research open access on transmission performance of ofdm ... · average power ratio (papr), and...

RESEARCH Open Access

On transmission performance of OFDM-basedschemes using MMSE-FDE in a frequency-selective fading channelHaris Gacanin1* and Fumiyuki Adachi2

Abstract

There has been greatly increasing interest in orthogonal frequency division multiplexing (OFDM) for broadbandwireless transmission due to its robustness against multipath fading. However, OFDM signals have high peak-to-average power ratio (PAPR), and thus, a power amplifier must be operated with a large input power backoff (IBO).Recently, OFDM combined with time division multiplexing (OFDM/TDM) using minimum mean square error-frequency domain equalization (MMSE-FDE) has been presented to reduce the PAPR, while improving the bit errorrate (BER) performance of conventional OFDM. In this article, by extensive computer simulation, we present acomprehensive performance comparison of OFDM-based schemes in a nonlinear and frequency-selective fadingchannel. We discuss about the transmission performance of OFDM-based schemes with respect to the transmitpeak-power, the achievable capacity, the BER performance, and the signal bandwidth. Our results show thatOFDM/TDM using MMSE-FDE achieves a lower peak-power and capacity than conventional OFDM, which meanssignificant reduction of amplifier transmit-power backoff, but with a slight decrease in signal bandwidth occupancy.

Keywords: OFDM/TDM, OFDM, capacity, power spectrum density, bit error rate, amplifier power efficiency

I. IntroductionIn a wireless channel, a signal propagates over a numberof different paths that give rise to a frequency-selectivefading, which produce severe inter-symbol interference(ISI) and degrades the transmission performance [1]. Tosolve this problem, intensive research effort on fre-quency domain channel equalization (FDE) is currentlyongoing in two directions: (i) orthogonal frequency divi-sion multiplexing (OFDM) [2], and (ii) single carrier(SC)-FDE [3]. To avoid the performance degradation ofOFDM due to high PAPR, the high transmit poweramplifier (HPA) must be operated with a large inputbackoff (IBO). Otherwise, the system performance interms of the bit error rate (BER), channel capacity,throughput, etc., may be degraded. The performance ofOFDM system over a nonlinear channel (e.g., HPA oramplitude limiter) has been analyzed in the recent lit-erature [4-6].

Of late, various approaches to reduce the PAPR ofOFDM have been proposed [7-12]. The conventionalOFDM and SC-FDE are compared in [13] with respectto their BER performances, PAPR, carrier frequency off-set, and computational complexity. In [14], the perfor-mance of clipped OFDM is analyzed in terms of thePAPR reduction capability and degradation of the chan-nel capacity. It was shown that the nonlinearity signifi-cantly degrades the channel capacity of OFDM due tothe high PAPR.Recently, OFDM combined with time division multi-

plexing (OFDM/TDM) [15] using minimum meansquare error FDE (MMSE-FDE) [16] was presented toreduce the PAPR, while improving the BER performanceof conventional OFDM. The PAPR problem, however,cannot be completely eliminated. OFDM/TDM usingMMSE-FDE transmits data over Nm (= Nc/K) subcar-riers, where Nc is the number of subcarriers in the con-ventional OFDM. A natural consequence is that thecapacity may decrease due to the reduced number ofsubcarriers. In particular, as stated in [14], the channelcapacity further decreases in a nonlinear channel due to

* Correspondence: [email protected] Division, Alcatel-Lucent Bell N.V., Antwerp, BelgiumFull list of author information is available at the end of the article

Gacanin and Adachi EURASIP Journal on Wireless Communicationsand Networking 2011, 2011:193http://jwcn.eurasipjournals.com/content/2011/1/193

© 2011 Gacanin and Adachi; licensee Springer. This is an Open Access article distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly cited.

mailto:[email protected]

http://creativecommons.org/licenses/by/2.0

the PAPR problem of OFDM. Hence, some additionalPAPR reduction technique must be applied.In [17], we analyzed the theoretical BER performance

of amplitude clipped and filtered OFDM/TDM usingMMSE-FDE. However, to unveil a potential of OFDM/TDM using MMSE-FDE, a more detailed transmissionperformance comparison in terms of transmit peak-power, the channel capacity and the spectrum splatter ofOFDM/TDM, and the conventional OFDM is required.To the best of our knowledge, such performance compar-ison between OFDM/TDM using MMSE-FDE and theconventional OFDM has not been reported.In this article, we provide a comprehensive perfor-

mance comparison between OFDM/TDM using MMSE-FDE and the conventional OFDM. A trade-off betweenthe transmit peak-power reduction (i.e., IBO reduction),the achievable capacity, the BER performance and thepower spectrum efficiency is discussed. We discussabout how, and by how much, OFDM/TDM usingMMSE-FDE improves the transmission performance incomparison with conventional OFDM system. Our aimis to show that OFDM/TDM using MMSE-FDE can beused in practical systems to overcome the high PAPRproblem of conventional OFDM at the cost of slightdecrease in spectrum efficiency. The capacity of OFDM/TDM using MMSE-FDE is obtained based on the Gaus-sian assumption of the OFDM/TDM signal amplitude.The remainder of this article is organized as follows.

