THE MAJOR limitation to the capacity of direct-sequence

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER An Improved Design of Chip Waveforms for B-Limited DS-CDMA Systems Ha H. Nguyen, Member, IEEE Abstract This paper introduces an efficient improved design of chip waveforms to minimize the multiple-access interference in b-limited direct-sequence code-division multiple-access (DS-CDMA) systems. For ease of implementation, the DS-CDMA system employs a time-limited chip waveform, as its b limitation is ensured by the low-pass filters at both the transmitter receiver ends. The design uses sinusoids to synthesize the timelimited chip waveform so that the portion of its spectrum across the specified bwidth is as flat as possible. It is shown that by using a simple series expansion (with only a few terms) the synthesized chip waveforms significantly outperform the spreading/despreading waveforms previously proposed, particularly for large values of the chip duration-bwidth product. Index Terms Multiple access, code-division multiple-access (CDMA), interference cancellation, chip waveform. I. INTRODUCTION THE MAJOR limitation to the capacity of direct-sequence code-division multiple-access (DS-CDMA) is multiple-access interference (MAI). To increase the system capacity, different techniques have been proposed for MAI cancellation. These techniques include multiuser detection (see [1]) the noise whitening approach [2], to name a few. In a single-user communication over an additive white Gaussian noise (AWGN) channel, the error performance depends on the energy, not the specific shape of the signaling waveform. In such a system, the selection of the signaling waveform is mainly determined by the spectral occupancy of the waveform. In contrast, in a DS-CDMA system, the signaling waveform, or chip waveform, affects not only the spectral occupancy, but also the error performance. This is because the statistical properties of the MAI depend on the actual shape of the chip waveform. Studying the effect of chip waveforms on the performance of DS-CDMA systems has recently received considerable attention. In [3], various time-limited chip waveforms are examined under the assumption that the channel bwidth is infinite. Since the bwidth of any practical system is limited, it is more useful to study compare different chip waveforms under some bwidth constraint. In [4], by using the family of prolate spheroidal wave functions (PSWFs) [5], the authors focus on the search for the optimum time-limited even chip waveform Manuscript received April 16, 2002; revised September 10, 2002, March 31, 2003, September 2, 2003, April 7, The author is with the Department of Electrical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada ( ha_nguyen@engr.usask.ca). Digital Object Identifier /TVT that minimizes the MAI subject to a fractional out-of-b energy bwidth constraint. More recently, the method in [4] has been extended to find an arbitrary single-chip waveform as well as double-chip waveforms for multirate DS-CDMA systems [6]. Although this method provides better time-limited chip waveforms as compared to other conventional ones, its main drawback is that the chip waveforms are constructed from PSWFs, which cannot be generated easily. Furthermore, the spectra of the chip waveforms are still not strictly b limited. For strictly b-limited DS-CDMA systems, the optimum chip waveform that minimizes the MAI was shown in [7] [8] to have a flat spectrum across the b. In [9], the family of sinc functions were used to synthesize the b-limited chip waveforms for quasi-synchronous CDMA systems corresponding to different density functions of the delay. Optimum chip waveforms that result in the minimum average bit-error rate (BER) for any delay profile were also found in [10] under the constraint of zero interchip interference (ICI). More specifically, it was shown in [10] that choosing the flat spectrum pulse with zero excess bwidth also results in the optimum system as far as the BER is concerned. Reference [11] shows that it is possible to improve the performance of DS-CDMA systems with a relaxation on the zero-ici constraint. A major problem with a b-limited chip waveform is the pulse s long duration in the time domain, which makes its generation complicated [12]. Instead of using a b-limited chip waveform, a b-limited DS-CDMA system can also be implemented using a timelimited chip waveform low-pass filters at both the transmitter receiver. Such systems were considered in [2] [12] [14]. With this configuration, the spectrum of the transmitted signal generally is not flat different techniques should be employed at the receiver to compensate for the inb spectrum of the received signal. For example, the