Beyond 3G Techniques of Orthogonal Frequency Division Multiplexing and Performance Analysis via...

International Journal of Advanced Pervasive and Ubiquitous Computing, 3(3), 1-13, July-September 2011 1

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Keywords: InverseFastFourierTransform(IFFT),MATLAB,OrthogonalFrequencyDivisionMultiplexing(OFDM),Single-CarrierTechnology,WirelessCommunications

INTRODUCTION

OFDM is kind of both multi-carrier and mul-tiplexing technique, which distributes a given channel into plurality of sub-channel. And each parallel transmitting sub-channel adopts single-carrier modulating. By this meaning, each sub-channel is flat relatively, and performs narrowband transmission. Signal bandwidth is less than related bandwidth, which eliminates interference between signal waveforms and im-proves frequency spectrum utilization because

of signal orthogonality, frequency spectrum overlap (Ramasami, 2002).

OFDM discards the way using traditional band filter to distribute sub-carrier, and adopting frequency modulation meaning to select the sig-nal waveforms that can keep orthogonality even while frequency spectrum aliasing. Therefore, OFDM is both modulating and multiplexing techniques.

For the traditional Frequency Division Multiplexing (FDM), guard band is used to avoid intercarrier interference (Figure 1), which induces frequency spectrum utilization. Whereas, OFDM system applies FFT technique into multi-carrier transmission system with

Beyond 3G Techniques of Orthogonal Frequency Division Multiplexing and Performance

Analysis via SimulationChunyanWang,StateIntellectualPropertyOffice,China

ABSTRACTAsoneofthetechniquesbeyond3G,becauseoftheeffectiveperformanceofhighspectrumutilizationandanti-fadingforfrequencyselectingandadoptedmulti-carriermodulationtechniquethatmeetstherequirementoftheexplosivetrafficcapacity,OrthogonalFrequencyDivisionMultiplexing(OFDM)hascarriedgreatweightinwirelesscommunications.ThispaperexpoundsOFDMtechnicalcharacteristicsandperformscomputersimulationontheOFDMsystembasedonInverseFastFourierTransform(IFFT)bymeansMATLAB.Duringthecourseofsimulation,comparisonbetweenOFDMandtraditionalsingle-carriertechnologyisperformed.Thesimulationresultshavegreatsignificanceforresearchandapplicationsinthefield.

DOI: 10.4018/japuc.2011070101

2 International Journal of Advanced Pervasive and Ubiquitous Computing, 3(3), 1-13, July-September 2011


orthogonal and aliasing frequency spectrum, so as to realize multiplex signal multiplexing and split conveniently. Here “orthogonal” indicates accurate mathematical relationship between carrier frequencies:

cos( ) cos( )( )

( )

sin(

2 2 20

2

00

0p p

p

mf t nf t dtTm n

m n

m

T

∫ ⋅ ==

≠

ff t nf t dtTm n

m n

mf t

T

T

00

0

00

2 20

2

) sin( )( )

( )

cos( )

∫ ⋅ ==

≠

p

p∫∫ ⋅ ==

≠

sin( )( )

( )2 2

00pnf t dt

Tm n

m n

(1)

and an important advantage of OFDM technique is that modulation and demodulation can be performed by adopting IFFT/FFT, so as to re-duce complexity for realizing the system.

TECHNIQUE PRINCIPLE

The essential technical principle is to divides one high speed data flow into plurality of low speed data flows. And the low-speed data flows are modulated by orthogonal frequency and transmit data simultaneously, thus wide band becomes narrow bands, and consequently, the

problem of selective fading can be solved. In addition, if adding a delayed protection to gen-erated OFDM signal, intersymbol interference can be figured out (Gong & Jia, 2002; IEEE Computer Society, 1999). The modulation principle in OFDM system is seen in Figure 2.

After the modulating of MQAM, MPSK or DPSK, etc., taking advantage of sub-carrier orthogonality, the original signal is demodu-lated. The principle is seen in Figure 3.

One OFDM symbol includes signals which are combined by multiple modulated sub-car-riers, and each sub-carrier can be modulated by PSK or QAM symbol. If N indicates the number of sub-channel, T indicates OFDM symbol density, di (i=0, 1, 2, …, N-1) indicates data symbol distributed to each sub-channel, and fc indicates the carrier frequency of the No. 0, rect(t)=1, |t|≤T/2, the original OFDM symbol can be indicated as following:

s t d rect t t T

j f i T t t

ii

N

s

c s

( ) Re{ ( / )

exp[ ( / )( )]},

= − −

+ −=

−

∑0

1

2

2p

(2)t t t ts s≤ ≤ +

s t t ts( ) = <0, or t t ts> +

OFDM output signal is described by equivalent baseband symbol:

Figure1.FDMfrequencydistribution



s t d ret t t T j i T t t

t t t T

ii

N

s s

s s

( ) = − − −

≤ ≤ +−

−

∑Re{ ( / )exp[ / ( )]},0

1

2 2p

ss t t t ort t ts s( ) = < > +0,

(3)

In the formula, the real pat and the imagi-nation part is respectively corresponding to the phase component and the orthogonal com-ponent, and in the real, multiplies the cosine component and the sine component separately, so as to generate a final synthetic OFDM signal by sub-channel signals (Figure 4).

