OCDD/CDMA: a new DS/CDMA with orthonormal code diversity detection

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 4, APRIL 2001 709

OCDD/CDMA: A New DS/CDMA with OrthonormalCode Diversity DetectionByoung-Hoon Kim and Byeong Gi Lee, Fellow, IEEE

Abstract—The paper presents a new spread spectrum com-munication system called orthonormal code diversity detection(OCDD)/CDMA system based on the novel concept ofor-thonormal-basis diversitywhich is a generalization of the existingspread spectrum diversity concepts such as path diversity andfrequency diversity. The OCDD/CDMA system is similar to theconventional DS/CDMA system in the transmitter structure, butis different in the receiver structure as it employs the extendedorthonormal basis-function set which is the union of the Walshbasis-functions multiplied by the PN sequences and, optionally,their delayed replicas. The received signal is matched to theextended basis functions, and the matched signal components arecombined together after individual channel compensation. Theproposed OCDD/CDMA system exhibits the bit error perfor-mance which is much improved over the conventional DS/CDMAsystem using the maximal ratio combing. In addition, it is robustto the chip timing error, which becomes more crucial in thefuture DS/CDMA systems having a higher data rate and smallerchip interval. From the simulation results, we confirm that theOCDD/CDMA system is a unique spread spectrum communica-tion technique that can effectively increase the diversity utilizationin the slowly fading channel, overcoming the inherent problems inthe DS/CDMA and OFDM/CDMA systems.

Index Terms—Diversity efficiency, diversity potential, diversityutilization, orthonormal basis diversity, orthonormal code diver-sity detection (OCDD)/CDMA.

I. INTRODUCTION

T HE DS/CDMA technique is perceived as a promisingsolution to the third generation personal communication

services (PCS) due to its inherent multipath and interferencesuppression capability along with other beneficial capabilitiessuch as capacity enhancement, soft hand-off, soft capacitycontrol, and information security. However, since the existingDS/CDMA systems are developed for dedicated voice services,its performance may degrade for the future voice-data inte-grated services that require much lowerbit error rate (BER)and much higher transmission rate [1].

In order to enhance the performance of the DS/CDMA systemin the third generation PCS environment, there have been pro-posed various new techniques [2]–[4]: For example, [2] and

Paper approved by B. Aazhang, the Editor for Spread Spectrum Networks ofthe IEEE Communications Society. Manuscript received May 25, 1998; revisedOctober 13, 1999. This paper was presented in part at the IEEE GLOBECOMConference, London, U.K., November 1996.

B.-H. Kim is with GCT Semiconductor, Inc., Seoul 156-712, Korea (e-mail:[email protected]).

B. G. Lee is with the School of Electrical Engineering and Computer Science,Seoul National University, Seoul 151-742, Korea (e-mail: [email protected]).

Publisher Item Identifier S 0090-6778(01)03154-3.

[3] employed the multiuser detection techniques that detect andeliminate the interferences of other users, instead of treatingthem as noise components, thus achieving a tremendous in-crease of system capacity; and [4] employed a new receiverstructure that can detect the DS/CDMA signal by adaptively ad-justing the receiver matched filter coefficients without knowingthe transmitter PN sequence. In addition, the spread spectrumdiversity technique can also render a very important means ofenhancing the performance of the CDMA system in the wirelessmultipath fading environment. It views, as the multiuser detec-tion technique did, the multipath interference as something uti-lizable to improve the system performance.

Aside from the efforts for enhancing the performance of theDS/CDMA system, a new CDMA technique, called theorthog-onal frequency division multiplexing(OFDM)/CDMA, has beenrecently developed for the indoor or mobile communicationsuse [5]–[9]. In this OFDM/CDMA system, each informationsymbol is transmitted over multiple subcarriers having differentfrequencies, and in the receiver each symbol subcomponent isindependently processed before being combined into a com-plete symbol. It is reported that the OFDM/CDMA system canachieve an improved bit error performance, which is even betterthan that of the conventional DS/CDMA system, by efficientlyutilizing the frequency diversity in the multipath channel [6],[7]. However, it has the drawbacks of inefficeint power con-sumption and complex implementation [8].

As such, the DS/CDMA and the OFDM/CDMA systems havedifferent observations on the multipath channel characteristics,thus forming two distinct diversity schemes—path diversity andfrequency diversity. In this paper, we are going to introduce anew DS/CDMA system calledorthonormal code diversity de-tection(OCDD)/CDMA system that employs an integrated formof the path and frequency diversities calledorthonormal-basisdiversity. This new diversity scheme, as will be fully discussedin the subsequent sections, enables us to further improve the biterror performance of the conventional DS/CDMA system in themultipath channel, while mitigating several existing problemsof the DS/CDMA and OFDM/CDMA systems.

