Article_The Alamouti scheme with CDMA-OFDMOQAM

8/8/2019 Article_The Alamouti scheme with CDMA-OFDM OQAM

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Hindawi Publishing CorporationEURASIP Journal on Advances in Signal ProcessingVolume 2010, Article ID 703513, 13 pagesdoi:10.1155/2010/703513

Research ArticleThe Alamouti Schemewith CDMA-OFDM/OQAM

Chrislin Lele,1 Pierre Siohan,2 andRodolpheLegouable2

1 CNAM, Laetitia group, 292, rue Saint Martin, 75141 Paris, France2 Orange Labs, 4, rue du Clos Courtel, BP 91226, 35512 Cesson S evigne Cedex, France

Correspondence should be addressed to Pierre Siohan, [email protected]

Received 23 June 2009; Revised 4 October 2009; Accepted 29 December 2009

Academic Editor: Behrouz Farhang-Boroujeny

Copyright 2010 Chrislin Lele et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper deals with the combination of OFDM/OQAM with the Alamouti scheme. After a brief presentation of theOFDM/OQAM modulation scheme, we introduce the fact that the well-known Alamouti decoding scheme cannot besimply applied to this modulation. Indeed, the Alamouti coding scheme requires a complex orthogonality property; whereasOFDM/OQAM only provides real orthogonality. However, as we have recently shown, under some conditions, a transmissionscheme combining CDMA and OFDM/OQAM can satisfy the complex orthogonality condition. Adding a CDMA component canthus be seen as a solution to apply the Alamouti scheme in combination with OFDM/OQAM. However, our analysis shows thatthe CDMA-OFDM/OQAM combination has to be built taking into account particular features of the transmission channel. Oursimulation results illustrate the 2 1 Alamouti coding scheme for which CDMA-OFDM/OQAM and CP-OFDM are compared intwo different scenarios: (i) CDMA is performed in the frequency domain, (ii) CDMA is performed in time domain.

1. Introduction

Increasing the transmission rate and/or providing robustnessto channel conditions are nowadays two of the main researchtopics for wireless communications. Indeed, much effortis done in the area of multiantennas, where Space TimeCodes (STCs) enable to exploit the spatial diversity whenusing several antennas either at the transmitting side orat the receiving side. One of the most known and usedSTC technique is Alamouti code [1]. Alamouti code hasthe nice property to be simple to implement while provid-

ing the maximum channel diversity. On the other hand,multicarrier modulation (MCM) is becoming, mainly withthe popular Orthogonal Frequency Division Multiplexing(OFDM) scheme, the appropriate modulation for transmis-sion over frequency selective channels. Furthermore, whenappending the OFDM symbols with a Cyclic Prefix (CP)longer than the maximum delay spread of the channel topreserve the orthogonality, CP-OFDM has the capacity totransform a frequency selective channel into a bunch of flatfading channels which naturally leads to various efficientcombinations of the STC and CP-OFDM schemes. However,the insertion of the CP yields spectral efficiency loss. Inaddition, the conventional OFDM modulation is based on

a rectangular windowing in the time domain which leads toa poor (sinc(x)) behavior in the frequency domain. Thus CP-OFDM gives rise to two drawbacks: loss of spectral efficiencyand sensitivity to frequency dispersion, for example, Dopplerspread.

These two strong limitations may be overcome by someother OFDM variants that also use the exponential baseof functions. But then, in any case, as it can be deducedfrom the Balian-Low theorem, see, for example, [2], it is notpossible to get at the same time (i) Complex orthogonality;(ii) Maximum spectral efficiency; (iii) A well-localized pulse

shape in time and frequency. With CP-OFDM conditions(ii) and (iii) are not satisfied, while there are two mainalternatives that satisfy two of these three requirementsand can be implemented as filter bank-based multicarrier(FBMC) modulations. Relaxing condition (ii) we get amodulation scheme named Filtered MultiTone (FMT) [3],also named oversampled OFDM in [4], where the authorsshow that the baseband implementation scheme can be seenas the dual of an oversampled filter bank. But if one reallywants to avoid the two drawbacks of CP-OFDM the onlysolution is to relax the complex orthogonality constraint. Thetransmission system proposed in [5] is a pioneering workthat illustrates this possibility. Later on an efficient Discrete


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2 EURASIP Journal on Advances in Signal Processing

Fourier Transform (DFT) implementation of the Saltzbergsystem [5], named Orthogonally Quadrature AmplitudeModulation (O-QAM), has been proposed by Hirosaki [6].To the best of our knowledge, the acronym OFDM/OQAM,where OQAM now corresponds to Offset QAM, appearedfor the first time in [7]. In [7] the authors also present an

invention of Alard, named Isotropic Orthogonal TransformAlgorithm (IOTA), and explicitly use a real inner productto prove the orthogonality of the OFDM/OQAM-IOTAmodem. A formal link between these continuous-time mod-ulation models and a precise filter bank implementation,the Modified Discrete Fourier Transform (MDFT) [8], isestablished in [9].

