Performance Analysis of COFDM in a Mobile Radio Channel Using the Signal Processing Worksystem

Juan Parra, Paul Fortier, Huu Tuê HuynhDépartement de génie électrique et de génie informatique

Université Laval, Québec, Canada, G1K 7P4Tel: (418) 656-3555, Fax: (418) 656-3159

email: juparra@gel.ulaval.ca, fortier@gel.ulaval.ca, huynh@gel.ulaval.ca

Abstract- In this paper, the performances of amulticarrier modulation (COFDM) system in an urbanmobile radio channel is analyzed using a computer-aidedanalysis tool called SPW. This multicarrier modulationsystem, with convolutional coding and interleaving,provides an extremely bandwidth efficient and multipathresistant transmission method. COFDM gives a remarkableperformance in selective Rayleigh channels at a muchhigher bit rate than conventional systems.

I. INTRODUCTIONDigital techniques have been used in sound program

production for many years now, and more recently they havebecome inexpensive enough to be introduced into the domesticconsumer market, leading to a wider public appreciation ofhigh-quality sound systems such as a Compact Disc (CD)digital audio system. Since the late 1980s, a new generation ofradio broadcasting systems are being developed in Europe.These Digital Audio Broadcasting (DAB) systems are based onproject Eureka 147. The objective of DAB is to deliver near-CDquality stereo audio programs to fixed and mobile receivers.

Digital broadcasting over terrestrial radio links experiencesevere problems due to the phenomena of multipathpropagation, fading effects and Doppler spread, especially inthe case of mobile receivers. So in DAB, the transmittedinformation must be insensible to any channel condition, underall circumstances. This is accomplished by a channel codingand modulation technique called: Coded Orthogonal FrequencyDivision Multiplexing (COFDM) [1], in which the echoes thatprovoke fading are used as a form of diversity such that theycontribute to reconstruct the original message with lowprobability of error.

In this paper, we analyze the performances of COFDM in anurban mobile radio channel using a computer-aided analysistool called SPW. The COFDM system is first presented inSection II. In Section III, we discuss channel modeling. Theresults of our simulations are presented in Section IV. Finally,we conclude the paper in Section V.

II. COFDM SYSTEMIn a conventional serial system, the symbols are transmitted

sequentially, with the frequency spectrum of each symbolallowed to occupy the entire available bandwidth. For instance,in the Rayleigh channel, several adjacent symbols may becompletely destroyed during a fade. So higher data rates can be

achieved only at the expense of degradation in performance.The delay spread imposes a waiting period that determineswhen the next pulse can be transmitted. This waiting periodrequires that the signaling be reduced to a rate much less thanthe channel coherence bandwidth to prevent intersymbolinterference (ISI).

Unlike serial systems that use only one carrier at a high-bitrate, the COFDM system splits the information over a largenumber of orthogonal subcarriers that are individually 4-DPSKmodulated at a relatively low-bit rate. The COFDM modulationsystem offers an excellent spectrum efficiency which is vital inapplications such as audio broadcasting, since the transmissionbandwidth is more likely to be squeezed in the alreadycongested radio frequency spectrum. Convolutional coding isused in conjunction with time and frequency interleaving toovercome fading. The diversity introduced by the interleavershas the effect of decorrelating errors at the input of a softdecision Viterbi decoder. The modulation and demodulationprocesses are carried out using FFT techniques. For furtherprotection, a guard interval is added to avoid intersymbolinterference and differential encoding is employed to ensureproper phase demodulation of each subcarrier at high vehiclespeeds.

The transmitted COFDM signal is then given by thefollowing equation:

(1)

where:

Ck = QPSK constellation points,N = number of subcarriers,fk = fo + k / ts, with fo the carrier frequency and ts the useful

symbol duration.

It can be shown that the sampled transmitted signal can bewritten as:

(2)

where

A = proportionality constant,mTe = sampling times at frequency 1/Te.

This type of modulation gives a signal composed of a sum oftruncated orthogonal sine waves. The signal spectrum is then

y t( ) Ckexp 2πi fkt( )k 0=

N 1–

∑=

y mTe( ) A FFT1–

Ck( )⋅=

composed of a sum of sinc functions regularly spaced over thefrequency band, resulting in a flat spectrum over that band.