This paper is organized as follows: In Section II, we establishthe concepts of diversity potential and orthonormal-basisdiversity through a rigorous examination of the current spreadspectrum diversity schemes. Based on these new concepts,we present the OCDD/CDMA system in Section III. Then inSection IV, we analyze the SNR performance of the proposedOCDD/CDMA system and carry out computer simulations toconfirm its performance improvements over the conventionalDS/CDMA system.

0090–6778/01$10.00 © 2001 IEEE

710 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 4, APRIL 2001

Fig. 1. Conventional DS/CDMA system employing MRC.

II. DIVERSITY POTENTIAL AND ORTHONORMAL-BASIS

DIVERSITY

To begin with, we will briefly review the spread-spectrumchannel model and the path and frequency diversity techniquesfor reference in subsequent sections. Then we will establish theconcept ofdiversity potentialand introduce the new diversitytechnique calledorthonormal-basis diversity.

A. Channel Models in Spread-Spectrum Systems

The baseband equivalent model of the continuous-timeRayleigh fadingwide-sense stationary uncorrelated scattering(WSSUS) channel is characterized as follows: The channeloutput at time caused by a unit impulse applied at time ,

, meets the autocorrelation relation [10]

(1)

where denotes the delay cross-power density func-tion. In most cases is factored into the product of thedelay-power profile and the fading characteristic ,with taking the uniform or exponentially-decaying profileand being determined by the Doppler power spectrum[11].

A continuous-time WSSUS channel having the delay spreadof , for the PN chip duration , can be approximated bythe -tapped discrete-time Rayleigh fading WSSUS channelmodel [12]–[14]

(2)

where denotes the oversampling factor (i.e., the number ofdiscrete samples in a chip interval), and . In addi-tion, ’s denote the independent complex gaussian randomprocesses representing the independent scatterings. The rela-tive average power and autocorrelation of are determinedrespectively by the delay-power profile and the Dopplerpower spectrum, as for the case of the continuous-time channel.

B. Path Diversity Versus Frequency Diversity

The conventional BPSK-modulated DS/CDMA system hasthe baseband equivalent structure depicted in Fig. 11 . In thissystem, the information bit stream is first band-spread by mul-tiplying a PN sequence which is unique to each user, andthen transmitted. The transmitted signal reaches the receiverafter being deformed by multipath fading,multiple access in-terference(MAI), and additive white gaussian noise(AWGN).The receiver first determines a few signal acquisition points (,

) based on the received signal power values,and then eliminates or suppresses the MAI and multipath inter-ference through a path-independent (i.e., acquisition point-inde-pendent) PN despeading process. The despread components areweighted by the complex conjugates of the respective estimatedpath gains , , then integrated, and finallycombined before final bit decision [10], [15].

1In this paper we assume themaximal ratio combining(MRC) technique ex-clusively for all concerned diversity systems as it renders the best bit error per-formance in the multipath fading channel. This implies that the channel consid-ered in this paper is slowly varying so that the channel parameters in the receivercan be accurately estimated.

KIM AND LEE: OCDD/CDMA: A NEW DS/CDMA H ORTHONORMAL CODE DIVERSITY DETECTION 711

Fig. 2. The OFDM/CDMA system employing MRC.

The basic OFDM/CDMA (or the multi-carrier CDMA)system has the structure shown in Fig. 2. In this system theinformation bit stream is first multiplied by the user-specificPN sequences , , with the period ,then converted to a parallel stream, and modulated by thesinusoidal carriers , , whose carrierfrequencies are separated by a multiple of Hz for theinformation bit duration . The resulting waveforms aresuperimposed themselves with the power reduced to andfinally transmitted. The receiver demodulates the receivedsignal in parallel streams and multiplies each demodulatedstream with the modified chip sequence , ,which is the channel-compensated version of the user-specificPN sequence . The modified chip sequence is determinedfor each parallel carrier by estimating the distortion of thepilot symbols that are transmitted periodically.2 The resultingparallel waveforms are integrated and combined before finalbit decision [5]–[7].