It is now recognized in a large number of applications,with cognitive radio being the most recent and importantone [10], that appropriate OFDM/OQAM pulse shapeswhich satisfy conditions (ii) and (iii) can be designed,and these can lead to some advantages over the CP-OFDM. However, most of these publications are related toa single user case and to Single-Input-Single-Output (SISO)systems. On the contrary, only a few results are availableconcerning more general requirements being related either tomultiaccess techniques or multiantenna, that is, of MultipleInput Multiple Output (MIMO) type. In a recent publication[11], we have shown that, under certain conditions, acombination of Coded Division Multiple Access (CDMA)with OFDM/OQAM could be used to provide the complexorthogonal property. On the other hand, it has also beenshown in [12] that spatial multiplexing MIMO could bedirectly applied to OFDM/OQAM. However, in the MIMOcase there is still a problem which has not yet found a fullyfavorable issue: It concerns the combined use of the popularSTBC Alamouti code together with OFDM/OQAM. Basicallythe problem is related to the fact that OFDM/OQAMby construction produces an imaginary interference term.Unfortunately, the processing that can be used in the SISOcase, for cancelling it at the transmitter side (TX) [13]or estimating it at the receiver side (RX) [14], cannotbe successfully extended to the Alamouti coding/decodingscheme. Indeed, the solutions proposed so far are not fullysatisfactory. The Alamouti-like scheme for OFDM/OQAMproposed in [15] complicates the RX and introduces aprocessing delay. The pseudo-Alamouti scheme recentlyintroduced in [16] is less complex but requires the appendingof a CP to the OFDM/OQAM signal which means thatcondition (ii) is no longer satisfied.

The aim of this paper is to take advantage of the orthog-onality property resulting from the CDMA-OFDM/OQAMcombination introduced in [11] to get a new MIMO Alam-outi scheme with OFDM/OQAM. The contents of our paperis as follows. In Section 2, after some general descriptionsof the OFDM/OQAM modulation in Section 2.1 and theMIMO Alamouti scheme in Section 2.2, we will combineboth techniques. However, as we will see in Section 2.3,the MIMO decoding process is very difficult becauseof the orthogonality mismatch between Alamouti andOFDM/OQAM. In Section 3, we propose to combine Alam-outi and CDMA-OFDM/OQAM in order to solve the prob-lem. Indeed, in [11], we have shown that the combination

of CDMA and OFDM/OQAM (CDMA-OFDM/OQAM) canprovide the complex orthogonality property; this interestingproperty is first recalled in Section 3.1. Then, two differentapproaches with Alamouti coding are proposed, by consid-ering either a spreading in the frequency (in Section 3.2)or in the time domain (in Section 4.2). When spreading

in time is considered, 2 strategies of implementing theAlamouti coding are proposed. Some simulation resultsfinally show that, using particular channel assumptions, theAlamouti CDMA-OFDM/OQAM technique achieves similarperformance to the Alamouti CP-OFDM system.

2. OFDM/OQAMandAlamouti

2.1. The OFDM/OQAM Transmultiplexer. The basebandequivalent of a continuous-time multicarrier OFDM/OQAMsignal can be expressed as follows [7]:

s(t) =M1m=0

nZ

am,ng(t n0)ej2mF0tm,n gm,n(t)

(1)

with Z the set of integers, M = 2N an even number ofsubcarriers, F0 = 1/T0 = 1/20 the subcarrier spacing, gthe prototype function assumed here to be a real-valued andeven function of time, and m,n an additional phase term suchthat m,n = jm+nej0 , where 0 can be chosen arbitrarily.The transmitted data symbols am,n are real-valued. Theyare obtained from a 22K-QAM constellation, taking the realand imaginary parts of these complex-valued symbols ofduration T0 = 20, where 0 denotes the time offset betweenthe two parts [2, 6, 7, 9].

Assuming a distortion-free channel, the Perfect Recon-struction (PR) of the real data symbols is obtained owing tothe following real orthogonality condition:

R

gm,n,gp,q

=R

gm,n(t)g

p,q(t)dt

=m,pn,q, (2)

where denotes conjugation, , denotes the innerproduct, and m,p = 1 if m = p and m,p = 0 ifm /=p. Otherwise said, for (m,n) /= (p, q), gm,n,gp,q is apure imaginary number. For the sake of brevity, we setgp,qm,n = jgm,n,gp,q. The orthogonality condition for theprototype filter can also be conveniently expressed using itsambiguity function

Ag(n,m) =

g(u n0)g(u)e2jmF0udu. (3)

It is well-known [7] that to satisfy the orthogonalitycondition (2), the prototype filter should be chosen such thatAg(2n, 2m) = 0 if (n,m) /= (0,0) and Ag(0,0) = 1.

In practical implementations, the baseband signal isdirectly generated in discrete time, using the continuous-time signal samples at the critical frequency, that is, withFe = MF0 = 2NF0. Then, based on [9], the discrete-time


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EURASIP Journal on Advances in Signal Processing 3

a0,n

a1,n

aM1,nPremodulation

IFFT

Polyphase

P/S S/P

Polyphase

FFT

Post

demodulation

.

.

.

.

.

.

Re{}

Re{}

Re{}

OQAM modulator OQAM demodulator

Figure 1: Transmultiplexer scheme for the OFDM/OQAM modulation.

OQAM

modulator

OQAM

demodulatorChannel Equalization

a0,n

aM1,n

a0,n

aM1,n

R

R

.

.

. ...

Figure 2: The transmission scheme based on OFDM/OQAM.

baseband signal taking the causality constraint into account,is expressed as

s[k] =M1m=0

nZ

am,ng(k nN)ej2m(k(Lg1)/2)m,n gm,n[k]

. (4)

The parallel between (1) and (4) shows that the overlap-ping of duration 0 corresponds to Ndiscrete-time samples.For the sake of simplicity, we will assume that the prototype

filter length, denoted Lg, is such that Lg = bM= 2bN, with bbeing a positive integer. With the discrete time formulation,the real orthogonality condition can also be expressed as:

R

gm,n,gp,q

=R

kZ

gm,n[k]gp,q[k]

=m,pn,q. (5)As shown in [9], the OFDM/OQAM modem can be

realized using the dual structure of the MDFT filter bank.A simplified description is provided in Figure 1, where it hasto be noted that the premodulation corresponds to a singlemultiplication by an exponential whose argument dependson the phase term m,n and on the prototype length. Note

also that in this scheme, to transmit QAM symbols of a givenduration, denoted T0, the IFFT block has to be run twicefaster than for CP-OFDM. The polyphase block contains thepolyphase components of the prototype filter g. At the RXside, the dual operations are carried out.

