jMulti-Carrier Spread-Spectrum and Related Topics!
`
`Spreading Sequences for Uplink and Downlink
`MC-CDMA Systems: PAPR and MAI Minimization
`
`STEPHANE NOBILET, JEAN-FRANi;OIS HELARD
`LCST/INSA, 20 Av. des Buttes de Coesmes, 35043 Rennes Cedex, France
`{ stephane.nobi/et, jeanjrancois.he/ard}@insa-rennes.fr
`
`DAVID MOTTIER
`Mitsubishi Electric ITE, 80 Av. des Buttes de Coesmes, 35700 Rennes, France
`mottier@rcl.ite.mee.com
`
`Abstract. This paper deals with spreading sequences selection for downlink and uplink Multi-Carner Code Division
`Multiple Access (MC-CDMA) systems with the aim of minimizing the dynamic range of the transmitted mulcicanier
`signal envelope and the multiple access interference. The crest factor of orthogonal and non-orthogonal sequences are
`compared analytically and by simulation for downlink and uplink phase shift keying MC-CDMA transmissions. Then,
`in order to minimize the multiple access interference produced by frequency selective channels, an optimized spreading
`sequence allocation procedure is presented. Finally. a selection of the spreading codes which jointly reduces the multiple
`access interference and the crest factor is proposed for downlink MC-CDMA systems.
`
`1
`
`INTRODUCTION
`
`In recent years, Multi-Carrier Code Division Multiple
`Access (MC-CDMA) has been receiving widespread inter(cid:173)
`ests for wireless broadband multimedia applications. Com(cid:173)
`bining Orthogonal Frequency Division Multiplex (OFDM)
`modulation and CDMA, this scheme benefits from the
`main advantages of both techniques [I]: high spectral ef(cid:173)
`ficiency, multiple access capability, robustness in case of
`frequency selective channels, high flexibility, narrow-band
`interference rejection, simple one-tap equalization, etc. In
`general, to reduce the Multiple Access Interference (MAI)
`in a synchronous system like the downlink mobile radio
`communication channel, the spreading sequences or codes,
`are chosen orthogonal. Besides, spreading sequences have
`to be selected in order to limit the dynamic range of the
`OFDM transmitted signal envelope, and therefore to miti(cid:173)
`gate the nonlinear distortions introduced by the high power
`amplifier.
`This paper deals with the selection of spreading se(cid:173)
`quences for the downlink and uplink of high rate cellular
`networks with the aim of jointly minimizing the MAI and
`the nonlinear distortions. The peak-to-average power ratio
`and the crest factor are used for the evaluation of the dy(cid:173)
`namic range of the transmitted Phase Shift Keying (PSK)
`modulated multicarrier signal envelope for various orthog(cid:173)
`onal and non-orthogonal spreading codes. Furthermore, in
`
`order to minimize the MAI, an optimized allocation pro(cid:173)
`cedure of the spreading sequences is described. Finally, a
`selection of the spreading codes, which jointly reduces the
`MAI and the non-linear distortions, is proposed.
`The paper is organized as follows. In Section 2, the
`considered MC-CDMA system is briefly described. Sec(cid:173)
`tion 3 presents the studied spreading sequences and the
`different selection criteria. In Section 4, crest factor ana(cid:173)
`lytical results for uplink and downlink contexts are devel(cid:173)
`oped. Section 5 presents simulation results on crest factors
`and performance evaluation in terms of bit error rate for a
`simulation environment similar to the ETSI BRAN HIPER(cid:173)
`LAN/2 physical layer. Conclusions are drawn in Section 6.
`
`2 SYSTEM DESCRIPTION
`
`In a MC-CDMA transmitter, as represented on Fig(cid:173)
`ure I, the data symbol D1(t), assigned to user j, is mul(cid:173)
`tiplied in the frequency domain by the spreading code
`SCj = [c1,j.c2.j,··· ,ck,f•··· ,cL,il· In this figure, the
`length L of the spreading code is equal to the num(cid:173)
`ber Ne of subcarriers, but this study is not limited to
`this particular case. However, the different results pre(cid:173)
`sented in this paper are given for L
`Ne. Af(cid:173)
`ter the multicarrier modulation, easily carried out by
`IFFf operation and the insertion of a guard interval, the
`
`Vol. 13, No. 5. Sep1ember-October 2002
`
`465
`
`ERIC-1006
`Ericsson v IV
`Page 1 of 10
`
`

