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`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999
`
`Spreading Sequences for Multicarrier
`CDMA Systems
`
`Branislav M. Popovi´c
`
`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 fre-
`quency domain. It is shown that the time-domain crosscorrelation
`function between the spreading sequences is not a proper interfer-
`ence 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, multi-
`carrier 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, char-
`acterized 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 mul-
`tiplied 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 com-
`plex conjugate of the complex spreading waveform used in the
`transmitter and integrated over the data symbol (i.e., spreading
`
`Fig. 2. Despreader/demodulator in MC-CDMA receiver.
`
`, as is shown in Fig. 2. The despreader
`waveform) period
`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 single-
`carrier 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
`0090–6778/99$10.00 ª
`
`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, 1998. 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 1998.
`The author is with Ericsson Research, S-164 80 Stockholm, Sweden (e-
`mail: branislav.popovic@era-t.ericsson.se).
`Publisher Item Identifier S 0090-6778(99)05022-9.
`
`1999 IEEE
`
`ERIC-1008
`Ericsson v IV
`Page 1 of 9
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`POPOVI ´C: SPREADING SEQUENCES FOR MULTICARRIER CDMA SYSTEMS
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`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 mini-
`mized. 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 wave-
`form 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 se-
`lection 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 nu-
`merical results. Finally, Section V summarizes some conclu-
`sions.
`
`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 asyn-
`chronous 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
`
`can be represented
`
`of user
`
`as
`
`Re
`
`(1)
`
`th signaling interval,
`is the data symbol in the
`where
`is the pulse shaping
`is the data symbol duration,
`waveform,
`, is the spreading
`,
`sequence assigned to the
`is the number of carriers,
`th user,
`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
`[8]:
`
`satisfies the following inequality
`
`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 mini-
`mization 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 in-
`terference cannot be modeled by the crosscorrelation function
`between the spreading sequences. It will be clear after the
`following consideration.
`The received baseband signal
`, delayed
`from user
`by
`with respect to the receiver timing of user
`, will be despread and demodulated in the receiver of user
`
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`920
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`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999
`
`as an interference signal
`
`, which can be represented as
`
`Re
`
`where
`
`and asynchronously depends on the overall multiple access
`interference (MAI) which is the sum of all
`pairwise
`interferences. The overall system performance is usually eval-
`uated through the average bit error probability
`, which is,
`assuming BPSK signaling over an AWGN channel, given by
`[10] and [11]
`
`(4)
`
`(5)
`
`where
`
`(10)
`
`are the two consecutive data bits
`and
`and
`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
`then if
`,
`the
`having unit energy,
`interference
`reduces to
`
`Re
`
`where sign depends on the data bit transmitted to user
`observed signaling interval, and
`
`(6)
`
`in the
`
`(7)
`
`, by neglecting the high-
`In the case of
`frequency cross-products in (4), the interference
`can
`be approximated as
`
`Re
`
`where
`
`(8)
`
`(9)
`
`is the
`is the data bit (spreading waveform) energy,
`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)
`
`is related to the number of occurrences
`The function
`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.
`
`is the measure of the instantaneous
`The function
`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
`
`III. SPREADING SEQUENCE SELECTION FOR A
`MODIFIED MC-CDMA SYSTEM
`A modification of the MC-CDMA system, called multi-
`carrier 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.
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`POPOVI ´C: SPREADING SEQUENCES FOR MULTICARRIER CDMA SYSTEMS
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`Fig. 3. Spectrum allocation in MC-SS system.
`
`and
`In the case of two asynchronous users
`, the instantaneous
`using the same spreading sequence
`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)
`
`is the energy of the sequence. A Huffman sequence
`where
`is characterized by the aperiodic autocorrelation central-to-
`, which is very high
`sidelobe ratio CSR
`for all Huffman sequences and increases with the increase of
`sequence length.
`the exceptional aperiodic autocorrelation
`Unfortunately,
`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
`[12] is
`Huffman sequence
`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
`and
`is shown below. By finding the Fourier transform of
`applying the well-known autocorrelation theorem, given by
`
`(15)
`
`it follows that the Huffman sequence Fourier spectrum mag-
`is equal to
`nitude
`
`The crest factor of the multicarrier spread spectrum waveforms
`based on Huffman sequences satisfies, according to (2) and
`(16), the following inequality:
`
`(16)
`
`CF
`
`CSR
`
`(17)
`
`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 (impulse-
`like) ambiguity function or the ideal aperiodic autocorrelation
`function cannot exist, but a large class of multilevel (non-
`constant envelope) sequences having almost ideal aperiodic
`autocorrelation function does exist. Any Huffman sequence
`,
`of length
`has the aperiodic
`
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`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
`
`properties and rather low crest factors, so these sequences will
`also be numerically evaluated in Section IV.
`
`CF
`
`CSR
`
`(18)
`
`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 com-
`plementary 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 se-
`quences [16] possess both the excellent ambiguity function
`
`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 se-
`quences. 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.
`
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`POPOVI ´C: SPREADING SEQUENCES FOR MULTICARRIER CDMA SYSTEMS
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`Fig. 6. Dynamic range of MC-CDMA waveforms.
`
`Fig. 7. Average bit error probability Pe in a MC-CDMA system with K = 4 simultaneous users.
`
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`924
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`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 se-
`quences produce significantly better average bit error probabil-
`ity 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].
`is
`Namely, it is shown in [15] that the parameter SC
`smallest for the set of Zadoff–Chu sequences, and it is highest
`can be used
`for the set of Walsh sequences. Therefore, SC
`as the performance indicator of the MC-CDMA systems, in
`the same way as the maximum absolute periodic crosscorre-
`lation value is used for performance prediction in DS-CDMA
`systems [11].
`parameter has similar values for
`However, if the SC
`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 per-
`formance than the more uniform PDF’s, even if these others
`. This is an explanation, illustrated
`have the smaller SC
`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-
`
`in the
`SS systems. The average bit error probability
`simultaneous users
`asynchronous MC-SS system, with
`using BPSK signaling over an AWGN channel, is shown in
`Fig. 9 for four different sequence families: Zadoff–Chu, inte-
`ger 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
`, and are obtained by replacing the
`lengths
`1
`only zero element in original Legandre sequence with
`1. The different cyclic shifts of the two possible binary
`or
`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 19.45 dB. In
`order to illustrate the connection between the multiple access
`curve corresponding
`performances and AFCSR values, the
`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 19.16 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 complemen-
`tary 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
`values, but many of them also produce relatively
`very low
`low crest factors. Generally, it is always possible to find a
`
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`
`Fig. 9. Average bit error probability Pe 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 multiple-
`access 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 addi-
`tional 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 sys-
`tems should not necessarily have a constant envelope, as op-
`posed to the DS-CDMA systems where the multilevel spread-
`ing sequences directly increase the signal dynamic range and
`therefore are not recommended. The significance of this con-
`clusion is illustrated by showing that the multicarrier spread
`spectrum waveforms based on the multilevel Huffman se-
`quences 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. 107–114.
`[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. 1670–1674.
`[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. 914–917.
`
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`926
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`
`Branislav M. Popovi´c was born in Belgrade,
`Yugoslavia, on April 11, 1958. 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.
`
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