Section II presents OFDM/TDM using MMSE-FDE sys-tem model. The computer simulation results and discus-sions are presented in Section III. Section IV concludesthe article.

II. System overviewIn this section, we begin with a brief overview of theconventional OFDM and later, OFDM/TDM usingMMSE-FDE is presented. The information bit sequenceof length M is channel coded with a coding rate R andmapped into the transmit data symbols, correspondingto quadrature phase shift keying (QPSK) modulationscheme. This sequence is divided into blocks {dm(i); i =0 ~ Nc - 1}, m = 0 ~ M/Nc - 1, with E[|dm(i)|

2] = 1,where E[·] denotes the ensemble average operation. Inthis study, without loss of generality, we consider atransmission of one block and thus, the block index mis omitted in what follows.

A. Conventional OFDMThe conventional OFDM system model is illustrated inFigure 1. In the conventional OFDM system, an Nc data-modulated symbol sequence {d(i); i = 0 ~ Nc - 1} is fed toJNc-point inverse fast Fourier transform (IFFT) to gener-ate an oversampled time-domain OFDM signal with Nc

subcarriers. Throughout this study, the oversampling

ratio J is used to approximate the time domain transmitsignal with high accuracy. After insertion of guard inter-val (GI) the signal is fed to pre-linearized HPA (i.e., thesignal is clipped and filtered by a soft-limiter model),where linear amplification is achieved until the saturationoutput power level Ps (normalized by the input signalpower). We assume that the amplifier saturation levelequals the clipping level. Finally, the signal is transmittedover a frequency-selective fading channel.At the receiver, after removing the GI, the Nc-point

FFT is applied to decompose the received signal into Nc

subcarriers {R(n); n = 0 ~ Nc - 1}. The distortion in thechannel has the effect of changing the phase and ampli-tude of each subcarrier, which is corrected by the singletap FDE through multiplication of the received signal R(n) by the equalization weight w(n) [2].

B. OFDM/TDM using MMSE-FDEThe OFDM/TDM transmission system model is illustratedin Figure 2. In OFDM/TDM the Nc-subcarrier OFDM sig-naling interval (i.e., OFDM/TDM frame) is divided into Kslots. A date-modulated symbol sequence {d(i); i = 0 ~ Nc

- 1} to be transmitted is divided into K subblocks eachhaving Nm (= Nc/K) data-modulated symbols. A time andfrequency symbol arrangement for conventional OFDMand OFDM/TDM is presented in Figure 3. The kth sub-block {dk(i); i = 0 ~ Nm - 1} is transmitted in the kth slot,where dk(i) = d(kNm+i) for k = 0 ~ K - 1. Then, JNm-pointIFFT is applied to generate the kth slot oversampled time-domain OFDM signal with Nm subcarriers as

sk(t) =√2P

Nm−1∑i=0

dk(i) exp{j2π t

i

JNm

}(1)

Dat

a m

odul

atio

n

JNc-p

oint

IFFT

GIInfo data

s(t)

(a) Transmitter

AWGN

-GI

…

Nc-p

oint

FFT

w(n)

R(n)

…

……

(b) Receiver

Figure 1 Conventional OFDM transmitter/receiver structure.


of 10

for t = 0 ~ Nm - 1, where P = Es/TcNm denotes thetransmit signal power. Es and Tc denote the data-modu-lated symbol energy and the sampling interval of theIFFT, respectively. The OFDM/TDM signal can beexpressed using the equivalent low-pass representationas

s(t) =K−1∑k=0

sk(t − kNm)u(t − kNm) (2)

for t = 0 ~ Nc - 1, where u(t) = 1(0) for t = 0 ~ Nm -1 (elsewhere). After insertion of the guard interval (GI),the OFDM/TDM signal is fed into pre-linearized HPAas in the case of conventional OFDM and transmittedover a frequency-selective fading channel.The OFDM/TDM signal propagates through the chan-

nel with a discrete-time channel impulse response h(τ)given as

h(τ ) =L−1∑l=0

hlδ(τ − τl), (3)

where hl and τl are the path gain and the time delay,respectively, of the lth path having the sample-spacedexponential power-delay profile with channel decay fac-

tor b (i.e.,E[|hg,l|2] = 1 − β

1 − βLβ l ). We assume that the

maximum time delay of the channel is less than the GIlength.At the receiver, Nc-point FFT is applied over the

entire OFDM/TDM frame [16] to decompose thereceived signal into Nc frequency components repre-sented by {R(n); n = 0 ~ Nc - 1}. One-tap MMSE-FDE[3] is applied to R(n) as

