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Performance of an Interl eaved Spread Sp ectrum OFDM System over Multipath Fading Channel s 1

Performance of an Interleaved SpreadSpectrum OFDM System over Multipath

Fading Channels

Pingzhou Tu1 , Xiaojing Huang2 , and Eryk Dutkiewicz3 , Non-members

ABSTRACT

In this paper we propose an interleaved spreadspectrum orthogonal frequency division multiplexing(ISS-OFDM) system and investigate its performanceover frequency selective multipath fading channels.The purpose is to exploit frequency diversity capabil-ity, develop an efficient spectrum spreading algorithm

and improve the system performance over frequencyselective multipath fading channels. At transmitter,a spectrum spread ISS-OFDM signal is generated byemploying OFDM modulation and interleaving tech-niques. At the receiver, two solutions including serialdemodulation and parallel demodulation for diver-sity combing are proposed, in which the received sig-nals are combined by using a maximum ratio combin-ing (MRC) technique. The simulation indicates thathigher frequency diversity is achieved, and the BitError Rate (BER) and Peak-to-Average Power Ratio(PAR) performances of the proposed ISS-OFDM sys-tem over frequency selective multipath fading chan-nels are improved significantly as compared with theconventional OFDM systems. Another unique char-acteristic is that the spectrum spreading factor anddiversity order provided by the system are reconfig-urable to achieve cognitive communications.

Keywords: Diversity, Interleaving, Spread spec-trum, OFDM, Fading channels

1. INTRODUCTION

Frequency selective fading is a dominant impair-ment in wireless communications. The channel fadingreduces received signal-to-noise ratio (SNR) and de-grades the bit error rate (BER). It also causes chan-nel delay spread and introduces inter-symbol inter-ferences (ISI) [1]. To combat the frequency selec-tive fading in wireless communications, diversity tech-niques must be resilient [2]. Orthogonal frequency di-vision multiplexing (OFDM) technique as one of themulti-carrier transmission techniques has extendedthe symbol duration and effectively reduced the ISIby inserting a cyclic prefix, which is greater than the

Manuscript received on June 25, 2007 ; revised on June 24,2008.1,2,3 The authors are with School of Electrical, Computer and

Telecommunication Engineering, University of Wollongong,Australia., E-mail: [email protected], [email protected] [email protected]

channel delays, before the signal is transmitted to thechannel [3;4]. However, its diversity potentials havenot been fully exploited yet.

Driven by OFDM applications against channel fad-ing and by enabling multipath diversity, some differ-ent forms of OFDM systems with different diversitytechniques have been proposed, such as the multiple-

input multiple-output OFDM (MIMO-OFDM) sys-tems [5], the frequency diversity OFDM (FD-OFDMor adaptive AFD-OFDM) systems [6-9], and thespread-spectrum multiple-carrier multiple-access (SS-MC-MA) [10]. Among these systems, the MIMO-OFDM is one of the most typical ones. It adopts avery commonly used method for achieving spatial di-versity by employing multiple antennas at both endsof wireless links. It holds the potential to drasticallyimprove the spectral efficiency and link reliability infuture wireless communications systems, and is re-garded as a particularly promising candidate for next-generation fixed and mobile wireless systems. How-ever, one major problem for MIMO-OFDM systemsis that the scalability of the diversity is very lim-ited. The other two methods, FD-OFDM and SS-MC-MA, use the same way of multiplying the trans-mitted data stream by an orthogonal spreading codebefore modulation in order to achieve frequency di-versity. The spectrum spreading is accomplished byputting the same data on all parallel subcarriers, pro-ducing a spreading factor equal to the number of sub-carriers. Although these systems enable full multi-path diversity, they need a large number of side infor-mation transmissions, which causes considerable rate

loss [11;12].In this paper we propose a method for achieving

frequency diversity and the corresponding receiver al-gorithms for diversity combining. The proposed sys-tem is called the interleaved spread spectrum orthog-onal frequency division multiplexing (ISS-OFDM)system. In this system, frequency diversity is en-abled by spread spectrum modulation and interleav-ing [13-15] techniques, rather than using multiple an-tennas, orthogonal codes, or other side information.At the transmitter, each data symbol modulates thecorresponding subcarriers multiple times, and severalreplicas bearing the same data information can beobtained. The replicas of the same data informationare interleaved sequentially and then transmitted indifferent time slots, instead of being added together.

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2 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.7, NO.1 February 2009

The interleaving operation results in signal spectrumbeing expanded into multiple subbands, each of whichcontains the same data information, so that frequencydiversity is achieved. After frequency selective chan-nel fading, the receiver can collect signal energy from

several signal subbands by using maximal ratio com-bining (MRC) techniques. Thus, the probability thatall signal components fade simultaneously is reducedconsiderably, leading to great system performancesuch as BER improvement [16-18].

With the increase of frequency diversity, anotherperformance improvement brought about is that thepeak-to-average power ratio (PAR) performance ofISS-OFDM system is reduced dramatically. As iswell known, one of the main disadvantages in conven-tional OFDM system is the large PAR of the trans-mitted signal [19;20], due to the addition of the mod-ulated signals by using Inverse Fast Fourier Trans-form (IDFT) operation. In ISS-OFDM system, sincethe information bearing subcarriers are interleavedinstead of superimposed, the PAR of the transmittedsignal is reduced significantly. Meanwhile, the num-ber of the total samples in one ISS-OFDM symbol in-creases greatly, which results in reduced signal powerspectrum density if the total signal energy remainsunchanged.