`

`S. Nobilet. J-F. Helard, D. Mottier
`
`signal S;(t) = ~( L~~1 Dj(t)ck,je 2i>rf•') is transmitted
`
`through a high power amplifier which has a limited peak
`output power [2].
`
`Non Linear
`power amplifier
`
`Figure I: MC-CDMA transmirrer for user J.
`
`In this study, we focus on the realistic case of frequency
`correlated Rayleigh fading channels. We assume that in(cid:173)
`ter symbol interference is avoided thanks to the insertion
`of a guard interval, which is longer than the delay spread
`of the channel. Moreover, frequency non-selective fading
`per subcarrier and time invariance during one OFDM sym(cid:173)
`bol are supposed. Besides, as we consider single-user de(cid:173)
`tection techniques, the complex channel response and the
`equalization coefficient for the subcarrier k of user j are
`respectively denoted hk,J and gk,J·
`
`Usually, for downlink transmissions, using orthogonal
`codes such as Walsh-Hadamard spreading sequences guar(cid:173)
`antees the absence of MAI in a Gaussian channel. How(cid:173)
`ever, in frequency selective fading channels, all the subcar(cid:173)
`riers of the MC-CDMA signal are received with different
`amplitude levels and different phase shifts, which gener(cid:173)
`ates MAI. To combat this interference, one may use vari(cid:173)
`ous Single-user Detection (SD), linear or nonlinear Multi(cid:173)
`user Detection (MD) techniques [3]. For downlink trans(cid:173)
`missions and for a given user terminal, the desired signal
`and the disturbing signals are affected by the same channel
`distortions. Then, it is easy, for example with the well(cid:173)
`known Zero Forcing SD, to benefit from the orthogonality
`between the spreading codes by multiplying the received
`signals by coefficients equal to the inverse of the channel
`frequency response.
`
`By contrast,
`the Nu
`transrruss1ons,
`for uplink
`MC-CDMA signals received at the base station from the
`Nu active users suffer from different degradations intro(cid:173)
`duced by the N ... independent channels. Consequently, us(cid:173)
`ing orthogonal codes for uplink transmissions is no longer
`mandatory and non-orthogonal codes may be considered.
`
`466
`
`3 SPREADING SEQUENCES AND SELEC(cid:173)
`TION CRITERIA
`
`Spreading sequences have to be selected in order to
`minimize on the one hand the Peak-to-Average Power Ra(cid:173)
`tio (PAPR) or the Crest Factor (CF) of the transmitted
`multi-carrier signal envelope and on the other hand the
`MAI in the receiver.
`
`3.1 SPREADING SEQUENCES
`
`Taking into account the uplink and downlink specifici(cid:173)
`ties, two kinds of sequences, orthogonal or non-orthogonal ,
`are investigated.
`
`3.1.1 Orthogonal sequences
`
`•Walsh-Hadamard sequences
`An important set of orthogonal codes is the Walsh(cid:173)
`Hadamard set. Walsh functions are generated using a
`Hadamard matrix, starting with H 1 = (+1]. The (L x L)
`Hadamard matrix is recursively built by :
`
`HL = [ HL/2
`HL/2
`
`(1)
`
`Then, the Walsh-Hadamard sequences are given by the
`rows or the columns of the matrix H L. These sequences are
`generally proposed for MC-CDMA synchronous systems
`due to their implementation facilities as depicted in [4].
`
`•Complementary Golay sequences
`Let (A;, 1 ~ i < p) be a set of finite sequences (±1)
`of length L and let iP A, A, ( k) denote the k-th element of
`the autocorrelation function of the sequence A;. A set of
`sequences is a complementary set if and only if (5]:
`
`p E l/•A,A, (k)::: 0,
`
`i : l
`
`(2)
`
`Golay sequences, both complementary and orthogonal.
`are recursively defined by the rows of the matrix CG L
`starting with CG2 (6]:
`
`CG2 = [ 1
`1
`1 -1
`
`] = [ A2 B2 ]
`
`(3)
`
`and more generally
`CGL = ( AL BL 1
`
`AL/2 BL/2
`
`with, ! At~ [ A,,, BL/2 ]
`
`BL= [ Al/2
`-A.L/2
`
`-BL/2 ]
`
`Bc,12
`
`(4)
`
`(5)
`
`ETT
`
`ERIC-1006 / Page 2 of 10
`
`

