SEVERAL types of code division multiple access (CDMA)

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1 918 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999 Spreading Sequences for Multicarrier CDMA Systems Branislav M. Popović Abstract The paper contains an analysis of the basic criteria for the selection of spreading sequences for the multicarrier CDMA (MC-CDMA) systems with spectrum spreading in the frequency domain. It is shown that the time-domain crosscorrelation function between the spreading sequences is not a proper interference measure for the asynchronous MC-CDMA users. Therefore, the spectral correlation function is introduced and, together with the crest factor and the dynamic range of the corresponding multicarrier waveforms, is used for the evaluation of MC-CDMA sequences. Some well-known classes of sequences, such as Walsh, Gold, Orthogonal Gold, and Zadoff Chu sequences, as well as Legandre and Golay complementary sequences, are evaluated with respect to the aforementioned basic criteria. It is also shown that the crest factors of the multicarrier spread spectrum waveforms based on the multilevel Huffman sequences are very close to or even lower than the crest factor of a single sine wave. Index Terms Ambiguity function, multicarrier CDMA, multicarrier spread spectrum sequences, spectral correlation function. Fig. 1. Spreader in MC-CDMA transmitter. I. INTRODUCTION SEVERAL types of code division multiple access (CDMA) systems based on the combination of direct sequence (DS) CDMA and orthogonal frequency division (OFDM) multiple access techniques are proposed recently [1]. Among them, the multicarrier CDMA (MC-CDMA) transmission scheme, characterized by a spreading operation in the frequency domain, is one which represents a qualitatively new spread spectrum technique, which is dual to DS-CDMA [2], [3]. However, a not so recognized fact is that spreading in the frequency domain is originally proposed rather earlier, the very first time in [4] as far as we know. The same type of spreading waveforms is also discussed in [5] later on. In the MC-CDMA scheme, the same data symbol is transmitted in parallel (spread) over carriers, each multiplied by a different element of the spreading sequence assigned to user. It is shown in Fig. 1. In the despreader, the input signal is multiplied by the complex conjugate of the complex spreading waveform used in the transmitter and integrated over the data symbol (i.e., spreading Paper approved by R. Kohno, the Editor for Spread Spectrum Theory and Applications of the IEEE Communications Society. Manuscript received July 10, 1997; revised October 5, This paper was presented in part at the IEE Colloquium on CDMA Techniques and Applications for Third Generation Mobile Systems, The Strand Palace, London, May 1997 and at the IEEE 5th International Symposium on Spread Spectrum Techniques and Applications, Sun City, South Africa, September The author is with Ericsson Research, S Stockholm, Sweden ( branislav.popovic@era-t.ericsson.se). Publisher Item Identifier S (99) Fig. 2. Despreader/demodulator in MC-CDMA receiver. waveform) period, as is shown in Fig. 2. The despreader is usually implemented by inverse discrete Fourier transform, whose output samples are multiplied by the complex conjugate of the corresponding spreading sequence elements and then summed. In general, the multicarrier transmission schemes have an increased peak-to-average power ratio (PAPR), as well as an increased signal dynamic range compared with the singlecarrier schemes. As the power amplifier has a limited peak output power, an increased PAPR reflects in a reduced power efficiency of the power amplifier, meaning that the average radiated power is reduced in order to avoid the nonlinear distortion of transmitted signal. Also, an increased signal /99$ IEEE

2 POPOVIĆ: SPREADING SEQUENCES FOR MULTICARRIER CDMA SYSTEMS 919 dynamic range reflects in an increased required range of linearity of power amplifier. These two drawbacks can be mitigated in the OFDM systems by a careful choice of carrier phases. The PAPR minimization consists of the minimization of the signal maximum absolute value, while for the dynamic range minimization the difference between the minimum and maximum values of complex signal envelope has to be minimized. The PAPR minimization, which has been the goal for all previously proposed phasing schemes, does not necessarily lead to the minimization of signal dynamic range, as is pointed out in [3]. The MC-CDMA systems offer, however, an additional degree of freedom for the PAPR and the dynamic range minimization. Namely, the phase optimization approach can be generalized so that also the carrier envelopes can be manipulated to produce multicarrier spread spectrum waveform with reduced PAPR or dynamic range. The reason lies in the fact that all carriers convey the same information stream. (In contrast to the OFDM systems where