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Joint Signal Precoding in the Downlink of Spread-Spectrum Systems André Noll Barreto, Member, IEEE, and Gerhard Fettweis, Senior Member, IEEE
Abstract—The downlink capacity tends to be the limiting factor in future communications systems. In this paper, we propose two schemes for the downlink of code-division multiple-access systems that help reduce the multiuser interference by jointly precoding the transmitted signal based on knowledge of the downlink channel. Methods that operate on blocks of bits will be first developed and a bitwise simplification of these for systems with large processing gains will be derived. The use of multiple transmit antennas will also be considered. These methods provide a substantial capacity increase without requiring complex multiuser detectors at the mobile terminals, and can be applied for instance to time-division duplex systems, which have reciprocal channels. Index Terms—Joint transmission, multiuser spread spectrum, precoding, pre-Rake, time-division duplex code-division multiple access (TDD-CDMA), transmission diversity.
I. INTRODUCTION
M
OBILE communications services are increasingly popular and cellular third-generation (3G) systems offering higher data rates and new data services are likely to be deployed worldwide in the next few years. Code-division multiple access (CDMA) based on direct-sequence spread-spectrum has been successfully employed in the cdmaOne cellular system [1] and it is emerging as the preferred technique for 3G, being part of the IMT-2000 standards [2]. Due to the expected increase in the traffic in the near future, capacity is one of the most critical issues in the design of mobile communications systems. This is particularly the case in the downlink since new data services like video on demand or Internet browsing tend to be largely asymmetric with much higher downstream bit rates. Multiuser detection techniques [3] have been extensively investigated in order to increase the capacity of spread-spectrum techniques, but these require somewhat complex algorithms, and their utilization in the downlink demands expensive mobile terminals with high power consumption, which should be avoided. If the channel impulse response is known to the base station before transmission, an alternative to multiuser detection is to transfer the system complexity to the base station and precode the signal such that the interference is minimized. Manuscript received June 22, 2001; revised November 27, 2001; accepted March 30, 2002. The editor coordinating the review of this paper and approving it for publication is Y.-D. Yao. This work was supported in part by Capes, Brazil, and by BMBF, Germany. This paper was presented in part at the ICC 2001, Helsinki, Finland, June 2001. A. N. Barreto was with the IBM Zurich Research Laboratory, CH-8803, Rüschlikon, Switzerland. He is now with ATL–Algar Telecom Leste S.A., Rio de Janeiro-RJ 22270–000 Brazil (e-mail: andré
[email protected]). G. Fettweis is with Dresden University of Technology, Mobile Communications Systems, D-01062, Dresden, Germany (e-mail: fettweis@ ifn.et.tu-dresden.de). Digital Object Identifier 10.1109/TWC.2003.811179
Such a priori knowledge of channel state information (CSI) is inherently available to the transmitter in time-division duplex (TDD) systems, in which the uplink and the downlink channels are reciprocal and, hence, the channel estimates obtained upon reception can be used for precoding in the transmission period. TDD will be used for instance in the unpaired-band mode of the 3G standard UMTS and diverse precoding techniques for TDD systems can be found in the literature [4]–[10]. If an increased signaling load is acceptable, the channel can be also known by the base station before transmission in frequency-division duplex (FDD) systems, provided channel state information is regularly sent by the mobile terminals through an uplink signaling channel. The channel variation in wireless communications can of course be a difficulty, but accurate a priori CSI can be obtained even in a mobile environment if prediction techniques are employed [11]. This is naturally possible only as long as the channel does not change too rapidly, i.e., if its coherence time is much larger than the TDD frame length or than the feedback signaling interval in an FDD system. This is however usually the situation for high-data-rate applications with portable devices, such as laptop computers, which are increasingly popular. The simplest way to use this a priori channel information in spread-spectrum modulation is to employ a pre-Rake [8]. In this technique, the channel matched filtering usually performed by a Rake receiver is transferred to the base station transmitter, such that just a simple one-finger receiver can be used at the mobile terminal. Even though the pre-Rake may increase the downlink capacity [4], [5] under certain conditions, the signals from different users are precoded individually with this method and no attempt is made to combat the multiuser interference. Multiuser interference within a cell can be nevertheless reduced or even eliminated if the signal is jointly optimized based on the knowledge of the data bits, spreading sequences and channel impulse response of every user. This concept is displayed in Fig. 1, where the function in Fig. 1(b) has to be optimized in terms of multiuser-interference minimization. In [12], such an approach was considered for a single-path channel only and a solution for the multipath channel was proposed by Vojcic and Jang in [13], which however requires the use of Rake receivers for a reasonable performance. Further joint precoding techniques were recently suggested in [14]–[17]. In Section II, our system model will be described. We will then derive in Section III the optimum precoding method such that the interference is completely eliminated with minimum transmit power. The resulting zero-forcing precoding technique was obtained independently by other authors [15]–[17], but using different criteria. We will also provide a new insight on the relationship between joint precoding and a pre-Rake.