`

`Spreading Sequences for Uplink and Downlink MC-CDMA Systems: PAPR and MAI Minimization
`
`where matrix AL et BL are of size L x L/2.
`For example, if L = 4:
`
`+l
`CG = +l
`+l
`[
`+l
`
`4
`
`+l +l
`-1 +1
`+l -1
`-1 -1
`
`-1 l +l
`
`.
`
`+1
`-1
`
`L + 2 Gold sequences of length L are available.
`Gold codes have correlation functions with three values
`{-1, -t(n), t(n) - 2}, where:
`
`(6)
`
`t(n) = {
`
`2 !!fl + 1
`
`for n odd
`
`2 ~ + 1
`
`for n even
`
`( 10)
`
`Moreover, Golay sequences are also complementary in
`two-two time (if j), i.e.:
`
`2L
`1/iA,A;(k) + ¢AjAj(k) = O
`{
`
`fork= 0
`
`fork# 0
`
`(7)
`
`• Orthogonal Gold sequences
`The orthogonal Gold sequences [7][8] are developed
`from a set of original Gold sequences, which contain ele(cid:173)
`ments of the alphabet { 1, -1}, by appending an additional
`"l" to the end of each sequence. The set OG(.) of L se(cid:173)
`quences of length L = 211 (with n mod 4 :f:. 0) of orthogo(cid:173)
`nal Gold codes is given by:
`
`OG(A, B) = (U, Vo, Vi, ... , VL-2)
`
`(8)
`
`with
`
`U =(A, 1)
`
`and where
`• A = (ao, ... , aL-2) and B = (bo, ... , bL-2) are a
`preferred pair of m-sequences of length L - 1,
`
`• TJ B is the sequence B after j-chip cyclic shift,
`
`• and $ is the modulo 2 addition operator.
`
`3.1.2 Non-orthogonal sequences
`
`• Gold sequences
`This family of Gold codes G(.) is constructed from a
`preferred pair of m-sequences of length L = 2" - 1 (with
`n mod 4 "f; 0) by adding modulo 2 these two m-sequences
`[9]:
`
`G(A, B) =(A, B, Vo, Vi, ... , VL-il
`
`(9)
`
`with
`
`and where A= (a 0 , ... , aL-d and B = (bo, ... , bL-d
`are a preferred pair of m-sequences of length L.
`
`• 'Zadoff-Chu codes
`The Zadoff-Chu codes are the special case of the gen(cid:173)
`eralized Chirp-Like polyphase sequences having optimum
`correlation properties. Indeed, Zadoff-Chu sequences of
`length L offer on the one hand an ideal periodic autocor(cid:173)
`relation, and on the other hand a constant magnitude (./I)
`periodic cross-correlation. They are defined by:
`
`ei1ff-(~+qk)
`
`for Leven
`
`(l l)
`
`Zcr(k) =
`
`{
`
`eJ2r( ~<\+I) +qk)
`for L odd
`where q is an)' integer, k = 0, 1, ... , L - 1 and r is the
`code index, prime with L [10]. Consequently, if L is a
`prime number, the set of Zadoff-Chu is composed of L - 1
`sequences.
`
`3.2 PEAK-TO-AVERAGE POWER RATIO AND CREST
`FACTOR
`
`The MC-CDMA technique offers many advantages but
`presents also a significant drawback, which is due to the
`multicarrier feature. Indeed, the MC-CDMA signal con(cid:173)
`sists of the sum of several subcarriers, which may result in
`a large dynamic transmitted signal. The envelope variation
`of a multicarrier signal can be estimated by the PAPR or
`the CF which are for a signal defined on the interval [O, T[
`equal to [I I]:
`
`=
`
`(12)
`
`As a power amplifier has a limited peak output power,
`an increased PAPR or CF results in a reduced average ra(cid:173)
`diated power in order to avoid nonlinear distortions. For
`the uplink mobile radio communication, each user's signal
`is transmitted by a different amplifier and the PAPR or CF
`of the spreading codes must be compared individually. By
`contrast, for the downlink, the different data multiplied by
`the orthogonal spreading codes of the Nu active users are
`added and transmitted synchronously by the same power
`
`Vol. 13. No. 5. September-October2002
`
`467
`
`ERIC-1006 / Page 3 of 10
`
`

