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Partial Parallel Interference Cancellation in Satellite Communications. Mohsen Ghotbi, Student Member, IEEE, and M. Reza Soleymani, Senior Member, IEEE.
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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 22, NO. 3, APRIL 2004

Multiuser Detection of DS-CDMA Signals Using Partial Parallel Interference Cancellation in Satellite Communications Mohsen Ghotbi, Student Member, IEEE, and M. Reza Soleymani, Senior Member, IEEE

Abstract—Multiuser detection (MUD) using parallel interference cancellation (PIC) technique provides a good complexity, latency, and performance compromise. This technique is suitable for satellite systems using either code-division multiple-access (CDMA) or a combination of time-division multiple-access (TDMA) and CDMA. We offer a new scheme that is a combination of soft and hard PIC detectors whose performance is superior to that of the other famous suboptimal detectors. In soft partial parallel interference cancellation (PPIC), in the first few stages, when the performance is still poor, the accurate knowledge of power and phase cannot be of much use. However, in the following stages, accurate power and phase estimation can improve the performance. This coincides with the time when the decisions are reliable enough to be used for parameter estimation. In our scheme, after a few stages of soft interference cancellation (IC), estimation of the parameters will start. Having these estimates, in the subsequent stages hard IC is performed. The complexity of this scheme grows linearly with the number of users. Moreover, this scheme is much faster than other receivers such as successive interference cancellation (SIC). PIC detectors are usually studied in equal-power case, i.e., a perfect power control scheme is assumed. In this paper, PIC detector in a near–far condition where user signals arrive at the receiver with different power levels is also investigated. Index Terms—Amplitude and phase estimation, direct-sequence code-division multiple-access (DS-CDMA), multiuser detection (MUD), partial parallel interference cancellation (PPIC).

I. INTRODUCTION

A

MONG spread-spectrum techniques the most popular one is the direct-sequence code-division multiple-access (DS-CDMA), where each active user’s data is modulated (multiplied) by a unique code [1]. When the signature waveforms assigned to different users are not orthogonal, each user suffers from the multiple-access interference (MAI) emanating from the other active users. In order to combat such an undesired matter, efforts have been made to mitigate MAI with the aim of reducing the biterror rate (BER). In this regard, Verdu devised an optimal maximum-likelihood (ML) receiver [2]. His devised receiver is an

Manuscript received December 15, 2002; revised July 1, 2003 and November 10, 2003. This work was supported in part by the Canadian Institute for Telecommunications Research (CITR) and in part by the Natural Science and Engineering Council (NSERC) under Grant OGPIN011. The authors are with the Wireless and Satellite Communications Laboratory, Department of Electrical and Computer Engineering, Concordia University, Montreal, QC H3G 1M8, Canada (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/JSAC.2004.823442

optimal one as it is based on the ML detection principle. This kind of detector sounds perfect as far as only a few users attempt to share the channel. Otherwise, the computational complexity grows exponentially with the number of users making this approach impractical to implement. Therefore, the goal of suppressing MAI has been compromised to find schemes that sacrifice optimality for easier-to-implement circuits while maintaining a satisfactory level of performance. As a result of such endeavors, some suboptimal multiuser detectors have been introduced in [3] and [4]. The first class of receivers with performance relaxation via simpler structures are linear multiuser detectors (LMUD) in which a linear mapping is applied to the outputs of the matched filters (MFs). The most familiar ones under this class are the decorrelator and minimum mean-squared error (MMSE) detectors. Such receivers have less complexity than that of the optimal ML receiver, however, they suffer from a main drawback of inverse cross-correlation matrix calculation. Such a computation must be done in real-time, which takes a large amount of memory when the number of users is high. Moreover, the necessity to guarantee the existence of inverse of the cross-correlation matrix makes the case more problematic. Thus, another class of multiuser detectors with still a better structure in the sense of complexity were proposed. The second suboptimal class of detectors are subtractive or interference-cancellation-based multiuser detectors. In this case, the interference of each user on the others is estimated, respread, and canceled from the received signal. This process is usually done through a multitude of stages giving these schemes the name multistage detectors. Successive interference cancellation (SIC) and parallel interference cancellation (PIC) detectors are well-known examples of this class of detectors. In the case of SIC, interferences are canceled sequentially, while, in PIC the interferences of all other users on each one are removed at once, which makes this scheme more attractive due to its higher speed. Recently, another kind of PIC called partial parallel interference cancellation (PPIC) has been proposed by Divsalar et al. In this scheme, instead of a complete cancellation of the interferences, the cancellation is done partially by introducing a partial cancellation coefficient that is always less than unity. It has been proven that the performance of PPIC is drastically better than that of the pure PIC [5]–[12]. Recently, some adaptive approaches to mitigate the MAI have been proposed ([13] and [14]). It is worth noting that although all kinds of subtractive multiuser detectors offer less complex structures compared with