The prototype filter has to be PR, or nearly PR. In thispaper, we use a nearly PR prototype filter, with length Lg =4M, resulting from the discretization of the continuous timefunction named Isotropic Orthogonal Transform Algorithm(IOTA) in [7].

Before being transmitted through a channel the basebandsignal is converted to continuous-time. Thus, in the rest ofthis paper, we present an OFDM/OQAM modulator that

delivers a signal denoted s(t), but keeping in mind that thismodulator corresponds to an FBMC modulator as shown inFigure 1.

The block diagram in Figure 2 illustrates our OFDM/OQAM transmission scheme. Note that compared toFigure 1, here a channel breaks the real orthogonalitycondition thus an equalization must be performed at thereceiver side to restore this orthogonality.

Let us consider a time-varying channel, with maximumdelay spread equal to . We denote it by h(t, ) in time,and it can also be represented by a complex-valued number

H(c)m,n for subcarrier m at symbol time n. At the receiver

side, the received signal is the summation of the s(t) signalconvolved with the channel impulse response and a noisecomponent (t). For a locally invariant channel, we candefine a neighborhood, denoted m,n, around the (m0,n0)position, with

m,n

=p,q

,pm,qn | H(c)m0+p,n0+q H(c)m0,n0,

(6)

and we also define m,n = m,n {(0,0)}.Note also that n and m are chosen according to the

time and bandwidth coherence of the channel, respectively.Then, assuming g(tn0) g(tn0), for all [0,],the demodulated signal can be expressed as [13, 14, 17]

y(c)m0 ,n0 = H(c)m0,n0am0 ,n0 + ja

(i)m0 ,n0

+ Jm0 ,n0 + m0 ,n0 (7)

with m0 ,n0 = ,gm0 ,n0 the noise component, a(i)m0 ,n0 , theinterference created by the neighbor symbols, given by

a(i)m0 ,n0 =

(p,q)m,nam0+p,n0+q

gm0,n0m0+p,n0+q,

(8)


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and Jm0 ,n0 the interference created by the data symbolsoutsidem,n.

It can be shown that, even for small size neighborhoods,if the prototype function g is well localized in time andfrequency, Jm0 ,n0 becomes negligible when compared to thenoise term m0 ,n0 . Indeed a good time-frequency localization

[7] means that the ambiguity function ofg, which is directlyrelated to the gm0 ,n0m0+p,n0+q terms, is concentrated around itsorigin in the time-frequency plane, that is, only takes smallvalues outside the m,n region. Thus, the received signalcan be approximated by

y(c)m0 ,n0 H(c)m0,n0am0 ,n0 + ja

(i)m0 ,n0

+ m0 ,n0 . (9)

For the rest of our study, we consider (9) as theexpression of the signal at the output of the OFDM/OQAMdemodulator.

2.2. Alamouti Scheme: General Case. In order to describe the

Alamouti scheme [1], let us consider the one-tap channelmodel described as

yk = hk,usk,u + nk, (10)

where, at time instant k, hk,u is the channel gain betweenthe transmit antenna u and the receive antenna and nkis an additive noise. We assume that hk,u is a complex-valued Gaussian random process with unitary variance. Onetransmit antenna and one receive antenna are generallyreferred as SISO model. We consider coherent detection, thatis, we assume that the receiver has a perfect knowledge ofhk,u.

The Alamouti scheme is implemented with 2 transmitand one receive antennas. Let us consider s2k and s2k+1 tobe the two symbols to transmit at time (time and frequencyaxis can be permuted in multicarrier modulation.) instants2k and 2k + 1, respectively. At time instant 2k, the antenna 0transmits s2k/

2 whereas the antenna 1 transmits s2k+1/

2.

At time instant 2k + 1, the antenna 0 transmits (s2k+1)/

2whereas the antenna 1 transmits s2k/

2. The 1/

2 factor is

added to normalize the total transmitted power. The receivedsignal samples at time instants 2k and 2k + 1 are given by

y2k = 12

h2k,0s2k + h2k,1s2k+1

+ n2k,

y2k+1

=

12h2k+1,0(s2k+1)

+ h2k+1,1(s2k)

+ n2k+1.(11)

Assuming the channel to be constant between the timeinstants 2k and 2k + 1, we get y2k

y2k+1

= 12

h2k,0 h2k,1h2k,1

h2k,0

H2k

s2ks2k+1

+ n2kn2k+1

.(12)

Note that H2k is an orthogonal matrix with H2kHH2k =

(1/2)(|h2k,0|2 + |h2k,1|2)I2, where I2 is the identity matrixof size (2, 2) and H stands for the transpose conjugate

operation. Thus, using the Maximum Ratio Combining(MRC) equalization, the estimates s2k and s2k+1 are obtainedas

s2ks2k+1

=

2

h2k,0

2

+

h2k,1

2

h2k,0 h2k,1

h2k,1

h2k,0

y2k

y2k+1

= s2ks2k+1

+ 2k2k+1

,(13)

where, 2k2k+1

= 2h2k,02 + h2k,12 h2k,0 h2k,1

h2k,1 h2k,0

n2kn2k+1

.(14)

Since the noise components n2k and n2k+1 are uncorrelated,E(|2k|2) = E(|2k+1|2) = 2N0/(|h2k,0|2 + |h2k,1|2), whereN0 denotes the monolateral noise density. Thus, assuming aQPSK modulation, based on [18], the bit error probability,denoted pb, is given by

pb = Q

h2k,02 + h2k,12

2

SNRt

, (15)where SNRt denotes the Signal-to-Noise Ratio (SNR) atthe transmitter side. When the two channel coefficients areuncorrelated, we will have a diversity gain of two [18].

