SIMULINK MODEL AND FPGA-BASED OFDM COMMUNICATION SYSTEM: A SIMULATION AND HARDWARE INTEGRATED...

September 8, 2010 14:25 WSPC/262-IJMSSC/S1793-9623 00025

International Journal of Modeling, Simulation,and Scientific ComputingVol. 1, No. 3 (2010) 369–404c© World Scientific Publishing CompanyDOI: 10.1142/S1793962310000250

SIMULINK MODEL AND FPGA-BASED OFDMCOMMUNICATION SYSTEM: A SIMULATIONAND HARDWARE INTEGRATED PLATFORM

LE KHOA DANG∗,‡, HUU PHUONG NGUYEN∗,LE NGUYEN BINH†,§ and DUC NHAN NGUYEN†

∗Faculty of Electronics and TelecommunicationsUniversity of Sciences, 227 Nguyen Van Cu St.

District 5, Ho Chi Minh City, Vietnam

†Department of Electrical and Computer Systems EngineeringMonash University, Clayton, Victoria 3800, Australia

‡[email protected]§[email protected]

Received 26 April 2010Accepted 13 June 2010

Ultra-broadband networks are currently attracting significant interests in employingwireless access and optical fiber access to the home and to the building at symbol ratereaching Gb/s. OFDM is a multicarrier modulation technique and considered to offersignificant reduction of the data symbol to be carried per carrier channel, especially inultra-high speed optical communications with bit rate reaching 100 Gb/s or even higher.This paper thus presents a novel and generic OFDM system employing both MATLABSimulink and FPGA-based development software platform for simulation as well as hard-ware implementation for the generation and detection of OFDM signals for wireless andoptical communications transmission media. Although the transmission medium is mod-eled with delay distortion filter in the baseband, this model would be valid for passbandsignals as the amplitude is represented by complex amplitude whose phase would be thephase of the carrier. The Simulink and hardware models presented hereunder are scal-able to much higher speed allowing possible implementation in multi-Giga samples persecond electronic processors. The sub-systems of the OFDM transmitter and receiver arepresented to demonstrate the feasibility of such models for ultra-wideband communica-tion systems such as wireless access and long haul optical fiber communication backbonenetworks.

Keywords: OFDM; FPGA; Viterbi codes and decoding; wireless communications; optical

communications.

1. Introduction

The advantages of OFDM (Orthogonal Frequency Division Multiplexing) have beenwell known; they are exploited to combat impairments in wireless and optical com-munication systems. The principal mechanism of OFDM is to generate parallel

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370 L. K. Dang et al.

orthogonal channels in the frequency domain, so each subcarrier carries a lowersymbol rate, thus providing efficient use of the spectrum and brick-wall-like prop-erty. Another superior feature of OFDM is to minimize the intersymbol interference(ISI) and interchannel interference (ICI). Wireless access rates reaching over 1 Gb/sper channel and more than 10 Gb/s per fiber channel are expected in the future.

Ultra-broadband networks are currently attracting significant interests; wire-less access and optical fiber access are provided to the home and to the building.There is a need for structures which can offer high speed and efficient generation anddetection schemes for hardware implementation of OFDM signals. FPGA offers pos-sibility of parallel structures and flexibility in this line of development.1–3 In recentyears, the fast development of electronic processors reaching several Giga-samples/shas allowed the exploration of hardware implementation operating in multi-Gb/stransmission systems. Therefore, there is a need for a software platform and thecorresponding hardware system which can be scalable to ultra-high speed OFDMcommunication systems.

This paper reports the implementation of OFDM transmitter and receivingsystems based on the Stratix Development kit EP1S25 and the associate softwarepackage DSP Builder of Alterra. The aim is to prove in principle the fast processingspeed which is scalable to ultra-broadband level for networking. MATLAB Simulinkis also used as a modeling platform for simulation of the hardware implementation.The models and prototype system presented here are applicable to both wireless andoptical communications. For optical communications systems, an optical modulator,the I-Q modulator, is used and fed by the signals generating the constellation fromthe electronic model/hardware system. Likewise these signals are fed to a poweramplifier and then antenna for wireless media.

EP1S254 is a high-speed device, it is suitable for system integration and appli-cations in telecommunications. It allows parallel processing, desired for imple-mentation in the physical layer that requires short delay/propagation time.Implementation sub-systems for OFDM such as coding, FFT/IFFT, cyclic prefixadder/remover, equalizer in the frequency domain, especially convolutional coderand Viterbi decoder, can be carried out without much difficulty and with efficiency.The noise generators and bit error rate counters are also implemented.

In our OFDM system, the parameters implemented are as follows: 256 subcar-riers, convolutional code 1

2 , modulation scheme either QPSK or 16 QAM, and thelength of prefix 1

4 .This paper is organized as follows. Section 2 gives a brief overview of the essential

features of OFDM techniques so as to bridge the MATLAB Simulink and hardwareimplementation based on FPGA described in Secs. 4 and 5. Section 3 briefly out-lines the wireless and optical guided transmission media for the OFDM systems.Section 6 describes the integration of the software and hardware for the experi-mental platforms. Section 7 then describes the hardware system and the resultsobtained by simulation and FPGA based hardware implementation. Finally, Sec. 9gives some conclusions and provides directions for future research.


Simulink Model and FPGA-Based OFDM Communication System 371

2. Overview of OFDM Techniques

2.1. Principles and generation of OFDM system signals

OFDM is a block transmission technique. The baseband sequence signals can becoded and modulated to the points of the constellation, for example binary phaseshift keying (BPSK), quadrature PSK (QPSK), quadrature amplitude modulation(QAM). Thus complex symbols are generated and assembled into blocks and mod-ulated to a group of subcarriers which are placed closely in the frequency spectrum.These subcarrier channels form an OFDM symbol. The data sequence can be con-trolled to occupy one or several carriers or all subcarrier channels of the OFDMsymbol. Thus the OFDM symbols are transmitted as a superposition of all thesesubcarrier channels.

Figure 1 depicts the sequences for construction of an OFDM symbol. The inputdata sequence {dl} is partitioned into N parallel data lines whose rate is thusreduced by N times via the serial to parallel converter (SPC). N is also equivalentto and assigned as the number of subcarriers. The bit sequence {di,k} is modulatedto form {am,k} signals where k is the index of the subcarrier, i is the index of thetime slot corresponding to the N bits parallel after going through the SPC, andm isthe time slot index corresponding to the N complex signals. The signals {am,k} arethen shaped to an appropriate form so as to limit the spectral width to the allow-able width of each subcarrier channel. They are then inserted with an appropriatesubcarrier φk(t) which is orthogonal to one another and can be expressed as

φk(t) = ej2πfkt, (1)

where fk is the corresponding frequency with respect to the kth subcarrier withinthe OFDM symbol.