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GHOTBI AND SOLEYMANI: MULTIUSER DETECTION OF DS-CDMA SIGNALS

LMUDs, their efficiency is inferior to that of the LMUD. Consequently, the latter receivers and specially the decorrelator detector (DD), serves as a reference to quantify the performance degradation of any newly proposed receiver. Henceforth, any step which is taken to raise the performance of SIC, PIC, and PPIC in each stage without adding any remarkable complexity, merit special attention. As a result, such a performance enhancement results in less stages of iteration which makes interference-cancellation-based detectors more promising for the thirdgeneration wireless receivers. A kind of SIC receiver using Gauss–Seidel method was introduced in [16]. The whole procedure is performed in two distinct steps of soft and hard iterative interference cancellation (IC) stages. The scheme proposed in this paper is also a combination of soft/hard detectors. However, instead of applying SIC, PPIC method is exploited. The first part of the structure of our detector comprises of soft cancelers. Once enough reliability on decided data is acquired (which is usually in the neighborhood of DD output), amplitude and phase estimation is performed. Eventually, the second part of the structure consists of hard IC stages. Through numerical simulation, it will be shown that our detector outperforms the DD. This paper is continued as follows. In Section II, the system model is formulated. Multistage soft and hard PPIC detectors will be explained in Sections III and IV, respectively. In Section V, the estimation of amplitude and phase is studied. Our proposed method is introduced through Section VI, and the near–far problem is discussed in Section VII. Some brief discussions about reliability and complexity will be covered by Sections VIII and IX, respectively. Finally, this paper is concluded in Section X.

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Fig. 1. DS-CDMA channel and receiver model.

II. SYSTEM MODEL users share a channel and the modulation is Assume that binary phase-shift keying (BPSK), the baseband model of the received signal can be written as Fig. 2.

Soft and hard outputs of correlators at the receiver.

user. Hence, the output of the th correlator under synchronous condition would be (Fig. 2) (1) , and are bit energy, inforwhere mation bit, signature waveform, and the carrier phase shift of th user, respectively. The ’s are the time delays of users at the receiver end. Under synchronous condition, we have . The noise is a complex additive white Gaussian noise (AWGN) with zero-mean and two-sided power watts per hertz for each real and spectral density (PSD) of imaginary components. The and with the du(bit duration) and (chip duration), respectively, ration of are assumed to be independent identically distributed (i.i.d.) and . random variables for The processing gain is . A simple representation of such a received signal is depicted in Fig. 1. At the receiver end, the arrived signal is passed through a group of correlators in order to recover the information stream transmitted by each

(2) where

(3) (4)

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Fig. 3.

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mth stage of a soft PPIC.

It is easy to see that is a complex Gaussian random variwatts per hertz. For able with zero-mean and variance of the sake of simplicity in notation, hereafter, we will consider the first user as the one of interest, and also, all notations are based . Hence, the soft output of the first coron one bit duration relator will turn out as

of the th stage detector (for user 1) that is sampled at can be shown as (8) As an example, for a single-stage detector (i.e., have

), we

(9) where (5) where the first, second, and the third terms denote the useful information, the MAI, and the noise component, respectively.

(10) and (11)

III. MULTISTAGE SOFT PPIC DETECTOR This type of detector does not need the knowledge of the parameters (e.g., amplitude and phase) of the users. According to Fig. 3, the output of the th stage of such a detector for the first user (as the one of interest) is

(6) where (7) and and denote the delayed versions of the received signal and the last stage output, respectively, and it is assumed that for the th stage detector, the received signal and the last stage outputs are delayed -bits and one-bit durations, respectively. The discrete-time notation for the output

It is noted that the structure of the soft PPIC detector which is introduced through Fig. 3 is different from what was depicted in [5] and [6], where the former scheme is easier to implement. Using (10) and (11) in (9) yields

GHOTBI AND SOLEYMANI: MULTIUSER DETECTION OF DS-CDMA SIGNALS

Fig. 4. Output of the multistage soft PPIC detector. N = 63; E =N = 2 .  = 0:3;  = 0:4;  = 0:5;  = 10 dB, K = 40, and 0 ' 0:6;  = 0:7;  = 0:8;  =  =  =  = 0:9.