2.3. OFDM/OQAM with Alamouti Scheme.Equation(9) indicates that we can consider the transmission

of OFDM/OQAM on each subcarrier as a flat fadingtransmission. Moreover, recalling that in OFDM/OQAM

each complex data symbol, d(c)m,n, is divided into two real

symbols, R{d(c)m,n} and I{d(c)m,n}, transmitted at successivetime instants, transmission of a pair of data symbols,according to Alamouti scheme, is organized as follows:

am,2n,0 =Rd

(c)m,2n

,

am,2n,1 =Rd

(c)m,2n+1

,

am,2n+1,0 = I

d

(c)m,2n

,

am,2n+1,1 = Id(c)m,2n+1,am,2n+2,0 = R

d

(c)m,2n+1

= Rd(c)m,2n+1 = am,2n,1,am,2n+2,1 =R

d

(c)m,2n

=Rd(c)m,2n = am,2n,0,am,2n+3,0 = I

d

(c)m,2n+1

= Id(c)m,2n+1 = am,2n+1,1,am,2n+3,1 = I

d

(c)m,2n

= I

d

(c)m,2n

= am,2n+1,0.

(16)


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We also assume that in OFDM/OQAM the channel gainis a constant between the time instants 2n and 2n + 3. Letus denote the channel gain between the transmit antenna iand the receive antenna at subcarrier m and time instant nbyhm,n,i. Therefore, at the single receive antenna we have

ym,2n = hm,2n,0am,2n,0 + ja(i)m,2n,0+ hm,2n,1

am,2n,1 + ja

(i)m,2n,1

+ nm,2n,0,

ym,2n+1 = hm,2n,0am,2n+1,0 + ja

(i)m,2n+1,0

+ hm,2n,1

am,2n+1,1 + ja

(i)m,2n+1,1

+ nm,2n+1,1,

ym,2n+2 = hm,2n,0am,2n+2,0 + ja

(i)m,2n+2,0

+ hm,2n,1

am,2n+2,1 + ja

(i)m,2n+2,1

+ nm,2n+2,0,

ym,2n+3 = hm,2n,0am,2n+3,0 + ja(i)m,2n+3,0+ hm,2n,1

am,2n+3,1 + ja

(i)m,2n+3,1

+ nm,2n+3,1.

(17)

Setting

zm,2n = ym,2n + j ym,2n+1,

zm,2n+1 = ym,2n+2 + j ym,2n+3,(18)

and using (16), we obtain

zm,2n = hm,2n,0d(c)m,2n + hm,2n,1d(c)m,2n+1+ hm,2n,0xm,2n,0 + hm,2n,1xm,2n,1 + m,2n,0,

zm,2n+1 = hm,2n,0d

(c)m,2n+1

+ hm,2n,1

d

(c)m,2n

hm,2n,0

xm,2n+2,0

+hm,2n,1

xm,2n+2,1

+m,2n+2,0,

(19)

where,

xm,2n,0 = a(i)m,2n+1,0 + ja(i)m,2n,0,

xm,2n,1 = a(i)m,2n+1,1 + ja(i)m,2n,1,

m,2n,0 = nm,2n,0 + jnm,2n+1,0,

m,2n,0 = nm,2n+2,0 + jnm,2n+3,0,

xm,2n+2,0 = a(i)m,2n+3,0 + ja(i)m,2n+2,0,

xm,2n+2,1 = a(i)m,2n+3,1 ja(i)m,2n+2,1.

(20)

This results in zm,2nzm,2n+1

z2n

= hm,2n,0 hm,2n,1

hm,2n,1 hm,2n,0

Q2n

d(c)m,2nd

(c)m,2n+1

d2n

+hm,2n,0 hm,2n,1 0 0

0 0hm,2n,1

hm,2n,0

K2n

xm,2n,0

xm,2n,1

xm,2n+2,0

xm,2n+2,1

x2n

+

m,2nm,2n+1

2n

.

(21)

We note that Q2n is an orthogonal matrix which issimilar to the one found in (12) for the conventional 2 1Alamouti scheme. However, the K2nx2n term appears, whichis an interference term due to the fact that OFDM/OQAMhas only a real orthogonality. Therefore, even without noiseand assuming a distortion-free channel, we cannot achievea good error probability since K2nx2n is an inherent noiseinterference component that, differently from the oneexpressed in (9), cannot be easily removed. (in a particularcase, where hm,2n,0 = hm,2n,1, one can nevertheless get rid ofthe interference terms.)

To tackle this drawback some research studies are beingcarried out. However, as mentioned in the introduction,

the first one [15] significantly increases the RX complexity,while the second one [16] fails to reach the objective oftheoretical maximum spectral efficiency, that is, does notsatisfy condition (ii). The one we propose hereafter is basedon a combination of CDMA with OFDM/OQAM and avoidsthese two shortcomings.

3. CDMA-OFDM/OQAMandAlamouti

3.1. CDMA-OFDM/OQAM. In this section we summarizethe results obtained, assuming a distortion-free channel, in[19] and [11] for CDMA-OFDM/OQAM schemes transmit-ting real and complex data symbols, respectively. Then, we

show how this latter scheme can be used for transmissionover a realistic channel model in conjunction with Alamouticoding.