The OFDM signals of N subcarriers can thus be represented as:

S′m(t) =

1√N

N−1∑k=0

am,kφk(t), 0 < t < NT, (2)

S-P-

Con

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Baseband signals

Bas

eban

d m

odul

atio

n

B

Σaseband signals

Baseband signals

Gua

rd b

and

inse

rtio

n

,i kd

,i Nd

,m ka

,m Na

1φ

kφ

Nφ

( )mS t′

DA

C ( )mS t

{ }ld

,1ma,1id

Fig. 1. Principles of construction of OFDM signals. DAC: digital to analog conversion. S-P: serialto parallel.



where am,k is the kth complex symbol, NT is the length of OFDM symbol containingN subcarriers, and T is the sampling interval. The subcarriers are equally spacedby ∆f = 1

NT , fk is estimated by

fk =k

NT. (3)

These fk values can then be mixed with the passband carrier, e.g. microwave orlightwave, to generate a set of orthogonal passband subcarriers. Each signal S

′m(t)

is equivalent to a point in the Euclidean N -dimensional space which is called thesignal space. Each point is thus represented by a set of values (am,1, am,2, . . . , am,N ).

In the case of continuous transmission, m is an integer and dependent on thelength of the input data. All multiplied signals are then added and the final sig-nal is the passband time-dependent modulated signal waves which can then betransmitted over the transmission medium. Due to the fact that fk is modulatedat the carrier frequency fk = k∆f Hz, the OFDM technique is commonly knownto be composed of N subcarriers, each carrying much lower speed data symbolsROFDM = RS/N with Rs as the original sampling rate or the bit rate of the inputdigital sequence. Thus for OFDM the bit rate of each subcarrier channel is thetransmission bit rate of the OFDM frame.

2.2. Implementation of OFDM system using IFFT/FFT

The multiplexing of subcarriers is not a major issue but the filtering of each subcar-rier channel is the principal task. Originally they were filtered by several bandpassfilters and thus their design and performance characteristics, especially the verysharp roll-off, cannot be easily satisfied. This deters the uses of OFDM in the ini-tial development phase till the proposal of using inverse discrete Fourier transform(IDFT)6 of the sequence ak, written as

S′m(nT ) =

1√N

N−1∑k=0

am,kej2π nk

N 0 ≤ n ≤ N − 1. (4)

Naturally IDFT is commonly available in almost every digital signal proces-sor. Likewise the demultiplexing of the subcarrier channel at the receiver can beeasily performed using DFT. This has facilitated the simplification for practicalimplementation of OFDM. Figure 2 depicts the implementation of OFDM signalsusing inverse Fourier transform IFFT and FFT which further simplify the genera-tion of orthogonal channels. Therefore, a FPGA-based system can assist with thisimplementation.

2.3. Cyclic prefix

Communication systems employing OFDM would face two main problems. Firstly,the channel separation between subcarrier channels is narrow and can easilylead to intercarrier interference (ICI). Secondly, OFDM symbols are continually



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Para

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con

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ion

Bas

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Gua

rd b

and

inse

rtio

n

,1id

,i kd

,i Nd

,1ma

,m ka

,m Na

( )mS t′

IFFT

( )mS t

DA

C

{ }ld

Fig. 2. Generic principles for the generation of OFDM using IFFT algorithm.

transmitted, so if the delay or distortion effects occur repeatedly, intersymbol inter-ference (ISI) would happen. So if the guard band consists of all “0”s, the processingcan minimize the ISI but not the ICI. Thus the prefix is suggested by Peled andRuiz6 in 1980 by copying parts of the message signal and inserting it to the begin-ning of the message signal. Therefore the problems of ISI and ICI can be resolved.

The notation ts is defined as the symbol period, and Ts is the symbol period plusprotection interval ∆G such that −∆G ≤ t < 0. Thus the OFDM signals includingthe prefix can be expressed as:

Sm(t) =1√N

N−1∑k=0

am,kφk(t), −∆G < t < NT. (5)

Usually the prefix is selected such that it is longer than the transmission delaytime of the transmission medium and can be tuned to achieve the maximum trans-mission quality. Thus the protection interval plays an important part in the miti-gation of the ISI and ICI. However by using the cyclic prefix, some energy must bepaid to this extra part of the signals to be transmitted. Naturally the total energyto be consumed by cyclic prefix OFDM signals would be now evaluated for eachsubcarrier channel as: ∫

|φk(t)|2dt =NT

NT − ∆G. (6)

Thus the SNR penalty per subcarrier channel at the receiver is given by

Eloss =NT

NT + ∆G. (7)

Hence the total SNR penalty at the receiver is given by:

SNRloss = −10 log10

(1 − ∆G

NT

). (8)

Therefore it is naturally expected that the longer the cyclic prefix interval, thehigher the SNR penalty.

In summary, the structure of the OFDM symbol is arranged as shown in Fig. 3.



Fig. 3. Structure of an OFDM symbol, including all subcarriers.

2.4. OFDM signal demodulation

The OFDM receiver can be considered to be composed of several demodulators;each one would be demodulated to passband signals carried by each subcarrier toits baseband equivalence. Then by superimposing all these baseband signals of allsubcarrier channels, the original data sequence can be recovered. The schematicdiagram representing the principles of signal recovery of OFDM signals is shown inFig. 4. We can easily observe that if all the functions φk(t) with k = 1, 2, . . . , N areorthogonal in pair, then the original set (am,1, am,2, . . . , am,N) can be recovered toits original values.

From the mathematical point of view, a set of functions can be consideredorthogonal if ∫ a

b

ψp(t) · ψ∗q (t)dt =

{k, p = q

0, p �= q .(9)

Here * denotes the complex conjugation. The orthogonality of the subcarriers canbe performed by the following: the pth carrier can be moved to the qth order by

S t

demodulation

demodulation

demodulation Tra

nsfo

rm s

ymbo

l to

bit s

eque

nce

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of G

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ban

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( )m′( )mS t

AD

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Received analog signals

{ }ld

Par

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l to

seri

al c

onve

rsio

n

,1id,1ma

Fig. 4. Principles of demodulation of OFDM signals.



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FFT

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Fig. 5. Schematic of the generation of OFDM signals using FFT.

multiplying it with the complex function ejpωSt in which wS = 2πfS = 2π 1TS

isthe spectral distance between the pth and qth order subcarriers. If all subcarriersare not desired and mixed to the frequency location given by a multiple numberof 1/TS, then the orthogonality ensures that they would result in a null numberafter integration over a symbol period. Thus the subcarriers must be separated bya multiple number of 1/TS so as to achieve orthogonality. Therefore similarly tothe operation given for the transmitting side can be used in the demodulation ofOFDM signals as depicted in Fig. 5.

3. Transmission Media: Wireless and Optical

3.1. Effects of transmission medium

Additive White Gaussian Noise (AWGN) transmission medium is considered tobe the simplest representing a generic model of the transmission medium whosenoise characteristics follow a Gaussian profile which most media for communicationswould follow, e.g. wireless and optical fibers. Note that when the optical fiber isoperating in the nonlinear region, the probability density function (pdf) is non-Gaussian and different treatment may have to be considered. A Gaussian pdf can beconsidered to offer zero average and a variance distributed about this null average.