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where (4) and being, respectively, the real and imagwith . inary parts of the th chip of the spreading sequence The spread signal of user over one block can be hence given by (5) (a)
(b)
where user
Fig. 1. Joint precoding concept.
We will see that full elimination of the interference is effective however only up to a certain number of users. With this in mind, in Section IV a novel iterative method based on the minimization of the mean square error will be proposed that is efficient independently of the number of users and allows for a scalable transmitter complexity. The analysis in Sections II to IV deals with blocks of bits, and the complexity of the algorithms investigated in these sections increases polynomially with the block size. In Section V, an alternative bitwise precoding scheme will be presented that reduces the algorithm complexity substantially and is suitable for systems with large spreading factors and many users. This was first proposed by the authors in [4] and it will be investigated here in connection with the precoding approaches taken in the previous sections. In Section VI, the application of the suggested algorithms to systems employing multiple antennas will be briefly investigated, and we will show that the algorithm complexity increases only slightly compared with a single-antenna system. Finally, in Section VII a brief conclusion will be made. II. SYSTEM MODEL We consider the transmission of a block of information code bits, with bits, which are coded into the coding rate. Let be the vector of transmitted code bits of user (1) denotes the th code bit of user . where We can also define the vector containing the bits of all the users (2) where is the number of users. Let be the bandwidth expansion factor in complex chips are spread by a complex sequence per data bit. Bits with spreading factor chips per code bit. Also let the represent the coding sequence corresponding to the vector th bit of the th user
(3)
is the
block spreading matrix of the th
.. .
.. .
..
(6)
.. .
.
In a system without precoding the multiuser transmitted signal vector, separated into real and imaginary parts, is given by (7) Now, let
be the composite vector of all spread signals (8)
where
is the
spreading matrix
.. . Also let be the addition matrix
.. .
..
.
.. .
identity matrix and
(9)
be the (10)
The transmitted signal vector from (7) can be alternatively represented in matrix notation by (11) As channel model we consider a multipath wireless channel represented by a baseband tapped delay line with tap spacing equal to the chip period. The channel changes slowly compared with the length of a transmission frame, so that it can be assumed to be time invariant within a frame. We consider data transmission with pulse shaping in band-limited channels, where the shaping filter satisfies the Nyquist criterion. Ideal sampling is also assumed, so that no interchip interference arises due to the filter. The sampled received signal at the th user’s mobile terminal is given by (12)
BARRETO AND FETTWEIS: JOINT SIGNAL PRECODING IN THE DOWNLINK OF SPREAD-SPECTRUM SYSTEMS
where is the complex gain of the th path of user , the number of resolvable paths, and the complex additive . Gaussian noise with variance Equation (12) can be rewritten in matrix notation as
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despreading. The decision variable vector with a Rake receiver is, hence, given by
(20) (13) is the real-valued noise vector containing where Gaussian-distributed independent samples with variance , is the matrix representing the transand mission channel of user . Assuming that the channel is constant during a transmission block, the channel matrix1 is
The same applies to a pre-Rake. In this case, the signal is modified at the transmitter by channel matched filtering after spreading, and the transmitted signal is given by (21) where
is the modified addition matrix (22)
.. .
.. .
..
.. .
.
(14)
where
a normalization factor to guarantee with that all users transmit with the same power. By substituting (21) into (17), we obtain the decision variable vector with a pre-Rake
(15) (23) and the real and imaginary parts of , rewith spectively. If we consider a system with conventional receivers at the mobile station, i.e., with no Rake receivers, then the decision variable at the decoder input is obtained by correlating the filtered with the spreading code over and sampled signal samples. In vector form, the decision variables of user are given by (16) The composite vector with the decision variables of all users can be also obtained using the addition matrix (17) where
.. .