III. CHANNEL MODELINGThe mobile radio channel is based on the propagation of

radio waves in a transmission environment. Due to groundirregularities and generally low antenna elevations, the directpath between the transmitter and receiver can be obstructed. Inaddition, typical wave phenomena like diffraction, scattering,reflection and absorption lead to a diffusion of a transmittedwave into a continuum of partial waves with differentamplitudes and phases. As a consequence, the transmittedsignal is attenuated and distorted. On the other hand, thescattering process depends on the geometrical andelectromagnetic surface properties (spatial surfaceirregularities, dielectric constant, and conductivity) and on theangle of arrival of the reflected waves. These properties showstrong variations in a realistic propagation environment such asurban and suburban, making an analytical treatment unfeasible.Hence a universal deterministic modeling of such channels isimpossible.

A semi-empirical method, based on both theoretical modelassumptions and on measured data, outlines a more promisingstrategy. The two-dimensional scattering function gives aconcentrated description of the stochastic behavior of aparticular scattering environment. The main mechanism of thephysical propagation process are identified, enabling areduction of the complex channel behavior to only a fewstatistical functions. The channel is thus described analyticallyby three functions: amplitude distribution, delay pathdistribution and Doppler spectrum for each path. With thesetools a characterization of the various channel configurationsfrom direct evaluation of measured data is possible.

Fig. 1 illustrates a hypothetical mobile propagation mediumand its associated scattering function.

Fig. 1 Link between scattering function and a given propagation medium.

Scattered signals arriving at the vehicle are Doppler shiftedby different amounts depending on the angle of arrival, whereasthe delay and relative power depend on the distance traveled bythe transmitted signal. The path labeled as ¿ comes directlyfrom ahead of the vehicle, shifting the signal by a positiveamount; the delay observed is the smallest of three and the

relative power is maximum, since there is a shortest pathbetween the transmitter and receiver. The path ¦ arrives almostperpendicular from a scatterer, resulting in a near-to-zeroDoppler shift and a longer delay with attenuated power. Finally,the path marked as Æ is the longest path coming from behindthe vehicle due to another scatterer, meaning that the signal isshifted negatively and has the largest delay with a minimumstrength.

The proposed model is a Rayleigh fading channel based ona statistical behavior of the channel power spectral density. Inthis model, some desired channel characteristics such as powerdelay profiles and power Doppler spectra are extracted frommeasured data and then statistically analyzed to generate ascattering function [2]. The scattering function is an averagepower spectral density function for the channel. The timeevolution of the power spectral density function is inducedusing an ad hoc method which imitates the desired timecorrelation characteristics for the channel.

The scattering function is defined by:

where RH (∆f, ∆t) is the channel autocorrelation function. Thechannel is assumed to be WSSUS, where the time delays for anytwo paths through the channel are uncorrelated and the time-delay function, h(t,τ), is a WSS random process. Theuncorrelated scattering assumption is satisfied for typicalmobile radio channels and, while they are not stationary in thestrict sense, they are approximately stationary for time periodson the order of the channel coherence time.

The characteristics of a fading communication channel canbe represented by a time-variant impulse response, h(t,τ) [2]. Arealization of the impulse response is generated by the inverseFourier transform of the square root of the power spectraldensity , P(τ, fD).

where the superscript m denotes the mth realization (mth samplefunction) of the underlying random process.

The following expression can be used to generate powerspectral density function realizations.

where r(m)(τ, fD) is mth realization of the Rayleigh-distributedrandom field defined as:

2

3

1 3

21

Scatterer

Paths

Mobile direction

Scattering Function

Doppler Hzdelay µs

Scat

tere

r

S τ fD,( ) =

RH f ∆f t ∆t,;,( )exp j2π∆fτ j2π∆tfD–( )dfdt

∞–

∞

∫∞–

∞

∫

hm( )

t τ,( ) Pm( ) τ fD,( )exp j2πfDt( )dfD

∞–

∞

∫=

Pm( ) τ fD,( ) r

m( ) τ fD,( )2S τ fD,( )=

rm( ) τ fD,( ) 1

2------- x

m( ) τ fD,( ) jym( ) τ fD,( )+=

x(m)(τ, fD) and y(m)(τ, fD) are realizations of two independentGaussian random fields with zero mean, unit variance and aconstant power spectral density height over the channelbandwidth. It follows that the phase θ(τ, fD) must be uniformlydistributed over 2π radians. Thus, the deterministic essence ofthe scattering function is related to the stochastic nature of thepropagation channel.