optimum noisewhitening receiver is proposed in [2] various spreading/despreading functions are introduced in [12], [14], [15]. For a given spreading function, the motivation to use a different despreading function in [12], [14], [15] is to make the crosspower spectrum density appear flat across the b. The results in [12] [14] illustrate that a significant MAI reduction can be obtained by using the hybrid spreading/despreading functions instead of the conventional rectangular pulse. However, there still is a wide gap between the MAI level achieved by the spreading/despreading functions in [12] [14] that of the theoretically optimum b-limited chip waveform. This inferiority is due to the specific structures of the spreading/despreading functions proposed in [12] [14]. This paper considers the same system model as in [2] [12] [14]. A better design of the time-limited chip waveforms is /04$ IEEE

2 1380 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 Fig. 1. System model for the kth tranceiver: (a) transmitter (b) receiver. proposed examined. This system uses the same chip waveform at both the transmitter the receiver, the waveform is designed to directly maximize the bwidth efficiency of the system. Since the design is based on the expansion in sinusoids, the proposed chip waveforms can be easily generated. Due to a higher degree of freedom that can be introduced into their structures, the proposed chip waveforms are more efficient than the spreading/despreading functions in [12], [14], [15]. More importantly, their performance approaches that of the optimal b-limited waveforms very closely. II. SYSTEM MODEL Consider a -user b-limited DS-CDMA system similar to the ones in [12] [14]. The transmitter receiver for user are shown in Fig. 1(a) (b), respectively. The b limitation of the system is ensured by the two analog low-pass filters. The data spreading signals are given by, are the bit the chip durations, respectively, for otherwise. is the chip waveform limited to has unit energy. Both the data signature sequences,, are modeled as sequences of independent rom variables taking values in with equal probability. There are chips in one bit interval, i.e.,. The th user s transmitted signal is, denotes convolution, is the average transmitted power, is the carrier frequency. The phases are modeled as independent uniform rom variables in the range. The received signal is given by, is AWGN with a two-sided power spectral density of is the delay of the th user. The user delays are modeled as rom variables uniformly distributed over, independent from one another independent from the s. The receiver in Fig. 1(b) is for the detection of, the th bit of the th user. In this figure, is the overall phase shift of user, while the despreading signal can be different from the spreading signal used at the transmitter. As in [12] [14], to simplify the analysis it is assumed that the filters are ideal low-pass filters. Ignoring the interchip interference, the signal-to- interference ratio (SIR) is given by [2], [12] SIR (1) is half the available bwidth of the system is called the bwidth efficiency factor [14]. This parameter is defined bounded as The function in (2) is the cross-power spectral density (PSD) of the spreading despreading signals, which can be found by taking the Fourier transform of the cross-correlation function. In [14], the ICI is accounted for by including an extra user the denominator of (1) is changed to. This, however, makes the SIR slightly pessimistic. It can be seen from (1) (2) that, in essence, measures the average MAI level in DS-CDMA systems. The equality in the second inequality of (2) is achieved when the magnitude of the cross-psd is a constant across the bwidth. This is exactly the guideline to select the hybrid spreading/despreading functions in [12], [14], [15]. Although they can provide a better MAI reduction capability, the spreading/despreading signals proposed in [12], [14], [15] are by no means optimal. Here, we consider the case the spreading/despreading signals are identical attempt to search for the chip waveform that directly maximizes the bwidth efficiency factor. When the spreading/despreading signals are the same, the cross-psd is proportional to, (2)