.. .
..
.
.. .
(18)
is the composite noise vector. and By substituting the signal from (11) into (17), we have the decision variable that is obtained with conventional transmission and no Rake receiver (19) It can be easily verified that Rake processing with maximum ratio combining is nothing but a channel-matched filtering, and can be therefore represented in the matrix notation as the mulbefore tiplication by the transpose of the channel matrix 1The channel matrix has been truncated in order that both r and s have the same length to facilitate the analysis.
III. OPTIMAL PRECODING FOR INTERFERENCE ELIMINATION With precoding we optimize the transmit signal according to a given performance criterion. One such criterion is to eliminate the multiuser and multipath interference. This means that we wish our decision variables to have the same values as they would in a single-user single-path system. Ignoring noise, and for any assuming a unit-gain channel, we want and , or, in vector form (24) There are several ways in which we can completely eliminate both the multiuser and the multipath interference, one solution was obtained for instance in [13]. Depending on the method employed, interference elimination requires a certain transmit that is usually greater than the one required with power conventional spreading. In real systems, however, power is limited, and the transmit power will have to be normalized to the available transmit power . Instead of the condition given in (24), the following decision variable will be obtained: (25) is the normalization factor. where If this normalization factor is less than one, this is reflected in a decrease of the signal-to-noise ratio (SNR) at the decision variable. With this in mind, the optimum precoding technique is the one that minimizes the transmission power before normalization , while satisfying the requirement of and, thus, maximizes interference cancellation given by (24). Given this constraint, we can search for the signal that minimizes the transmit signal energy of a block (26)
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Fig. 2. Block precoding for interference elimination with minimum transmit power.
We have a set of constraints from (24). Considering that no Rake receiver is employed at the mobile station, these constraints can be expressed in vector form as follows: (27) This is a constrained minimization problem that can be solved . We must, thus, obtain using Lagrange multipliers if the vector that minimizes the Lagrange function
Fig. 3.
Performance of joint precoding with interference elimination.
Different link quality requirements can be accommodated with this techniques, for instance if some users require a lower bit-error rate (BER) or suffer from a greater intercell interference. In this case, we can change the condition in (24) to (33)
(28) where is the vector of Lagrange multipliers with length that can be obtained from the minimization constraints. The minimization of (28) can be made by taking the root of , i.e., we want to find such that the gradient of (29) The solution is straightforward (30) By substituting (30) into the constraints from (27), we obtain the Lagrange multipliers (31) where
is the
correlation matrix (32)
Comparing (30) with (21), we can see that the optimum transmitter is nothing less than a set of independent pre-Rakes applied on the modified nonbinary information signal given by , which is just a linear transformation of the data vector . The transmitter concept is displayed in Fig. 2. It should be mentioned here that this is equivalent to a zero-forcing multiuser detector [18], and it will be called zero-forcing precoder henceforth in this work. Furthermore, it must be mentioned that the same transmitter equations were obtained through different methods in [15]–[17]. The same conclusions taken here for a system with conventional receivers apply also when a Rake receiver is employed, in which case the channel H in (30) and (32) should be substituted . with the equivalent channel
where is a diagonal matrix whose elements correspond to the required receive-signal amplitude for each user. The precoding in (31). solution will then be found by replacing with Simulation Results The precoding scheme presented here was simulated and its performance compared with the ones obtained with a conventional system employing Rake receivers and with the Vojcic–Jang precoding proposal [13], which also requires Rake receivers for a reasonable performance. Our proposal is investigated both with and without Rake receivers. We consider a direct-sequence spread-spectrum system with quaternary phase-shift keying (QPSK) modulation, bandwidth expansion , and orthogonal spreading without channel factor ). Since QPSK is employed, there are coding ( possible orthogonal sequences. More codes can be however orthogonal generated if we multiply each group of at most sequences by different scrambling codes, which are random codes in the simulations. A six-path channel model was chosen in which the mean path gains decay exponentially ( 1.6 dB dB. per path) and the SNR is The results are shown in Fig. 3. We can see that the proposed method can significantly improve the system performance compared with a system employing conventional transmitters and Rake receivers. It can be also observed that, given the same receiver configuration with Rake receivers, our method outperforms substantially the Vojcic–Jang method. This happens because the latter applies the precoding on the bits before spreading and hence does not make use of any channel matched prefiltering as in our proposal. It will not be derived here, but it can be shown that both methods have about the same . The precoding methods can however complexity