the carriers convey different information streams and therefore should have equally shared energy.) Consequently, the spreading sequences for MC-CDMA systems should not necessarily have a constant envelope, as opposed to the DS-CDMA systems where the multilevel spreading sequences directly increase the signal dynamic range and therefore are not recommended. The significance of this conclusion will be illustrated in Section III by showing that the multicarrier spread spectrum waveforms based on multilevel Huffman sequences can have a lower PAPR than a single sine wave. It can be shown that the single user synchronization in an MC-CDMA system does not depend on the autocorrelation or other properties of the spreading sequence [6], which is an advantage compared with conventional CDMA systems. However, the mutual interference between the asynchronous users in the MC-CDMA systems does depend on the properties of spreading sequences, but the crosscorrelation function (even or odd) between the discrete sequences is not a proper measure of the mutual interference, as it is in the conventional DS- CDMA. This will be discussed in the next section. The paper is organized as follows. In Section II, the selection criteria for the MC-CDMA systems are defined. In Section III, the spreading sequence selection for a modified MC-CDMA system, so-called multicarrier spread spectrum (MC-SS) system, is discussed. Section IV presents some numerical results. Finally, Section V summarizes some conclusions. II. SELECTION CRITERIA FOR MC-CDMA SEQUENCES There are three basic properties of the multicarrier spread spectrum waveforms which are of interest for the comparison between the different classes of sequences for the asynchronous MC-CDMA systems: a) the peak-to-average power ratio, b) the dynamic range of complex signal envelope, and c) the mutual interference. The PAPR parameter of a signal is defined as the ratio of peak to average signal power. An alternative measure of the signal envelope compactness, which will be used further on, is so-called crest factor [7], [8], defined as the ratio of signal envelope peak to rms value, i.e., CF PAPR. The transmitted signal of user can be represented as Re where is the data symbol in the th signaling interval, is the data symbol duration, is the pulse shaping waveform,,, is the spreading sequence assigned to the th user, is the number of carriers, and is the frequency spacing between the adjacent carriers. For simplicity, only BPSK signaling is considered, with the rectangular pulse shape of duration and of unit energy. The crest factor of satisfies the following inequality [8]: (1) CF (2) where is the Fourier spectrum of the spreading sequence, and is the energy of the same sequence. The dynamic range DR is the ratio of maximum to minimum value of complex signal envelope. The dynamic range can also be defined in terms of Fourier spectrum magnitude of the spreading sequence, i.e., DR (3) If the spreading sequence has a constant envelope, the minimization of the crest factor reduces to the problem of finding carrier initial phases which minimize the signal maximum absolute value. Until now, two major analytical constructions for the initial phases of a multitone signal have been proposed. The first one is basically a chirp-like phase construction [7]. The other construction is based on pairs of binary or polyphase complementary sequences [8]. Naturally, these sequences are candidates for the application in asynchronous MC-CDMA systems. The interference between perfectly mutually synchronized users in the MC-CDMA system depends on the zero delay crosscorrelation between spreading codes. This situation exists in a down-link mobile radio channel, in which case the best performance can be expected when the set of orthogonal sequences is employed for spreading. When the users are asynchronous, or only partially mutually synchronized, as is the case in the up-link mobile radio channel, the mutual interference cannot be modeled by the crosscorrelation function between the spreading sequences. It will be clear after the following consideration. The received baseband signal from user, delayed by with respect to the receiver timing of user, will be despread and demodulated in the receiver of user