R(n) = R(n)w(n), (4)

where w(n) is the equalization weight given by [16]

w(n) =H∗(n)

|H(n)|2 +(EsN0

)−1 , (5)

where H(n) and N0 denote the Fourier transform ofthe channel impulse response and the single-sided addi-tive white Gaussian noise (AWGN) power spectrumdensity (PSD), respectively.The time-domain OFDM/TDM signal is recovered by

applying Nc-point IFFT to {R(n); n = 0 ∼ Nc − 1} and

then, the OFDM demodulation is carried out using Nm-point FFT to obtain decision variables

{dk(i); i = 0 ∼ Nm − 1}[16]. For channel decoding, thelog-likelihood ratios (LLRs) are computed before decod-ing [18].We note here that OFDM/TDM using MMSE-FDE

for K = 1 (i.e., Nm = Nc) reduces to the conventionalOFDM system with Nc = 256 subcarriers.

III. Performance analysisWe first develop a mathematical model for PAPR distri-bution of OFDM/TDM signal and then, we develop theexpression for the capacity of OFDM/TDM usingMMSE-FDE.

A. PAPR of OFDM/TDMThe baseband oversampled OFDM/TDM signal given by(2) is considered. The PAPR of the observed OFDM/TDM frame is defined as the ratio of the peak power tothe ensemble average power and can be expressed as

PAPR =max{|s(t)|2}t = 0∼JNc−1

E{|s(t)|2} . (6)

The expression for PAPR distribution of OFDM/TDMis derived based on assumption that JNm-point IFFTsize is large enough so that real and imaginary part of

Dat

a m

odul

atio

n

JNm

-poi

nt IF

FT

Fram

e ge

nera

tion

GI per frame

Info data

s(t)

(a) Transmitter

AWGN

-GI

…

OFDM/TDMdemod.

Nc-p

oint

FFT w(n)

R(n)

…

Nc-p

oint

IFFT

MMSE-FDE

(b) Receiver

Figure 2 OFDM/TDM transmitter/receiver structure.

t

f

d(0)d(1)

d(15)

td(3)

d(2)

d(1)

d(0)

d(7)

d(6)

d(5)

d(4)

d(11)

d(10)

d(9)

d(8)

d(15)

d(14)

d(13)

d(12)

f

(a) Conventional OFDM (Nc=16) (b) OFDM/TDM (Nc=16; Nm=4, K=4)

Figure 3 Time and frequency data arrangement.


of 10

the kth time slot OFDM signal sk(t), for t = 0 ~ JNm - 1,are samples of zero-mean statistically independentGaussian process with unit variance. Hence, the ampli-tudes {r(t) (= |sk(t)|); t = 0 ~ JNm - 1} are independent-and-identically distributed (i.i.d.) Rayleigh random vari-ables [1].Cumulative distribution function (cdf) F(lk) of the

PAPR lk for the kth slot is given by

F(λk) =[1 − exp (−λk)

]JNm . (7)

We assume that the block data-modulated symbols {dk

(i); i = 0 ~ Nm - 1} and k = 0 ~ K - 1 are statisticallyindependent, so that the OFDM/TDM signal is gener-ated from K statistically independent OFDM signals.Hence, the PAPR probability of OFDM/TDM is givenby

FOFDM/TDM(λ) ={1 − [

1 − exp(−λ)JNm]}K

. (8)

It can be seen from (8) that the PAPR of OFDM/TDM decreases as K increases. For K = 1, the aboveexpression collapses to the PAPR expression for theconventional OFDM. The above PAPR probabilityexpression given by (8) together with computer simula-tion results is evaluated in the next section.

B. Channel capacity of OFDM/TDM using MMSE-FDEFrom here on, we analyze capacity of the OFDM/TDMusing MMSE-FDE based on the assumption that non-linear distortion caused by power amplifier is Gaussian.We assume perfect channel knowledge.Using the Bussgang theorem [5,6], the received

OFDM/TDM signal can be expressed as

R (n) = αS (n)H (n) + αI (n) + Sc (n)H (n) +N (n) . (9)

where S(n), H(n), I(n), Sc(n), and N(n) denote theFourier transform of transmitted OFDM/TDM signal,the channel gain, the inter-slot interference (ISI), thenonlinear distortion, and zero mean AWGN process,respectively, having single-sided power spectrum densityN0. a denotes the attenuation constant that can be well

approximated as α = 1 − exp (−P2s ) +

√πPs2 erfc (Ps)[4-6],

where Ps is the HPA power saturation level (normalizedby the input average signal power), and

erfc[x] = 2√π

∫ ∞

xexp(−t2)dt is the complementary error

function.After MMSE-FDE, the time-domain OFDM/TDM sig-

nal is recovered by applying Nc-point IFFT to

{R(n); n = 0 ∼ Nc − 1} and then, OFDM demodulationis carried out by Nm-point FFT to obtain decision vari-ables:

dk(i) =

√2EsTcNm

αdk(i)