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eliminate the interference only if the number of users is less of the system, in this case than the degrees of freedom , and beyond this value these methods collapse. For a small number of users the BER with joint precoding and without Rake receivers drops compared with a single-user scenario. This happens because in our simulations the total transmitted power is proportional to the number of users, , with the single-user transmit power. The i.e., precoding algorithm is very efficient for few users, and interference-free transmission is possible with a transmit power less is then larger than one, than . The normalization factor and, as we can see in (25), this results in a greater amplitude of the decision variable compared with a single-user scenario and, hence, in a higher SNR. As the number of users increases, it becomes more difficult to eliminate the interference and the normalization factor must be reduced, with a corresponding decrease in the amplitude of the decision variable. With Rake receivers the joint-precoding performance looks different. For a single user the precoder will obtain the solution that maximizes the SNR after the Rake receiver, and its performance is similar to the one obtained with the combination of a pre- and a post-Rake [5] or with an eigenprecoder [9], [10]. The combination of multipath channel and Rake receiver can be seen, however, as an equivalent channel with a longer impulse response. In a multiuser environment, this increases the interference and makes its elimination more difficult for the precoder than without Rake receivers at the mobile terminals. This is nevertheless only true for a small number of users, since if no Rake receivers are employed the multipath distortion has to be compensated by pre-Rakes, as shown in Fig. 2, which destroys the code orthogonality. Because this is not needed when Rake receivers are employed, a great deal of the code orthogonality can be preserved, which makes the precoding algorithm more effective as the number of interfering users increase. IV. PRECODING WITH POWER CONSTRAINT The precoding technique proposed in Section III is able to completely eliminate the multiuser and the multipath interference. However, as seen in the simulation results from Fig. 3, in power limited systems the price to pay for this interference elimination at high traffic loads is a substantial reduction in the SNR at the decision variable, which is not compensated by the interference cancellation. Furthermore, the algorithm can only be applied if the number of users is less than the number of degrees of freedom in the system. This is particularly relevant if is employed, since in this case the a channel coding of rate number of degrees of freedom, and hence the maximum number of users supported by the previous precoding scheme, is reduced . We propose here that in order to overcome to this problem we can restate the optimization problem. In Section III, we tried to transform a multiuser multipath system into a single-user system with additive white Gaussian noise (AWGN) by precoding the signal with minimum transmit power. With power limitation we should instead try to minimize the mean square error caused by interference (34) with a constraint on the transmit power.
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A statistical minimization of the mean square error considering the receiver noise is also possible but of little practical interest, since the noise power and the intercell interference at the mobile receivers are usually not known at the transmitter. With conventional receivers without Rake filtering the function to be minimized is (35) The power limitation can be expressed by the following constraint: (36) is the maximum signal energy allowed in a block. where We have seen in Section III that the optimum algorithm in terms of power minimization with interference elimination consists of a pre-Rake applied on a modified data vector (37) We may infer that this is also the case if we want to minimize the mean square error with limited power, and instead of , we can searching for the optimum vector of dimension , such that the transmit optimize the vector of dimension signal is given by (37). and, hence, one approach to The mean square error that eliminates the this problem is to try to obtain the vector ] with minimum transmit interference [i.e., such that power, as done in Section III. If the constraint from (36) can be satisfied for , then the problem is already solved, otherwise, with the maximum allowed energy, i.e., we can minimize . This problem can also be satisfying the constraint solved using Lagrange multipliers. We must now minimize the Lagrange function (38) where is the Lagrange multiplier. The value of that minimizes this function is the root of the , which, since the factor must also be calcugradient of lated, has to be solved through a nonlinear system with variables, for which to our knowledge there is no closed-form solution. One alternative to the approach above is to use the method of penalty functions [19]. With this method we define a new function to be minimized which includes a penalty function that approaches infinity if the constraint is not satisfied. Furthermore, the penalty function is chosen such that the new function be differentiable in order to facilitate the analysis. We can use for instance a square law penalty function, and in this case the new function to be minimized is if if
(39)
. where is a real valued constant such that for If (36) has to be satisfied, then we must optimize . We can, however, consider (36) to be a weak constraint, might be since a block with energy slightly higher than acceptable if this results in a much smaller mean square error. We can, thus, consider to be a parameter that determines how strict the power limitation is.