In reality, wireless signals transmitted from the base station (BS) to the mobilestation (MS) would be affected by several factors of the transmission medium,especially the fading effect due to diffraction and reflection of the electromagneticwaves to the objects of the environment. If the mobile receiver is moving, then aDoppler frequency shift would exist at

fD = fDmax cos(α) with fDmax = vfc

c, (10)

where v is the relative velocity of the MS to the BS. fc is the carrier frequency, c isthe velocity of light in vacuum, α is the angle of the direction of movement of theMS with respect to the BS.



( )x t0τ

0 ( )tα 1( )tα ( )k tα

( )y t

( )L tα

Σ

2τ kτ Lτ

Fig. 6. Delay model for transmission of purely delay effects such as wireless transmission andpolarization mode dispersion in single mode optical fibers.

A generic model of the transmission medium with multipath delays can bedepicted as shown in Fig. 6 in which x(t) represents the transmitted signals, y(t)is the output of the transmission medium, τk is the kth delay time, αk(t) is theattenuation factor of the kth delay path, and L is the number of delay paths. For thecase of single mode optical fibers, the delay is contributed by different travel timesof the two polarized modes. This is the fundamental property of the weak guidingof lightwaves in modern single mode fiber whose refractive index difference is verysmall (∼3× 10−4). Furthermore, the random imperfection of the cross section areaof the circular core enhances the fluctuation of the difference of the delay timesbetween the two polarized modes.

The difference is the delay time and delay path is strongly dependent on themedium. Thus we can define a coherence bandwidth as the frequency interval gen-erated by the maximum delay time given by the medium as

(∆f)C =1

τmax, (11)

where τmax is the maximum delay time of the flat fading or nonselective fading. Onthe other hand, we would have frequency selective fading. When interference andDoppler effect occurs, the shifting in the subcarrier can be related to a coherenttime defined as

(∆t)C =1

(2fDmax), (12)

where fDmax is the maximum Doppler frequency. If the coherent time is less thanone period of the original data, then the fading is fast fading. Otherwise it is slowfading.

3.2. Equalization of OFDM signals

In an OFDM system, the data at the input must be transformed and coded toN parallel sources. These OFDM symbols would then be transformed by IFFTand then by FFT back to the time domain and the superimposition to obtain thesignal s(t). For simplification, we can bypass the generation of the OFDM signaland assume that s(t) is the OFDM signal which is transmitted to a channel whose



impulse response is h(t) and output is r(t). In the case of AWGN n(t), we have

r(t) = h(t) ∗ s(t) + n(t). (13)

Correspondingly in the frequency domain we have

R(f) = H(f) · S(f) +N(f), (14)

where S(f) is the frequency domain representation of the OFDM signal. The recov-ery of S(f) is thus mainly filtering of the noises contributed by N(f).

Thus the equalization can be implemented after the FFT subsystem, and onlythe multiplication or division operations are needed and not integration or differ-entiation. This offers significant advantages in signal processing in real time.

The effectiveness of OFDM technique depends on the shifting of the frequencyand phase of the subcarriers. If Doppler effects exist in the transmission medium,then the phase lock loop at the receiver front may have to be used. If errors infrequency and phase happen, then the rotation of the constellation of the receivedsignals would happen and the detection must be corrected. The third problem isthat the clock signals of the ADC and DAC at the front end of the transmitter andreceiver can be different, thus creating some extension of the OFDM symbol whichmay be different from symbols to symbols. Thus there must be a synchronizationof the symbols. These problems affect the recovery of the transmitted signals andmust be dealt with.

The use of the cyclic prefix can solve the problem of synchronization of thesymbols. Furthermore, if the delay time varies and is less than the cyclic prefix timeinterval, then one can use this interval to assist the synchronization of the OFDMsymbols. Then the FFT with N points from this location would significantly reducethe mismatch in the subcarrier phase. Once the synchronization is complete, theeffects of shift in the frequency and phase due to the Gaussian noises can be resolvedby increasing the spectral distance between the subcarriers. However, the techniqueemployed in this work is to insert pilot carriers at the known subcarrier location inOFDM symbols. This technique is described in the next subsection.

3.3. Pilot signals

At the receiver end, the received and original values of the pilot allow the esti-mation of the effects of the transmission at the frequency location of these pilotsand thus one can deduce the effects of the transmission medium on all subcarrierchannels of the OFDM symbol. The original OFDM symbols can then be recoveredwithout much difficulty. The pilots can be inserted into OFDM symbols as shownin Fig. 7. The frequency spacing between pilots must follow the sampling rules inthe frequency and time domain.

As mentioned above, the change of frequency of the transmission medium isdependent on the maximum delay time of the medium. Let rf be the sampling



Fig. 7. Representation of pilots in the time domain and frequency domain.

ratio in the frequency domain and ∆f be the spacing between the subcarriers, thenthe spacing between the pilots must satisfy:

rf =1

Df∆fτmax≥ 1. (15)

Thus the minimum sampling ratio must be rf = 1. When rf < 1, the transmissionchannel cannot be fully recovered via the pilots.

Similarly in the frequency domain, the spacing between the pilots must satisfy

rt =1

2fDmaxDt(TS + ∆G)≥ 1, (16)

where fDmax is the maximum frequency of the Doppler effects.The estimation of the frequency response of the transmission medium H(f)

is useful especially when OFDM is used in the transmission system due to thefrequency operation of the OFDM signals. That means that one can operate onR(f) instead of r(t). This is quite easy with the implementation using digital signalprocessors.

Now let Spilot(f) be the frequency distribution of the known pilots in the OFDMsymbol. At the receiver end, when the received R(f) is known, the pilot locationscan be derived by

Rpilot(f) = Spilot(f) ·Hpilot(f) +N(f). (17)



For the sake of simplicity, we can ignore the noises due to AWGN, then

Rpilot(f) = Spilot(f)Hpilot(f). (18)

Hence the frequency response of the transmission medium evaluated at the locationsof the pilots is given as

Hpilot(f) =Rpilot(f)Spilot(f)

. (19)

From Hpilot(f), the overall frequency response H(f) of the transmission channelcan be derived by using available techniques such as Wiener–Hop filtering or othercomplex filtering methods.

There are several possibilities of inserting pilot carriers into the spectrum ofOFDM signals as proposed in Refs. 7 and 8. Each scheme offers its strong pointdepending on the transmission characteristics of the transmission channel. Thusthere is possibility for further research in the allocation of the pilots, especiallywhen single mode optical fibers and online optical amplifiers are employed in thesystems in which the nonlinear phase noises and quadratic distortion characteristicsof the fibers are combined with the random noises (ASE = amplified stimulatedemission) of in-line cascaded optical amplifiers.

4. OFDM Systems Design

4.1. Structures of OFDM symbols

OFDM symbol is defined as a set of subcarrier channels whose number determinesthe number of the FFT and IFFT to be used. First, the data carrier is employedfor transmission. Second, the pilot carriers would be used for synchronization andestimation of the effects of the transmission medium. Finally, the null subcarrier forprotection band and DC carrier can be added. The usefulness of the protection bandensures the sharp roll-off of the “brick-wall-like” passband of the OFDM symbol.