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Fig. 5. Output of the multistage soft PPIC detector for different stages and 2  .  = 0 :3 ;  = system loads. N = 63; E =N = 8 dB, and 0 ' 0 :4 ;  = 0 :5 ;  = 0 :6 ;  = 0 :7 ;  = 0 :8 .





(12) where the first, second, and the third components of (12) are useful information, residual interference, and the noise, respectively. Similarly, for a two-stage detector, we have (13) Substituting (9) into (13) after some manipulation yields

(14) As it is seen, for more interference cancellation stages, the expression for the corresponding output in terms of the output becomes more complicated. (The output for a of the MF general -stage soft PPIC detector can be found in [15]). Therefore, instead of an analytical study of multistage detector, we will take advantage of computer simulations. In all simulations, pure random signature sequences will be used. Fig. 4 shows the output of the soft PPIC detector for up to ten soft interference dB, cancellation stages. In this figure,

Fig. 6. Comparison of the performance of a seven-stage soft PPIC detector ' 2 , and equal power. with BPSK single user. N = 63; K = 40; 0  = 0 :3 ;  = 0 :4 ;  = 0 :5 ;  = 0 :6 ;  = 0 :7 ;  = 0 :8 ;  = 0 :9 .





and , and the number of active users is assumed to be 40. For this figure and all simulations throughout is taken from [6] and as the this paper, the first PIC factor stages go higher, this factor is increased accordingly. In order to achieve a good confidence level which will be calculated later, 100 packets of 10 000 bits will be run for each simulation. Otherwise, it will be explicitly specified for different packets. It is seen that after some stages, improving the performance is not possible. In fact, as it will be seen later, the performance saturates in the vicinity of DD output. Fig. 5 depicts the number of active users versus BER. It is easily discernible that these two figures support each other; after a few stages (five or six stages), as the steps are taken into further stages, the performance does not improve significantly. Fig. 6 compares a seven-stage PPIC detector with the case of BPSK single user. Note that the knowledge of users’ amplitudes and phases have not been taken into consideration yet.

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Fig. 7. The

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mth stage of a hard PPIC detector. IV. MULTISTAGE HARD PPIC DETECTOR

When a hard cancellation detector is used, the knowledge of the amplitude and phase of each user has a key role in obtaining a good performance. The less accurate the knowledge of parameters is, the more is the resulting interference. Therefore, having no IC is better than wrong IC. According to Fig. 7, the output of the th stage for the first user is

(15) where

Fig. 8. Output of the multistage hard PPIC detector. N = 63; E =N = 7 dB, 0 ' 2 , and K = 40.  = 0:3;  = 0:4;  = 0:5;  = 0:6;  = 0:7;  = 0:8;  =  = 1 1 1 =  = 0:9.



and are the soft and hard estimates of an -stage detector output for the th user, respectively. Similar to the soft cancellation case, the discrete-time version is of the output of the th stage at



and

(16) where

It is noted that since in the hard cancellation case, the knowledge of parameters is used, the performance of such a detector is better than its soft cancellation counterpart assuming that the reliability of the used parameters is high enough. Numerical sim-

ulation validates our claim and in less stages, the output of detector gets its highest possible performance. Fig. 8 shows the dB, output of the hard PPIC detector when , and . Fig. 9 shows the performance of different stages of hard IC detector for different amounts of system load. Eventually, the probability of error for different levels of signal-to-noise ratio (SNR) has been depicted through Fig. 10. It is noted that a perfect estimation is assumed for these figures. As pointed out at the beginning of this section, having a good knowledge of the amplitude and phase of each user has a profound impact on the performance of the hard PPIC detector. Hence, when the estimation of such parameters with good accuracy is practical, the performance could be superior to that of the soft PPIC detector where no knowledge of parameters is

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by the enhanced thermal noise rather than the MAI. Therefore, the th bit of the th user’s signal can be shown as (17) where [16] , we get by

. If both sides of (17) are multiplied (18)

Now, if (18) is averaged over a block of data which need not be very long, the effect of noise will be eliminated effectively.