3 920 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999 as an interference signal Re, which can be represented as and asynchronously depends on the overall multiple access interference (MAI) which is the sum of all pairwise interferences. The overall system performance is usually evaluated through the average bit error probability, which is, assuming BPSK signaling over an AWGN channel, given by [10] and [11] where (4) where (10) (5) and and are the two consecutive data bits transmitted by user during the observed time interval in the receiver of user. The complex conjugation is denoted by *. Assuming that is the rectangular pulse of duration having unit energy, then if, the interference reduces to Re (6) where sign depends on the data bit transmitted to user observed signaling interval, and in the In the case of, by neglecting the highfrequency cross-products in (4), the interference can be approximated as where (7) Re (8) The function is the measure of the instantaneous mutual interference between different users in the MC-CDMA system. This function will be called the spectral correlation function [15]. It can be calculated as the Fourier spectrum of the complex sequence,. For the special case when the users are perfectly synchronized, the spectral correlation function reduces to the zero-shift crosscorrelation between the corresponding spreading sequences. It should be noted that a function similar to the spectral correlation function is obtained in [9] from the continuous-time correlation function of periodic bandlimited signals. However, only the synchronous correlation case is further discussed in [9]. According to (6), the spectral correlation function is analogous to the even crosscorrelation function in DS-CDMA systems. The odd spectral correlation function given by (9) is analogous to the odd crosscorrelation function in DS-CDMA systems, i.e., it holds. A single user receiver performance in the multiple access system with simultaneous users transmitting continuously (9) is the data bit (spreading waveform) energy, is the additive white Gaussian noise (one-sided) power spectral density, while is the MAI probability density function (PDF). The function is obtained by -fold convolution of pairwise interference PDF, i.e., (11) The function is related to the number of occurrences of each possible value of obtained for all pairs of sequences within a given set of spreading sequences. For the practical evaluation of, it is necessary to limit the number of possible spectral correlation values, which is equivalent to the quantization of the pairwise interference function. The continuous delay variable also has to be quantized, so some fast Fourier transform algorithm can be used for the calculation of (7). In Section IV, the function is calculated for a few different classes of spreading sequences, assuming 64 quantization values within the range SC SC, where SC and SC are the minimum and the maximum spectral correlation magnitudes found for a given set of sequences. The delay variable is quantized into NFFT values. III. SPREADING SEQUENCE SELECTION FOR A MODIFIED MC-CDMA SYSTEM A modification of the MC-CDMA system, called multicarrier spread spectrum (MC-SS) system, has been recently proposed [3] to achieve the reduced signal dynamic range for all users in the system. In such a system, the same spreading sequence is assigned to all users, but each user has a different carrier frequency offset. It is shown in Fig. 3. All the users will have the same, reduced signal dynamic range if only a single appropriate spreading sequence is found. The constant envelope complex spreading sequences producing the MC-SS signals with a dynamic range of about 6 db (typically the dynamic range of OQPSK signaling with raised cosine filtering) have been found by using a specific numerical method [3]. It is claimed in [3] that the mutual interference between the different users depends only on the aperiodic autocorrelation function sidelobes of a common spreading sequence. However, this is true only if the users are synchronized.

4 POPOVIĆ: SPREADING SEQUENCES FOR MULTICARRIER CDMA SYSTEMS 921 Fig. 3. Spectrum allocation in MC-SS system. In the case of two asynchronous users and using the same spreading sequence, the instantaneous interference signal after despreader in the receiver of user can be represented as [15] Fig. 4. Ambiguity function of a Huffman sequence, N =7. autocorrelation function given by [12] (14) elsewhere (12) The function is equivalent (after the trivial change of variables) to the ambiguity function of sequence, well known from the radar literature. For the special case of perfectly synchronized users, the function reduces to the aperiodic autocorrelation function of a common spreading sequence. A single user receiver performance in the asynchronous MC-SS system with simultaneous users can be evaluated by using the methodology described in Section II. The pairwise interference PDF in an MC-SS system is strongly related to the properties of the ambiguity function of the spreading sequence. The ambiguity function central-to-sidelobe ratio (AFCSR), defined as AFCSR (13) turns out to be an excellent indicator of the MC-SS multiple access performance, as will be shown in Section IV. A spreading sequence having either the ideal (impulselike) ambiguity function or the ideal aperiodic autocorrelation function cannot exist, but a large class of multilevel (nonconstant envelope) sequences having almost ideal aperiodic autocorrelation function does exist. Any Huffman sequence, of length has the aperiodic where is the energy of the