthogonal user signals from the other cell. Thus, the goal was more to ensure satisfactory performance of the equalizers
[6]
[7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
H. Holma and A. Toskala, Eds., Wideband CDMA for UMTS, John Wiley and Sons, New York, 2000. S. Verdu, Multiuser Detection, Cambridge University Press, Cambridge, UK, 1998. A. Klein, “Data detection algorithms specially designed for the downlink of CDMA mobile radio systems,” in Proc. IEEE Veh. Technol. Conf., Phoenix, USA, May 4–7 1997, vol. 1, pp. 203–207. C. D. Frank and E. Visotsky, “Adaptive interference suppression for direct-sequence CDMA systems with long spreading codes,” in Proc. Annual Allerton Conf. Commun., Contr., Computing, Allerton House, Monticello, USA, Sept. 23-25 1998. I. Ghauri and D. T. M. Slock, “Linear receivers for the DS-CDMA downlink exploiting orthogonality of spreading sequences,” in Proc. 32th Asilomar Conf. on Signals, Systems and Comp., Asilomar, CA, Nov. 1–4 1998, vol. 1, pp. 650–654. K. Hooli, M. Latva-aho, and M. Juntti, “Multiple access interference suppression with linear chip equalizers in WCDMA downlink receivers,” in Proc. IEEE Global Telecommun. Conf., Rio de Janeiro, Brazil, Dec. 5–9 1999, vol. 1, pp. 467–471. K. Hooli, M. Latva-aho, and M. Juntti, “Performance evaluation of adaptive chip-level channel equalizers in WCDMA downlink,” in Proc. IEEE Int. Conf. Commun., Helsinki, Finland, June 2001, pp. 1974–1979. K. Hooli, M. Juntti, M.J. Heikkilä, P. Komulainen, M. Latva-aho, and J. Lilleberg, “Chip-level channel equalization in WCDMA downlink,” Eurasip J. Applied Sign. Proc., to appear, 2002. K. Hooli and M. Juntti, “Interference suppression in wcdma downlink by symbol-level channel equalization,” in Proc. European Sign. Proc. Conf., to appear, Toulouse, France, Sept. 3–6 2002. T. Krauss and M. Zoltowski, “MMSE equalization under conditions of soft hand-off,” in Proc. IEEE Int. Symp. Spread Spectrum Techniques and Applications, Parsippany, USA, Sept. 6–8 2000, vol. 2, pp. 540–544. S. Werner and J. Lilleberg, “Downlink channel decorrelation in CDMA systems with long codes,” in Proc. IEEE Veh. Technol. Conf., Houston, USA, July 16–19 1999, vol. 2, pp. 1614–1617. L. Mailaender, “Low-complexity implementation of CDMA downlink equalization,” in Proc. IEE Int. Conf. 3G Mobile Commun. Tech., London, UK, Mar. 26-28 2001. S. Haykin, Adaptive Filter Theory, Prentice Hall, Upper Saddle River, NJ, USA, 3rd edition, 1996. A. Rontogiannis and S. Theodoridis, “An adaptive LS algorithm based on orthogonal Householder transformations,” in Proc. IEEE Int. Conf. Electron., Circuits, Syst., 1996, pp. 860–863. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall, Englewood Cliffs, NJ, USA, 1993. A. Paulraj and C. Papadias, “Space-time processing for wireless communications,” IEEE Signal Processing Mag., vol. 14, no. 6, pp. 49–83, Nov. 1997.