(19)

Fig. 9. Output of the multistage hard PPIC detector for different stages and 2 .  = 0:3;  = system loads. N = 63; E =N = 7 dB, and 0 ' 0:4;  = 0:5;  = 0:6;  = 0:7;  = 0:8;  = 0:9.





where the exact equality holds in the absence of noise. In order is unknown and needs to be estimated in to find (19), somehow. The approach which is followed for the estimation purpose is the same as what is proposed in [16]. It is assumed lie in . Whenever that the phase shifts of users ), difthe risk of phase ambiguity exists (i.e., ferential coding can be used in order to avoid this matter. It is into two intervals of useful to split the interval of and such that in is greater than , while in the first interval, the second interval, is greater than . VI. COMBINED SOFT AND HARD MULTISTAGE DETECTOR

Fig. 10. Comparison of the performance of a seven-stage hard PPIC detector 2  .  = 0 :3 ;  = with BPSK single user. N = 63; K = 40, and 0 ' 0 :4 ;  = 0 :5 ;  = 0 :6 ;  = 0 :7 ;  = 0 :8 ;  = 0 :9 .





assumed. Consequently, seeking an approach to estimate the parameters with good accuracy and, of course, offering an easy to use method, merit special attention. V. AMPLITUDE AND PHASE ESTIMATION As we know, the outputs of MFs are more contaminated by MAI than by the thermal noise. Therefore, as far as there exists a large amount of such an interference affecting each user, the estimation of amplitude and phase pertaining to each user is not feasible. Hence, we primarily try to lower the interference through multistage soft PPIC detector since this type of detector does not require any information about the parameters. This approach is continued until obtaining better performance is not achievable. At this point, the estimation of users’ parameters with good accuracy is feasible provided that the SNR is high enough. Now, it is assumed that users are mostly corrupted

So far, we have introduced soft PPIC detector, parameter estimation, and hard PPIC detector. As a novel approach, one may employ a combination of the aforementioned methods. We will call this new scheme as soft and hard partial parallel interference cancellation (SHPPIC) detector. Such a scheme, takes three steps in order to generate a final output. As a first step, some stages of soft IC are in place until obtaining better performance is not possible. Through numerical simulations, it is shown that the performance of this first step is the same as that of the DD which is usually considered as a good reference to compare. At this point, parameter estimation will be done, and eventually a few stages of hard cancellation will complete the procedure. Fig. 11 shows the block diagram of the and denote the number of proposed method, where required soft and hard stages, respectively. It is claimed that the performance of the detector obtained in this manner, surpasses the performance of the DD as the numerical simulations justify this. Furthermore, in order to have a fair comparison, conditions (e.g., number of users, processing gain, SNR, and phase shifts of ) remain the same as in [16]. Fig. 12 compares the performance of our proposed method with SIC and DDs. It is notable that in both cases of either perfect or proposed estimation method, the efficiency is better than or equal to the SIC method which has been proposed in [16]. Also, it is noted that in this figure, after stage 10, the performance starts to degrade for the case that uses the estimation algorithm. The reason is that, since the estimation algorithm does not give a perfect estimate of parameters, after some stages, it seems that some useful information is also canceled. It should be mentioned that although the soft PPIC detector cancels the MAI, it enhances the thermal noise which similar to the DD results in

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Fig. 13. Performance comparison of a ten-stage SHPPIC with MF [16], DD [16], SIC [16], and single-user case. N = 31; E =N = 7 dB, ' = 0, and equal power.  =  = 0:3;  =  = 0:4;  =  = 0:5;  = 0 :6 ;  = 0 :7 ;  = 0 :8 ;  = 0 :9 .

Fig. 11.

Combined SHPPIC detector.

In Fig. 13, a performance comparison is demonstrated for different system loads. It is seen that our proposed scheme outperforms other multiuser detectors when the number of active users is high. One may raise the question that when the system load is not high, the performance of SHPPIC detector seems inferior to SIC method. Indeed, when the number of simultaneous users is low, we do not have to proceed through as many stages as in the case of high system load. This is because there is less interference affecting each user, and taking further steps through IC stages results in more useful data cancellation rather than IC. As a result, if we adjust our detector to make the number of stages proportional to system load (less stages for low system load and vice versa), the performance of our proposed method will always be better than that of the other detectors. In Fig. 14, a performance comparison between a ten-stage (seven soft and three hard stages) SHPPIC and BPSK single-user detectors is depicted. It should be noted that since we are dealing with a multiuser channel, the MAI dominates the thermal noise. Therefore, for the equal-power case, in order to reach the same performance as that of the DD, the number of stages is practically independent of the SNR. VII. NEAR–FAR PROBLEM

Fig. 12.