3.1.1. Transmission of Real Data Symbols. We denote byNc the length of the CDMA code used and assume thatNS = M/Nc is an integer number. Let us denote by cu =[c0,u cNc1,u]T, where ()T stands for the transposeoperation, the code used by the uth user. When applyingspreading in the frequency domain such as in pure MC-CDMA (Multi-Carrier-CDMA) [20], for a user u0 at agiven time n0, NS different data are transmitted denotedby: du0 ,n0 ,0, du0 ,n0,1, . . . , du0,n0,NS1. Then by spreading with


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x0,n

xM1,n

Real datadu,n

Spreading

infrequency O

QAM

modulator

ChannelDespreading

infrequencyO

QAM

demodulator

Equalization

Re{}

Im{}

du,n

iu,n

Figure 3: Transmission scheme for the CDMA-OFDM/OQAM system with spreading in frequency of real data.

the cu codes, we get the real symbol am0,n0 transmitted atfrequencym0 and time n0 by

am0 ,n0 =U1u=0

cm0/Nc ,udu,n0 ,m0/Nc, (22)

where U is the number of users, / the modulo operator,and the floor operator. From the am0 ,n0 term, thereconstruction of du,n0 ,p (for p [0,NS 1]) is insuredthanks to the orthogonality of the code, that is, cTu1cu2 =u1,u2; see [21] for more details. Therefore, noise taken apart,the despreadingoperator leads to

du,n0,p = Nc1m=0

cm,uapNC+m,n0 . (23)

In [19], it is shown that, since no CP is inserted, thetransmission of these spread real data (du,n0 ,p) can be insured

at a symbol rate which is more than twice the one usedfor transmitting complex MC-CDMA data. Figure 3 depictsthe real CDMA-OFDM/OQAM transmission scheme forreal data and a maximum spreading length (limited bythe number of subcarriers), where after the despreadingoperation, only the real part of the symbol is kept whereasthe imaginary component iu,n is not detected. This schemesatisfies a real orthogonality condition and can work for anumber of users up to M.

3.1.2. Interference Cancellation. A closer examination of theinterference term is proposed in [11] assuming that theCDMA codes are Walsh-Hadamard (W-H) codes of length

M = 2N = 2n, with n an integer. The prototype filterbeing of length Lg = bM, its duration is also given by theindicating function I|nn0|


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Alamoutiprocessing

peruser

persub-carrier

or time

Spreading

Spreading

OQAM

modulator

OQAM

modulator

sn,0

sn,M/21

.

.

.

.

.

.

.

.

.

Figure 5: An Alamouti CDMA-OFDM/OQAM transmitter.

AlamoutiCDMA-OQAM

decoding

DespreadingOQAMdemodulator

sn,0

sn,M/21...

... ...

Figure 6: An Alamouti CDMA-OFDM/OQAM receiver.

with 2 antennas with indexes 0 and 1, respectively, and if weapply Alamouti coding scheme to every user u data, denotingbysk,uthe main stream of complex data for user u, we have

at time 2k,

d(c)2k,u,0 =

s2k,u2

d(c)2k,u,1 =

s2k+1,u2

,

at time 2k + 1,

d(c)2k+1,u,0 =

s2k+1,u2

d(c)2k+1,u,1 =

s2k2.

(34)

For a flat fading channel, ignoring noise, the despreadedsignal for user u is given by

z(c)n,u = hn,0d(c)n,u,0 + hn,1d(c)n,u,1. (35)Hence, z(c)2k,u

z(c)2k+1,u

= 1

2

h2k,0 h2k,1h2k+1,1

h2k+1,0 s2k,u

s2k+1,u

.(36)

This is the same decoding equation as in the Alamoutischeme presented in Section 2.2. Hence, the decoding could

20151050

SNR

Alamouti with CDMA-OFDM/OQAM

Alamouti with CP-OFDM

104

103

102

101

100

BER

Figure 7: BER for the complex version of the Alamouti CDMA-

OFDM/OQAM with spreading in frequency domain, versus Alam-outi CP-OFDM for transmission over a flat fading channel.

be performed in the same way. Figures 5 and 6 present theAlamouti CDMA-OFDM/OQAM transmitter and receiver,respectively.

3.2.3. Performance Evaluation. We compare the proposedAlamouti CDMA-OFDM/OQAM scheme with the AlamoutiOFDM using the following parameters:

(i) QPSK modulation

(ii) M= 128 subcarriers(iii) maximum spreading length, implying that the W-H

spreading codes are of length Nc = 128,(iv) flat fading channel (one single Rayleigh coefficient for

all 128 subcarriers);

(v) the IOTA prototype filter with length 512,

(vi) zero forcing one tap equalization for both transmis-sion schemes,

(vii) no channel coding.

Figure 7 gives the performance results. As expected, bothsystems perform the same.

4. Alamouti andCDMA-OFDM/OQAMwithTime Domain Spreading

In this section, we keep the same assumptions as the onesused for the transmission of complex data with a spreadingin frequency. Firstly, we again suppose that the prototypefunction is a real-valued symmetric function and also thatthe W-H codes are selected using the procedure recalled inSection 3.1.2.


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x0,n

xM1,n

Complex data

d(c)u,n

Spreading

intime O

QAM

modulator sT(t) y(t)

Channel

OQAM

demodulator

Equalization

Despreading

intime

a0,n

aM1,nZ

(c)u,n

Figure 8: Transmission scheme for the CDMA-OFDM/OQAM system with spreading in time of complex data.