The paper is organized as follows. First, the sys-tem model is described in section 2. Then, the OFDMsignal generation process with both time diversityand frequency diversity is described in section 3, and

the signal diversity characteristics are analyzed in thefrequency domain and time domain. In section 4, thecorresponding two receiver models are proposed. Sec-tion 5 is devoted to system performance simulationand discussion, in which the system average bit errorprobability and computational complexity are given.Finally, conclusions are drawn in section 6.

2. SYSTEM MODEL

As is well known, when signals are propagated ina frequency selective multipath fading channel, thepresence of reflecting objects and scatters in the chan-

nel creates a constantly changing environment thatdissipates the signal energy in amplitude, phases andtime. These effects result in multiple versions of thetransmitted signal, which are received by the receiverat different times from different multipaths, displacedwith respect to one another in time and spatial ori-entation.

Fig.1 displays the ISS-OFDM baseband model.We assume that the channel is frequency selectivewith slow fading, and the noise is additive whiteGaussian noise (AWGN) with zero mean. The databit to symbol mapping scheme can be any of M-arymodulation. To demonstrate the system performanceimprovement, in this paper we take only quadraturephase shift keying (QPSK) as the mapping methodto simulate the generation of ISS-OFDM signal and

compare the system performance. A cyclic prefix(CP) is also added to preserve the orthogonality ofthe subcarriers and eliminate intersymbol interfer-ence (ISI) between consecutive ISS-OFDM symbols.

We now illustrate the function of each module

showed in Fig. 1. The function of the transmitteris to generate an ISS-OFDM signal with time andfrequency diversities. The complex QPSK data sym-bols to be transmitted are first divided into an N by1 vector, where N is the number of subcarriers. Thisvector modulate N subcarries in parallel by using thecomplex exponential spreading (CES) technique, andthen the spread signals are interleaved to form anISS-OFDM symbol of N2 samples. After a cyclicprefix insertion and filtering, the ISS-OFDM signaly(m) (also represented by Y(k) in the frequency do-main) with spectrum spreading is transmitted intothe frequency selective multipath fading channel withimpulse response h(m) (denoted as H(k) in the fre-quency domain). Meanwhile, the AWGN noise v(m)(denoted as V(k) in the frequency domain) is addedto the signal. After being distorted by the fadingchannel, the signal is filtered and CP removed, andthen demodulated. The output of the demodulatoris equalized and combined to form a decision variableUk by employing maximal ratio combining (MRC)technique.

Fig.1: Baseband system model

We assume that the transmitted ISS-OFDM signalbandwidth BISSOFDM is greater than the coher-

ence bandwidth (f)c, BISSOFDM (f)c thusthe channel can be considered as a frequency-selectivefading channel. The channel model can be expressedin the form

h(m) =N21i=0

i(m)(m mi)

where i(m) is the multipath fading channel attenua-tion factor on the mth path and mi is the propagationdelay for the mth path. Correspondingly, the channelfrequency response is written as

H(k) =N21m=0

h(m)ej2N2

km. (1)

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After the transmitted signal, denoted as y(m),passes through the fading channel, the received equiv-alent low-pass signal is viewed as the convolution be-tween h(m) and y(m) plus noise as follows

r(m) = h(m)

y(m) + v(m) (2)

where v(m) represents the complex-valued whiteGaussian noise process corrupting the signal. In fre-quency domain, Equation (2) is equivalent to the out-put of the DFT demodulator.

R(k) = H(k) Y(k) + V(k) (3)where R(k), Y(k), H(k) and V(k) denote the fre-quency representations of the received signal r(m),the transmitted signal y(m) the channel impulse re-sponse h(m) and the noise v(m), respectively.

3. DIVERSITY IN ISS-OFDM SIGNALS

3.1 Transmitter Model

Fig. 2 shows the transmitter model, which in-dicates the generation process of ISS-OFDM signalwith time diversity and frequency diversity. Letai(i = 0, 1, , N) denotes the ith complex-valuedsymbol of the N QPSK symbols to be transmitted.The N QPSK symbols are modulated by the CESmodulator, and then interleaved by the interleaver to

form the ISS-OFDM signal with time diversity andfrequency diversity. Time diversity is achieved byCES modulation and frequency diversity is obtainedby interleaving.

3.2 Time Diversity of ISS-OFDM Signals

After serial to parallel conversion the N 1 par-allel QPSK symbols modulate the corresponding Nsubcarriers. If the ISS-OFDM symbol period is Ts,fi =

iTs

denotes the ith subcarrier frequency of the N

orthogonal subcarriers, and ai modulates the ith sub-carrier at time t = nNTs, n = 0, 1, , N1, where isthe sampling time index. The modulated symbol onthe ith subcarrier and the nth time instant is writtenas follows,

yi(n) = aiej2fit = aie

j2ni/N. (4)

In the ISS-OFDM symbol duration Ts, each ele-ment of the N 1 data symbol vector modulates thesame corresponding subcarrier N times, so that Nelements in the vector generate an N N samplematrix after modulation. In consequence, N replicasof each data symbol are produced in symbol durationTs

by CES modulation, and the time diversity of theISS-OFDM symbol is achieved. Fig. 3 displays theprocess of achieving time diversity in the ISS-OFDMsystem with subcarrier number N = 4.