Performance comparison of SHPPIC with SIC [16] and DD [16].

N = 31; E =N = 11 dB, K = 20; ' = 0, and equal power.  =  = 0:3;  =  = 0:4;  =  = 0:5;  =  = 0:6;  =  = 0:7;  =  = 0:8;  =  = 0:9. an error floor. Therefore, in order to get a performance that is acceptable for data application in the satellite communications, our proposed scheme should be cascaded with an error-control encoder and decoder at the transmitter and the receiver sides, respectively.

One of the main issues contributed to CDMA in general, and to PIC or PPIC detectors, in particular, is the near–far issue where the interference originating from the strong users worsen the situation of information transmitted by the weak users. Among multiuser detection techniques, PIC and PPIC detectors are vulnerable to this matter. Since these detectors are attractive due to their simple structure, any effort to make them more resistant against the near–far problem, is of great interest. One method that has been proposed recently is to split the users into groups with (ideally) the same power [17]. Fig. 15 shows the block diagram of such an approach. As it is seen, IC is done in PIC form inside the groups, while between the groups cancellation will be in the form of SIC.

GHOTBI AND SOLEYMANI: MULTIUSER DETECTION OF DS-CDMA SIGNALS

Fig. 14. Comparison of the performance of a ten-stage (seven-stage soft and three-stage hard IC) SHPPIC detector with BPSK single user. N = 31; K = 20; ' = 0, and equal power.  =  = 0:3;  =  = 0:4;  =  = 0:5;  = 0:6;  = 0:7;  = 0:8, and  = 0:9.

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Fig. 16. A comparison of a seven-stage soft HIC and a seven-stage soft PPIC detectors. N = 15, and ' = 0.  = 0:3;  = 0:4;  = 0:5;  = 0 :6 ;  = 0 :7 ;  = 0 :8 ;  = 0 :9 .

received power. The first group to detect is the one with the strongest power. As soon as the outputs pertaining to this group are available, they will be exploited to detect the second strongest group of users. This procedure is continued until the last group of users with the weakest received power level is detected, and similar to the PPIC case, in order to obtain a better performance, this procedure can be done through a multitude of stages. This will be called multistage HIC detector. Fig. 16 shows the performance of an HIC detector where all . This is the worst phase shifts are assumed to be zero case and for random phase shifts the MAI would be less. In this figure, it is assumed that there are two groups each of which includes five users with the SNRs of 5.5 and 11 dB. This situation is compared with the equal power cases where in the first case there are ten users with the SNRs of 5.5 dB, and in the second case, there are ten users with the SNRs of 11 dB. As it is expected, the performance for the strong users in near–far case is better than the performance of equal-power case since in the former, there are less numbers of strong active users. On the other hand, the performance of the weak users approaches the performance of equal power case, although these weak users experience a large amount of interferences coming from the strong users. VIII. RELIABILITY OF THE NUMERICAL RESULTS

Fig. 15.

Block diagram of the multistage HIC detector.

This scheme is called hybrid interference cancellation (HIC) detector. In this approach, the positive aspects of SIC and PIC are combined such that the resulting scheme is less complex and more tolerant to the situations where the user signals arrive with different power levels at the receiver. It is noted that in the HIC scheme, before any cancellation, groups of equal power users are sorted according to their

At this point, we have a brief discussion about the confidence interval of the simulation results. As an example, let us choose dB in Fig. 14 for SHPPIC detector. The the point of is defined as cost function if error if no-error The confidence interval for the probability of 0.9 is defined as [15], [19], and [21] (20)

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where

(21) As it was mentioned earlier, simulation is run for 100 packets of 10 000 bit sequences. Therefore