4.1. CDMA-OFDM/OQAM with Spreading in the TimeDomain. Let us first consider a CDMA-OFDM/OQAMsystem carrying out a spreading in the time domain, thatis, on each subcarrier m the data are spread over the timeduration frame length. Let us consider Lf the length of theframe, that is, the frame is made ofMdata in the frequencydomain and Lf data in time domain. Nc is the length of thespreading code. We assume that NS = Lf/Nc is an integernumber. Let us denote by: cu = [c0,u cNc1,u]T thecode used by the uth user. Then, for a user u0 at a givenfrequency m0, NS different data are transmitted denotedby: du0 ,m0,0,du0 ,m0 ,1, . . . ,du0 ,m0 ,NS1. By spreading with the cucodes, we get the real symbol am0,n0 transmitted at frequencym0 and time n0 by

am0,n0 =U1u=0

cn0/Nc ,udu,m0 ,n0/Nc, (37)

where U is the number of users. From the am0,n0 term, thereconstruction of du,m0 ,p (for p [0,NS 1]) is insuredthanks to the orthogonality of the code, that is, cTu1cu2 =u1,u2, see [21] for more details. Therefore, the despreadingoperator leads to

du,m0 ,p = Nc1n=0

cn,uam0 ,pNc+n. (38)

We now propose to consider the transmission of complex

data, denoted d(c)m,u,p, using U well chosen W-H codes. In

order to establish the theoretical features of this complexCDMA-OFDM/OQAM scheme, we suppose that the trans-mission channel is free of any type of distortion. Also, forthe sake of simplicity, we now assume a maximum spreading

length (in time domain, Lf = Nc). We denote by d(c)m,u thecomplex data and bya

(c)m,n,u

=cn,ud

(c)m,u the complex symbol

transmitted at time n0 over the carrier m and for the codeu. As usual, the length of the W-H codes are supposed to bea power of 2, that is, Lf = 2L = 2q with q an integer.

The block diagram of the transmitter is depicted inFigure 8. For a frame containing 2L OFDM/OQAM datasymbols, the baseband signal spread in time, can be writtenas

sT(t) =2L1n=0

2N1m=0

xm,ngm,n(t)

with xm,n =U1u

=0

a(c)m,n,u =U1u

=0

cn,ud(c)m,u.

(39)

In (39), we assume that the phase term is m,n = jm+n as in[7]. Let us also recall that the prototype function g satisfiesthe real orthogonality condition (2) and is real-valued andsymmetric, that is, g(t) = g(t). To express the complexinner product of the base functions gm,n, using a similarprocedure that led to (24), we get

gm,n,gp,n0 = mp,nn0 + j(p,n0)m,n I

|n

n0

|


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Considering the W-H codes, we obtain

z(c)m0 ,u0 = d(c)m0 ,u0

+ j

U1u=0

2N1m=0,m /=m0

d(c)m,u

2L1q=0

2L1n=0

cq,u0cn,u(m0 ,q)m,n

.

(46)

In [11], for W-H codes of length 2L, we have shown that forn /=n0,

2L1p=0

2L1m=0

cp,u0cm,u(p,n0)m,n+n0 = 0, (47)

where (p,n0)m,n is given by

(p,n0)m,n =I

(1)m(n+n0)jm+npn0Ag

nn0,mp

. (48)

To prove the result given in (47), we had the followingrequirements:

(i) W-H codes satisfy the set of mathematical propertiesthat are proved in [11].

(ii) Since g is a real-valued function, Ag(n,0) is realvalued and the ambiguity function of the prototypefunction g also satisfies the identities Ag(n,m) =(1)nmAg(n,m) and Ag(n,m) = Ag (n, m).

Using these results, (47) can be proved straighforwardly.It is worth mentioning that the above requirements are

independent of the phase term and thus are satisfied in thecase of the CDMA-OFDM/OQAM system with spreading in

time. It can also be shown that the modification of the phaseterm m,n leads to the substitutions n m and p + m n + n0, in obtaining (48) from (41). Accordingly the secondterm on the right hand side of (46) vanishes and we obtain

m0,u0, z(c)m0 ,u0 = d(c)m0,u0 . (49)

4.2. Alamouti with CDMA-OFDM/OQAM with Spreading inTime. Now, if we consider the CDMA-OFDM/OQAM withspreading in time, contrary to the case of a spreading infrequency domain, as long as the channel is constant duringthe spreading time duration, we can perform despreadingbefore equalization. At the equalizer output we will have a

complex orthogonality. Indeed, considering at first a SISOcase, if we denote by hm,i the channel coefficient betweena single transmit antenna i and the receive antenna atsubcarrier m, the despreaded signal is given by

z(c)m,u = hm,id(c)m,u,i, (50)

where d(c)m,u,i is the complex data of user u being transmitted

at subcarrier m by antenna i. Thus, we can easily apply theAlamouti decoding scheme knowing the channel is constantfor each antenna at each frequency. Otherwise said, themethod becomes applicable for a frequency selective channel.Actually two strategies can be envisioned.

(1) Strategy 1. Alamouti performed over pairs of frequencies. Ifwe consider a system with 2 transmit antennas, 0 and 1, andif we apply the Alamouti coding scheme to every user u data,that is, if we denote bysm,u the main stream of complex datafor user u, then we have the following at subcarrier 2m:

d

(c)

2m,u,0 =s2m,u

2

d(c)2m,u,1 =

s2m+1,u2

(51)

and at subcarrier 2m + 1,

d(c)2m+1,u,0 =

s2m+1,u2

d(c)2m+1,u,1 =

s2m2.