Depending on practical systems, the number of subcarriers of each portion of themessage symbol may vary. For example, the symbol structure of Standard 802.16can be {28 zero, 100 data, zero, 100 data, 27 zero} where the data are imbedded withpilot at special locations of −88,−63,−38,−13, 13, 38, 63, 88. Each complex datasequence, when imbedded into the symbol, would be indexed from −128 to +127.

4.2. Estimation of the design parameters

In order to design OFDM symbols, we need to specify the following parameters:BW: spectral width of OFDM symbol; Nused: number of subcarriers to be used inan OFDM symbol; n: the sampling factor, together with BW and Nused the spec-tral width of the carrier can be specified based on the symbol time as defined inEq. (3); G: ratio between CP and the symbol time; NFFT: number of FFT pointswhich are selected to be in the order of 2N and greater with N being an integer.NFFT is greater than Nused; Fs: sampling frequency, Fs = floor(n·BW/8000)·8000;



∆f: spectral separation between subcarriers; Tb: useful symbol time period, Tb =1/∆f ; Tg: guard time interval (GI), Tg = GTb; Ts: time interval between OFDMsymbols Ts = Tb + Tg; sampling time: Tb/NFFT = 1/Fs; length of the cyclicprefix: ∆G.

When designing the system using the OFDM technique, one need to implementthe following.

First, the cyclic prefix (CP) must be selected as small as possible in order tominimize the energy loss and ensure that the transmission speed is greater thanthe delay time τ . Secondly, the length of the OFDM symbol must be much longerthan the response time τ of the transmission channel given by

NT � τ ⇒ N � τ

T= τBW. (20)

Thirdly, OFDM is very sensitive to ICI so the subcarrier spacing 1NT should be

considered as the best when it is greater than the frequency shift due to Dopplereffect fD so that the subcarrier orthogonality would remain satisfied.

1NT

� fD ⇒ N 1T · fD

=BW

fD. (21)

Thus,

τBW N BW

fD. (22)

This is the condition to be satisfied to determine the number N of subcarriers.Further we can deduce that the channel delay time τfD 1, meaning that thesmaller the delay of the transmission channel τ , the wider the frequency band withno change in the passband and the greater the coherent time.

4.3. Simulation and FPGA-based models

This section outlines briefly the transmission system employing the OFDM tech-nique, including the software platform and the hardware demonstration. Thedetailed description of the function of each block of the system and an introductionto the DSP Builder and DSP development are given.

4.4. OFDM communication system models

The OFDM transmission system integrating both the hardware and FPGA-basedplatform is shown in Fig. 8 which consists of a randomizer/derandomizer, channelencoder/decoder, IQ mapper/IQ demapper, symbol OFDM, signal OFDM, channelestimation, and an equalizer.

Data used for inspection of the system generating the randomizer are storedin some allocated memory. SingalTap of Altera FPGA interfaced via the StandardJoint Test Action Group (JTAG) is used for the inspection and control of theoperation of the whole system. Digital signals are converted to analog form viathe DAC and then monitored using the spectrum analyzer. The system processes



Fig. 8. Hard- and software experimental platform of the OFDM digital transmission systems.

signals at the baseband level; thus the signal spectrum is evaluated on the I- andQ-components.

4.5. Functionalities of OFDM system blocks

The principal function of a communication system is to transport information withan assurance of the bit error rate (BER) as pre-determined. Therefore the OFDMsystem consists of the following blocks:

The randomizer blocks. At the randomizer the input data initially would be splitinto groups of “1”s and “0”s with a distribution by using XOR and a random bitpattern generation. The bit pattern generation block would be associated with thepseudo-random bit sequence (PRBS) generator. The effects of the randomizer areto avoid identical bit patterns so as to avoid the difficulty in recovery of signals toits original bit sequence. The derandomizer at the receiver performs reverse processof the randomizer.

Channel encoder. This is the most important block and plays the major part inthe coding and assists in the recovery of the decoder block with redundancy bits. Inthis work the convolutional coder employed is associated with the Viterbi algorithmto ensure perfect corrections of error. Turbo algorithm can also be employed tofurther improve the performance of the decoder.

IQ mapper block. This block converts the bits into a set of bit patterns corre-sponding to the states of the constellation of modulation scheme. In OFDM this iscalled the mapper which can be formed to further increase the bit rates and hencethe spectral efficiency by higher order or level of the constellation. QPSK or M-aryQAM can be used. In the reverse process the demapper is used to transform theconstellation points back to the bit pattern.

OFDM symbol generator block. After conversion of the bit sequence into sym-bol, the serial bit sequence would be converted to parallel blocks and assembled



with pilots or DC symbol and protection symbol; these symbols form the OFDMsymbol. Each symbol represents a frequency spectrum so as to superimpose on thesubcarriers.

OFDM signal block. The OFDM symbol would then be IFFT-transformed togenerate OFDM signals. Thus OFDM signal is a combination of all the spectraof the OFDM symbols. Afterwards the IFFT cyclic prefix would be inserted atthe beginning to form the OFDM signal for transmission over the channel. Thesesignals are converted to the analog form via the DAC and then converted to thewireless or optical domain depending on the transmission medium.

The transmission channel is simulated using delay and summation to representthe delay paths of signals over a wireless medium. If optical fiber is used, then theSchrodinger equation of the complex amplitude would be used in association withthe split step process to propagate the OFDM signals. The noises are modeled usingAWGN method.

Other blocks in the receiving ends would be formed with their operations in areverse order and in complement to those described for the transmitting end blocks.

4.6. DSP Builder and FPGA-based systems for OFDM

The software platform used in this work is the DSP Builder of Alterra for digitalsignal processing applications. The Builder is operating in a MATLAB Simulinkenvironment. Available blocks in DSP Builder facilitate the development of thecommunication system. Simulink blocks can also be integrated to analyze simulatedresults and monitor signals at different sections and blocks of the model. Mostimportantly, the DSP Builder can convert the design block systems into VHDL,allowing the storage and copying of data and their integration to form the designdata for hardware implementation. Furthermore, the DSP Builder would also allowus to conduct simulation of filtering and more complex functions by using MegaCoreFunctions available in the builder.

MATLAB Simulink9 generates the model, integrating the blocks of DSP Builderwith those of the Simulink. The Register Transfer Level (RTL) expresses the simu-lation model and the DSP Builder supports the ModelSim by TCL scripts. CreatedVDHL format model can be used by other software packages for simulation ifdesired.

The files obtained from the DSP Builder Signal Compiler can be combined withRTL. The DSP Builder supports TCL scripts for automatic integration with othersoftware packages such as Quartus II, Synplify, or LeonardoSpectrum. The designplatform in this work is written in the Quartus II software environment.