Fig.2: Transmitter model

Fig.3: Time diversity of ISS-OFDM signals withsubcarrier number N=4

Mathematically, the matrix can be expressed as

[yi(n)] =

y0(0), y0(1), , y0(N 1)y1(0), y1(1), , y1(N 1)

yN1(0), yN1(1), , yN1(N 1)

=

a0ej200/N, a0e

j201/N, , a0ej20(N1)/Na1e

j200/N, a1ej201/N, , a1ej20(N1)/N

aN1e

j200/N, aN1ej201/N,

, aN1e

j20(N1)/N

(5)

Let WniN , where WN = ej 2

N , denote the ith

sub-carrier at the nNTs time instant, and

Diag(ai) =

a0, 0, . . . 00, a0, 0 . . . 0................0, 0, . . . aN1

.

Thus, Equation (5) can be rewritten as,

a0W

00N , a0W

01N , . . . , a0W

0(N1)N

a1W10N , a1W11N , . . . , a1W

1(N1)N

. . .

aN1W(N1)0N , aN1W

(N1)1N , . . . , aN1W

(N1)(N1)N

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= Diag(ai)

WniN

. (6)

Equation (6) indicates one way of implementingCES modulation, by which the N transmitted datasymbols at the input of the modulator are rearrangedinto the diagonal elements of a diagonal matrix. Sincethe input signal of the modulator is in the form of adiagonal matrix, the output signal is an NN samplematrix as denoted in Equation (5).

3.3 Frequency Diversity of ISS-OFDM Sig-

nals

After CES modulation, the N N samples areshifted in time and placed on different time slots toform a serial sequence of length N2 in the time do-main. This operation is a process of interleaving.Here, different interleaving algorithms can be em-ployed such as pseudo random interleaving, periodic

interleaving and convolutional interleaving. In thefollowing, we discuss the periodic interleaving pro-cess. The periodic interleaving can be realized byshifting N modulated subcarriers on different timeslots and adding them together. For instance, the ith

subcarrier of the N subcarriers is shift by i , where is the time interval, = TsN2 , then, the N shiftedsubcarriers are interleaved to form one ISS-OFDMsymbol with N2 samples. The mth sample in theISS-OFDM symbol, denoted by y(m), m = nN+ i =0, 1, , N2 1, can be mathematically written asfollows,

y(m) =Ni=1

Nn

yi(n)[m i nN] ,

where [m nN i] =

1,f or m = nN + i0,f or m = nN + i.

is the unit impulse. Expressing m = nN + i, y(m),can be simplified in the form

y(m) = y(nN + i)

= yi(n). (7)

The mathematical equations above can be inter-preted as follows. All N samples in a column ofthe N N matrix are taken out from the N Nmatrix, shifted in time, and then placed in differenttime slots, instead of being superimposed together asin conventional OFDM systems. Due to the shiftingin time for each sample, the phase of each subcar-rier is shifted. In the frequency domain, the signalspectrum is expanded to N subbands, each of whichcontains N orthogonal subcarriers modulated by thesame transmitted data symbols. Therefore, the ISS-OFDM signals frequency diversity is obtained. Fig.4 displays the spectrum of ISS-OFDM signals withsubcarrier number N = 4. It is seen that the modu-lated data symbol on the ith(in this case i = 1, 2, 3, 4)subcarrier appears in all N = 4 subbands.

The frequency domain representation of the ISS-OFDM signal can be obtained by taking discreteFourier transform (DFT) of the signal in the timedomain.

Y(k) = DF T(y(m))

= DF T(y(nN + i))

=N21

nN+i=0

y(NN + i)ej2n2

(nN+i)k.

That is,

Y(k) =N1n=0

N1i=0

y(nN + i)ej2N2

(nN+i)k. (8)

Substituting y(nN + i) from Equation (7) intoEquation (8), we have

Y(k) =N1n=0

N1i=0

yi(n)ej 2

N2(nN+i)k. (9)

Substituting yi(n) from Equation (4) into Equa-tion (9) yields

Y(k) =N1n=0

N1i=0

aiej 2N

niej2N2

(nN+i)k

= NN1i=0

aiej 2N

ki 1

N

N1n=0

ej2N

(ki)n

((ki)N

.

That is

Y(k) = Nn1i=0

aiej 2

N2ki((k i)N), (10)

where

((k i)N) 0, k = pN + i1, k = pN + i .Equation (10) can be also rewritten as

Y(pN+i) = N aiej 2

N2(pN+i)i, p = 0, 1, , N1. (11)

Equation (11) indicates that each data symbol aiis modulated on the ith subcarrier in every subband,and the signal spectrum is spread N times. The spec-trum spread signal contains N subbands and each ofwhich bears the same information. Fig. 4 shows thespectrum of the ISS-OFDM signal with subcarriersnumber N = 4. It shows that the ISS-OFDM sig-nal contains 4 subbands, each subband carries thesame information. The order of frequency diversityachieved is 4.

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Fig.4: Spectrum of ISS-OFDM symbol with subcar-rier number N = 4.

4. DIVERSITY COMBINING OF ISS-OFDM

SIGNALS

At the receiver, the received signal is firstly fil-tered by using a root raised cosine filter. The filteris matched to the transmitter filter, so that the over-all effect of filtering is that of a raised cosine filter-ing. The passband of the receiver filter is designed tobe flexibly reconfigurable according to the system re-quirements. One or more subbands of received signalcan be selected through the receiver filter. Assum-ing that all the N subbands of the received signal are

passed through the filter, the diversity combining canbe implemented in two receiver solutions. One is theserial demodulation mode; the other one is paralleldemodulation mode.