From the figure, it is known that respective N times modulating are not in the real calcula-tion, and for the generator, that is similar to perform one IFFT, but for the receiver, modu-lating part is similar to performs one FFT.

Figure 5 describes an embodiment that one OFDM symbol includes three sub-carriers, in which all the sub-carriers have same amplitude and phase. Each sub-carrier includes integer multiple periods in one OFDM symbol period, and every two adjacent sub-carriers differs one period. This characteristic can explain the or-thogonality between sub-carriers as following:

Figure2.OFDMmodulationprinciple

Figure3.OFDMdemodulationprinciple



1 100T

j t dtm nm nn

T

exp( ),,

w ==≠

∫ (4)

In the formulation, the carrier j is de-modulated, and integrated within time length T;

dT

jjTt t d x j

Tt t dt

Td

j s ii

N

T

t T

sS

s

= − − −

=

=

−+

∑∫1

2 21

11

1

exp[ ( )] [ ( )]π ω

iiT

t T

i

N

ss

s

ji jTt t dt djexp[ ( )

+

=

−

∫∑−

− =0

1

2π

(5)

Thus, carrier j is demodulated to restore the expected symbols. For other carriers, be-

cause that frequency difference is ( )i jT

- in one integral interval to generate integral mul-tiple of periods, the integration result is zero (Guo & Li, n. d.; Tamaki & Tomohisa, 2002).

The orthogonality can be explained at the angle of frequency domain. According to the formulation (5), each OFDM symbol includes plurality of non-zero sub-carriers in period T.

therefore, the spectrum can be viewed as a convolution for the rectangular pulse spectrum in period T and a group of δfunctions at each sub-carrier frequency. The rectangular pulse spectrum amplitude is sin [ ]c fT function, and the zero is in the point at which the frequency is integral multiple 1/T (Figure 6). Aliasing sub-channels multiply each other on rectangu-lar pulse to results in sine function spectrum. At the maximum of each sub-carrier, all other sub-carriers spectrum is exactly zero. Because during the course of modulating OFDM symbol, each sub-carrier frequency maximum, corre-sponding to the points, is calculated so as to extract every sub-channel symbol from mul-tiple aliasing sub-channel symbols, thus avoid-ing interference from other sub-channels.

In accordance with Figure 6, OFDM sym-bol meets the Nyquist criterion, that is to say that the spectrum interference does not exist among the multiple sub-channels. Accordingly, in frequency domain, the spectrum maximum of a sub-channel corresponds to zero points of other sub-channels, which can avoid Inter-Carrier Interference (ICI).

Figure4.OFDMsystemprimarymodeldiagram



KEY TECHNIQUES

As a technique beyond 3G, OFDM has follow-ing key techniques.

1. Synchronization of Time Domain and Frequency Domain

OFDM system is sensitive to offset of timing and frequency, especially under the circumstance that FDMA, TDMA and CDMA etc. multiplexing in combination. Downlink synchronization is simple relatively, and easy to implement. In the uplink, signals from different mobile stations must arrive at the Base Station (BS), so that the inter-carrier orthogonality can be insured. That is important especially.

Figure5.OFDMsymbolthatincludesthreesub-carriers

Figure6.OFDMfrequencyspectrum



2. Channel Estimation

In OFDM system, there are two points in channel estimation: pilot information selection and channel estimator designation. Because the wireless channel is fading channel and channel tracking must be continuous, the pilot informa-tion must be transmitted constantly. Channel estimator designation requires low-complexity and nice pilot tracking capability.

3. Channel Encoding and Interleaving

For improving digital communications system performance, channel encoding and interleaving are general technical meaning. Channel encoding avoids random errors in channels and channel interleaving avoids burst error in fading channel.

4. Depressing Peak-to-Average Power Ratio (PAPR)

In OFDM signal time domain, orthogonal N sub-carrier signals overlay each other. When all the maximum of the N sub-carrier signals add together, the OFDM signal generates a peak, and the peak power is N times of the average power. Though the peak power value occurs seldom, however, for transmitting undistorted OFDM signal at high PAPR, the transmitter requires High Power Amplifier (HPA) with high linearity degree. Therefore, a high PAPR depresses OFDM system performance greatly, as well as the real allocation (Ramasami, 2002).