[1Nc

Nc−1∑n=0

H(n)

]+ μk(i) (10)

withH(n) = H(n)w(n) . In the above expression, μk(i)denotes the kth slot composite noise (i.e., the sum ofnonlinear component, AWGN, and residual ISI afterFDE). We approximate μk(i) as a zero-mean complex-valued Gaussian process and that μk(i) is uncorrelatedwith dk(i). Thus, the variance of μk(i) can be computedas

2σ 2 =2α2EsTcNc

Nc−1∑n=0

∣∣∣∣∣H(n) − 1Nc

Nc−1∑m=0

H(m)

∣∣∣∣∣2

|(n)|2

+2EsNm

TcNc

Nc−1∑n=0

[1 − exp(−P2

s ) − α2] |H(n)|2|(n)|2

+2N0

TcNc

Nc−1∑n=0

|w(n)|2|(n)|2,

(11)

where

(n) =1Nm

sin{πNm

n−KiNc

}sin

{π n−Ki

Nc

} × exp{jπ

[(2k + 1)Nm − 1

] n − KiNc

}. (12)

We note here that the first term in (11) denotes theresidual ISI, and it is omitted in the case of the conven-tional OFDM.For the given Ps and Es/N0, the ergodic channel capa-

city C[Es/N0, Ps] in bps/Hz over a Rayleigh channel canbe computed as [1]:

C[Es/N0,Ps] = E[C

(EsN0

,Ps, {H(n)})]

=

∞∫0

· · ·∞∫0

C[EsN0

,Ps, {H(n)}]

℘[{H(n)}] ×∏n

dH(n),(13)

where C(Es/N0, {H(n)}) and ℘ [{H(n)}] denote the con-ditional channel capacity given by [1]:

C[EsN0

,Ps, {H(n)}]=

1Nc

Nc−1∑n=0

log2

[1 + γ

(EsN0

,Ps, {H(n)})]

. (14)

and the joint probability density function of {H(n); n =0 ~ Nc - 1}, respectively. A closed or convenient expres-sion for numerical calculation has not been found forintegral in (13), and thus, we resort to a differentapproach. The signal-to-noise plus interference-and-dis-tortion ratio g (·) of OFDM/TDM using MMSE-FDE isfirst computed using (10) as

γ

(EsN0

,Ps, {H(n)})=2α2 Es

TcNm

∣∣∣∣ 1Nc

∑Nc−1n=0 H(n)

∣∣∣∣2

2σ 2.(15)


of 10

Using (15), we can write (13) as

C[EsN0

,Ps

]=

1Nc

∞∫0

· · ·∞∫0

Nc−1∑n=0

log2

[1 + γ

(EsN0

, {H(n)})]

× ℘[{H(n)}]∏n

dH(n). (16)

The evaluation of the ergodic capacity is done byMonte Carlo numerical-computation method as follows.A set of path gains {hl; l = 0 ~ L - 1} is generated using(3) to obtain channel gains {H(n); n = 0 ~ Nc - 1}. Then,the capacity given by (16) is computed using (15) forthe given set of channel gains {H(n)} as a function ofthe Es/N0 and the normalized saturation level Ps of thepower amplifier. This is repeated a sufficient number oftimes to obtain the average capacity.

Iv. Numerical evaluation and discussionsWe assume an OFDM/TDM frame size of Nc = 256samples, GI length of Ng = 32 samples, and ideal coher-ent quadrature phase shift keying (QPSK) data modula-tion/demodulation. As the propagation channel, weassume an L = 16-path block Rayleigh fading channelhaving the exponential power-delay profile with channeldecay factor b. It is assumed that the maximum timedelay of the channel is less than the GI length. Theinformation bit sequence length is taken to be M =1024 bits. A (2048, 1024) low-density parity check(LDPC) encoder [19] is assumed with code rate R, andsum product algorithm (SPA) decoder having columnweight = 1, and row weight = 8. A rate R = 1/3 turboencoder with constraint length 4 and (13, 15) recursivesystematic convolutional (RSC) component encoders isapplied, while the parity bit sequences are punctured toobtain coding rate of 1/2. The turbo coded bit sequenceis interleaved before data modulation. A block interlea-ver used as channel interleaver in the simulation is ofsize 2a and 2b block interleaver, where a and b are themaximum allowable integers for a given sequence sizeso that we can obtain an interleaver as close as possibleto a square one. The internal interleaver for turbo cod-

ing is S-random

(S = N

12

)interleaver. Log-MAP

decoding with eight iterations is carried out at thereceiver.