4.1 Diversity Combining in Solution I: Serial

Demodulation

4.1...1 Frequency Domain Representation of Re-ceived Signals in Serial Demodulation Mode

Fig. 5 shows the receiver structure of solutionI, which is realized by using one DFT operation of

size N2

. After CP remove and DFT demodulation,the output of the demodulator is equalized, and thencombined by maximal ratio combining (MRC) tech-nique.

Fig.5: Serial demodulation and combination

Substitute Y(k) from Equation (10) into Equation(3), the received diversity signal at the input of thereceiver in the frequency domain is rewritten as fol-lows

R(k) = NN1i=0

ai((k i)N)ej2N2

kiH(k) + V(k), (12)

where k = 0, 1, , N2

1.According to Equation (12), the output of the se-

rial demodulation is as follows

R(pN + i) = N aiC(1)i,p + V(pN + i), (13)

where

C(1)i,p = e

j 2N2

(pN+i)iH(pN + i),

p = 0, 1, , N 1, i = 0, 1, , N 1.

It can be observed from Equation (13) that R(pN+i) can be decomposed into N groups. Each groupforms one subband which consists of subcarriers,and each subcarrier consists of N the correspondingweighted signal and noise. Generally, we assume thatthe received signal contains M subbands, M N,and use the M subbands to demodulate the trans-mitted signal. The structure of R(pN + i) can beillustrated in Fig. 6.

The transmitted data symbol ai, i = 0, 1, , N1, can be recovered from R(pN+i), p = 0, 1, , M1, which can be expressed in matrix form as follows:

R(i)R(N + i)

...R((M1)N+i)

= N

C(1)i,0

C(1)i,1...

C(1)i,M1

ai+

V(i)V(N + i)

...V((M1)N+i)

.

According to the above matrix equation, a mini-mum mean squared error (MMSE) estimate of ai canbe obtained as follows:

ai=1

N

C(1)

i,0 C(1)i,1 C(1)i,M1

C(1)i,0

C(1)i,1...

C(1)i,M1

+ 1SN R1

.

C(1)

i,0 C(1)i,1 C(1)i,M1

R(i)R(N + i)

...R((M 1)N + i)

= 1N

M1q=0

C

(1)

i,qM1p=0

C(1)i,p 2 + 1SN RR(q+ i),

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where SN R is the signal-to-noise ratio before theMMSE equalization.

To analyze the system BER performance, the nor-malized MMSE can be expressed as

2min=

SN R

C

(1)i,0 C

(1)i,1 C(1)i,M1

C(1)i,0

C(1)i,1...

C(1)i,M1

+1

1

=1

SN RM1p=0

C(1)i,p 2 + 1.

Therefore, the output signal-to-noise ratio afterMMSE equalization is

out =1 2min

2min=

1

2min 1SN R

M1p=0

C(1)i,p 2 .Assuming QPSK modulation for data symbols and

making a Gaussian distribution approximation forthe intersymbol interference after MMSE equaliza-tion, we finally obtain the expression for the averageBER using the Q function

P(MMSE)e = E(Qout) (14)where E() denotes ensemble average over channel co-efficients.

Fig.6: The structure of R(pN + i)

4.1...2 Diversity Combining

From Equation (13), we see that a data symbolai is transmitted on different subcarriers and expe-riences independent fading. Thus, another effectiveway to gain frequency diversity is to directly use themaximal ration combining (MRC) technique to col-lect signal energy from all information bearing sub-cariers. In this way the system diversity can be madefull use of and the best system performance can beachieved.

Similar to the above MMSE equalization, we as-sume that only M subbands, M N, are used torecover the transmitted data symbols. The MRCprocess proceeds as follows. First, we multiply the

conjugated channel coefficient C(1)

i,p with the receivedR(pN + 1) to compensate the channel phase shiftand weight the information bearing subcarrier witha gain proportional to the signal strength. Then, allthe weighted subcarriers corresponding to the same

data symbol a are combined to produce the decisionvariable U

(1)i for the detection of ai. That is,

U(1)i =

M1p=0

C(1)i,p R(pN + i).

To analyze the BER performance of the MRC tech-nique, we substitute R(pN+ i) in the above equationwith Equation (13) and have

U

(1)

i = N

M1

p=0

C(1)i,p 2

ai +

M1

p=0 C

(1)

i,p V(pN + i).

The output signal-to-noise ratio after MRC can beobtained as

(1) =

N

M1p=0

C(1)i,p 22

E|ai|2

E

M1p=0

C(1)i,p V(pN + 1)

2

=

M1p=o

C(1)i,p 22

N2E|ai|2

M1p=0

C(1)i,p 2 E|V(pN + i)|2

=M1p=0

C(1)i,p 2 SNR,

where SN R =N2E

|ai|2

E|V(pN + i)|

2

is the signal-to-

noise ratio before MRC.For QPSK modulated data symbols, the average

error probability can be therefore written as:

PMRCe = E

Q

(1)

. (15)

From Equation (14) and Equation (15) we see thatthe MMSE equation and the MRC have the sameperformance for the serial demodulation.