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but it can be avoided through the precoding method with power constraint. This has a good performance even for a high number of users beyond , outperforming by far conventional transmission with Rake receivers or the method presented in Section III. For a small number of users the behavior of power-constrained joint precoding is similar to the one obtained with interference elimination, namely that a reduction in the BER can be achieved. Moreover, the performance is dependent on the number of iterations performed in the optimization algorithms, thus allowing a scaling of the signal quality for transmitters with different complexities. V. BITWISE PRECODING
Fig. 4.
Performance of joint precoding with power constraint.
The optimum that minimizes taining the root of its gradient
can be found by ob-
if if
(40)
, then is the root of a cubic equation over , for which to our knowledge there is no closed-form sonulution either. We can, however, minimize the function merically, for instance through the conjugate-gradient method [19], which is an iterative method that converges quadratically to the function minimum. In practice, the minimization must be performed in real time and we have to define then a maximum number of iterations of the numerical algorithm that can be executed in the available time, and the complexity of the algorithm is . Constrained-power precoding was derived here considering that no Rake receivers are employed, but the same development would apply otherwise. All we would have to do then is to use instead of in the the equivalent channel matrix algorithm. If
Simulation Results The numerical method proposed here was simulated considering that no Rake receivers are employed and the results are shown in Fig. 4. The bandwidth expansion factor is the same ), but this time part of the as in the previous section ( spreading is accomplished through a convolutional code of rate , thus reducing the degrees of freedom of the problem ). The same channel is also considered, ( but, as channel coding is employed, the SNR can be reduced dB with similar BERs. to The precoding scheme from Section III was also simulated for conventional receivers, and, as already noticed, its performance collapses as the number of users approaches . Since coding is employed, this limitation is now much more critical,
The block precoding techniques presented in the previous sections can be very efficient in increasing the capacity of CDMA spread-spectrum systems, but due to their high complexity, their implementation is in practice limited to systems with a small number of users and short data blocks. We can however use the same joint precoding concepts proposed so far and perform them bitwise. If the spreading gain is large compared with the number of paths, the interference between bits caused by multipath propagation can be neglected and we can use the same algorithms for each bit at a time. In this case, the precoding has to be performed once every bit only. Considering for instance the zero-forcing algorithm, operations are needed in a block of code bits if the signal is precoded bitwise, which is a significant reduction in the comoperations required by plexity compared with the block precoding. This bitwise method was previously investigated by the authors in [4]. We can also consider the interference between the bits in our precoding scheme if there are no Rake receivers at the mobile terminals. In this case, neglecting the thermal noise, the decision vector corresponding to the th bit is (41) where
.. .
.. .
..
.
.. .
(42)
is the channel matrix, as defined in (14) and (18), but truncated to a bit interval. is the addition matrix, the transmitted signal corresponding to the interference caused by the other bits. the th bit and The truncation of the channel matrix has negligible effects if the channel delay spread is small compared with a bit interval, but for small spreading gains and many resolvable paths this truncation becomes noticeable and would make this approach unfeasible. Considering that no Rake processing is made and that the ), channel impulse response is not longer than one bit ( is caused by the previous bit only the interbit interference and it can be given by (43)
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where is the channel matrix applied on the previous bit with diagonal elements of dimension
.. .
.. .
.. .
.. .
..
.. .
.. .
.. .
.. .
.. .
.
.. .
(44) When joint precoding is applied to the th bit, we have already knowledge of the optimized signal obtained for the preand we can take it into account in the previous bit coding algorithm. Suppose we want to completely eliminate the interference with no power constraint, then we must satisfy the equality (45)
Fig. 5. factor.