A. Bit error rate issueThe BER performance with and without channel codingas a function of the average signal energy per bit-to-AWGN power spectrum density ratio Eb/N0 = 0.5 × R ×(Es/N0) × (1 + Ng/Nc) is illustrated in Figure 4. In oursimulation, we consider turbo and LDPC channel enco-ders with rate R = 1/2. As seen from Figure 4a, thecoded BER of conventional OFDM (K = 1) is betterthan OFDM/TDM with K = 16 (64) (i.e., 1.4 (0.15) dBlower Eb/N0 is required to achieve BER = 10-4). Unlike

uncoded case where the BER decreases as K increases,with turbo coding, a trade-off is present among fre-quency diversity gain, coding gain due to better fre-quency interleaving effect, and orthogonality distortionbetween consecutive slots within OFDM/TDM frame;for higher (lower) K, the coding gain is lower (higher)due to the reduced frequency-interleaving effect, whilehigher (lower) frequency diversity gain is obtained. Con-sequently, for turbo-coded case, the appropriate para-meter K may be chosen to achieve the same BER asconventional OFDM while still giving the lower PAPR.It can be seen from the Figure 4b that the LDPC-coded

1.E-04

1.E-03

1.E-02

1.E-01

0 5 10 15 20 25 30 35Average Eb /N 0 (dB)

Ave

rage

BER

K=1 (OFDM)K=4K=8K=16K=64K=256 (SC)

OFDM (K=1)K=4K=8K=16K=64SC (K=256)

K

K

f DT s=0.0014, QPSK, L =16, β=0 dB

uncoded

coded

Turbocoded(R =0.5)

(a) Turbo coded

1.E-04

1.E-03

1.E-02

1.E-01

0 5 10 15 20 25Average E b /N 0 (dB)

Ave

rage

BER

K=

LDPC coded

(R=0.5)

uncoded

QPSKL=16β=0 dB

OFDM (K =1)

f D T s =10-4

MMSE-FDE

4

1664

(b) LDPC coded

Figure 4 BER versus Eb/N0.


of 10

BER performance is almost the same irrespective of thedesigned parameter K.Figure 5 illustrates the average BER performance of

OFDM/TDM with MMSE-FDE as a function of theamplifier’s saturation power level Ps normalized by theinput signal power for Eb/N0 = 30 dB with K as a para-meter. The figure shows that OFDM/TDM can be usedto reduce the required IBO, while achieving the betterBER than the conventional OFDM. For example, if therequired BER = 10-3, then the conventional OFDM (K =1) cannot achieve this performance irrespective of Ps.Hence, to achieve BER = 10-3 with reduced IBO, we canuse OFDM/TDM. When K increases from 16 to 32, theHPA power saturation level Ps can be reduced from 7 to1 dB for BER = 10-3, respectively. Note that K = 64 canachieve BER = 10-3 irrespective of Ps. This is because asK increases, the PAPR of the OFDM/TDM signalreduces, and the signal is less degraded in the HPA. It isseen from Figure 5 that as K increases the requiredpeak-power (i.e., IBO) of OFDM/TDM is reducing; forthe average BER = 10-4, IBO can be reduced by about1.3, 2.9 and 5.1 dB, compared to the conventionalOFDM, when K = 4, 16, and 64, respectively, as shownin Figure 5. The worst performance is achieved with theconventional OFDM (K = 1) due to large PAPR.

B. Power efficiency issueIn this section, we discuss about the peak-power that isproportional to the PAPR of the transmitted signal. Bydefinition, it can be shown that the theoretical PAPR ofOFDM/TDM is proportional to the number of subcar-riers Nm (= Nc/K). The PAPR values (in decibels) of

OFDM/TDM and conventional OFDM, which representthe required IBO for QPSK constellation are given inTable 1. It is seen from the table that the PAPR ofOFDM is as large as 24 dB, while, for OFDM/TDMwith K = 4 and 16, the PAPR reduces to 18 and 12 dB,respectively. Although the PAPR increases linearly withthe number of subcarriers Nm, the probability that sucha peak will occur decreases exponentially with Nm.Figure 6 illustrates the theoretical and computer-simu-

lated complementary cdf (ccdf) of PAPR for OFDM/TDM as a function of K when Nc = 256. The theoreticalccdf of OFDM/TDM and the conventional OFDM arecomputed using (8). Also presented below are the com-puter simulation results for the OFDM/TDM signaltransmission to confirm the validity of the theoreticalanalysis. Computer simulation results for ccdf of PAPRare obtained over 20 million OFDM/TDM frames. Afairly good agreement with theoretical and computer-simulated results is seen, which confirms the validity ofour PAPR analysis based on the Gaussian approximationof the OFDM/TDM signal. It can be seen from the fig-ure that, as K increases, the PAPR10% level, by which thePAPR of OFDM/TDM exceeds with a probability of10%, is about 9, 8, 6.5, and 3 dB for K = 1 (OFDM), 4,16, and 256 (SC), respectively.We also consider the required peak transmit power