4.1...3 Diversity Performance

After normalization, SN R and Eb/N0 have the re-

lation SN R = 2M Eb

N0(Refer to Appendix), the sys-

tem BER performance expression in Equation (15)can be rewritten as:

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P(MRC)e = E

Q

M1

p=0

C(1)i,p 2 1M EbN0 . (16)

4.2 Solution II: Parallel Demodulation byDFT

The demodulation in Solution I using single DFTis straightforward to realize. However, the computa-tional complexity in Solution I is relatively high.

In order to reduce the complexity, we propose Solu-tion II, a parallel demodulation method by employingmultiple DFTs. The parallel demodulation methodconsists of cyclic prefix removal, deinterleaver, de-modulation, and maximum ratio combining. Com-pared with the serial demodulation, the difference isthe number of DFTs employed. In the parallel DFT

solution, the demodulation is realized by employingN DFTs of size N, rather than a single DFT of sizeN2.

4.2...1 Frequency Domain Representation of Re-ceived Signals in Parallel Demodulation Mode

Fig. 7 shows the receiver structure for SolutionII using parallel demodulation, which is realized byusing N parallel DFTs, each of which is of size N .We assume that the signal in the time domain at thereceiver input is known. To obtain the data vector foreach DFT operation, the time domain signal is splitinto N groups, each group is demodulated by usingan DFT operation with the size N .

In order to compensate the channel distortion us-ing frequency domain equalization, we must find outthe relationship among each parallel DFT output, thechannel coefficient, and the transmitted data symbol.For doing that, the first step is to express the receivedsignal in the time domain at the input of the receiverin terms of the channel frequency response and thetransmitted data symbol.

The signal in the time domain at the input of thereceiver can be obtained by conducting the inverseDFT (IDFT) of size N2 on R(k), i.e.,

r(m) = IDFT(R(k)) =1

n2

N21k=0

R(k)ej2N2

km. (17)

Fig.7: Parallel demodulation and combination

Substituting R(k) from Equation (12) into Equa-tion (17), the received signal in the time domain r(m)can be rewritten as:

r(m) =1

N

N21

k=0N1

i=0aie

j 2N2

(im)((i k)N)H(k)

+1

N2

N21k=0

V(k)ej2N2

km (18)

After the time domain signal is received, it is thende-interleaved. The de-interleaved process is exactlythe same as the method discussed in Solution I.

After de-interleaving, the signal in the time do-main is split into N data streams, each of which canbe demodulated using one DFT operation. Thus, todemodulate the NN data samples simultaneously,parallel DFTs, each of size N, are needed. In thisway, the demodulation of the received signal is com-pleted by employing N parallel DFT operations. Thedeinterleaved signals can be written as:

ri(n) = r(nN + i) = r(m), i = 0, 1, , N 1,n = 0, 1, , N 1,

To derive the frequency domain representation ofri(n), we can perform the DFT operation on ri(n).

The output of the demodulation can be obtained asfollows:

Ri(k) =N1n=0

ri(n)ej 2

Nkn

=

N1n=0

r(nN + i)ej2N

kn.

where k = 0, 1, , N 1. It must be noted thatthe definition of k in the above equation is a differentvariable from that of R(k) in Solution I, in whichk = 0, 1, , N2 1.

Substituting r(m) in Equation (18) in to the aboveequation, Ri(k) can be written as follows:

Ri(k) =1

N

N1n=0

NN1k=0

N1i=0

aiej 2

NNk(inNi)

((k

i, )N)H(k

) +1

N

NN1k=0

V(k

)

ej2NN

k(nN+i)

ej2N

kn

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=

N1k=0

N1i=0

ai ej 2NNk(ii)((i k)N)H(k) 1N

1

N

N1

n=0ej

2N (k

k)n

((kk)N)

+1

N N

NN1

k=0V(k)ej

2NN

ki

1

N

N1n=0

ej2N

(kk)n

((kk)N)

Since k k must be integer multiples of N, i.e., kk = qN, we express k = qN + k, and Ri(k) becomes

Ri(k) =N1

i=0 aiNN1

k=0 H(k)ej2NN

k(ii)

((i k)N)((k k)N) k=qN+k

+1

N

NN1k=0

V(k)((k k)N) k=qN+k

ej2NN

ki

=N1i=0

ai

N1q=0

H(qN + k)ej2NN

(qN+i)(ii)

((qN + k i)N) i=k

+ 1N

N1q=0

V(qN + k)ej 2NN (qN+i)i.

Again, since qN + k i must be integer multiplesof N, we have i = k and Ri(k)is finally expressed as

Ri(k) = ak

N1q=0

H(qN + k)ej2NN

(qN+i)(ki)

+1

N

N1

q=0V(qN + k)ej

2NN(qN+k)i

= ak

N1q=0

ej2N

q(ik)H(qH + k)ej2NN

i(ki)

C

(2)k,j

+1

N

N1q=0

V(qn + k)ej2NN

(qN+k)i

vk,i

= akC(2)k,i + vk,i. (19)

Where C(2)k,i =

N

1q=0

ej2N

(ik)H(qN + k)ej2NN

i(ki)

is an equivalent channel coefficient and vk,i =

1

N

N1q=0

V(qN + k)ej2NN

(qN+k)i is the independent ad-

ditive noise.Now the relationship among each demodulated

outputRi

(k

), the equivalent channel coefficientC

(2)

k,i,

transmitted signal ak, and noise vk,i is clearly shownin Equation (19).

4.2...2 Diversity Combining and Performance

The MRC technique for Solution II is very similarto the one used in Solution I. After the parallel DFTs,

the decision variable U(2)k for the detection of ak is

calculated by

U2k =N1

i=0C

(2)k,i Ri (k) .