By substituting (41) into (45), we have the following condition: (46) This can be solved for example through the zero-forcing precoding method by making (47) where
Performance of bitwise precoding with large bandwidth expansion
VI. PRECODING WITH MULTIPLE ANTENNAS The use of multiple transmit antennas can be considered with a few small changes in the system matrices. These will be briefly discussed in this section. We consider here the vector notation from Section II and extend it to systems employing multiple antennas at the base station transmitter. transmit antennas at the base station Suppose we have the transmitted signal at the th antenna. The overall with transmit signal can be expressed in vector form as
(48) The same applies for the minimization with power constraint, where the function to be minimized is now
(49) This approach cannot be carried out if a Rake receiver or a pre-Rake is employed, because Rake processing is equivalent to a noncausal channel-matched filtering and, thus, the interbit interference is caused both by the previous and by the following bit. In this situation, a block precoding scheme as the ones presented in Section III and Section IV must be employed if we desire to cancel out the interference. Simulation Results The reduced complexity of bitwise precoding makes it feasible for systems with a larger number of users too, in which the intersymbol interference is not very significant, independently of the frame length. In Fig. 5, performance results for a system with , convolutional coding of bandwidth expansion factor , and orthogonal spreading are displayed. The rate dB is considered. six-path channel model with SNR Both zero-forcing precoding and the iterative precoding with power constraint were considered. If the spreading gain is large, as in this case, the effect of intersymbol interference is insignificant and quite good results can be achieved with bitwise joint precoding, as we can observe in Fig. 5.
(50) be the matrix describing the channel between the th Let transmit antenna and the mobile terminals of every user, as described by (18). Then, if conventional one-finger receivers are used, the vector of decision variables at the mobile terminals can be given by (51) where (52) and
.. .
.. .
..
.
.. .
(53)
with defined in (10). The system equation (51) is the same as for a system employing a single transmit antenna, except for the extended channel, addition and transmit signal matrices. If we apply, for instance, the optimization algorithm from Section III considering multiple antennas we will end up with the following optimum solution for the transmit signal: (54)
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where (55) with
the correlation matrix (56)
The computation of the transmit signal in (54) and of the correlation matrix in (56) are indeed more complex than the ones necessary for the single antenna case, but most of the algorithm complexity arises from the matrix inversion in (55). By comparing the expressions for the correlation matrices with a single and with multiple antennas in (32) and (56), respectively, we see that they have the same dimension and hence the same complexity for the matrix inversion. The same applies for the other algorithms investigated in this paper, multiple antennas can be taken into account with only a marginal increase in the computational complexity. The capacity achieved with joint precoding employing multiple antennas will be however not addressed in this work and is a matter for future studies. VII. CONCLUSION We have shown in this paper that if channel state information is available before transmission in the downlink, which is the case in TDD-based systems, the multiuser and multipath interference in direct-sequence spread-spectrum communications can be reduced or even eliminated by appropriate precoding before transmission. Two such block precoding schemes were suggested here, as well as a bitwise adaptation of them with reduced complexity for systems with large spreading factor. We have seen that substantial capacity gains can be achieved this way without requiring the use of complex multiuser detection at the mobile terminals. A critical issue for the proposal is the acquisition of reliable channel state information, which may be difficult in time-variant channels, and the performance of these methods in the presence of channel estimation errors is yet to be investigated. REFERENCES [1] “Mobile station-base station compatibility standard for dual-mode wideband spread-spectrum cellular systems,”, TIA/EIA-IS95B, July 1997. [2] T. Ojanperä and R. Prasad, “An overview of air interface multiple access for IMT-2000/UMTS,” IEEE Commun. Mag., vol. 36, pp. 82–86, Sept. 1998. [3] D. Koulakiotis and A. H. Aghvami, “Data detection techniques for DS/CDMA mobile systems: A review,” IEEE Pers. Commun., vol. 7, pp. 24–34, June 2000. [4] A. N. Barreto and G. Fettweis, “On the downlink capacity of TDD CDMA systems using a pre-Rake,” in Proc. Global Telecommunications Conf. (GLOBECOM), Rio de Janeiro, Brazil, Dec. 1999, pp. 117–121. [5] , “Performance improvement on DS-spread spectrum systems using a pre- and a post-Rake,” in Proc. Int. Zurich Seminar on Broadband Communications, Zurich, Switzerland, Feb. 2000, pp. 39–46. [6] R. Benjamin, I. Kaya, and A. Nix, “Smart base stations for ‘dumb’ time-division duplex terminals,” IEEE Commun. Mag., pp. 124–131, Feb. 1999. [7] R. Esmailzadeh, M. Nakagawa, and E. Sourour, “Time-division duplex CDMA communications,” IEEE Pers. Commun., vol. 4, pp. 51–56, Apr. 1997.