The DSP Development Stratix EP1S25 is used. These are the kits employed todesign applications of digital signal processing by DSP builder or HDL languages.The kit comprises Stratix DSP Development Board, QuartusII software package,DSP Builder, and IP core MATLAB/Simulink. Main devices are incorporated on



the Stratix EP1S25 with the main device 25660 logic elements at the fastest speed,packaged with FineLine BGA and a total memory of 1,944,576 bit RAM.

The development kit consists of (i) two ADC-12-bit, maximum sampling rate 125Msamples/s, 2-complement data converter, frequency of input signals greater than1MHz, peak-to-peak input amplitude 2V; (ii) two DAC-14-bit, operating speed165MHz, conversion to analog signals from digital form, peak-to-peak amplitudeof 1V; 2Mb SRAM with 7.5-ns synchronization, each SRAM with 18 address lines,36 data bus and 1MB 32 Mbit flash memory.

In general the library of the DSP Builder consists of a number of blockswhose functionalities include4: Library “AltLab”, Block “SignalCompiler”, Block“SignalTap II Analysis”, Library “Arithmetic”, Library “Board”, Library “Com-plex Type”, “Gate and Control”, Library “IO and Bus”, “Rate Change”, Library“Storage”, and Library “MegaCore”.

5. OFDM System Platform

This section gives the principal function of the design and associated blocks ofthe OFDM system including I/O ports, randomizer, convolutional code block, andstructures of OFDM symbol. Employment of the cyclic prefix is based on 802.16.

5.1. Random generation of data signals

5.1.1. Principles of generation

The logic diagram of the randomizer would consist of a shift register and two exclu-sive OR gates. The principles of operations of this block are briefly described above.

5.1.2. Design of the pseudo-random generator

The MATLAB Simulink model of the generator is given in Fig. 9, it is integrated inthe DSP Builder. The pseudo-random binary sequence generator can be constructedin this block using the sequence “1 + X14 + X15”. The pseudo-random sequence

Fig. 9. Schematic diagram of the randomizer.



can be generated from the initial sequence set “100101010000000”. The input isXORed with the output of the pseudo-random binary sequence generator. Thesignals ena and rst enable the reset and rest of the pseudo-random generator. Thederandomization at the receiver can be done by passing the signals again throughthe randomnizer. In this work the input is in the form of binary sequence, thusthere is no need for the conversion from the decimal form to the binary form.

5.2. Channel encoding

The encoder is shown in Fig. 10 for generation of the convolutional code withthe determined speed of 1

2 . The length of the encoder is seven symbols and thepolynomial used is G1 = 171OCT and G2 = 133OCT. The encoder is formed byusing six tap delays and two XOR gates with five inputs. In CC is the input of theencoder and out CC1 and out CC2 are the two outputs corresponding to G1 andG2. The signals ena and rst are for enabling and resetting the encoder.

5.3. Decoding using Viterbi algorithm

The decoder is designed using Viterbi algorithm. The algorithm consists of fourmain blocks: branch metric, add compare and select, survivor path metric, tracebackand output decoding block.

The branch metric is used to estimate the Hamming distance of the bits, e.g. 2bit if the speed of codes is R = 1

2 with branches. The summation block conductsselective addition and is responsible for estimating the total Hamming distance ofthe branches in the current state and it keeps only the shortest distance branch.This block selects and determines the optimum sequence. The traceback and outputdecoding block is responsible for selection, rechecking the sequence at the optimumstate and determine the output sequence which is the decoding sequence of thealgorithm.

Figure 11 shows the decoding techniques model using MegaCore so as to con-struct the decoder using Viterbi algorithm. The Viterbi algorithm is based on thebest suitable sequence. Therefore the determination of the length of the sequence

Fig. 10. Encoder for generation of convolutional code.



Fig. 11. Schematic of the decoder using Viterbi algorithm on MATLAB Simulink.

influences the effectiveness of the decoder. If the length is too long, then there wouldbe more numerical operations, increasing the memory storage and the delay time.On the other hand, if the length is too short, then it limits the error correctionpotential of the algorithm.

5.4. Signal constellation

5.4.1. Constellation

Constellation is the modulation technique to transform the sequence of m bit intoa complex phasor in the form of a + jb. The number of bits m depends on thenumber of states of the constellation. For example, a 16-QAM has four bits persymbol, which has 16 points on the constellation. The mapper uses the method ofmodulation but the modulation function rests at the IFFT and the DAC at theoutput. There are a number of methods for constructing the mapper by using thelook-up table based on data stored in ROM memory. In this work, the mapper usesthe structure of look-up tables which are classified for the I- and Q-components.The data used for forming the constellation are stored in the look-up table. Theoutput values vary from −1 to +1. The output of the DAC is represented by a 14-bitword. Thus, this work normalizes the sequence into fixed point arithmetic values.Figure 12 shows the MATLAB Simulink model of the constellation generator.

5.4.2. Reconstruction from constellation

At the receiving end, the constellation points representing the states of the OFDMsymbols at the output of the transmission medium, are accumulated. Thus the con-stellation demodulator must set the decision levels so as to determine the constel-lation points of the receiver. The demapper is constructed using Verilog language.The decision point is based on the shortest Euclidean distance to the received sig-nals. When QPSK modulation is used, the demapper can simply determine by



Fig. 12. MATLAB Simulink model for QPSK modulation.

Fig. 13. Schematic of the modulator using 16-QAM by MATLAB Simulink.

evaluating the most significant bit of the bit sequence received which is the signbit of the received sequence. For the 16-QAM multilevel modulation scheme, thedemapper is designed based on the rule of IF-THEN. The output data are fed intothe FIFO and then into the decoder. In the OFDM symbol there are 192 data val-ues to be transmitted. Thus the FIFO needs 192 memory pair shift registers so asto store the I- and Q-component values. Figure 13 illustrates the Simulink modelof the demapper for the 16-QAM modulation.

5.5. OFDM symbols

An OFDM symbol consists of the data payload, the pilot, and the “0” patching upvalues and the inserted symbol pilots. These pilots are used to estimate the effectsof the transmission medium at the receiving end.

5.5.1. Generation of pilot signals

In order to generate the pilot, we need to use the pseudo-random generator/randomizer. The polynomial for the PRBS is (1 +X9 +X11) as shown in Fig. 15.The coefficients of the polynomial are based on 10101010101B. The pilot signals for



Fig. 14. Demapper block.

Fig. 15. Generation of pilot signals.

the kth OFDM symbol can be derived from the value wk. The interleaving valuescan be determined as c−88 = c−38 = c13 = c38 = c63 = c88 = 1 − 2wk and c−63=c−13 = 1 − 2(!wk).

The Simulink model for generating the pilots is given in Fig. 15 which consistsof a LFSR block to generate random sequence, a block for generating the locationof !wk and finally the arithmetic operator to generate (1− 2wk) or (1 − 2(!wk)). Ifwe index the symbol from 0 to 255 then the values −63 and −13 would become 65and 115 which are the time indices for determining the location of the bit in theOFDM symbol. The signal “ena” and “rst” are used for enabling and resetting thecircuitry. The pilot signal is the output of the block.