sequence. A Huffman sequence is characterized by the aperiodic autocorrelation central-tosidelobe ratio CSR, which is very high for all Huffman sequences and increases with the increase of sequence length. Unfortunately, the exceptional aperiodic autocorrelation function of Huffman sequences does not guarantee the high value of the ambiguity function central-to-sidelobe ratio AFCSR. As an example, the ambiguity function of the integer Huffman sequence [12] is shown in Fig. 4. However, an almost ideal aperiodic autocorrelation function of Huffman sequence provides an extremely low crest factor of the corresponding multicarrier spread spectrum waveform, as is shown below. By finding the Fourier transform of and applying the well-known autocorrelation theorem, given by (15) it follows that the Huffman sequence Fourier spectrum magnitude is equal to (16) The crest factor of the multicarrier spread spectrum waveforms based on Huffman sequences satisfies, according to (2) and (16), the following inequality: CF CSR (17)

5 922 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999 Fig. 5. Crest factors of MC-CDMA waveforms. The crest factor of complex multicarrier spread spectrum waveforms based on Huffman sequences is equal to CF (18) CSR The dynamic range of multicarrier spread spectrum waveform obtained from a Huffman sequence is, according to (3) and (16), equal to DR CSR CSR (19) For example, the integer Huffman sequence has CSR, and the corresponding multicarrier spread spectrum waveform has CF (2.98 db), which is lower than for a single sine wave (3.01 db). The corresponding dynamic range is DR db. Another family of spreading sequences which might be attractive for the MC-SS systems consists of the Golay complementary sequences. Any Golay complementary sequence produces an MC-SS waveform with the crest factor always less than or equal to 6 db [8]. The AFCSR of a Golay sequence is rather higher than for a Huffman sequence of the same or similar length, so it is to be expected that the multiple access performances of an MC-SS system are better with Golay sequences than with Huffman sequences. This will be verified in Section IV. Finally, cyclically shifted versions of binary Legandre sequences [16] possess both the excellent ambiguity function properties and rather low crest factors, so these sequences will also be numerically evaluated in Section IV. IV. NUMERICAL RESULTS The four families of sequences, most frequently evaluated in conventional DS-CDMA systems, are evaluated with respect to the crest factor, the dynamic range, and the average bit error probability which they produce in the MC-CDMA system. Those classes are: Walsh, Gold, Orthogonal Gold [13], and Zadoff Chu sequences [14]. The chirp-like phase constructions, mentioned in Section II and used for the crest factor minimization of the multitone signals, are closely related to the Zadoff Chu polyphase sequences. If the sequence length is a prime number, the set of Zadoff Chu sequences have the best possible periodic crosscorrelation function, having constant magnitude equal to. It is shown in [11] that they provide the lowest average bit-error probability in DS-CDMA system compared with other deterministic spreading sequences. The corresponding crest factors are shown in Fig. 5. It can be seen that the set of Zadoff Chu sequences produces the best crest factors, while the set of Walsh sequences produces the worst. The dynamic range is shown in Fig. 6, only for the sets of Gold and Zadoff Chu sequences, because the other two sets produce the MC-CDMA waveforms having the envelopes fluctuating down to the zero value. It can be concluded that the Zadoff Chu sequences on average produce the lower dynamic range. The average bit error probability in the asynchronous MC-CDMA system, with simultaneous users using BPSK signaling over an AWGN channel, is shown in Fig. 7 for different sequence families.

6 POPOVIĆ: SPREADING SEQUENCES FOR MULTICARRIER CDMA SYSTEMS 923 Fig. 6. Dynamic range of MC-CDMA waveforms. Fig. 7. Average bit error probability P e in a MC-CDMA system with K =4simultaneous users.

7 924 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999 Fig. 8. Pairwise interference PDF. It can be seen that the Orthogonal Gold and Zadoff Chu sequences produce significantly better average bit error probability than Walsh and Gold sequences. These results are basically in agreement with the prediction based on the (normalized by ) maximum spectral correlation magnitude (SC ) [15]. Namely, it is shown in [15] that the parameter SC is smallest for the set of Zadoff Chu sequences, and it is highest for the set of Walsh sequences. Therefore, SC can be used as the performance indicator of the MC-CDMA systems, in the same way as the maximum absolute periodic crosscorrelation value is used for performance prediction in DS-CDMA systems [11]. However, if the SC parameter has similar values for the different sequence families, the