From Fig. 14, for

dB, we get

In order to calculate

from (21), we need to find

and

to the class of IC detectors and takes advantage of a simple structure whose complexity grows linearly with the number of users per bit per stage]. Therefore, this sort of structure seems [ more promising when the system load is moderate to high. However, since this method employs the SIC, it is compulsory to detect users one by one. The drawback in this situation is the latency, which makes such a scheme too slow for a large number of users. Finally, in what was proposed in this paper, although the complexity of each stage is higher than SIC approach, it still per bit per stage), and since there is no grows linearly ( need to wait for updated data as in SIC scheme, our proposed method is much faster which makes our scheme more attractive for satellite communications. In addition, when the partial can(which are always less than one and cellation coefficients somehow independent of SNR for equal-power case) are chosen properly (for more details refer to [20]), the number of stages will be less. Obviously, this results in more savings in terms of latency, as well as complexity. X. CONCLUSION

substituting in (21), yields

Finally, using (20), we get

Similarly, for the confidence level of %99, we have

Finally, in order to get some points with higher SNRs, the simulation of our proposed method is run for 100 packets of 100 000 bits. Other conditions remain the same as in Fig. 14. and for The resulting outputs are 11 dB and 12 dB, respectively. IX. COMPLEXITY ISSUE For the sake of comparison, in what follows, the computational complexity of some well-known schemes is studied. First of all, the complexity of the optimal (ML) multiuser detector is subject to exponential growth as the number of users increases per bit]. Such a receiver, as mentioned before, suits [ the situations where the number of users is small. Otherwise, it turns out to be too complicated to implement. Another receiver is DD, which is classified under the linear group. It has a complexity proportional to the square of the number of inper bit]. Hence, this approach is attracterfering users [ tive for the case where the system load is low to moderate. Gauss–Seidel (SIC) soft/hard detector proposed in [16] belongs

A new scheme for MUD using a combination of SHPPIC with parameter estimation was presented in this paper. Our proposed method can be applied to the evolutionary satellite communication systems that uses a combination of TDMA and CDMA (slotted CDMA in [18]). The placement of our detector at payload’s receiver section would be after bandpass filtering of the received signal and before channel error-control decoding. There are some advantages contributed to our proposed scheme. First of all, the computational complexity of our proposed method is linear in the number of users which is much less than that of the ML and linear multiuser detectors. Second, the first part of our proposed method applies multistage soft PPIC detector. This type of detector does not require any knowledge of users’ parameters which makes this scheme easy to implement. The resulting performance of such a multistage detector is almost equal to that of the DD. We applied a simple method to estimate the parameters whose accuracy is good for a moderate SNR, and finally, using multistage hard PPIC detector, the overall performance of our proposed method is far better than that of DD which is usually used to gauge the performance of suboptimum detectors. We also studied an HIC detector which is more resilient in near–far conditions. Simulation results demonstrated the excellent performance of our proposed method. As a result, our approach can be considered as a satisfactory alternative considering the complexity, performance, and latency aspects since, it is less complex than the DD with a better performance; and it is faster than the SIC receiver. REFERENCES [1] R. Prasad and T. Ojanpera, “A survey on CDMA: Evolution towards wideband CDMA,” IEEE Spread Spect. Appl., vol. 1, pp. 323–331, Sept. 1998. [2] S. Verdú, Multiuser Detection, 1st ed, Cambridge, U.K.: Cambridge Univ. Press, 1998. [3] S. Moshavi, “Multi-user detection for DS-CDMA communications,” IEEE Commun. Mag., vol. 34, pp. 124–136, Oct. 1996. [4] A. Duel-Hallen, J. Holtzman, and Z. Zvonar, “Multiuser detection for CDMA systems,” IEEE Pers. Commun., vol. 2, pp. 46–58, Apr. 1995.