`

`S. Nobilet, J-F. Helard, D. Mottier
`
`amplifier at the base station. So, in that case, the quantity,
`which is of interest for the comparison between the dif(cid:173)
`ferent classes of sequences, is the global CF (GCF) of the
`global transmitted signal:
`
`GCF (~S;(t))
`
`Nu
`max I:sj(t)
`j=l
`
`2
`
`2
`
`( 13)
`
`}:_ 1T Nu
`
`T a
`
`I:sj(t) dt
`j::::l
`
`3.3 MULTIPLE ACCESS INTERFERENCE
`
`A simple MAI limitation technique for downlink syn(cid:173)
`chronous MC-CDMA transmission system, which consists
`in an optimized spreading sequence assignment, has been
`proposed in [l2J. Considering SD techniques, the analytic
`expression of the MAI power associated to user j for the
`case of a synchronous MC-CDMA transmission is given
`by:
`
`0"~11.1,1 =(Nu -
`
`l)Rj(O)L +
`
`a
`
`L-1
`2R(l) "\""' w(j,m)w(j,m) +
`J ~ k
`k+l
`k::::l
`
`L-2
`
`2R1(2) L wij,m)wJ/+';) + ...
`
`( 14)
`
`k=l
`
`11,m
`2Rj(L - l)w[j,m)w~,m)
`
`where Ri ( i)
`is
`the
`autocorrelation defined
`as
`Rj(P - q) = E[ap,J·aq,j]. ak,J = hk,j·gk,j is the coef(cid:173)
`the subcarrier k after equalization,
`ficient affecting
`uYmi ==ck,j·Ck,m defines the product between the chip
`element used by users j and m at the subcarrier k, and
`Nu S l is the number of active users.
`Whatever the frequency correlation of the transmis(cid:173)
`sion channel, the MAI minimization procedure detailed
`in (121
`leads to retain a subgroup of Nu spreading
`sequences for which the minimum number of transi(cid:173)
`tions ( + l / - 1) among each possible product vector
`wU,mi = (w[J,m), w~J,m), ... , w~·m)) is maximum. In(cid:173)
`deed, each product vector w(j,m) can have between 0 and
`L - 1 transitions. So depending on the set of selected
`spreading sequences, the set of corresponding product vec(cid:173)
`tors has a given minimum which can be different from
`the minimum of an other set. And we select the set of
`spreading sequences which offer the minimum correspond(cid:173)
`ing product vectors which is maximal. In that case. the sum
`over m of negative terms /3}.m of Equation ( 14) decreases.
`
`which reduces the MAI due to large positive value a. Here,
`wU.m) must be understood as a measure of the ability to
`mitigate interference between users j and m. Thus, this
`first criterion aims at minimizing the largest degradation
`among two distinct users. Nevertheless, we may obtain
`several equivalent optimized subgroups. Then, the selec(cid:173)
`tion procedure can include a complementary criterion in
`order to further reduce the MAL
`For that purpose, as a complementary criterion, we
`compare the three following approaches :
`
`• Complementary criterion: MEAN
`which consists in maximizing the average number
`of transitions among the different product vectors
`wU.m), which ensures a minimization of the sum
`of terms /11 'm.
`
`• Complementary criterion: STD
`aiming at minimizing the standard deviation of the
`number of transitions among the different product
`vectors w(j,m). The application of this complemen(cid:173)
`tary criterion further avoids privileging a given user.
`
`• Complementary criterion: 2"d order
`which consists in maximizing the minimum number
`of transitions ( + 1/ - 1) among each possible second
`order product vectors
`·w(j,m) w(j,m))
`ur'(j,m) _ (tu(j,m) ·w(j,m)
`• · · · ' L-3 • L-1
`n
`-
`1
`'
`3
`and
`"V"(j,m) -
`w(j,m) ·tu(j,m))
`(w(j,m) w(j,m)
`4
`L
`·
`, · · · , L-2 1
`::?
`'
`y
`-
`According to the first criterion, the minimization of
`the sum of negative terms /3j,m results in a maxi(cid:173)
`mization of the sum of other negative terms /j,m of
`equation ( 14 ). Hence, in order to mitigate this effect,
`this last approach aims at minimizing the sum over
`m of /j,m which further reduces the MAI.
`
`Criteria based on MAI are expected to be all the more
`efficient as the channel is frequency correlated [ 12].
`
`4 CREST FACTOR ANALYTICAL RESULTS
`
`4.1 UPLINK CONTEXT
`
`In uplink context, the MC-CDMA signal, which is
`transmitted thanks to a high power amplifier for user j, is
`given by:
`
`( 15)
`
`where fk = fa + J.:/T, Tis the "useful" duration of the
`MC symbol of the transmitted signal !:Jj ( t), 1\fc is the num(cid:173)
`ber of subcarriers and I Dj (t) I = 1, as we consider PSK
`modulations.
`
`468
`
`ETT
`
`ERIC-1006 / Page 4 of 10
`
`