because it is an important design parameter of transmitpower amplifiers. For conventional OFDM transmission,high PAPR causes signal degradation due to nonlinearpower amplification, and the BER performance degrades.Figure 7 illustrates the BER performance of the codedOFDM/TDM using MMSE-FDE as a function of thepeak transmit power with K as a parameter. We con-sider the PAPR10% level, which the PAPR of OFDM/TDM exceeds with a probability of 10%. PAPR10% areabout 8.5, 7.2, and 5.7 dB for K = 1, 16, and 64, respec-tively. It is seen from the figure that for turbo code theconventional OFDM (K = 1) gives the worst perfor-mance due to the large PAPR. As K increases therequired peak-power (i.e., IBO) of OFDM/TDM is redu-cing; for the average BER = 10-4, IBO can be reduced byabout 1.3, 2.9, and 5.1 dB, compared to the conventionalOFDM, when K = 4, 16 and 64, respectively, as shownin Figure 4. In the case of LDPC codes the performanceimprovement is slightly larger in comparison withturbo-coded performance. We note here that the

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0 1 2 3 4 5 6 7 8P s (dB)

Ave

rage

BER

K=1256 (SC)L=16E b /N 0=30 dB

MMSE-FDEK =1 (OFDM)

4

16

64

Figure 5 BER versus Ps.

Table 1 PAPR comparison between OFDM/TDM andconventional OFDM

Parameters Nc = 256, Nm = Nc/K PAPR level (dB)

Conventional OFDM K = 1, Nm = 256 24.08

OFDM/TDM K = 4 (16), Nm = 64 (16) 18.06 (12.04)


of 10

performance improvement presented above is paid withlower spectral efficiency as presented in the nextsection.

C. Channel capacity issueThe channel capacity in bps/Hz is illustrated in Figure 8as a function of the amplifier’s saturation power level Psnormalized by the input signal power with K as a para-meter for Eb/N0 = 30 dB (for a low Eb/N0 the achievablecapacity is almost the same irrespective of K, and thecapacity trade-off as a function of K cannot beobserved). The capacity of OFDM/TDM using MMSE-FDE is illustrated in Figure 8 as a function Ps for theaverage bit energy-to-AWGN power spectrum densityratio Eb/N0 = 30 dB, where Eb/N0 = 0.5 × (Es/N0) × (1+Ng/Nc). The figure shows that for lower Ps (<8 dB), theperformance of OFDM/TDM using MMSE-FDE with K= 4, 16 and 64 outperforms the conventional OFDM (K= 1), while the best capacity is achieved with SC-FDE (K= 256) payed by the lower signal bandwidth occupancy.On the contrary, for higher Ps (>8 dB) the highest capa-city is achieved with the conventional OFDM (K = 1),while the lowest is achieved with SC-FDE (K = 256).

D. Channel code rate issueHere, the impact of different code rates on the BER per-formance with K as a parameter is evaluated by compu-ter simulation. Figure 9 illustrates the BER performanceas a function of design parameter K for both turbo- andLDPC channel-coding techniques. It can be seen from

the figure that the impact of K on the BER performancewith different code rates is not high for both channelencoders. We note here that the impacts of differentdecoding strategies are not taken into consideration, andit are out of the scope of this study.

E. The channel frequency-selectivity issueAs said earlier, the performance improvement ofOFDM/TDM is attributed to the frequency-diversityeffect achieved by the MMSE-FDE. This suggests that

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10 11 12

PAPR (dB)

Prob

[PA

PR>a

bsci

ssa]

OFDM (K =1)

K =16

K =4

SimulationTheory

SC (K =256)

Figure 6 PAPR distribution of OFDM/TDM.

1.E-04

1.E-03

1.E-02

1.E-01

5 10 15 20Peak E b /N 0 (90%) (dB)

Ave

rage

BER

K=1K=4K=16K=64

Turbo coded (R=0.5)

QPSKL=16β=0 dBf D T s =10-4

MMSE-FDE

OFDMK =4K =16K =64

Uncoded

(a) Turbo coded

1.E-04

1.E-03

1.E-02

1.E-01

5 10 15 20Peak E b /N 0 (90%) (dB)

Ave

rage

BER

K=1K=4K=16K=64

QPSKL=16,β=0 dBf D T s =10-4

MMSE-FDE

LDPC coded(R =0.5)

OFDMK =4K =16K =64

Uncoded

(b) LDPC coded

Figure 7 BER versus Peak Eb/N0.


of 10

the BER performance depends on the channel frequencyselectivity. The measure of the channel selectivity is thedecay factor b of the channel power-delay profile. Thedependency of the achievable BER performance on b isshown in Figure 10 for both turbo and LDPC encoders.As was expected, as b becomes larger, the performanceof OFDM/TDM with higher K degrades for both enco-ders due to less frequency-diversity effect resulting fromthe weaker frequency selectivity. It can be also seenfrom the figure that in the case of LDPC channel enco-der, the BER performance of OFDM/TDM is morestable in comparison with the performance of turbochannel encoder.