5.5.2. Assembly and separation of symbols

The assembly and separation of the constituents of OFDM symbols are implementedas shown in Figs. 16 and 17, respectively.

The arrangement of the data sequence of OFDM symbols is based on StandardIEEE 802.16 and defined as follows: {28 “0”s, 100 data, zero, 100 data, 27 “0”s} inwhich the locations of the pilots are at c−88, c−63, c−38, c−13, c13, c38, c63 and c88.Verilog language is used to generate this arrangement. The inputs of assembler arethe index of the symbol, the data to be transmitted, pilot and zeros for patching and



Fig. 16. Generation of OFDM symbols by combining of constituents.

Fig. 17. Separation of constituents of OFDM signals.

data for the I- and Q-components as shown in Fig. 16. The output of this assembleris IFFT-transformed to generate OFDM signals with control timing signals as shownin Figs. 17 and 18. The disassembling of the OFDM signals at the receiving endcan be implemented with the input to the FFT block. The data information is thenfed into the equalizer as shown in the separator of Fig. 19.

Fig. 18. OFDM generator.



Fig. 19. Schematic of the Separator of OFDM signals.

5.6. Transmission medium and evaluation of OFDM signals

5.6.1. Transmission medium models

The AWGN transmission channel is structured in a software platform and storedin memory. The output signals with cyclic prefix inserted would be superimposedwith noises (Figs. 20 and 21).

5.6.2. Equalizer

The equalization block is shown in Fig. 22. The estimation of transmission mediumfrom the pilots is received for setting of the coefficients of the equalizer, which areupdated from time to time.

Fig. 20. Generation block for cyclic prefix insertion.



Fig. 21. Noise generation and superposition.

Fig. 22. Estimator for transmission channel and equalization.

5.6.3. Error analyzer

The error analyzer is shown in Fig. 23. It is used to estimate the bit error rate(BER) of the decoded data sequence as compared to the original data sequence atthe transmitting end.

5.6.4. Control signals

The monitoring of the performance of the hardware system is incorporated in alook-up table. Our OFDM signals carry 256 subcarriers in which 55 values at the



Fig. 23. BER counter and analyzer.

Fig. 24. Generation of control signals.

beginning and at the end of the symbol are patched up with zeroes. Thus, with eightpilots used, the total number of bits for data payload would be 192. Convolutioncode is used with a factor of 1

2 . Figure 24 shows the structure of the block for controlsignals generation.

5.7. Hardware implementation

The schematic of an OFDM system developed in this work is shown in Fig. 25.Similar shaded blocks are used to indicate the block and its counterparts atthe transmitting and receiving ends respectively. The functions of each block aredescribed in the previous section. The functions of the blocks of this diagram arelisted in Table 1.

6. Simulation and Experimental Platform

The OFDM signals are monitored by the software platform SignalTap which isintegrated in the hardware system, in particular the FPGA-based section. Theresults obtained are then displayed on a desktop computer. SignalTap also updatessignals in real time. The development board is also updated via software platformboard using JTAG standard. In order to study the functions and performancesof each block of the system as described above, we monitored and accumulated



Fig. 25. Schematics of OFDM systems as constructed on DSP Builder.

data at the inputs and outputs of each block.11,12 Delay adjustments are made tocompensate for the data accumulation. This section thus presents the experimentalresults obtained including the monitoring of the spectra of OFDK system via anexternal spectrum analyzer.

6.1. Randomizer

The data passing by the randomizer twice would give the same sequence at theinput. Once randomized, the data are indexed with “1” or “0” which appear con-tinuously. Figure 26 depicts the waveforms of the data sequence at the input andoutput of the randomizer after one and two passing. This confirms the workingprinciples of the randomizer as described above.

6.2. Encoder

The input randomized data sequence would be encoded using convolutional codeprinciples with a coding speed of 1

2 . After coding, noises are superimposed by abit-complementary transmission channel. At this stage the probability of error is14 with an error sequence of “01000100”. After this the Viterbi algorithm is usedto decode the encoded data sequence; the decoded sequence must be the same asthe original data sequence. Figure 27 shows the performance of the encoder withthe input data sequence, its output after the encoder, and then the output of thedecoder which is identical with its original image. Thus this confirms the workingof the encoder developed using FPGA-based processor. The coding speed of 1

2

means that for each bit entering the encoder, there would be two bits following thepattern g1 and g2 which are represented as a pair of bits (g1g2) where g1 is the most



Table 1. Description of blocks of the OFDM systems (Fig. 25).

Blocks Functions Data lines

Names Functions

Sink Generating data for

transmission andcontrol signals

index out Indexing of symbol

rd data Reading data after constellation at theFIFO

Ena Enabling data outputdata out Output data

Randomizer Randomization ofdata sequence

ena Enabling processingin ran Data to be randominzed — inputrst Reset

ChannelEncoder

Encoding ena Enabling processingin cc Data to be encoded — inputrst Resetout cc1 Output g1= 171oct

out cc2 Output g2= 133oct

Mapper Mapping toconstellationpoints

rd data Retrieve data from FIFO memorywr data Writing data to FIFO memoryin map Data input to be mapped to constellation

pointssclr Erase FIFO memoryout mapI In phase output of mapper — points states

of constellationout mapQ Quadrature phase output

AssemblingSymbolOFDM

Generating OFDMsymbol byassembling dataand inserting pilotand zero patching

index Symbol indexin dataI Inphase inputin dataQ Quadrature phase inputout I Inphase outputout Q Quadrature phase output

SignalOFDM

Generating OFDMsignals by IFFT

index in Symbol indexin real Real inputin imag Imaginary inputout real Real outputout imag Imaginary outputout sop Start of fame at outputout rst Reset output for new symbol

Cyclic Prefix Insert cyclic prefix in real Real inputin imag Imaginary inputsclr Erase index of data at outputout real Output realout imag Output imaginary

RemoveCyclicPrefix

Removing cyclicprefix

in real Input realin imag Input imaginaryout real Output realout imag Output imaginarysop rx Start frame at receiving end after

removing CPeop rx End of frame at receiving end



Table 1. (Continued)

Blocks Functions Data lines

Names Functions

Signal

OFDM

Decomposition of

OFDM signals byFFT

in realrx Input real

in imagrx Input imaginaryin sop Start of receiving frameIn eop End of receiving frameout realrx Output realout imagrx Output imaginarysop rx Start of frame output

DisassemblingSymbolOFDM

Decomposition ofOFDM signals tocollect data, pilot

in realrx Inphase inputin imagrx Quadrature phase inputsop rx Start of output framdata I Inphase outputdata Q QUadrature phase outputpilot I Inphase pilot outputpilot Q Quadrature phase pilot outputwr data Writing into FIFO memoryindex Index of received data

Equalizer Estimation oftransmission channelcharacteristics

data I Inphase input datadata Q Quadrature input datapilot I Pilot inphase inputpilot Q Quadrature pilot inputrx I Inphase outputrx Q Quadrature phase output

Demapper Conversion ofconstellation pointsto data sequence

rx I Inphase input datarx Q Quadrature phase input datawr data Writing into FIFO memoryrd data Reading data from FIFOdata out Data output after mapping to

constellation

ChannelDecoder

Decoding usingViterbi algorithm

in dec Input data to be decodedsink val Enabling decodingout dec Output of decoderout ena Enable output of decoder

Derandomizer Decoding byde-randomization

in ran Input data to be decodedena Enabling randomnizationout ran Randomnized Data

significant bit and g2 is the least significant bit. The clock period of the decoderis four times longer than the recovery temporal length. Thus for a recovery lengthof 42, the length of the decoder is 7, and a delay time of the decoder is 168 clockintervals. This would allow us to set the delay time for comparison between theinput encoded data sequence and that of the output of the decoder. The sequencewaveforms in Fig. 27 can then be confirmed to demonstrate the working of theencoder and decoder. Note that for every four bits transmitted, there would be oneerror bit and this error bit is corrected by the Viterbi algorithm.