`

`Spreading Sequences for Uplink and Downlink MC-CDMA Systems: PAPR and MAI Minimization
`
`The maximum power of the signal Si(t) is defined by
`the maximum square absolute value of Si(t) equal to:
`
`max JSj (t) 12 = max llR (~ Dj (t)ck,je
`
`?
`
`2
`
`i"kt/T e2i"/ot) 1·
`
`IC:r(t)J 2
`
`:::; 2£
`
`(21)
`
`where C:i:(t) is the inverse Fourier transform of any com(cid:173)
`plementary Golay sequence.
`So, the upper bound for the Golay sequences crest fac(cid:173)
`tor is given by:
`
`< max Dj (t) L c1o,je2i>rkt/T
`
`Ne
`
`< max It c1o,je2;,,.1<1/Tl2
`
`I
`
`k=l
`
`k=l
`< max!Cj(t)! 2
`
`2
`
`1
`
`je2i,,./ot/2
`
`CF Golay (Sj (t)) $ 2
`
`(22)
`
`where,
`
`Ne
`
`Cj(t) = L ci.,je2i1rkt/T
`
`k=l
`
`(
`
`is nothing else than the inverse Fourier transform of the
`sequence scj assigned to user j.
`.
`As the mean square value of the signal amplitude Si (t)
`equals to Nc/2, from Equatjon (12), we obtain the upper
`bound for the crest factor for an uplink MC-CDMA signal
`[ 11][13]:
`
`CF(Sj(t))$
`
`2
`max !Ci (t) 1
`L/2
`
`(18)
`
`• Walsh-Hadamard sequences
`According to Equation (18), we need to evaluate the
`maximum square absolute value of the inverse Fourier
`transform of the Walsh-Hadamard sequence SCj. Un(cid:173)
`doubtedly,
`this value is maximum when the Walsh(cid:173)
`Hadamard sequences are only composed of elements + 1.
`Consequently, max ICi(t)l2 = £ 2 and the upper bound for
`the Walsh-Hadamard crest factor is given by:
`
`(19)
`
`• Golay sequences
`For each pair of complementary sequences assigned to
`users i and j (i # j), by calculating the inverse Fourier
`transform of Equation (7) and applying the well-known au(cid:173)
`tocorrelation theorem [13], we obtain the following rela(cid:173)
`tion:
`
`(16)
`
`(17)
`
`• Gold sequences
`Gold codes have three-valued correlation properties.
`Thus, autocorrelation function of any Gold sequence can
`be overestimated by:
`
`r/Ja,a(k) $ { L
`t(n) - 2
`
`fork= 0
`
`fork# 0
`
`(23)
`
`By applying the autocorrelation theorem, we obtain the
`inverse Fourier transform of any Gold sequence and then:
`
`{ L[t(n) -
`
`l] + 2 -
`
`t(n)
`
`fort= 0 ·
`
`L~t(n)+2
`
`fort¥:- 0
`
`(24)
`
`?
`
`ICa(t)!-:::;
`
`Hence,
`
`max1Ca(t)j 2 $ L[t(n) -
`
`l] + 2 -
`
`t(n)
`
`(25)
`
`It follows that the upper bound of Gold codes crest fac(cid:173)
`tor is given by:
`
`CFGo1d (Si(t)) $
`
`2 [t(n) - 1 - t~) + i] (26)
`
`• 7.adoff-Chu sequences
`The autocorrelation function of Zadoff-Chu codes· is
`defined to be ideal, i.e.:
`
`L
`1/Jzc.,Zcr (k) = O
`{
`
`fork= 0
`
`fork-/:- 0
`
`(27)
`
`From (20), it follows that:
`
`Vol. 13, No. 5, September-October2002
`
`(20)
`
`By applying the autocorrelation theorem, we can obtain
`the inverse Fourier transform of any Zadoff-Chu sequence
`and then:
`
`469
`
`ERIC-1006 / Page 5 of 10
`
`