shapes of corresponding pairwise interference probability density functions have the determinate influence on the system performance. As it is remarked in [10], the PDF shapes approaching a triangular, or generally, an impulse-like shape will provide better performance than the more uniform PDF s, even if these others have the smaller SC. This is an explanation, illustrated by Fig. 8, why the Orthogonal Gold sequences produce lower multiple access interference in MC-CDMA systems than the Zadoff Chu sequences of the similar length, although the Zadoff Chu sequences have some lower SC. The performance results shown in Fig. 7, obtained for Gold and Zadoff Chu sequences when applied in a MC-CDMA system, can be directly compared with the corresponding results obtained for a DS-CDMA system [11, Fig. 6]. It can be seen that the Gold sequences provide practically the same performances in both systems, while the Zadoff Chu sequences have better performances in DS-CDMA systems. Finally, it would be interesting to compare the multiple access performances of asynchronous MC-CDMA and MC- SS systems. The average bit error probability in the asynchronous MC-SS system, with simultaneous users using BPSK signaling over an AWGN channel, is shown in Fig. 9 for four different sequence families: Zadoff Chu, integer Huffman, binary Legandre [16], and Golay complementary sequence [17]. The binary Legandre sequences used for the evaluation, having the same two-level periodic autocorrelation as the original, ternary Legandre sequences, exist for prime lengths, and are obtained by replacing the only zero element in original Legandre sequence with 1 or 1. The different cyclic shifts of the two possible binary Legandre sequences of length 31 are searched in order to obtain the maximum AFCSR. The maximum obtained AFCSR for the binary Legandre sequences of length 31 is db. In order to illustrate the connection between the multiple access performances and AFCSR values, the curve corresponding to another cyclic version of Legandre sequence with a lower AFCSR is also shown in Fig. 9. Similarly, all possible Golay complementary sequences of length 32 are searched in order to find those with the maximum AFCSR values. The maximum obtained AFCSR for the Golay complementary sequences of length 32 is db. The average bit error probability in an MC-SS system is at moderate to high signal-to-noise ratios inversely proportional to the AFCSR of the spreading sequence: the lowest values correspond to the spreading sequences with the highest AFCSR s, such as Legandre and Golay sequences. It turns out that the MC-SS system using Legandre or Golay complementary sequence outperforms the best corresponding MC-CDMA system (using the set of Orthogonal Gold sequences). The cyclic versions of binary Legandre sequences provide not only very low values, but many of them also produce relatively low crest factors. Generally, it is always possible to find a

8 POPOVIĆ: SPREADING SEQUENCES FOR MULTICARRIER CDMA SYSTEMS 925 Fig. 9. Average bit error probability P e in an MC-SS system with K =4 simultaneous users. cyclic shift of the binary Legandre sequence which produces the crest factor less than 5 db. The Zadoff Chu sequences have ridge-type ambiguity function, which consequently has very low AFCSR, and which is the reason for the worst MC-SS multiple access performances, as shown in Fig. 9. V. CONCLUSIONS The even and odd spectral correlation functions, analogous to the corresponding functions in DS-CDMA systems, are introduced as the basic measures of the mutual interference between the pairs of users in the MC-CDMA system. Based on these functions, the pairwise interference probability density function is determined for the MC-CDMA signals obtained from four different families of spreading sequences, and the corresponding average bit error probabilities for the multipleaccess BPSK signaling over AWGN channel are calculated. The four families of sequences Walsh, Gold, Orthogonal Gold, and Zadoff Chu sequences most frequently evaluated in conventional DS-CDMA systems, are evaluated with respect to the crest factor, the dynamic range, and the average bit error probability. Taking into account all three performance measures, the Zadoff Chu sequences seem to be the optimum choice for the spreading sequences in the asynchronous MC- CDMA systems. The average bit error probability in the asynchronous MC-SS system, having a single spreading sequence for all users in the system, is evaluated for four different sequence families: Zadoff Chu, integer Huffman, binary Legandre, and Golay complementary sequence. It is found that is at moderate to high signal-to-noise ratios inversely proportional to the ambiguity function central-to-sidelobe ratio AFCSR of the spreading sequence: the lowest values correspond to the spreading sequences with the highest AFCSR s, such as Legandre and Golay sequences. It turns out that the MC- SS system