h(t,τ) is a concatenation of realizations and each realization is aconcatenation of time-invariant impulse responses. Threeproperties validate the model. First, the channel impulseresponse has a Rayleigh distribution, since r(τ, fD) is Rayleighdistributed. Second, the channel model has a scattering functiongiven by S(τ, fD), as desired. Third, the Fourier transform existsfor many realistic choices of the scattering function.

IV. SIMULATION RESULTSWe performed numerous Monte Carlo simulations to

estimate the Bit Error Rate (BER) under different channelconditions. The mobile radio channel was chosen to be a typicalurban type for all simulations where channel parameters werenot to be varied. Since the characteristics of the scatteringfunction change according to the physical structure of themobile environment, it follows that we change the scatteringfunction parameters in order to evaluate the COFDM systemperformances.

It it worth mentioning that we use a software especiallydesigned to simulate communication systems. The SignalProcessing WorkSystem (SPW) provides a unified graphicaluser interface for all aspects of system design and simulation.SPW is responsible for generating the simulation program,executing the simulation program and displaying the results.The simulations are carried out in the time domain by iterativecalculation. In this way, we only have to concentrate onproblem definition, results analysis, and design iterations.

In Table 1, we display the mobile radio channel parametersalso necessary to estimate the BER. Notice that the delay profileand Doppler spectrum types were chosen in such a manner forsimplicity of implementation. Nevertheless, these types fit theclass of urban mobile radio channels.

The COFDM parameters used in our simulations are similarto those proposed by Le Floch [1]. Table 2 shows all importantCOFDM parameters used in our simulation to estimate theBER.

We estimated the Eb /No vs BER performance of a COFDMsystem for different values of the delay spread, leaving theDoppler spread fixed and for different values of the Dopplerspread leaving the delay spread fixed. We also compared the

COFDM system to serial modulation systems. For all computersimulations perfect interleaver synchronization was assumed.

TABLE 1

MOBILE RADIO CHANNEL PARAMETERS.

TABLE 2

COFDM SYSTEM PARAMETERS.

In Fig. 2, we display the results obtained for values of thedelay spread, S, equal to 0.2, 1.0, 5.0 and 10.0 µs. The bestperformance is for S = 1.0 µs. This can be explained by sayingthat the existence of multipaths is a form a diversity thatcontributes to improve the performance of COFDM, and thatparticular value of the delay spread produces the best diversitycombination of the simulated S values.

hm( )

t τ,( ) =

S τ fD,( )rm( ) τ fD,( )exp j2πfDt( )dfD

fDmin

fDmax

∫

Delay profile type

Doppler spectrum type

Delay profile range 0 < τ ≤ 7S

Delay spread values 0 < S ≤ 10 µs

Doppler spectrum range |fD| ≤ fDmax

Doppler spread values 0 ≤ fDmax ≤ 185 Hz

Operating frequency 1 GHz

Number of subcarriers 448

FFT size 512

Symbol duration 64 µs

Guard interval 16 µs

Carrier frequency 1 GHz

Global bandwidth 7 MHz

Bit rate 5.6 Mbits/s

Subcarrier modulation 4-DPSK

Subcarrier bandwidth 15625 Hz

Spectral efficiency 0.8 bits/Hz/s

Convolutional code R =1/2, K = 7, dfree = 10

Generator Polynomials 171 & 133

Viterbi decoding 8-level soft decision

Path memory 100

Block interleaver: rows 896

Block interleaver: columns 896

P τ( ) exp τ S⁄–( )=

S fD( ) 1

1 fD fDmax⁄( )2–

-----------------------------------------------=

Fig. 2 BER performance for different values of the delay spread.