[8] R. Esmailzadeh, E. Sourour, and M. Nakagawa, “Pre-rake diversity combining in time-division duplex CDMA mobile communications,” IEEE Trans. Veh. Technol., vol. 48, pp. 795–801, May 1999. [9] R. Irmer, A. N. Barreto, and G. Fettweis, “Transmitter precoding for spread-spectrum signals in frequency-selective fading channels,” in Proc. 3G-Wireless, San Francisco, CA, June 2001. [10] J.-B. Wang, M. Zhao, S. D. Zhou, and Y. Yao, “A novel multipath transmission diversity scheme in TDD-CDMA systems,” IEICE Trans. Commun., vol. E-82B, pp. 1706–1709, Oct. 1999. [11] A. Duel-Hallen, S. Hu, and H. Hallen, “Long-range prediction of fading signals,” IEEE Signal Processing Mag., vol. 15, pp. 62–75, May 2000. [12] L. Wilhelmsson and K. S. Zigangirov, “Coordinated pre-coding for the forward-link in DS-CDMA,” in Proc. Global Telecommunications Conf. (GLOBECOM), Phoenix, AZ, Nov. 1997, pp. 1509–1513. [13] B. R. Vojcic and W. M. Jang, “Transmitter precoding in synchronous multiuser communications,” IEEE Trans. Commun., vol. 46, pp. 1346–1355, Oct. 1998. [14] M. Brandt-Pearce and A. Dharap, “Transmitter-based multiuser interference rejection for the down-link of a wireless CDMA system in a multipath environment,” IEEE J. Select. Areas Commun., vol. 18, pp. 407–417, Mar. 2000. [15] P. W. Baier, M. Meurer, T. Weber, and H. Troger, “Joint transmission (JT), an alternative rationale for the downlink of time division CDMA using multielement transmit antennas,” in Proc. Int. Symp. Spread Spectrum Techniques and Applications. Newark, NJ: NJIT, Sept. 2000, pp. 1–5. [16] “Tx diversity with joint predistortion,” Tech. Rep. Tdoc 3GPP TSGR1#6(99)918, 3GPP, July 1999. [17] M. Joham and W. Utschick, “Downlink processing for mitigation of intracell interference in DS-CDMA systems,” in Proc. Int. Symp. Spread Spectrum Techniques and Applications, NJ: NJIT, Sept. 2000, pp. 15–19. [18] A. Klein and P. W. Baier, “Linear unbiased data estimation in mobile radio systems applying CDMA,” IEEE J. Select. Areas Commun., vol. 11, pp. 1058–1066, Sept. 1993. [19] G. Grosche, V. Ziegler, D. Ziegler, and E. Zeidler, Teubner-Taschenbuch der Mathematik—Teil II. Leipzig, Germany: Teubner, 1995.
André Noll Barreto (S’96–M’01) received the B.Eng. and the M.S. degrees from the Catholic University (PUC), Rio de Janeiro, Brazil, in 1994 and 1996 respectively, and the Ph.D. degree (summa cum laude) from the Dresden University of Technology, Germany, in 2001, all in electrical engineering. He was working as a Postdoctoral Fellow at the IBM Zurich Research Laboratory, since October 2000. He is now with ATL–Algar Telecom Leste S.A., Rio de Janeiro, Brazil. His current research interests include signal preprocessing and antenna diversity schemes for spread spectrum and OFDM.
Gerhard Fettweis (S’82–M’90–SM’98) received the M.Sc./Dipl.-Ing. and Ph.D. degrees in electrical engineering from the Aachen University of Technology (RWTH), Germany, in 1986 and 1990, respectively. From 1990 to 1991 he was a Visiting Scientist at the IBM Almaden Research Center, San Jose, CA, working on signal processing for disk drives. From 1991 to 1994, he was a Scientist with TCSI, Berkeley, CA, responsible for signal processor developments for mobile phones. Since September 1994, he holds the Mannesmann Mobilfunk Chair for Mobile Communications Systems at Dresden University of Technology, Dresden, Germany. Since 1999, he is CTO of Systemonic, a startup spun out of Dresden University of Technology focusing on broadband wireless chip-sets. Dr. Fettweis is an Elected Member of the SSC Society’s Administrative Committee since 1999, and the IEEE ComSoc Board of Governors from 1998 to 2000, respectively. He has been an Associate Editor for IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II and an Associate Editor for IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS: Wireless Series. Over the years he has organized and been on the program committee of numerous IEEE workshops and conferences.