To analyze the BER performance of the MRC tech-nique, we substitute Ri(k) in the above equation withEquation (19) and have

U(2)k =

N1i=0

C2k,i2 ak + N1i=0

C(2)k,i vk,i.

The output signal-to-noise ratio after MRC can beobtained as

(2) =

N1

i=0 C(21)k,i

2

2

E|ak|2

E

N1i=0

C(2)k,i vk,i

2

=

N1i=0

C(2)k,i 22

E|ak|2

N1i=0

C(21)k,i 2 E|vk|2

=N1

i=0 C(2)k,i

2SNR,

where SN R =E|ak|2

E|vk,i|2

is the signal-to-noise ratiobefore MRC.

Similar to Solution I, the average error probabilitycan be written as:

P(MRC)e = E

Q

(2)

. (20)

5. SYSTEM PERFORMANCE

5.1 PAR Performance and Analysis

Assume that the number of subcarriers N = 32,and the data symbol mapping scheme uses QPSK.

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The use of the other mapping methods would leadsto different relation between SNR and Eb/N0. Conse-quently, the system BER performance would be dif-ferent, but the total trend would keep unchanged.

After the modulation, an NN matrix is formed,the modulated subcarriers in the matrix are inter-leaved and placed on different time slots to form aserial sequence. The sequence is pulse shaped bypassing through a root raised cosine filter and thusan ISS-OFDM signal y(t) is generated. The PAR ofy(t) can be written as

=max

|y(t)|2E[|y(t|2)] , (21)

where max[] is the maximum instantaneous power ofthe ISS-OFDM signal and E[] is the expected value.

The generated ISS-OFDM signal has N2

samplesand contains N subbands, each of which contains Nsubcarriers and carries the same data information.The transmitter is designed so that M subbands areselected, M = 0, 1, , N respectively, and thus thetransmitted signal contains M subbands. To observethe PAR performance, we select the signal bandwidthwith M = 1, 2, 4, 8, 16 and 32 subbands respectively(M is the spreading factor), and the filtered signal isoversampled by a factor of four, which is commonlyused to estimate the PAR of an analogy signal fromits samples. The actual PAR of the continuous-timesignal can not be determined by using Nyquist sam-

pling rate. In order to evaluate the PAR performanceof the transmitted signal, the signal should be over-sampled by a factor of four, which is sufficient to pro-duce accurate PAR [23].

According to Equation (21), we can compute thePAR performance curves as shown in Fig. 8 showsthe ISS-OFDM transmitted signal PAR performancewhen PAR exceeds a certain threshold PAR0 with theincrease of the spectrum spreading factor M from 1to 32.

It can be seen from Fig. 8 that with the increaseof the number of subbands, the PAR performance

is improved considerably. The most right-hand-sidecurve shows the PAR performance of ISS-OFDM sig-nal when M is equal to 1, in this case, the ISS-OFDMsignal is in fact a conventional OFDM signal.

As M increases to 2, 4, 8, 16, and 32 respectively,the PAR gains are 0.5dB, 1.5 dB, 3.5 dB, 5 dB and7 dB respectively. Therefore, the PAR of the ISS-OFDM signal is greatly reduced compared to PAR ofthe conventional OFDM signal.

5.2 Diversity Scalability

A distinct feature in the ISS-OFDM system is thesignal diversity scalability. Since the signal spectrumis very wide and contains N subbands, each of whichcontains the same data information, any one or moresubbands can be used to demodulate the transmitted

Fig.8: PAR performance for ISS-OFDM signals

Compared to the conventional OFDM

information according to the system requirement andchannel condition. At the transmitter, if we config-ure the transmitter filter so that the signal spectrumis spread M times, M N, where L is the lengthof multipath channels, the system frequency diver-sity order would be M. We assume that the numberof the subcarriers of the ISS-OFDM is N, then themaximum spectrum spread factor is and the maxi-mum diversity capability of the ISS-OFDM system isN. The more the diversity capability is provided by

the system, the better BER performance the systemcan achieve. But if the diversity capability providedby the system is more than the channel multipath L,the extra diversity capability provided by the systemis redundant. That is to say, if M > L, the diversityof the ISS-OFDM system is limited to the channelmultipath length , which is shown in Fig. 9

Fig.9: Diversity scalability

The scalability performance of diversity has arange of applications. One of the potential applica-tions is to be applied to dynamic spectrum-sharingmanagement system for the efficient and effective uti-lization of the spectrum. If there are one or moresubbands interfered, the system can jump to theother non-interfering subbands to complete commu-nications and the interfered frequency subbands canbe easily avoided. For some unlicensed users in somespectrum subbands, the system can adapt its systemfrequency to the spectrum holes detected by spectrumscanning devices. As indicated in Fig.10, the system

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Fig.13: BER performance after interfered subbands

removed adaptively in fading channels.

different systems working in the same allocated fre-quency band without interference. Other Perfor-mances, such as power efficiency, are also improvedto some extent in ISS-OFDM system.

6. CONCLUSION

In this paper, we have investigated the diver-sity performance of an interleaved spread spectrumOFDM system including transmitter signal genera-tion, two receiver solutions and system performance.The investigation shows that the combination ofspread spectrum modulation and interleaving tech-niques is an efficient way of implementing spectrumspread and achieving frequency diversity. Since thespread spectrum modulation and interleaving tech-niques are jointly employed, the frequency diversityand time diversity are efficiently developed and uti-lized.