`

`S. Nobilet, J-F. Helard, D. Mattier
`
`According to the Cauchy-Schwartz inequality, we ob(cid:173)
`tain an upper bound for the maximum power of S(t):
`
`(28)
`
`Substitution of Equation (28) into Equation ( 18) yields
`the Zadoff-Chu crest factor given by:
`
`CFZadoff-Chu ( Sj ( t)) = V2
`
`(29)
`
`• Crest factors bounds summary
`Table l gives the different values of the crest factor in
`terms of the spreading sequences family used.
`
`Table 1: Crest factor bounds of uplink MC-CDMA signals for dif(cid:173)
`ferent spreading sequences of length L.
`
`Walsh-Hadamard
`
`'
`i
`i
`i
`' i
`
`I
`
`Golay
`
`Gold
`
`Zadoff-Chu
`
`~ v'2L
`
`~2
`
`~ J2[t(n) -1- ~ + t]
`= v12
`
`As far as orthogonal Gold codes are concerned, no ex(cid:173)
`ploitable bound can be obtained from the autocorrelation
`function.
`
`4.2 DOWNLINK CONTEXT
`
`In downlink context, the signal S( t) which is transmit-
`ted thanks to a power amplifier is the contribution of all
`users. So, in that case, the quantity that needs to be esti-
`mated is the Global Crest Factor (GCF) defined by Equa-
`tion (13)_
`The maximum power of the signal S(t) is equal to:
`
`Nu
`max\S(t)\ 2 = max L Sj(t)
`j=l
`
`2
`
`max !II (%D;(t)C;(t)<'"1
`•')
`
`le3;.,.. Jot 12
`
`2
`
`2
`
`Nu
`< max LDi(t)Cj(t)
`j=l
`
`Nu
`< max L Dj(t)Cj(t)
`i=l
`
`(30)
`
`where Cj ( t) is given by Equation ( 17).
`
`470
`
`max/S(t)/' < max{~ ID;(t)I' % IC;(t)I'}
`". max { N, (% IC; (t)l 2
`
`) }
`
`(31 J
`
`As the mean square value of the signal amplitude S(t)
`equals to NuNc/2, the upper bound for the global crest
`factor for a downlink MC-CDMA signal is given by:
`
`GCF (S(t)) ~
`
`L
`
`(32)
`
`For instance, let us apply Expression (32) to the case of
`Golay sequences where !(among N,,, sequences are com(cid:173)
`plementary. According to the properties of Golay codes
`(Equation (20)), we obtain:
`
`max{% /C;(t)I'} = K · 2L + (N - K) · 2L
`2
`u
`
`L(2Nu - K)
`
`(33)
`
`Consequently, the upper bound for the Golay codes
`global crest factor can be expressed as:
`
`GCF(S(t)) ~ y'2(2Nu - K)
`
`(34)
`
`5 SIMULATION RESULTS
`
`5.1 CREST FACTOR MINIMIZATION
`
`the CF of orthogonal and non(cid:173)
`this section,
`In
`orthogonal spreading sequences has been evaluated by sim(cid:173)
`ulation in the case of PSK modulated MC-CDMA sig(cid:173)
`nals.-Figure 2 represents the individual CF obtained for dif(cid:173)
`ferent orthogonal spreading sequences of sequence. length
`L = 32: Walsh-Hadamard, orthogonal Gold and Golay
`codes. As expected from Equation (22), it can be seen
`that Golay sequences individually produce the best CF (al(cid:173)
`ways equal to 2), while the W-H sequences produce the
`worst. Indeed, W-H crest factor ranges from 4 to 8, which
`is in accordance with the upper bound equal to v'2I = 8
`obtained analytically. Similar results have been achieved
`for different sequence lengths L = 16, 64, 128. Then, for
`uplink applications using orthogonal sequences, as far as
`the dynamic range of the transmitted signal is concerned,
`
`ETI
`
`ERIC-1006 / Page 6 of 10
`
`

`

`Spreading Sequences for Uplink and Downlink MC-CDMA Systems: PAPR and MAI Minimization
`
`it is more advisable to use Golay sequences than Walsh(cid:173)
`Hadamard sequences, which are however considered in
`most uplink systems.•
`
`s,-~--.~~--,-~~-,-~~-.----;::==::=:====c:::===:=;i
`-+- Walsh-Hadamard
`_._.Golay
`-
`0
`
`nalGold
`
`6
`
`5.2 GLOBAL CREST FACTOR MINIMIZATION
`
`For the synchronous downlink, it is necessary to esti(cid:173)
`mate the PAPR or the GCF of the global transmitted sig(cid:173)
`nal as defined by Equation (13). Figures 4 and 5 show the
`GCF of the global signal transmitted by the base station,
`which corresponds to the synchronous addition of the dif(cid:173)
`ferent users' signals. The results are presented for W-H
`and Golay codes (L = 16) versus the number Nu of active
`users. For each number Nu of active users, the GCF of the
`subsets offering the minimum and the maximum value for
`all the data symbol subsets are calculated, which represents
`2Nu .CJ:i,, ::3 294 720 possibilities for L = 16 and Nu = 8.
`
`Sequence Number [ j)
`
`Figure 2: Crest Factor of orthogonal spreading sequences
`(L = 32).
`
`s,-~--..~~--.-~~-,--~~-r-~~i;:::==:::::::i====::;i
`-
`Zadotf-Chu
`--- Gold
`
`8
`
`7
`
`6
`
`5.5
`
`5
`
`4.5
`
`0 4
`~ ... 3.5
`;;
`! 3
`u
`~2.5
`a 2
`1.5
`
`0.5
`
`00
`
`i l
`
`2
`
`4
`
`12
`10
`8
`8
`Number of users ( Nu )
`
`......_ Max GCF
`-+- MlnGCF
`
`14
`
`16
`
`18
`
`Figure 4: Global Crest Factor of Golay codes ( L = 16).
`
`As expected, the difference between the minimum and
`the maximum GCF is larger for W-H codes than for Golay
`codes. Furthermore, a good selection of the W-H codes
`allows to keep the GCF lower than 2.6 from 2 to 16 users
`while the GCF of Golay codes increases with Nu. In this
`case, using W-H codes is appropriate to limit the PAPR of
`the transmitted signal envelope for the downlink.
`
`:.~
`
`5
`
`10
`
`15
`20
`Sequence Number ( j)
`
`25
`
`30
`
`35
`
`Figure 3: Crest Factor of non-orthogonal spreading sequences
`(L=31).
`
`As regards non-orthogonal codes for uplink applica(cid:173)
`tions, Zadoff-Chu complex sequences with constant mag(cid:173)
`nitude periodic crosscorrelation functions equal to L, have
`a lower CF than Gold sequences. Indeed, Zadoff-Chu se(cid:173)
`quences CF is constant and equal to V2 while Gold codes
`CF is about 3 as shown on Figure 3 and inferior to the upper
`bound equal to 3.94 according to Equation (26).
`
`5.3 MAI MINIMIZATION
`
`The spreading sequence allocation procedure based on
`the MAI criteria has been validated by simulation for a
`downlink MC-CDMA synchronous transmission over !111
`indoor propagation channel. A 64 FFT-based OFDM
`modulation, W-H or Golay spreading sequences of length
`L = 16, SD based on Minimum Mean Square Error Com(cid:173)
`bining (MMSEC) and perfect power control are consid(cid:173)
`ered. As the minimum number of transitions among each
`possible product vector within a subgroup of Nu spreading
`sequences is exactly the same for W-H and Golay codes,
`the performance in tenns of MAI for optimised Nu load
`subsets are strictly identical with both sequences families.
`The simulation environment is inspired by ETSI BRAN
`
`Vol. 13, No. 5, September-October2002
`
`471
`
`ERIC-1006 / Page 7 of 10
`
`