3 NGUYEN: AN IMPROVED DESIGN OF CHIP WAVEFORMS FOR BAND-LIMITED DS-CDMA SYSTEMS 1381 is the Fourier transform of. In this case, the factor in (2) can be rewritten as Note that the maximization of (3) is invariant to the scaling of the chip waveform. Therefore, by imposing the constraint instead of a unit-energy constraint, maximizing (3) is equivalent to minimizing. The objective function in (3) shows that for the DS-CDMA systems under consideration, only the inb portion of the spectral density of the chip waveform is important. Before closing this section, it should be emphasized that the design of the spreading waveforms for the system model in [12], [14], this paper can never yield the truly optimal waveform with flat spectrum across the b. However, the main interest in [12], [14], this paper is to develop practical designs for the chip waveforms that perform as close as possible to the theoretically optimal chip waveform. (3). With the above expansion, it has been implicitly assumed that the chip waveform satisfies. This is a desirable property since it makes the signals less susceptible to transient high-order harmonic generation by hardware circuitry. Phase continuity is also important in relation to nonlinear amplification [4]. Using the expansion in (5), the problem of finding the chip waveform to minimize (3) reduces to a finite-dimensional optimization problem in unknowns. Obviously, one expects that a better approximation of the theoretically optimal chip waveform is obtained with a larger value of. Interestingly, numerical results in Section IV show that for all the values of in the range of interest, is enough to practically achieve the maximum MAI suppression capability of the optimal chip waveform. As noted earlier, it is more convenient to impose the constraint on the chip waveforms, which can be written in terms of as III. PROBLEM FORMULATION To search for the time-limited chip waveform that maximizes (3), the series-expansion technique is employed. First, the family of PSWFs appears to be a natural choice for series expansion due to its high concentration in the frequency domain. However, the complicated generation of PSWFs make them less practical. For the CDMA systems in Fig. 1, since b limitation is guaranteed by the low-pass filters, it is not necessary to use the complicated PSWFs. Instead, the family of time-truncated sinusoids is used to approximate the chip waveform. These functions form a complete set for all continuous functions time limited to, more importantly, they can be generated very easily. Let. To simplify the calculation of the objective function introduce the shifted ( possibly negated) versions of, defined by With this constraint, the objective function is can be written as (6) if is odd if is even Let. Note that when is odd, is an even function is real. On the other h, when is even, is an odd function is purely imaginary. Write when when. Then (4) version of. Now approximate the delayed with a finite series expansion as (7) (5) (8)

4 1382 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 (9) (10) Given, all the integrals in (6), (8), (9), (10) can be precomputed easily. The design of the chip waveforms can be formulated as follows. Problem 1: Find coefficients that minimize (7) subject to the constraint in (6). The above can be solved numerically; for example, by sequential quadratic programming (SQP) routines in the MATLAB optimization toolbox [16]. IV. RESULTS AND COMPARISONS This section presents some results obtained from solving Problem 1. To avoid locally optimal solution, the optimization routine is run times (with rom starting values in each run) the best result is kept. Performance comparison to the spreading/despreading waveforms proposed in [12], [14], [15] (which consider the same system model) is also made. Note that the system in [4] is a time limited, while that in [10] uses the theoretically optimum b-limited chip waveform whose performance is the best that can be achieved by the proposed design. The specific waveforms for comparison are as follows. 1) The rectangular chip pulse is used at both the transmitter receiver [2]. The auto-psd of the rectangular spreading signal is. 2) The same chip waveform is used at the transmitter receiver. It consists of three terms [14],, the coefficients, are chosen to flatten the spectrum of. For this chip waveform, the auto-psd is [14] (11) 3) The rectangular chip pulse is used at the transmitter a family of stepping chip waveforms (SW) is used at the receiver [12], [15]. The cross-psd is given by [12] Fig. 2. Plots of bwidth efficiency factors versus WT. (12) is a tunable parameter. Both 2) 3) reduce to case 1) when, respectively. A. Comparison of Bwidth Efficiency Factor Fig. 2 plots the bwidth efficiency factors achieved by different spreading/despreading techniques. As in [6] [15], the range of interest for is over [0.5, 3]. For a given processing gain, the value of is proportional to the total system bwidth the larger value of means a wider-b DS-CDMA system [15]. For both the three-term Rect./SW schemes, the parameters are optimized to maximize for each value of. It can be seen from Fig. 2 that using three-term Rect./SW chip waveforms improves the spectral efficiency