By investigating two receiver algorithms of serialdemodulation and parallel demodulation methods,we showed that both two receiver algorithms can re-

cover transmitted signal very well in terms of systemBER performance, but the parallel demodulation insolution II can reduce the computational complexitygreatly and its structure is flexible to be reconfigured.Parallel demodulation method is more preferable forthe proposed system.

Compared to other previous spread spectrumOFDM, ISS-OFDM has superior performance interms of system BER and PAR, reconfigurable struc-ture, and flexible system bandwidth. It realizes spec-trum spread by combination of spread spectrum mod-ulation and interleaving techniques, rather than con-ventional frequency hopping or orthogonal spreadcode. It does not degrade the range of communi-cations or need to transmit side information.

The proposed ISS-OFDM system can be used in

ultra-wideband communications. It is also expectedto be used in cognitive radio adaptive modulationtechniques.

References

[1] J. G. Proakis, Digital Communications, 4 ed.New York, USA: Mc Graw Hill, 2000.

[2] R. Novak and W. A. Krzymien, Diversity Com-bining Options for Spread Spectrum OFDM inFrequency Selective Channels, Wireless Com-munications and Networking Conference, vol. 1,pp. 308-314, 2005.

[3] M. Welborn, Frequency Hoppers and FCCUWB Rules, IEEE P802. 15 Wireless PersonalArea Networks, vol. IEEE P802.15-03/271r22003.

[4] A. Batra et al., Multi-band OFDM Physi-cal Layer Proposal Area Networks (WPANs),IEEE P802. 15-03/26r2, IEEE P802. 15 Wire-less Perosnal Area Networks, pp. 1-69, 2003.

[5] R. S. Blum, Y. Li, and J. H. Wintersand Q. Yan, Improved Space-Time Codingfor MIMO-OFDM Wireless Communications,IEEE Transactions on Communications, vol. 49,no. 11, pp. 1873-1878, 2001.

[6] R. Novak and W.A.Krzymien, SS-OFDM-F/TA System Packet Size and Structure for HighMobility Cellular Environments,, 2 ed 2003, pp.1438-1444.

[7] J. Qaddour and D. Leonard, Beyond 3G: Up-link Capacity Estimation for Wireless Spread-Spectrum Orthogonal Frequency Division Mul-tiplexing (SS-OFDM), Global Telecommunica-tions Conference, vol. 7, pp. 4139-4141, 2003.

[8] S. W. Kim, K. H. Yoon, R. G. Jung, and J. W.Son and H. G. Ryu, Adaptive Frequency Di-versity OFDM (AFD-OFDM) CommunicationNarrow-Band, Joint Conference of 10th Asia-Pacific Conference on Communications and 5thInternational Symposium on Multi-DimensionalMobile Communicaitons, vol. 1 and 2, pp. 834-

838, 2004.[9] R. Novak and W. A. Krzymien, An Adaptive

Downlink Spread Spectrum OFDM Packet DataSystem with Two-Dimensional Radio ResourceAllocation: Performance in Low-Mobility Cel-lular Environments, Wireless Personal Multi-media Communications, 2002. The 5th Interna-tional Symposium on, vol. 1, pp. 163-167, 2002.

[10] S. Kaiser and K. Fazel, A Flexible Spread-Spectrum Multicarrier Multiple-Access Systemfor Multi-Media Applications, Personal, Indoorand Mobile Radio Communications, vol. 1, pp.100-104, 1997.

[11] G. J. Saulnier and Z. Ye and M. J. Medley,Performance of a Spread Spectrum OFDM Sys-tem in a Dispersive Fading Channel with Inter-

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ference, Military Communications Conference,vol. 2, pp. 679-683, 1998.

[12] P. Xia and S. Zhou and G. B. Giannakis,Bandwidth- and Power-Efficient MulticarrierMultiple Access, IEEE Transactions on Com-

munications, vol. 51, no. 11, pp. 1828-1836, 2003.[13] V. G. S. Prasad and K. V. S. Hari, Inter-

leaved Orthogonal Frequency Division Multi-plexing System, Acoustics, Speech, and SignalProcessing, vol. 3, p. III-2745-III-2748, 2002.

[14] P. Tu and X. Huang and E. Dutkiewiz, ANovel Approach of Spread Spectrum in OFDMSystems, International Symposium on Commu-nications and Information Technologies, ISCIT06, pp. 487-491, 2006.

[15] A. D. S Jayalath and C. Tellambura, Use ofdata permutation to reduce the peak-to-average

power ratio of an OFDM signal, Wireless Com-munications and Mobile Computing, vol. 2, pp.187-203, 2002.

[16] O. Edfors, M. Sandell, J. J. V. D. Beek, and S.K. Wilson and P. O. Borjesson, OFDM ChannelEstimation by Singular Value Decomposition,IEEE Transactions on Communications, vol. 46,no. 7, pp. 931-938, 1998.

[17] P. Xia and S. Zhou and G. B. Giannakis, BERMinimized OFDM Systems with Channel In-dependent Precoders, IEEE Transactions onCommunications, vol. 51, no. 11, pp. 1828-1836,

2003.[18] L. Wan and V. K. Dubey, BER Performance

of OFDM system Over Frequency NonselectiveFast Ricean Fading Channels, IEEE Transac-tion Letters, vol. 5, no. 1, pp. 19-21, 2001.