`

`S. Nobilet, J-F. Helard, D. Monier
`
`I
`
`• \
`\
`\ I
`
`0.5
`
`a
`s
`12
`10
`Number of user.i ( Nu )
`
`14
`
`16
`
`18
`
`Figure 5: Global Crest Faetor of Walsh-Hadamard codes
`(l = 16).
`
`HfPERLAN/2 specification. The signal bandwidth is equal
`to 20 MHz and the propagation channel, issued from spec(cid:173)
`ifications published in [ 14]. has a coherence bandwidth
`equJ.l to 2 56 MHz.
`
`~
`CZl
`
`"'
`
`e, •JSS
`I
`I
`o.osf
`
`n 045r
`I
`I
`i
`0.041
`
`i
`0.035~
`' I
`0.03l
`
`0.0251
`
`0.02
`0
`
`~ Bad allocation
`.- Cl!>t. allocation - Cornplemllf'tary clirerion: MEAN
`' -+- Cl!>t. allocalion - Complemefllaly cliterion: STD
`...- Opt. allocation - Complementa cliterion: 2nd ordM
`
`2
`
`4
`
`10
`8
`6
`Number ol users ( Nu)
`
`12
`
`14
`
`16
`
`Figure 6: 8 ER versus the number Nu of active users for
`Eo/ No = 6 dB; Ne = 64. l = 16, MMSEC detec(cid:173)
`tion.
`
`Figure 6 represents the Bit Error Rate (BER) averaged
`over the active users versus the number Nu of active users
`for Eb/No = 6 dB and for different subsets matching the
`selection criteria defined in Section 3.3. Users' signals
`have the same power. As a bad allocation case, we con(cid:173)
`sider the subset defined by a minimum number of transi(cid:173)
`tions in each possible product vector W(i,Jl. As in [12],
`we confirm the gain obtained by the optimization of the
`spreading sequence allocation procedure. A bad allocation
`results in a BER close to 4.8 io- 2 for any number Nu
`of users varying from 2 to 16 whereas optimized alloca-
`
`tions leads to lower BER, increasing almost linearly with
`Nu. However, the BER performance obtained with the
`three complementary criteria are really close. We can only
`notice a slight difference from Nu = 9 to 16 in favor of
`the 2"d order criterion curve. Consequently, using a com(cid:173)
`plementary criterion based on MAI to further optimize the
`selection does not provide significant BER gain.
`
`5.4
`
`JOINT MAI AND GCF MINIMIZATION
`
`With the aim of optimizing the performance of the
`downlink transmission system, we propose a selection of
`spreading sequences based on a joint minimization of the
`MAI and the GCF. Figure 7 shows the GCF of W-H codes
`for the synchronous downlink. Curves (1) and (2) already
`presented in Figure S corresponding to the maximum and
`the minimum GCF are given as reference.
`
`•
`
`6
`
`5.5
`
`5
`
`4.5
`g 4
`u
`~3.5
`in
`!
`(.)
`~2.5
`5!
`.
`\!l 2
`
`3
`
`1.5
`
`0.5
`
`00
`
`_.. Max GCF (1)
`Min GCF(2)
`....... Min MAl-GCF 3)
`
`..
`
`.... ..... _.., - ... -. - .. - ...
`
`2
`
`4
`
`12
`10
`8
`6
`Number of users ( Nu)
`
`14
`
`16
`
`18
`
`Figure 7: Joint minimization: Global Crest Factor of Walsh(cid:173)
`Hadamard subsets which minimize first rhe MAI and the
`GCF
`
`Curve (3) gives the GCF of subsets which minimize
`first of all the MAI according to the first criterion and then
`the GCF. It can be noticed that there is only a slight differ(cid:173)
`ence with curve (2) for 4 and 6 users.
`Furthermore, as shown in Figure 8, the BER perfor(cid:173)
`mance obtained by these subsets are really close to the per(cid:173)
`formance of the subsets derived from MAI-based comple(cid:173)
`mentary criteria. Then, it is shown that it is possible to
`select the subset in order to jointly minimize the MAI anti
`theGCF.
`
`6 CONCLUSION
`
`For a given transmission context (number of users; up(cid:173)
`link or downlink) and depending on the criterion which
`is privileged in each application, i.e., minimization of the
`
`472
`
`ETT
`
`ERIC-1006 / Page 8 of 10
`
`