5. Channel Equalization

In general fading environment, because the OFDM technique has diversity characteristic of multi-path channel, therefore OFDM does not equalize. But in high scattering channel, channel memory length is great; therefore the Cyclic Prefix (CP) must be long enough so as to avoid the ICI, however, the CP length results in energy lost. Accordingly, adding equalization can be considered to reduce CP length. That

means to improve frequency utility at the cost of increasing system complexity.

PERFORMANCE ANALYSIS VIA SIMULATION

In 1971, Weinstein and Ebert apply DFT to multi-carriers transmission system, which realizes multi-path signal multiplexing and de-composition of multi-path signal. Consequently, OFDM attracts great attention and is regarded as a beyond 3G hot technique in future mobile communications. In this part, in accordance with OFDM system model based on IFFT/FFT, numerical analysis software MATLAB is ad-opted to perform a mass of computer simulation. The simulation results embody OFDM system characteristic and performance intuitively (You, 2002; Gong & Jia, 2002).

Simulation Model

Figure 7 describes an OFDM system flow using MATLAB simulation. Wherein, the input data is binary data, and after baseband modulating (16QAM), mapping to be symbol data (d dN0 1~ - ), S/P converting, the parallel data is converted to be time domain sample point by IFFT/FFT.

Channel simulation describes some wire-less channel generality characteristic, e.g., noise, multi-path. The noise is generated by adding random data to transmitting data. The multi-path is generated by copying the channeling with time-delay and fading. Definitively, the OFDM performed P/S converting is generated by alias-ing plurality sub-channels, which results in great PAPR. When going through a nonlinear device, spread spectrum and band distortion emerges much. Accordingly, the peak clipping must be performed. After performing S/P con-verting to the serial data, the receiver executes FFT converting to the parallel data to acquire corresponding frequency domain data, and fi-nally, after base-band demodulating (16QAM) and P/S converting, binary data is recovered.

During perform the simulation, there are the following hypothesis premises: ideal



synchronization of the transmitting side and the receiving side, and ideal channel estima-tion; channel fading is flat, which means the channel is regarded as being constant in one OFDM symbol. Table 1 describes the simula-tion parameters.

SIMULATION RESULTS ANALYSIS

Figure 8 describes the simulation of binary data input/output and OFDM transmitting/receiving. The binary input data is performed 16QAM modulation as Figure 9, and the output data corresponds to the time domain signal waveform at B point in Figure 8.

Figure 8(c) and (d) is the waveform of OFDM signal going through two-path Gauss channel and recovered binary data separately. Sub-figure (c) corresponds to point F, (d) cor-responds to point H. Comparing sub-figure (c) (d) with (b) (a) respectively, it is knowable that received OFDM signal waveform and recovered binary data all have weak distortion because that OFDM has great reflection of mitigating multi-path.

The S(t) may have two expression;

S t a t b tn c n c( ) = −cos( ) sin( )w w (6-1)

S t a jb en nj f tc( ) = +( )

Re 2p (6-2)

Figure7.Simulationdiagram



The equation 6-1 corresponds to the 16QAM output waveform in Figure 8. The equation 6-2 is complex symbol data (d d dN0 1 1, ,,... - N is number of sub-carriers) generated after signal constellation mapping. After IFFT converting, the OFDM transmission wave-form (time-amplitude) described in Fig-ure 8(b), namely, the wave-form at point C in Figure 7, is generated. The base-band signal at

point C: y t d e t Tn

jnTt

n

N

( ) =

≤ ≤

=

−

∑Re ,2

0

1

0p

.

During the simulating, by adding random data complying with Gaussian to simulate chan-nel noise and copying the transmitting signal consider fading and delay to simulate two-path channel, Figure 10 describes the simulation of two-path Gauss channel.

OFDM is kind of special multi-carrier, and for comparing with single-carrier modulating, modulation of 16QAM is adopted in the simu-lation. By simulating sub-carrier waveform receiving and binary data recovery, the com-parison of OFDM system performance and single-carrier is reflected.

Table1.Simulationparameters

Simulation parameter Parameter value

FFT_size 128

Num_carrier 32 (fft_size/4)

Signal constellation 16QAM

Channel model Two-path Gauss channel

Figure8.Binarydatainput/output,andOFDMsignaltransmitting/receiving



(i) Selection of single-carrier modulation model

In OFDM system, sub-carrier modulating model may be MPSK, MQAM, or DQPSK. When source-rate, sub-carrier parameter and channel bandwidth are ensured to be invariable, in different SNR, the simulation of OFDM sys-tem of additive white Gaussian noise (AWGN) high speed voice-data compatible transmission is described in Figure 10. The modulation model and encoding rate are seen in Table 2.