significantly over the conventional Rect. pulses. Also observe from Fig. 2 that, although the more-complicated Rect./SW scheme was originated from the three-term scheme, it is only slightly superior when. As expected, the performance of the proposed chip waveforms improves as increases. The proposed chip waveforms corresponding to (i.e., consisting of two terms) is slightly inferior to the three-term pulses. However, a significant improvement over both the three-term Rect./SW schemes is obtained when (i.e., with only four terms) the optimal bwidth efficiency of one is practically achieved with. This is especially true for large values of (i.e., wider-b DS-CDMA systems). For examples, comparing to the Rect./SW scheme, the proposed chip waveforms can improve the spectral efficiency by 25%, 43%, 54% at,, respectively. The results presented in Fig. 2 are best understood by examining the cross- (or auto-) PSDs of different spreading/despreading techniques, plotted in Figs Except for the case of Rect. pulse, plotted in these figures are the cross- (or

5 NGUYEN: AN IMPROVED DESIGN OF CHIP WAVEFORMS FOR BAND-LIMITED DS-CDMA SYSTEMS 1383 Fig. 3. Cross-PSDs of different schemes: WT =1:0. Fig. 5. Chip waveforms designed with L =3;W T =2:0: without with inb power constraint. Fig. 4. Cross-PSDs of different schemes: WT =2:0. auto-) PSDs optimized for each of the values of. It can be seen that the PSDs of the proposed chip waveforms are fairly constant over each bwidth range under consideration. In contrast, the (cross-) PSDs corresponding to either Rect. pulse, three-term, or Rect./SW waveforms generally are nonflat. Also, except for the PSDs of the three-term chips at, these (cross-) PSDs always have spectral nulls at multiples of. These spectral nulls cause the inefficiency in wider-b DS-CDMA systems (when ) of the spreading/despreading schemes proposed previously. Problem 1 was also solved for the family of even chip waveforms by setting in (6) (7). It is interesting to observe that, although the best chip waveforms are neither even nor odd (about ), the best even chip waveform performs very closely to that of the best arbitrary chip waveforms, especially when large values of are used. For example, with, the bwidth efficiency factors of the best arbitrary even waveforms are , respectively. Thus for all practical purposes, the even chip waveforms might be preferred. For example, Fig. 5 plots the best chip waveforms obtained with. B. Comparison of Error Performance The evaluation of bit-error probabilities for DS-CDMA systems is a problem of long interest. Over the past few decades, substantial research has been devoted to approximations, bounds, or exact calculations for the error performance of DS-CDMA (see [17] the references therein). Among these different techniques, Holtzman s simplified improved Gaussian approximation (SIGA) has received much attention since its publication [18]. Holtzman s SIGA was originally described for DS-CDMA systems using a time-limited rectangular chip waveform (with no low-pass transmit/receive filters). It was recently developed verified for b-limited DS-CDMA systems in [17]. Other approximation techniques for evaluating the error performance of b-limited DS-CDMA systems can also be found in [19] [21]. Due to its simplicity excellent accuracy, the SIGA approach is used in this paper. This approximation is given by [18], [17] (13) is the power of the signal component; is the noise variance;, respectively, are the mean stard deviation of the MAI variance conditioned on all users delays phase shifts. The expressions of, for systems employing different spreading/despreading functions are given in Appendix II of [17]. If both the spreading despreading waveforms are the same as in the proposed design, then (14) (15)

6 1384 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 is a more dominant parameter than MAI at low signal-to-noise ratio. Fig. 6. BER performance of different spreading/despreading schemes. (16) (17) is the energy per bit. The ratio between gives the signal-to-background noise ratio SNR. It should be noted that the above SIGA was developed for zero-ici chip waveforms. For chip waveforms that do not satisfy the Nyquist criterion, the above results might serve as a lower bound to the actual performance. As mentioned earlier, the ICI can also be accounted for by including an extra user [13], [14] or be totally ignored if is large [2], [12]. To compare the BER performance, consider a DS-CDMA systems with. Since is large, ICI can be ignored. Fig. 6 plots the error performance of different spreading/despresding schemes computed with SIGA 1 for two DS-CDMA systems, one with the other with. Fig. 6 shows that for narrower-b system the proposed