`

`Spreading Sequences for Uplink and Downlink MC-CDMA Systems: PAPR and MAI Minimization
`
`5.5 10- 1 ,--~=================;i
`-
`Opt Allocation - Complementary criterion: 2nd order
`-+- Min MAI - GCF
`
`ACKNOWLEDGEMENT
`
`4.5 10-1
`ffi
`
`<Xl
`
`3.5 io- 1
`
`The authors would like to express their thanks to the
`anonymous reviewers for their suggestions and useful con(cid:173)
`tributions. Furthermore, the authors, Stephane Nobilet and
`Jean-Fran~ois Helard from INSA Rennes, would like to
`thank Mitsubishi Electric ITE and Ff R&D/DMR which
`support and contribute to this study.
`
`I
`3 io- 1 ._· _
`0
`
`_.__ _
`2
`
`_.__ _ _,_ _ _,_ _ _._ _
`4
`6
`8
`10
`Number of users ( Nu)
`
`__.__ _
`12
`
`__.__ _
`14
`
`___._ _
`16
`
`__.
`18
`
`Figure 8: Joint minimization: BER versus the number Nu of ac(cid:173)
`tive users/or Eb/No = 6dB; Ne= 64, L = 16, MM(cid:173)
`SEC detection.
`
`MAI or minimization of the dynamic range of the transmit(cid:173)
`ted signal envelope, the optimum spreading sequence sub(cid:173)
`sets may be different. In this paper, we propose to select
`spreading sequences subsets that jointly reduce the MAI
`and the CF of the MC-CDMA signal.
`For uplink applications, with regard to orthogonal se(cid:173)
`quences, the low CF of the Golay codes is undoubtedly
`an advantage compared to W-H codes, whereas a selec(cid:173)
`tion based on MAI minimization cannot be applied since
`the channels from active mobile stations to the dedicated
`base station are independent. As regards non-orthogonal
`codes used for uplink transmissions, it is worth mention(cid:173)
`ing the very low CF of the complex Zadoff-Chu sequences
`which is besides constant and equal to J2 for any sequence
`length.
`For the downlink, it has been shown that a good se(cid:173)
`lection of the subsets leads to a reduction of the global
`crest factor specially with Walsh-Hadamard codes which
`are confirmed to be the best candidates in that case. More(cid:173)
`over, it is possible to shortlist the subgroups which mini(cid:173)
`mize the MAI, i.e.
`the BER, according to the first MAI
`criterion and then to select the subgroup offering the mini(cid:173)
`mal GCF. So, an optimum subset which jointly minimizes
`the MAI and the GCF of the transmitted signal can be ob(cid:173)
`tained for any load.
`Finally, this study which was originally devoted to a
`single cell environment, will be extended to a multi-cell
`context taking into account the scrambling process. In the
`same way, it is then possible in that case to select:
`
`- a couple made up of a scrambling code and a spread(cid:173)
`ing code which minimizes the CF for uplink applica(cid:173)
`tions.
`
`- a subset offering the minimal GCF and a minimized
`MAI for downlink applications.
`
`Manuscript received on April 5, 2002.
`
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`
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