F. Transmit signal bandwidth issueIn this section, our focus is on the spectral efficiencyof the OFDM/TDM and conventional OFDM. ThePSD is computed over a sequence of 64,000 frameswith J = 16 oversampled OFDM/TDM waveform andaveraged 106 times. Figure 11 illustrates the PSD ofOFDM/TDM (K = 4 and 16) and conventional OFDM(K = 1) with the amplifier’s power saturation level Ps =4 dB. It is seen from the figure that OFDM/TDMachieves a lower spectral efficiency in comparison withthe conventional OFDM; the spectral efficiencydecreases as K increases. This is because OFDM/TDMsignals have discontinuity in their waveforms withinthe OFDM/TDM frame and cause a higher-order spec-tral spreading. However, a better PSD of conventionalOFDM is achieved at a cost of higher PAPR and BER,as discussed above.

G. Complexity issueThe computational complexity of OFDM/TDM hasbeen evaluated in [20] by using the number of therequired complex multiplications of IFFT/FFT operationas the comparison metric. It has been shown that thecomplexity of OFDM/TDM transmitter is lower thanthe complexity of its receiver, while the complexities oftransmitter and receiver for the conventional OFDM arealmost the same. On the other hand, the total (i.e.,transmitter/receiver) complexity of OFDM/TDM is

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18P s (dB)

Bps

/Hz

O

MMSE-FDE

L=16E b /N 0=30 dB

4K =1

(OFDM)

256 (SC)

1664

Figure 8 Impact of Ps on capacity.

1.E-09

1.E-07

1.E-05

1.E-03

1.E-01

0 32 64

Ave

rage

BER

K

BER (0.5)BER (0.66)BER (0.75)

QPSKL=16β=0 dBfDTs=10-4

Turbo codeR=0.5R=0.66R=0.75

Eb/N0=12 dB, MMSE-FDE

1.E-09

1.E-07

1.E-05

1.E-03

1.E-01

0 32 64

Ave

rage

BER

K

R=0.5R=0.66R=0.75

LDPC codeR=0.5R=0.66R=0.75

QPSKL=16β=0 dBfDTs=10-4

MMSE-FDE, Eb/N0=12 dB

(a) Turbo coded

(b) LDPC codedFigure 9 BER versus K.


of 10

larger in comparison with the complexity of the conven-tional OFDM [20].

V. ConclusionIn this article, we have analyzed and discussed a trade-off between the peak-power reduction, the channelcapacity, and the spectrum efficiency for OFDM/TDMusing MMSE-FDE was presented. It was shown that theOFDM/TDM reduces the peak-transmit power (i.e.,IBO) for the same BER, but with a slight increase inPSD in comparison with the conventional OFDM. Itwas also shown that OFDM/TDM using MMSE-FDE

can be designed to achieve a higher capacity with alower PAPR in comparison with the conventionalOFDM in a nonlinear and frequency-selective fadingchannel. Hence, OFDM/TDM using MMSE-FDE pro-vides flexibility in designing an OFDM-based systems.

AcknowledgementsThis study was supported in part by 2010 KDDI Foundation Research GrantProgram.

Author details1Motive Division, Alcatel-Lucent Bell N.V., Antwerp, Belgium 2GraduateSchool of Engineering, Tohoku University, Sendai, Japan

Competing interestsThe authors declare that they have no competing interests.

Received: 4 July 2011 Accepted: 2 December 2011Published: 2 December 2011

References1. JG Proakis, Digital communications, 3rd edn. (McGraw-Hill, New York, 1995)2. S Hara, R Prasad, Multicarrier Techniques for 4G Mobile Communications

(Artech House, Norwood, MA, 2003)3. D Falconer, SL Ariyavisitakul, A Benyamin-Seeyar, Eidson B, Frequency-

domain equalization for single-carrier broadband wireless systems. IEEECommun Mag. 40, 58–66 (2002)

4. M Friese, On the degradation of OFDM signals due to peak-clipping inoptimally predistorted power amplifiers, in Proceeding of IEEE GlobeCom, vol.2. (Sydney, Australia, 1998), pp. 939–944