From Figure 10, under the circumstance that EBR, sub-carrier and protection interval

are same, for OFDM system, sub-carrier QAM modulation model is better than PSK modula-tion model.

(ii) Performance of single-carrier (16QAM) and OFDM

In Figure 11, as an example, 16 QAM sin-gle-carrier modulation system performs binary data recovery and QAM transmitting/receiving waveform are simulated. Comparing sub-figure (c), (d) in Figure 11 with (c), (d) in Figure 8, it is knowable that receiving waveform and data recovery distorts greatly. That embodies that, in

Figure9.16QAMmodulationprinciple

Figure10.SNR-BERgraphs



OFDM system, the performance of anti-delay, anti-noise and anti-multipath interference is better than the single-carrier modulation system.

Figure 11 shows the simulation result of signal spectrum after FFT converting to OFDM, QAM signal. Comparing the sub-figure (a) with (b), it is knowable that the two has various greed of distortion after through two-path Gauss channel. Meanwhile, comparing Figure 12(c) with Figure 13(c), it is knowable that perfor-mance of anti-multipath effect of OFDM system is better than that of single carrier modulation system. Figure 12(a) and Figure 13(a) are spectrums of OFDM, QAM transmitting signal waveform after FFT converting. At the angle

of spectrum utilization, OFDM sub-carrier spectrum has close distribution and concen-trated energy.

During channel simulating, adding inde-pendent Gauss binary data with 0 mean and variance s2 , channel noise is simulated. Figure 14 describes energy distributing for 16 QAM received signal constellations corresponding to different noise power, wherein, sub-figure (a), (b), (c) is respectively corresponding to received signal distribution when σ = 0.1, 0.3, 0.5.

The simulating results indicate; on low noise power (σ is small), the signal energy distributes centrally, and with the noise power

Table2.Modulationmodelandencodingrate

Sub-carrier Modulation Model Convolution Coding Efficiency

DQPSK Uncoded

16PSK 1/2

16QAM 1/2

64QAM 1/3

Figure11.Sub-carrierrecoversinputbinarydata



Figure12.FFTofOFDMsignal

Figure13.FFTofQAMsignal



Figure14.16QAMreceivedsignalconstellationanddecisionboundary



level rising, the proportion of noise component increases and signal energy distribution tends to be decentralized, and BER affection to OFDM system is larger accordingly.

CONCLUSION

The paper expounds OFDM technical charac-teristic, and performs computer simulating to OFDM system based on FFT/IFFT by means of MATLAB. During the course of simulation, comparation between OFDM and single-carrier technique (16QAM) is described in detail.

Generally speaking, because of the sub-carrier orthogonality, OFDM system reduces inter-carrier interference, and also increases spectrum utilizations. By adopting IFFT/FFT to modulate/demodulate signal, complexity of realizing the communications system is depressed. The low-speed data stream is modu-lated on orthogonal frequency and transmitted in the meantime, which changes the wide band to be narrow band, consequently, the problem of frequency selective fading is solved. By comparing with single-carrier system, it is embodied that OFDM has more advantage in fields of resisting multi-path interference and channel fading, and spectrum utilization.

Because that OFDM system has the advantages that sing-carrier communication system and traditional FDM system does not have, OFDM is considered as one of the most important techniques beyond 3G. In OFDM

technical field, it is necessary to research further the techniques of time-frequency do-main synchronization, channel encoding and interleaving, depressing PAPR and channel estimation, etc.

REFERENCES

Gong, J., & Jia, H. (2002). OFDM technique and simulation analysis thereof. Railway Newspaper,24(3).

Guo, Y., & Li, J. (n. d.). Mobilecommunications. Sichuan, China. PressofXianElectronicScience&TechnologyUniversity.

IEEE. Computer Society. (1999). IEEE 802.11a1999.Part11:WirelessLANMediumAccessControl(MAC) and Physical Layer (PHY) Specification. Washington, DC: Author.

Ramasami, V. C. (2002). Orthogonal frequencydivisionmultiplexing. Retrieved from http://www.cetuc.puc-rio.br/~amanda.cunha/projeto/OFDM/Tutorial%20de%20Orthogonal%20Frequency%20Division%20Multiplexing.pdf

Saliga, S. V. (2000). An introduction to IEEE 802.11 Wireless LANs. In ProceedingsoftheIEEERadioFrequency Integrated Circuits Symposium (pp. 11-14).

Tamaki, S., & Tomohisa, W. (2002). Technicalnotes:MagnaDesignNet. Retrieved from http://www.magnadesignnet.com/en/booth/technote/ofdm/

You, X. (2002). Chinese mobile communicationdevelopmentinthefuture.

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