(a) (b)

(c)

Fig. 26. Experimental observation of the randomizer. (a) Original data sequence. (b) Randomizeddata sequence. (c) De-randomized data sequence.

(a) (b)

(c) (d)

Fig. 27. Experimental signals obtained at the encoder. (a) Original data sequence. (b) Encodeddata sequence. (c) Encoded data with added noises. (d) Decoded data sequence.

6.3. Signal processing at the transmitter

The data sequence at the output of the transmitting end is formed by the rando-mizer. It is fed into the input of the encoder, the mapper for mapping to the con-stellation points, assembling into OFDM symbol and cyclic prefix. Furthermore, theoutput of DAC is a unipolar signal; thus addition of DC component and conversionto bipolar is required. Each OFDM symbol is transmitted within 320 clock periods;hence the obtained waveforms are presented in 320 clock periods.

6.3.1. Encoder

Because the randomized data sequence consists of 192 binary bits, in order to ensurethe right error correction of the 7-bit-long error encoder, we need to path a “0” atthe end of the bit sequence.



(a) (b)

(c)

Fig. 28. Data input to the mapper and after the mapper for mapping to the constellation forQPSK modulation. (a) Input data sequence to the mapper. (b) Inphase component sequence atthe output of the mapper. (c) Quadrature phase component sequence at the output of the mapper.

6.3.2. Constellation transformer

The encoded data sequence would then be transformed to the states of the constel-lation using the mapper. With the convolutional encoding of 1

2 , the output of theencoder is a 2-bit pair, or two bits per symbol state, which is equivalent to one stateof QPSK. Figure 28 shows the experimental waveform monitored at the output ofthe encoder, consistent with the constellation mapper. The results obtained for theI- and Q-components with fixed points are consistent.

6.3.3. Forming OFDM symbols

Figure 29 shows the observed waveforms of the block performing the assembling ofdata and pilot and zero patching for OFDM symbol, which consists of 256 points

(a) (b)

(c) (d)

Fig. 29. Structure of an OFDM symbol. (a) Rearranged data in the I-component to bypass pilotlocation. (b) Q-component. (c) Final OFDM symbol in I-axis. (d) Final OFDM symbol in Q-axis.



with a structure of {28 “0”s, zero, 100 data bits, zero, 100 data bits, 27 “0”s}. Inthis structure, the data-bit sequence consists of eight pilots at the locations of c−88,c−63, c−38, c−13, c13, c38, c63 and c88. These pilots are not standardized. Thus,they would have values greater than the data bits. The input data sequence wouldbypass the locations of these pilots and the inserted pilot. The output of the OFDMsymbol block is consistent with its symbol structure.

6.3.4. Generation of OFDM signals

After forming the OFDM symbol, the IFFT would be used to form OFDM signals(Fig. 30). Both I- and Q-data sequences are fed into the real and imaginary inputsof the IFFT block. Thus the output of the IFFT is a complex sequence and we mayobserve the PAPR effects of the waveform at this output as described in the sectionabove.

6.3.5. Insertion of cyclic prefix

Figure 31 shows the waveform after insertion of cyclic prefix. The length of thecyclic is 1

4 . The cyclic is inserted at the beginning of OFDM signals. The data at

(a) (b)

Fig. 30. OFDM signals. (a) I-component. (b) Q-component.

(a) (b)

(c) (d)

Fig. 31. Transmitted signals before and after adding cyclic prefix after 192 clock period delay.

(a) I-component without cyclic prefix. (b) Q-component without cyclic prefix. (c) I-componentwith cyclic prefix. (d) Q-component with cyclic prefix.



(a) (b)

Fig. 32. Combined OFDM signals. (a) I-component signal. (b) Q-component signal.

(a) (b)

(c)

Fig. 33. Transmitted signals after AWGN channel. (a) Random noises generated by the rando-mizer. Superimposed signals and noises of (b) the I-component, and (c) the Q-component.

the end would be copied to the beginning so as to form a signal with 320 intervalsin the time domain. These signals are then passed through the DAC to give thebaseband OFDM signals. The output of the DAC is unipolar 14 bit thus the IFFTwould be set up so that there is unipolar waveform at the output of the IFFT. TheDC component would be added with an appropriate value of 8192. Figure 32 showsthe waveform after this superposition.

6.3.6. Transmitted signals

The signals at the transmitter would be added with noises which have a natu-ral probability density distribution to mimic the AWGN channel noises that arenormally presented in wireless transmission medium or polarization dispersion andoptically amplified fiber cascaded spans. Figure 33 shows the transmitted signalsafter superimposing noises to give a SNR of 20 dB. Naturally when the signals passthrough the medium, errors would occur. However, the decoder can perform errorcorrection.

6.4. Processing of signals at the receiving ends

The first block at the receiving end of the OFDM system has the responsibilityof removing the cyclic prefix. In this work the removal is done by controlling the



start of “sop” and finish of the frame “eop”. These two signal indicators indicatethe FFT to receive only 256 values of the OFDM signal frame. The output of theFFT would then be fed to the blocks responsible for disassembling the OFDMsymbols, demapping the constellation points, decoding and error correction andderandomization. At the same time the output of the receiving end block would becompared with the data sequence at the transmitting end and error counting wouldbe performed to obtain the BER of the system.

6.4.1. FFT transform to recover OFDM symbol

OFDM signals are passed through the FFT so as to receive the data sequence asshown in Fig. 34. Due to superimposition of the noises on the signal, correction isimplemented at the decoder using the Viterbi algorithm.

6.4.2. Disassembling OFDM symbol block

The OFDM signals are then disassembled into data, pilot and eliminated zero patch-ing sections. The pilot parts would be used to estimate the distortion effects of thetransmission channel and then used for the equalizer of the receiving end section.Figure 35 shows the waveforms obtained at the transmitting and receiving ends atthe assembling block and disassembling block.

6.4.3. Constellation and encoder

The output of the disassembling block would be fed into the constellation mapper.The output would be a pair of bits for QPSK modulation states on the constellation.With the errors accumulated, the Viterbi algorithm associated with the decoder cancorrect without much difficulty, as proven in our experimental system.