[19] C. Schurgers and M. B. Srivastava, A System-atic Approach to Peak-to-Average Power Ratioin OFDM, Proc. SPIE, vol. 4474, no. 11, pp.454-464, 2001.

[20] S. B. Slimane, Peak-to-Average Power Ra-tio Reduction of OFDM Signals Using Broad-band Pulse Shaping, http://citeseer. ist. psu.

edu/438615. html, pp. 889-893, 2002.[21] S. Haykin, Cognitive Radio: Brain-EmpoweredWireless Communications, IEEE Journal onSelected Areas in Communications, vol. 23, no.2, pp. 201-219, 2005.

[22] B. Ackland, D. Raychaudhuri, M. Bushnell, C.Rose, and I. Seskar, High Performance Cogini-tive Radio Platform with Intergeated Physi-cal and Network Layer Capabilities (InterimTechnical Report), WINLAB, Rutgers Univer-sity,2005.

[23] A. D. S Jayalath and C. Tellambura, In-terleaved PC-OFDM to Reduce the Peak-to-average Power Ratio, in Advanced Signal Pro-cessing for Communication Systems, Springer,Netherlands, pp. 239-250, 2007.

Pingzhou Tu received the bachelor de-gree in computer science and applica-tions from Harbin Engineering Univer-sity, China, in 1991 and master degree incomputer architecture from HuazhongUniversity of Science and Technology,China, in 1999 and Ph.D degree from

University of Wollongong, Australia, in2008. From 1991 to 2004 he workedfor Wuhan Marine Communication Re-search Institute China as an engineer

and senior engineer in the fields of marine communications.He has completed lots of research and development projectson marine communications in the fields of wired and wirelesscommunication. From 2005 to 2008 he was doing Ph.D in Uni-versity of Wollongong. His current research interests includewireless communication networks, digital signal processing.

Xiaojing Huang was born in Hubei,China, on 3 October, 1963. He received

his Bachelor of Engineering, Master ofEngineering, and Ph.D. degrees fromShanghai Jiao Tong University, Shang-hai, China, in 1983, 1986, and 1989,respectively, all in electronic engineer-ing. From 1989 to 1994, he worked inthe Electronic Engineering Departmentof Shanghai Jiao Tong University, wherehe had been a Lecturer since 1989 and

an Associate Professor since 1991. Form 1994 to 1997, he wasthe Chief Engineer with Shanghai Yang Tian Science and Tech-nology Co. Ltd., Shanghai, China. In 1998, he joined the Mo-torola Australian Research Centre, Botany, NSW, Australia,where he had been a Senior Research Engineer since 1999 anda Principal Research Engineer since 2003. Since 2004, he hasbeen an Associate Professor in the School of Electrical, Com-puter and Telecommunications Engineering at the University

of Wollongong, Wollongong, NSW, Australia. He also holds anumber of visiting positions in Shanghai Jiao Tong University,Chinese Academy of Science, and the Commonwealth Scien-tific and Industrial Research Organisation. His research inter-ests are in communications theory, digital signal processing,and wireless communications networks. He is a member of theInstitute of Electrical and Electronics Engineers.

Eryk Dutkiewicz received his Bach-elor of Engineering degree in Electri-cal and Electronic Engineering from theUniversity of Adelaide in 1988, his Mas-ter of Science in Applied Mathematicsdegree from the University of Adelaidein 1992 and his PhD in Telecommuni-cations from the University of Wollon-gong in 1996. From 1988 to 1992 heworked at the Overseas Telecommuni-cations Corporations Research Labs in

Sydney developing pioneering broadband multimedia telecom-munications systems based on ATM networking. From 1992to 1999 he worked at the University of Wollongong conductingresearch and teaching activities in the area of telecommunica-tions and mobile networks. From 1999 to 2004 he worked atMotorola Labs in Sydney where he became the Manager of theWLAN Technologies Laboratory. The Laboratory conductedR&D of wireless technologies for Motorolas home networking,public safety and semiconductor products. From 1999 to 2004he worked at Motorola Labs in Sydney where he became theManager of the WLAN Technologies Laboratory. The Labo-ratory conducted R&D of wireless technologies for Motorolashome networking, public safety and semiconductor products.While with Motorola Labs he was an active member of theIEEE 802.11 standards organizations contributing to the suc-cessful WiFi standards. He is currently a Professorial Fellow at

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the University of Wollongong in charge of the Wireless Tech-nologies Laboratory. He has had research contracts in the areaof next generation wireless technologies with Motorola Inc.,USA, Agere Systems Ltd Australia and Freescale Semiconduc-tor Inc, USA. Prof. Dutkiewicz holds visiting appointments atthe Chinese Academy of Sciences in Beijing and at the Shang-hai Jiao Tong University. His current research interests in-

clude Quality of Service in broadband wireless networks andoptimization of wireless sensor networks.

APPENDIX

The relationship between SN R and Eb/N0 de-pends on the symbol mapping mode. In this paper,we only consider this relationship based on QPSKmapping mode. In Solution I, according to Fig. 6,

SN R =2x2v

=M N 2xMN 2v

=M N 2x T MNM N 2v T M N

= Es NM N 2v T MN = Es NN0 1T T MN = 2M E

bN0

.

Thus, the relationship between SN R andEbN0

can

be expressed as

SN R =2

M

EbN0

.

This relationship between SN R andEbN0

also ap-

plies to the Solution II.

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