(52)

Then, considering a flat fading channel, the despreadedsignal for user u is given by

z(c)m,u = hm,0d(c)m,u,0 + hm,1d(c)m,u,1. (53)

Therefore, we get z(c)2m,uz

(c)2m+1,u

= 1

2

h2m,0 h2m,1h2m+1,1

h2m+1,0 s2m,u

s2m+1,u

.(54)

That means, when assuming the channel to be flat over twoconsecutive subcarriers, that is, h2m,i = h2m+1,i for all i, wehave exactly the same decoding equation as the Alamoutischeme presented in Section 3.2, by permuting the frequency

and time axis. Then, the decoding is performed in the sameway.

(2) Strategy 2. Alamouti performed over pairs of spreadingcodes. In this second strategy, we apply the Alamouti schemeon pairs of codes, that is, we divide the Ucodes in two groups(assumingUto be even). That is, we process the codes by pair(u0,u1). We denote by sm,u0 ,u1 the main stream of complexdata for user pair (u0,u1). At subcarrier m, antennas 0 and 1transmit

d(c)m,u0 ,0 =

sm,u0 ,u12

,

d(c)m,u0 ,1 = sm+1,u0 ,u12 ,

d(c)m,u1 ,0 =

sm+1,u0,u12

,

d(c)m,u1 ,1 =

sm,u0 ,u12

.

(55)

At the receiver side we get,

z(c)m,u0

z

(c)m,u1

= 12

hm,0 hm,1hm,1

hm,0

sm,u0 ,u1sm+1,u0 ,u1

. (56)


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2520151050

SNR

Alamouti-CDMA-OFDM/OQAM (str ategy2)

Alamouti-CDMA-OFDM/OQAM (str ategy1)

Alamouti CP-OFDM

105

104

103

102

101

100

BER

Figure 9: BER for two complex versions of the Alamouti CDMA-OFDM/OQAM with spreading in time domain, versus AlamoutiCP-OFDM for transmission over the 4-path frequency selectivechannel.

18161412108642

SNR

Alamouti-CDMA-OFDM/OQAM (strategy1)

Alamouti-CDMA-OFDM/OQAM (strategy2)

Alamouti CP-OFDM

104

103

102

101

100

BE

R

Figure 10: BER for two complex versions of the Alamouti CDMA-OFDM/OQAM with spreading in time domain, versus AlamoutiCP-OFDM for transmission over the 7-path frequency selectivechannel.

Then, we do not need to consider the channel constantover two consecutive subcarriers. We have exactly the samedecoding equation as the Alamouti scheme presented inSection 3.2. Hence, the decoding is performed in the sameway.

We have tested two different channels considering eachtime the same channel profile, but with different realizations,between the 2 transmit antennas and one receive antenna.The Guard Interval (GI) is adjusted to take into account thedelay spread profiles corresponding to a 4-path and to a 7-path channel. The 4-path channel is characterized by the

following parameters:

(i) power profile (in dB): 0, 6, 9, 12,(ii) delay profile (in samples): 0, 1, 2, 3,

(iii) GI for CP-OFDM: 5 samples,

and the 7-path by

(i) power profile (in dB): 0,6, 9, 12, 16, 20, 22,(ii) delay profile (in samples): 0, 1, 2, 3, 5, 7, 8,

(iii) GI for CP-OFDM: 9 samples;

We also consider the following system parameters:

(i) QPSK modulation,

(ii) M= 128 subcarriers,(iii) time invariant channel (no Doppler),

(iv) the IOTA prototype filter of length 512,

(v) spreading codes of length 32, corresponding to theframe duration (32 complex OQAM symbols),

(vi) number of CDMA W-H codes equals to 16 in

complex OFDM/OQAM, with symbol duration 0and this corresponds to 32 codes in OFDM, withsymbol duration 20, leading to the same spectralefficiency

(vii) zero forcing, one tap equalization,

(viii) no channel coding.

In Figures 9 and 10, the BER results of the AlamoutiCDMA-OFDM/OQAM technique for the two proposedstrategies are presented.

The two strategies perform the same until a BER of103 or 102 for the 4 and 7-path channel, respectively.

For lower BER the strategy 2 performs better than thestrategy 1. This could be explained by the fact that strategy1 makes the approximation that the channel is constantover two consecutive subcarriers. This approximation leadsto a degradation of the performance whereas the strategy2 does not consider this approximation. If we compare theperformance of Alamouti CDMA-OFDM/OQAM strategy2 with the Alamouti CP-OFDM, we see that both systemperform approximately the same. It is worth mentioningthat however the corresponding throughput is higher for theOFDM/OQAM solutions (no CP). Indeed, it is increasedby approximately 4 and 7% for the 4 and 7-path channels,respectively.


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5. Conclusion

In this paper, we showed that the well-known Alam-outi decoding scheme cannot be directly applied to theOFDM/OQAM modulation. To tackle this problem, weproposed to combine the MIMO Alamouti coding scheme

with CDMA-OFDM/OQAM. If the CDMA spreading iscarried out in the frequency domain, the Alamouti decodingscheme can only be applied if the channel is assumedto be flat. On the other hand, for a frequency selec-tive channel, the CDMA spreading component has to beapplied in the time domain. For the Alamouti scheme withtime spreading CDMA-OFDM/OQAM, we elaborate twostrategies for implementing the MIMO space-time codingscheme. Strategy 1 implements the Alamouti over pairs ofadjacent frequency domain samples whereas the strategy2 processes the Alamouti coding scheme over pairs ofspreading codes from two successive time instants. Strategy2 appears to be more appropriate since it requires lessrestrictive assumptions on the channel variations acrossthe frequencies. We also made some performance compar-isons with Alamouti CP-OFDM. It was found that, undersome channel hypothesis, the combination of Alamoutiwith complex CDMA-OFDM/OQAM is possible withoutincreasing the complexity of the Alamouti decoding process.Furthermore, in the case of a frequency selective channel,OFDM/OQAM keeps its intrinsic advantage with a SNRgain in direct relation with the CP length. To find asimpler Alamouti scheme, that is, without adding a CDMAcomponent, remains an open problem. Naturally, some otheralternative transmit diversity schemes for OFDM/OQAM, asfor instance cyclic delay diversity, could also deserve furtherinvestigations.