chip waveform (designed with ) is superior to the Rect. scheme, while it performs slightly worse than the three-term scheme. For wider b system, the proposed scheme significantly outperforms both the Rect. three-term schemes at high signal-to-noise region. The inferiority of the proposed scheme at low signal-to-noise region can be explained by the fact that the proposed scheme achieves a smaller value of SNR SNR 1 The summation in (17) is truncated at 650 so that considerable accuracy can be obtained. C. Chip Waveform Design With an Inb Power Constraint Although the optimal bwidth efficiency can be practically achieved, Figs. 3 4 show that a large portions of the powers of the spreading/despreading signals are filtered by the low-pass filters. For a system with smaller value of, the portion of the power being filtered becomes larger. This could result in a performance degradation when nonideal low-pass filters are used in practice. It also reduces the SNR value degrades the system performance at the low signal-to-noise region (i.e., when AWGN is more dominant than MAI). In order to minimize these effects, a constraint on the inb power of the spreading/despreading signals can be introduced. Let be the required fraction of the power of the spreading/despreading signals found inside the b of Hz. Then, the inb power constraint can be written exactly as in (6), with the only difference being that the right-h-side is instead of 1. With the inb power constraint, it is then necessary to also consider the unit-energy constraint of the chip waveform. Fig. 7 illustrates the impact of the additional inb power constraint on the bwidth efficiency of the proposed chip waveforms designed with. Two observations can be made: 1) the factor increases as increases (this is in contrast to Fig. 2) 2) a more stringent constraint on the inb power results in a larger reduction in bwidth efficiency of the chip waveform, especially for small values of. This provides a tradeoff between the MAI AWGN suppression capabilities of the proposed scheme. Also shown in Fig. 7 is the bwidth efficiency of the threeterm chip waveform with the inb power constraint (the circles, crosses, squares correspond to % %, %, respectively). More precisely, three coefficients (, ) are optimized to maximize the bwidth efficiency factor, subject to the inb power unit-energy constraints. It is interesting to note that the bwidth efficiency of this chip waveform approaches that of the proposed chip waveforms very closely when is small (less than about 1.4 for 90% 99% inb power requirements less than about 1.6 for 99.9% inb power requirements). But for larger, the bwidth efficiency of the three-term chip waveform quickly decreases is clearly inferior to that of the proposed chip waveforms. This is again due to the spectral nulls of the PSD of the three-term chip waveform. The chip waveforms designed for 90%, 99%, 99.9% power constraints with are shown in Fig. 5. As in the case of no power constraint, although the best chip waveforms are neither even nor odd around, limiting the chip waveforms to be even only reduces the bwidth efficiency factors slightly. For example, with %, the best arbitrary even chip waveforms achieve of , respectively. It has been observed that the more stringent the power constraint, the more ripples the PSD possess in the passb. The ripples generally increase the ICI level. For the proposed design that uses the same chip waveform for spreading despreading, it can be shown (see

7 NGUYEN: AN IMPROVED DESIGN OF CHIP WAVEFORMS FOR BAND-LIMITED DS-CDMA SYSTEMS 1385 Fig. 7. Bwidth efficiency factor F achieved by the proposed chip waveforms (designed with L =3with without power constraint) three-term chip waveforms (with power constraint). high signal-to-noise region. Finally, it should be noted that the performance of the proposed waveforms with an inb power constraint could be improved by increasing the value of in the design. Fig. 8. Performance comparison of the proposed scheme (designed with without power constraint) the optimum chip waveform. [8]) that the effect of ICI on is to add the ICI term into the integral in the denominator of (3). Numerical results based on SIGA show that, for the specific systems under consideration with, ICI has almost no influence on the error performance. Nevertheless, by adding an extra user to account for the ICI, Fig. 8 compares the error performance of the proposed scheme designed for, without with a power constraint. The tradeoff between AWGN suppression MAI cancellation can be clearly seen when changing the amount of inb power. Among the specific designs, the constraint of 90% inb power yields the best compromise since it improves the BER performance at low signal-to-noise