GHOTBI AND SOLEYMANI: MULTIUSER DETECTION OF DS-CDMA SIGNALS

[5] D. Divsalar, M. K. Simon, and D. Raphaeli, “Improved parallel interference cancellation for CDMA,” IEEE Trans. Commun., vol. 46, pp. 258–268, Feb. 1998. [6] D. Divsalar and M. Simon, “Improved CDMA performance using parallel interference cancellation,” California Inst. Technol., Jet Propulsion Lab., Pasadena, CA, Tech. Rep., Oct. 1995. [7] R. M. Buehrer and S. P. Nicoloso, “Comments on partial parallel interference cancellation for CDMA,” IEEE Trans. Commun., vol. 47, pp. 658–661, May 1999. [8] P. Shan and T. S. Rappaport, “Parallel interference cancellation (PIC) improvements for CDMA multiuser receivers using partial cancellation of MAI estimates,” in Proc. IEEE GLOBECOM 98, vol. 6, pp. 3282–3287. [9] T. Suzuki and Y. Takeuchi, “Near-decorrelating multistage detector for asynchronous DS-CDMA,” IEICE Trans. Commun., vol. E81-B, pp. 553–564, Mar. 1998. [10] A. N. Fawzy, A. W. Fayez, and M. M. Riad, “Optimization of partial parallel interference cancellation (PPIC) factor in CDMA systems,” in Proc. IEEE Systems, Man, Cybernetics Conf., vol. 4, Nashville, TN, Oct. 2000, pp. 2375–2380. [11] M. J. Borran and M. N. Kenari, “An efficient detection technique for synchronous CDMA communication systems based on the expectation maximization algorithm,” IEEE Trans. Veh. Technol., vol. 49, pp. 1663–1668, Sept. 2000. [12] R. M. Buehrer, “On the convergence of multistage interference cancellation,” in Proc. IEEE Asilomar Sig. Sys. Comp., vol. 1, 1999, pp. 634–638. [13] S. R. Kim, Y. G. Jeong, J. G. Lee, and I. K. Choi, “Incorporation of adaptive interference cancellation into parallel interference cancellation,” in Proc. IEEE Vehicular Technology Conf., vol. 2, Houston, TX, May 1999, pp. 1242–1245. [14] M. Honig and M. K. Tsatsanis, “Adaptive techniques for multiuser receivers enhanced signal processing with short codes,” IEEE Signal Process. Mag., pp. 49–61, May 2000. [15] M. Ghotbi, “Multiuser detection of DS-CDMA signals using parallel interference cancellation in wireless communications,” M.S. thesis, Concordia Univ., Montreal, QC, Canada, Dec. 2001. [Online]. Available: www.ece.concordia.ca/~mohsen/publications/htm. [16] Z. Feng and C. Schlegel, An iterative CDMA multiuser detector with embedded phase/amplitude estimation. [Online]. Available: www.ee.ualberta.ca/%7eschlegel/publications.html. [17] 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. [18] C. G. F. Valadon, G. A. Verelst, P. Taaghol, R. Tafazolli, and B. G. Evans, “Code-division multiple access for provision of mobile multimedia services with a geostationary regenerative payload,” IEEE J. Select. Areas Commun., vol. 17, pp. 223–237, Feb. 1999.

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[19] M. D. Srinath, P. K. Rajasekaran, and R. Viswanathan, Introduction to Statistical Signal Processing with Applications. Englewood Cliffs, NJ: Prentice-Hall, 1996. [20] D. Guo, L. K. Rasmussen, and T. J. Lim, “Linear parallel interference cancellation in long-code CDMA multiuser detection,” IEEE J. Select. Areas Commun., vol. 17, pp. 2074–2081, Dec. 1999. [21] M. Ghotbi and M. R. Soleymani, “Partial parallel interference cancellation of DS-CDMA satellite signals with amplitude and phase estimation,” in Proc. IEEE GLOBECOM, Taipei, Taiwan, Nov. 2002, pp. 2882–2886.

Mohsen Ghotbi (S’00) received the B.Sc. degree from Sharif University of Technology (S.U.T.), Tehran, Iran, in 1992 and the M.Sc. degree from Concordia University, Montreal, QC, Canada, in 2001, both in electrical engineering. He is currently working toward the Ph.D. degree at Concordia University. From 1992 to 1998, he was with consulting engineers companies in Iran as an electrical design engineer. His research interests include CDMA systems for wireless and satellite communications, specifically, multiuser detection and interference cancellation areas.

Mohammad Reza Soleymani (S’78–M’78–SM’99) received the B.S. degree from the University of Tehran, Tehran, Iran, in 1976, the M.S. degree from San Jose State University, San Jose, CA, in 1977, and the Ph.D. degree from Concordia University, Montreal, QC, Canada, in 1987, all in electrical engineering. From 1987 to 1990, he was an Assistant Professor with the Department of Electrical and Computer Engineering, McGill University, Montreal. From October 1990 to January 1998, he was with Spar Aerospace Ltd. (currently EMS Technologies Ltd.), Montreal, QC, Canada, where he had a leading role in the design and development of several satellite communication systems. In January 1998, he joined the Department of Electrical and Computer Engineering, Concordia University, as an Associate Professor. His current research interests include wireless and satellite communications, information theory, and coding.