Acknowledgments

The authors would like to thank the reviewers and Pro-fessor Farhang-Boroujeny for their careful reading of ourmanuscript and for their helpful suggestions. This workwas partially supported by the European ICT-2008-211887project PHYDYAS.

References

[1] S. M. Alamouti, A simple transmit diversity technique forwireless communications, IEEE Journal on Selected Areas inCommunications, vol. 16, no. 8, pp. 14511458, 1998.

[2] H. Bolcskei, Orthogonal frequency division multiplexingbased on offset QAM, in Advances in Gabor Analysis,Birkhauser, Boston, Mass, USA, 2003.

[3] G. Cherubini, E. Eleftheriou, and S. Olcer, Filtered multitonemodulation for very high-speed digital subscriber lines, IEEE

Journal on Selected Areas in Communications, vol. 20, no. 5, pp.10161028, 2002.

[4] R. Hleiss, P. Duhamel, and M. Charbit, Oversampled OFDMsystems, in Proceedings of the International Conference onDigital Signal Processing (DSP 97), vol. 1, pp. 329331,Santorini, Greece, July 1997.

[5] B. R. Saltzberg, Performance of an efficient parallel datatransmission system, IEEE Transactions on CommunicationTechnology, vol. 15, no. 6, pp. 805811, 1967.

[6] B. Hirosaki, An orthogonally multiplexed QAM systemusing the discrete Fourier transform, IEEE Transactions onCommunications Systems, vol. 29, no. 7, pp. 982989, 1981.

[7] B. Le Floch, M. Alard, and C. Berrou, Coded orthogonalfrequency division multiplex, Proceedings of the IEEE, vol. 83,pp. 982996, 1995.

[8] T. Karp and N. J. Fliege, MDFT filter banks with perfectreconstruction, in Proceedings of IEEE International Sympo-sium on Circuits and Systems (ISCAS 95), vol. 1, pp. 744747,Seattle, Wash, USA, May 1995.

[9] P. Siohan, C. Siclet, and N. Lacaille, Analysis and designof OFDM/OQAM systems based on filterbank theory, IEEETransactions on Signal Processing, vol. 50, no. 5, pp. 11701183,2002.

[10] B. Farhang-Boroujeny and R. Kempter, Multicarrier commu-nication techniques for spectrum sensing and communicationin cognitive radios, IEEE Communications Magazine, vol. 46,

no. 4, pp. 8085, 2008.[11] C. Lele, P. Siohan, R. Legouable, and M. Bellanger, CDMA

transmission with complex OFDM/OQAM, EURASIP Jour-nal on Wireless Communications and Networking, vol. 2008,Article ID 748063, 12 pages, 2008.

[12] M. El Tabach, J.-P. Javaudin, and M. Helard, Spatial datamultiplexing over OFDM/OQAM modulations, in Proceed-ings of the IEEE International Conference on Communications(ICC 07), pp. 42014206, Glasgow, Scotland, June 2007.

[13] J.-P. Javaudin, D. Lacroix, and A. Rouxel, Pilot-aided channelestimation for OFDM/OQAM, in Proceedings of the IEEEVehicular Technology Conference (VTC 03), vol. 3, pp. 15811585, Jeju, South Korea, April 2003.

[14] C. Lele, J.-P. Javaudin, R. Legouable, A. Skrzypczak, and P.

Siohan, Channel estimation methods for preamble-basedOFDM/OQAM modulations, in Proceedings of the 13thEuropean Wireless Conference (EW 07), Paris, France, April2007.

[15] M. Bellanger, Transmit diversity in multicarrier transmissionusing OQAM modulation, in Proceedings of the 3rd Interna-tional Symposium on Wireless Pervasive Computing (ISWPC08), pp. 727730, Santorini, Greece, May 2008.

[16] H. Lin, C. Lele, and P. Siohan, A pseudo alamouti transceiverdesign for OFDM/OQAM modulation with cyclic prefix,in Proceedings of the IEEE Workshop on Signal Processing

Advances in Wireless Communications (SPAWC 09), pp. 300304, Perugia, Italy, June 2009.

[17] D. Lacroix-Penther and J.-P. Javaudin, A new channel esti-mation method for OFDM/OQAM, in Proceedings of the7th International OFDM Workshop (InOWo 02), Hamburg,Germany, September 2002.

[18] D. Tse and P. Viswanath, Fundamentals of Wireless Communi-cation, Cambridge University Press, Cambridge, Mass, USA,2004.

[19] C. Lele, P. Siohan, R. Legouable, and M. Bellanger,OFDM/OQAM for spread spectrum transmission, in Pro-ceedings of the International Workshop on Multi-CarrierSpread-Spectrum (MCSS 07), Herrsching, Germany, May2007.

[20] K. Fazel and L. Papke, On the performance of convolu-tionnally-coded CDMA/OFDM for mobile communication


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system, in Proceedings of the Symposium on Personnal, Indoorand Mobile Radio Communications (PIMRC 93), pp. 468472,Yokohama, Japan, September 1993.

[21] E. H. Dinan and B. Jabbari, Spreading codes for directsequence CDMA and wideband CDMA cellular networks,IEEE Communications Magazine, vol. 36, no. 9, pp. 4854,1998.


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Article_The Alamouti scheme with CDMA-OFDMOQAM