region, while practically approach the optimal performance at V. CONCLUSION An effective simple design of time-limited chip waveforms for b-limited DS-CDMA systems has been introduced in this paper. The design provides time-limited chip waveforms based on series expansion in sinusoids, the b limitation of the systems is guaranteed with the low-pass filters. It has been demonstrated that the proposed chip waveforms can practically achieve the optimal bwidth efficiency. They are superior to all the spreading/despreading techniques previously proposed for the same CDMA system model, both in terms of MAI cancellation BER performance. The design of the chip waveforms with practical inb power constraint was also presented. ACKNOWLEDGMENT The author would like to thank the anonymous reviewers for their constructive comments that help in improving the presentation of this paper. REFERENCES [1] S. Verdú, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, [2] A. M. Monk, M. Davis, L. B. Milstein, C. W. Helstrom, A noisewhitening approach to multiple access noise rejection-part I: Theory background, IEEE J. Select. Areas Commun., vol. 12, pp , June [3] P. I. Dallas F.-N. Pavlidou, Innovative chip waveforms in microcellular DS/CDMA packet mobile radio, IEEE Trans. Commun., vol. 44, pp , Nov [4] M. A. Lolsi W. E. Stark, DS-CDMA chip waveform design for minimal interference under bwidth, phase, envelope constraints, IEEE Trans. Commun., vol. 47, pp , Nov

8 1386 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 5, SEPTEMBER 2004 [5] D. Slepian H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis, uncertainty I, Bell Syst. Tech. J., vol. 40, pp , [6] T. Luo, S. Pasupathy, E. S. Sousa, Interference control chip waveform design in multirate DS-CDMA communication systems, IEEE Trans. Wireless Commun., vol. 1, pp , Jan [7] J. S. Lehnert, Chip waveform selection in offset-quaternary direct-sequence spread-spectrum multiple-access communications, M.S. thesis, Univ. Illinois, Urbana, [8] A. J. Viterbi, Very low rate convolutional codes for maximum theoretical performance of spread-spectrum multiple-access channels, IEEE J. Select. Areas Commun., vol. 8, pp , May [9] V. M. DaSilva E. S. Sousa, Multicarrier orthogonal CDMA signals for quasisynchronous communications systems, IEEE J. Select. Areas Commun., vol. 12, pp , June [10] J. H. Cho J. S. Lehnert, An optimal signal design for b-limited asynchronous DS-CDMA communications, IEEE Trans. Inform. Theory, vol. 48, pp , May [11] W. Gao, J. H. Cho, J. S. Lehnert, Chip waveform design for DS/SSMA systems with aperiodic rom spreading sequences, IEEE Trans. Wireless Commun., vol. 1, pp , Jan [12] Y. Huang T. S. Ng, Capacity enhancement of b-limited DS-CDMA system using weighted despreading function, IEEE Trans. Commun., vol. 47, pp , Aug [13] J. E. Salt S. Kumar, Effects of filtering on the performance of QPSK MSK modulation in D-S spread spectrum systems using RAKE receivers, IEEE J. Select. Areas Commun., vol. 12, pp , May [14] L. Yu J. E. Salt, A hybrid spreading/despreading function with good SNR performance for b-limited DS-CDMA, IEEE J. Select. Areas Commun., vol. 8, pp , Oct [15] Y. Huang T. S. Ng, A DS-CDMA system using despreading sequences weighted by adjustable chip waveforms, IEEE Trans. Commun., vol. 47, pp , Dec [16] T. Coleman, M. A. Branch, A. Grace, Optimization Toolbox. Natick, MA: The Mathwork, Inc., [17] G. Zang C. Ling, Performance evaluation for b-limited DS-CDMA systems based on simplified improved Gaussian approximation, IEEE Trans. Commun., vol. 51, pp , July [18] J. M. Holtzman, A simple, accurate method to calcualte spread-spectrum multiple-access error probabilities, IEEE Trans. Commun., vol. 40, pp , Mar [19] Y. C. Yoon, A simple accurate method of probability of bit error analysis for asynchronous b-limited DS-CDMA systems, IEEE Trans. Commun., vol. 50, pp , Apr [20], An improved gaussian approximation for probability of bit error analysis of asynchronous b-limited DS-CDMA systems with BPSK spreading, IEEE Trans. Wireless Commun., vol. 1, pp , July [21] J. H. Cho, Y. K. Jeong, J. S. Lehnert, Average bit-error-rate performance of b-limited DS/SSMA communications, IEEE Trans. Commun., vol. 50, pp , July Ha H. Nguyen (M 01) received the B.Eng. degree from Hanoi University of Technology, Hanoi, Vietnam, the M.Eng. degree from the Asian Institute of Technology, Bangkok, Thail, the Ph.D. degree from the University of Manitoba, Winnipeg, Canada, in 1995, 1997, 2001, respectively. He has been with the Department of Electrical Engineering, University of Saskatchewan, Saskatoon, Canada, as an Assistant Professor since His research interests include digital communications, spread-spectrum systems, error-control coding.