using Legandre or Golay complementary sequence outperforms the best corresponding MC-CDMA system (using the set of Orthogonal Gold sequences) It is also shown that the MC-CDMA systems offer an additional degree of freedom for the crest factor and the dynamic range minimization, in a way that also the carrier envelopes can be manipulated in addition to the carrier initial phases to obtain the desired multicarrier spread spectrum waveform. Consequently, the spreading sequences for MC-CDMA systems should not necessarily have a constant envelope, as opposed to the DS-CDMA systems where the multilevel spreading sequences directly increase the signal dynamic range and therefore are not recommended. The significance of this conclusion is illustrated by showing that the multicarrier spread spectrum waveforms based on the multilevel Huffman sequences can have a lower crest factor than a single sine wave. REFERENCES [1] R. Prasad and S. Hara, An overview of multi-carrier CDMA, in Proc. 4th Int. Symp. Spread Spectrum Techniques and Applications (ISSSTA 96), Mainz, Sept. 1996, pp [2] G. Fettweis, A. S. Bahai, and K. Anvari, On multi-carrier code division multiple access (MC-CDMA) modem design, in Proc. VTC 94, Stockholm, June 1994, pp [3] V. Aue and G. P. Fettweis, Multi-carrier spread spectrum modulation with reduced dynamic range, in Proc. VTC 96, Atlanta, Apr./May 1996, pp

9 926 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999 [4] A. Baier, P. W. Baier, and M. Pandit, Spread-spectrum waveforms simplifying transform domain signal processing, Proc. Inst. Elect. Eng., vol. 132, no. 7, pt. F, pp , Dec [5] P. J. White and M. Ahtee, A new class of spreading waveforms for CDMA, in Proc. 2nd Int. Symp. Spread Spectrum Techniques and Applications (ISSSTA 92), Yokohama, Nov./Dec. 1992, pp [6] J. H. Yooh and V. K. Wei, On synchronizing and detecting multi-carrier CDMA signals, in Proc. ICUPC 95, Tokyo, Nov. 1995, pp [7] E. V. D. Ouderaa, J. Schoukens, and J. Renneboog, Peak factor minimization of input and output signals of linear systems, IEEE Trans. Instrum. Meas., vol. 37, pp , June [8] B. M. Popović, Synthesis of power efficient multitone signals with flat amplitude spectrum, IEEE Trans. Commun., vol. 39, pp , July [9] T. P. McGree and G. R. Cooper, Upper bounds and construction techniques for signal sets with constrained synchronous correlation and specified time-bandwidth product, IEEE Trans. Inform. Theory, vol. IT-30, pp , Mar [10] D. Rogers and B. Davis, Code properties: Influences on the performance of a quaternary CDMA system, in Proc. 3rd Int. Symp. Spread Spectrum Techniques and Applications (ISSSTA 94), Oulu, July 1994, pp [11] A. W. Lam and F. M. Ozluturk, Performance bounds for DS/SSMA communications with complex signature sequences, IEEE Trans. Commun., vol. 40, pp , Oct [12] J. N. Hunt and M. H. Ackroyd, Some integer Huffman sequences, IEEE Trans. Inform. Theory, vol. IT-26, pp , Jan [13] B. M. Popović, Efficient despreaders for multicode CDMA systems, in Proc. ICUPC 97, San Diego, Oct , 1997, pp [14], Generalized chirp-like polyphase sequences with optimum correlation properties, IEEE Trans. Inform. Theory, vol. 38, pp , July [15], Spreading sequences for multi-carrier CDMA systems, in IEE Colloquium CDMA Techniques and Applications for Third Generation Mobile Systems, London, May 19, 1997, pp. 8/1 8/6. [16] S. R. Gottesman, P. G. Grieve, and S. Golomb, A class of pseudonoiselike pulse compression codes, IEEE Trans. Aerosp. Electron. Syst., vol. 28, pp , Apr [17] S. Z. Budisin, New complementary pairs of sequences, Electron. Lett., vol. 26, no. 13, pp , June 21, Branislav M. Popović was born in Belgrade, Yugoslavia, on April 11, He received the Dipl.Ing., M.Sc., and Ph.D. degrees in electrical engineering from the University of Belgrade, Belgrade, Yugoslavia, in 1983, 1989, and 1993, respectively. From 1984 to 1994, he was with the Institute of Microwave Techniques and Electronics (the former Institute of Applied Physics), Belgrade, working in the field of digital signal processing for pulse compression radars, spread-spectrum radio communications, and systems for the reconnaissance and jamming of radars and frequency-hopping radios. From March 1994 to December 1995, he was with the R&D Department of Ericsson Radio Access AB, Stockholm, Sweden, where he was engaged in the design and implementation of the base station signal processing algorithms for the analog cellular systems. In December 1995, he joined the Radio Core Unit Research at Ericsson Radio Systems AB (presently Ericsson Research), Stockholm, to work on new radio access techniques and signal processing algorithms for the CDMA cellular systems. There he was also involved in the standardization of WCDMA air interface for the third generation cellular systems. He is the inventor or coinventor of ten pending patents related to CDMA cellular systems. He has published more than 30 journal and conference papers.