(a) (b)

(c) (d)

Fig. 34. Data waveforms after FFT. (a) I-channel waveform of OFDM symbol at the transmittingend. (b) Q-channel waveform at the transmitting end. (c) I-component of OFDM signals at thereceiving end. (d) Q-component of the OFDM signals at the receiving end.



(a) (b)

(c) (d)

Fig. 35. Comparison of OFDM symbol at the transmitting and receiving ends. (a) I-componentdata sequence of one symbol at the transmitting end. (b) Q-component data sequence of onesymbol at the transmitting end. (c) I-component data sequence of one symbol at the receivingend. (d) Q-component data sequence of one symbol at the receiving end.

6.5. System performance

6.5.1. System parameters and resources used

The speed of the operating system is set at 100MHz for the complete OFDMsystem. The number of FFT points is 256 with a cyclic prefix of 1

4 . Thus therewould be 320 value levels of the signal and 320 clock pulses for transmitting onesymbol OFDM. In the 256 values to be set at the IFFT, there are 192 useful datalocations. The system employs the convolutional code of Hamming distance of 1

2 andQPSK modulation scheme with 2 bits/state. Thus the useful speed of the systemis 60Mb/s.

FPGA is used for the design of systems and facilitates the setting of the operat-ing condition of the system, as well as interfaces to various sections of the board forthe transmitting and receiving ends. The details of the FPGA are listed in Table 2.The number of logic elements is 17,389 with a total LAB of 2020. Thus with thepotential of the DSP Development Kit and Devices Stratix EP1S25, we can design

Table 2. Resources of the development systems.

STT Resources Use

1 Total logic elements 17,389/25,660 (68%)2 Total registers 14,900/29,168 (51%)3 Total LABs 2020/2566 (79%)4 I/O pins 54/598 (9%)5 M512s 19/224 (8%)6 M4Ks 136/138 (99%)7 Total memory bits 460,520/1,944,576 (24%)8 Total RAM block bits 637,632/1,944,576 (33%)



and implement OFDM communication system or any other digital communicationsystems with equivalent complexity.

6.5.2. Spectra of OFDM signals

The wireless transmission channel can be modeled as a set of delay paths andinterference of signals. For optical guided wave channel, the distortion effects aremainly due to chromatic and polarization dispersion effects, as well as nonlinearself phase modulation effects. One must address the fact that such models areapplicable to passband communication systems. For example, in the case of opticalcommunication systems, the lightwave frequency is very high in the tera-Hz rangeand it is very difficult for the digital computing systems to operate if we include andsample the data at this speed. Indeed it must be a few ten-times higher than thecenter frequency of the carrier. Thus the common “complex” amplitude signals areused to represent the envelope of the signals. The phase of the carrier is includedas the complex part of the amplitude. The signals are observed at the output ofthe DAC.

The spectra of OFDM signals generated by MATLAB Simulink section undernoiseless and noisy conditions are shown in Figs. 36 and 37 respectively. The moni-tored OFDM spectra at the output of the digital to analog converter of the FPGAboard are shown in Fig. 38, at the receiver output that indicates the agreementof the analysis and simulation. There are some deviations of the spectra, possi-bly due to electromagnetic interference. The modulation is QPSK with the I- andQ-channels monitored. Implementation of M-ary PSK would also be possible with-out much difficulty. The frequency scale in Fig. 37 is normalized to 80MHz; thebandwidth of the OFDM system is 64MHz which agrees well with the experimentalspectrum in Fig. 38. It is noted that the MATLAB observation point is at the posi-tion where no cyclic prefix has been added. Clearly the spectrum indicates the truerepresentation of the composite data signal waveforms. The roll-off of the spectrumobserved in this experiment (Fig. 38) is due to the roll-off characteristics of the

(a) (b)

Fig. 36. Spectra of noiseless OFDM signals as obtained on MATLAB Simulink. (a) I-component.(b) Q-component. Normalized frequency.



Fig. 37. Nonnormalized spectrum of OFDM signals superimposed with noises as observed onMATLAB Simulink platform. Note that no cyclic prefix is included at this observation.

(a) (b)

Fig. 38. Spectra of received signals as observed at the output of the DAC on a spectrum analyzer.(a) I-channel at 8.7 dB/div. (b) Q-channel at 8.7 dB/div.

low-pass filtering of the DAC subsystem at the transmitting side. This could becorrected without much difficulty.

7. Concluding Remarks and Further Research

In this paper, we have demonstrated an OFDM communication platform usingboth MATLAB Simulink and software development facilities of an FPGA-baseddevelopment hardware to prove the principles and performances of systematicblocks of the system for generation of OFDM symbols, encoding, and mapping



to QPSK symbols with the possibility of upgrading to 16-QAM models of trans-mission medium. The use of pilots has enabled the estimation of the transmissionmedium characteristics and hence their employment in the equalizer at the receiver.The waveforms are monitored at the transmitting end blocks and at the receivingend so as to confirm the working principles of the design of various blocks of theOFDM communication systems.

The models presented in this paper will be modified and integrated into aMATLAB development platform for simulation of OFDM signals transmissionthrough optically amplified multi-span optical fiber communication systems.13 Thiswill be used to study various OFDM signaling techniques to combat impairmentand associated mitigation technqiues for ultra-long transmission without using dis-persion compensating modules and associated optical amplifiers. These works willbe reported in the future.

Furthermore, the developed system reported here would be expanded to includeall kinds of wireless transmission media and channel estimation for broadbandwireless access for the 4G wireless communication networks with the bit rate reach-ing 1 Gb/s and above.

For long-haul optical amplifed fiber transmission systems, we identify the fol-lowing issues/problems for further research:

• Techniques for the reduction of the peak to average values of OFDM signals inorder not to drive the optical modulator into the nonlinear region, especially whenan optical interferometric modulator is used. Optical phase modulator may beused in association with clamping of the peak amplitude. The error contributionto the signal recovery due to this clamping will be studied and investigated bysimulation.

• The model developed in this paper will be integrated with a MATLAB Simulinkplatform for multi-span optically amplified fiber transmission to study theseeffects and the mitigation techniques to reduce the impairment.

• Under long-haul multi-span transmission, OFDM will suffer the effects of lin-ear chromatic dispersion and polarization mode dispersion, and nonlinear effectssuch as self-phase modulation, cross-phase modulation and four-wave mixing.However, we believe that the self-phase modulation effects will affect the I- andQ-components of the passband OFDM signals and the cross-phase modulationeffects will create interchannel interference effects in the frequency domain ofadjacent optical channels (i.e. at different wavelengths of systems employing densewavelength division multiplexing).

• Mitigation techniques will be employed to overcome the distortion effects iden-tified above such as equalization of OFDM, especially the equalization in thefrequency domain.

• A parallel bank of these FPGA-based processors will be structured to formextremely wideband signals for modulating an I–Q optical modulator forlong-haul optical transmission, metropolitan or access optical Internet operat-ing with multi-Gb/s bit rates.



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