5. P Banelli, S Cacopardi, Theoretical analysis and performance of OFDM signalsin nonlinear AWGN channels. IEEE Trans Commun. 48(3), 430–441 (2000)

6. D Dardari, V Tralli, A Vaccari, A theoretical characterization of nonlineardistortion effects in OFDM systems. IEEE Trans Commun. 48(10), 1755 (2000)

7. R O’Neill, LB Lopes, Envelope Variations and Spectral Splatter in ClippedMulticarrier Signals, in Proceedings of the 1995 IEEE International Symposiumon Personal, Indoor and Mobile Radio Communications (PIMRC 1995),Toronto, Canada, pp. 71–75 (11-14 September 1995)

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3 4 5Channel Decay Factor (dB)

Ave

rage

BER

K=1 (OFDM)K=4K=16K=64

L=16, f D T s =10-4, E b /N 0=8 dB

K =1 (OFDM)K =4K =16K =64

Uncoded

Turbo coded(R=0.5)

QPSKMMSE-FDE

(a) Turbo coded

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3 4 5Channel Decay Factor (dB)

Ave

rage

BER

K=1 (OFDM)K=4K=16K=64

L=16, f D T s =10-4, E b /N 0=8 dB

K =1 (OFDM)K =4K =16K =64

Uncoded

LDPC coded(R=0.5)

QPSKMMSE-FDE

(b) LDPC coded

Figure 10 BER versus channel decay factor b.

-30

-25

-20

-15

-10

-5

0

4 5Normalized frequency

PSD

(dB

)

Series3

00 5

0.51 5

1

OFDM(K=1)

K=4

00 5

0.51 5

1

Ps=4 dB

K=16Nc=256Nm=Nc /K

Figure 11 PSD performance.


of 10

8. AE Jones, TA Wilkinson, SK Barton, Block coding scheme for reduction ofpeak to mean envelope power ratio of multicarrier transmission scheme.Elect Lett. 30(22), 2098–2099 (1994)

9. BS Krongold, DL Jones, PAR reduction in OFDM via active constellationextension. IEEE Trans Broadcasting 49(3), 258–268 (2003)

10. SH Muller, JB Huber, OFDM with reduced peak-to-average power ratio byoptimum combination of partial transmit sequences. Elect Lett. 33(5),368–369 (1997)

11. RW Bauml, RFH Fisher, JB Huber, Reducing the peak-to-average power ratioof multicarrier modulation by selected mapping. Elect Lett. 32(22),2056–2057 (1996)

12. P Van Eetvelt, G Wade, M Tomlinson, Peak to average power reduction forOFDM schemes by selective scrambling. Elect Lett. 32(21), 1963–1964(1996)

13. Z Wang, X Ma, G Giannakis, OFDM or single-carrier block transmission. IEEETrans Commun. 52(3), 380–394 (2004)

14. H Ochiai, H Imai, Performance analysis of deliberately clipped OFDM signals.IEEE Trans Commun. 50(1), 89–101 (2002)

15. CV Sinn, J Gotze, M Haardt, Common architectures for TD-CDMA andOFDM based mobile radio systems without the necessity of a cyclic prefix,in Proceedings of the MS-SS Workshop, DLR, Oberpfaffenhofen, Germany(24–25 September 2001)

16. H Gacanin, S Takaoka, F Adachi, OFDM combined with TDM usingfrequency-domain equalization. J Commun Netw. 9(1), 34–42 (2007)

17. H Gacanin, F Adachi, PAPR advantage of amplitude clipped OFDM/TDM.IEICE Trans Commun. E91-B(3), 931–934 (2008)

18. C Berrou, A Glavieux, P Thitimajshima, Near optimum error correctingcoding and decoding: Turbo codes. IEEE Trans Commun. 44(10), 1261–1271(1996)

19. T Wadayama, A coded modulation scheme based on low density paritycheck codes. IEICE Trans Commun. E81-B(10), 1–5 (2001)

20. H Gacanin, S Takaoka, F Adachi, Bit error rate analysis of OFDM/TDM withfrequency-domain equalization. IEICE Trans Commun. E89-B(2), 509–517(2006)

doi:10.1186/1687-1499-2011-193Cite this article as: Gacanin and Adachi: On transmission performanceof OFDM-based schemes using MMSE-FDE in a frequency-selectivefading channel. EURASIP Journal on Wireless Communicationsand Networking 2011 2011:193.

Submit your manuscript to a journal and benefi t from:

7 Convenient online submission

7 Rigorous peer review

7 Immediate publication on acceptance

7 Open access: articles freely available online

7 High visibility within the fi eld

7 Retaining the copyright to your article

Submit your next manuscript at 7 springeropen.com


of 10

http://www.springeropen.com/

http://www.springeropen.com/

research open access on transmission performance of ofdm ... · average power ratio (papr), and...

Documents