Fig. 3 shows the BER performance for some values of themaximum Doppler shift, fDmax, such as 0, 46, 111 and 185 Hz.The best performance corresponds to the vehicle moving at aspeed of 120 km/h (fDmax = 111 Hz). This outcome is explainedby the fact that the mobile speed introduces an additionaldiversity that helps to improve the system coding up to a certaindegree. When the speed is slower than 120 km/h, say 50 km/h(46 Hz), the performance is slightly degraded, and a little moredegradation results when the vehicle is not moving at all, i.e.fDmax = 0 Hz. In this case, the frequency interleaver is the onlysource of diversity in the frequency domain, but it stillguarantees an excellent performance for the COFDM system.On the other hand, at a higher speed (fDmax = 185 Hz), thechannel varies so fast that the differential detection becomesless effective.

Fig. 3 BER performance for different values of the Doppler spread.

Considering the problem of data transmission through atypical urban channel, some authors have pointed out thatclassical modulation systems such as 4-DPSK and FSK lead toan irreducible BER [3]. Even in the case where the channel isneither frequency-selective nor time-selective, the BER vs. Eb /No is known to decrease slowly; more than 35 dB is needed foran uncoded 4-DPSK system to achieve a BER of 10-4. This isshown in Fig. 4.

Fig. 4 Various system BER performances in Rayleigh fading channels.a) Uncoded 4-DPSK (2.4 Kbits/s) time-selective Rayleigh fading;b) Uncoded 4-DPSK (15.625 Kbits/s) nonselective Rayleigh fading;c) TCM 8-DPSK (2.4 Kbits/s) time-selective Rayleigh fading;d) Coded 4-DPSK (15.625 Kbits/s) selective Rayleigh fading;e) COFDM (5.6 Mbits/s) selective Rayleigh fading.

We also show the performance of an interleaved differentialTCM system over fading channels [4]. For a non-selectivefading channel, the TCM system performs relatively well,needing a little more than 17 dB to attain a BER = 10-4; on theother hand, for a time-selective Rayleigh channel, the bestinterleaved system performance has an error floor close to 10-4

(see Fig. 4). This irreducible BER is a consequence of twoindependent phenomena: frequency selectivity and the timevariation of the channel characteristics. The first will causeintersymbol interference as soon as the data tends to increase,while the second will cause degradation in the phase estimationas soon as the data rate tends to be too low.

V. CONCLUSIONWe have analyzed the performances of COFDM in an urban

mobile radio channel using SPW. The channel was modelledusing the scattering function. In mobile radio channels, theCOFDM system can be considered to be immune to selectivefading caused by the multipath propagation and the Dopplerspread, as long as the multipath spread is not too the large andthe Doppler spread is less than 185 Hz or, equivalently, vehiclesthat do not surpass 200 km/h.

VI. REFERENCES[1] B. Le Floch, R. Halbert-Lasalle, D. Castellain, “Digital sound broad-

casting to mobile receivers”, IEEE Transactions on Consumer Elec-tronics, vol. 35, no. 3, pp. 493-503, August 1989.

[2] R. L. Mickelson, K. C. Yeh, P. Argo, T. J. Fitzgerald. “A Rayleigh Fad-ing Channel Simulator”, Ionospheric Effects Symposium, pp. 327-334,Washington D.C., May 4-6 1994.

[3] J. C.-I. Chuang, “The Effects of Time Delay Spread on Portable RadioCommunications Channels with Digital Modulation”, IEEE Journal onSelected Areas in Communications, vol. SAC-5, no. 5, pp. 879-889,June 1987.

[4] F. Edbauer, “Performance of Interleaved Trellis-Coded Differential 8-PSK Modulation over Fading Channels”, IEEE Journal on Selected Ar-eas in Communications, vol. SAC-2, no. 1, pp. 51-76, January 1984.

Delay spread 0.2 µs -----

1.0 µs

5.0 µs

10.0 µs *o

0.2 µs -----

1.0 µs

5.0 µs

10.0 µs *

o

Delay spreadDoppler spread 0 Hz -----

46 Hz

111 Hz

185 Hz

*

o

a

bc

d

e