In view of diversity techniques, the DS/CDMA system isa path-diversity system, and the OFDM/CDMA system is

2More specifically, if the subcarriera (i) exp(j! t) arrives at the receiverwith the amplitude gainh , the modified chip sequenced (i) is determined tobe(a (i)h ) . This MRC process yields the best bit error performance in themultipath channel but degrades the MAI suppression capability. Refer to [7] fordetails.

a frequency-diversitysystem. These two different diversitytechniques stem from two different interpretations of thesame multipath channel as follows: The DS/CDMA focuseson the time-axis impulse response profile of the multipathchannel. It first decomposes the profile in PN-chip unit, thendetermines the path-gain of each component based on eachdecomposed profile, and finally combines the path-resolvedsignal components after multiplying by their correspondingdetermined gains. This decomposition technique is possibleowing to the sharp time-axis autocorrelation pattern of thePN sequence. In contrast, the OFDM/CDMA focuses on thefrequency-axis selective distortion property of the multipathchannel. It first resolves the frequency spectrum in the unit ofsubcarrier frequency separation, then allocates an independentgain on each subcarrier component based on the frequencydistortion pattern, and finally combines them all. As such, thetime-axis and frequency-axis approaches have been employedin an exclusive manner, with most communication systemsthus being designed on this basis. Recently, however, somedifferent approaches employingKarunen-Loeve(K-L) expan-sion or wavelet based signal analysis have been investigatedfor their potential capabilities to overcome some defects of theconventional time- or frequency-based signal analyses. [10],[11], [17], [18].


C. Diversity Potential and Orthonormal Basis Diversity

From the standpoint of the signal dimension, a given WSSUSchannel itself can be considered as an infinite dimensional time-frequency space formed by an infinite number of bases with un-correlated random gains. When a spread spectrum signal passesthrough the channel, however, it is affected by a finite dimen-sional subspace of the channel that corresponds to the signalspace (i.e., finite time-frequency space) itself.3 This means thatthe increase of the signal time-bandwidth potentially providesthe spread spectrum receiver with an increased amount of in-dependent information on the transmitted data. In this context,we definediversity potentialto be the ratio of the total infor-mation (on the transmitted data) included in the received spreadspectrum signal to themaximal informationobtainable out of asingle optimal basis function.4

As most communication receivers cannot utilize all the infor-mation embedded in the received signal, we define, in parallelwith the concept of diversity potential, thediversity utilizationof a spread spectrum receiver to be the ratio of the total infor-mation obtainable by employing all the basis functions in thereceiver to the total information included in the received spreadspectrum signal.5 According to this definition, the increase ofthe diversity utilization is directly connected to the improvementof the bit error performance.

As an estimate of the effective diversity gain per basis, we ad-ditionally define thediversity efficiencyof a spread spectrum re-ceiver to be the total information obtainable in the receiver nor-malized by the maximal information and divided by the numberof employed basis functions.6 Then, the diversity efficiency de-creases as the number of bases increases, in general, due to thedecrease of the incremental information. For a fixed number ofbases, the receiver employing the K-L basis functions is sup-posed to have the largest diversity efficiency. However, it shouldbe noted that the diversity efficiency alone cannot provide a suit-able criterion for the efficiency comparison of different diversitysystems because the receiver complexity depends not only onthe number of the employed orthonormal bases but also on thecomplexity of realizing the individual basis.

As examined above, the spread spectrum diversity receivercan be characterized by the receiver orthonormal-basis func-tions. In the conventional DS/CDMA rake receiver, the delayed

3The dimension of the signal space is about2BT for a signal with bandwidth2B and time durationT . For more details of the signal dimension and signalspace, refer to [19].

4More rigorously, if we expand the received spread spectrum signalinto the form r(t) = r � (t) using the corresponding K-L or-thonormal basis functionsf� (t)g arranged in decreasing order of thecoefficient powerE(jr j ), then the diversity potentialD is defined byD = E(jr j )=E(jr j ).

5Let ~g , i = 0; 1; . . . ; K � 1, denote the coefficients that are ob-tained by projecting the spread spectrum signalr(t) into the signalspace formed by K receiver orthonormal basis functions~� (t),i = 0; 1; . . . ;K � 1. Then the diversity utilizationD (K ) is de-fined by D (K ) = E(j~g j )= E(jr j ). Note that thediversity utilization gets maximized when the firstK K-L basis functions aretaken, due to the optimal truncation property of the K-L expansion [11], [17].

6WhenK orthonormal bases are employed, the diversity efficiencyD (K )is defined byD (K ) = E(j~g j )=K E(jr j ). Note that the rela-tionD (K ) = D �D (K )=K holds among the three diversity elements.

replicas of the transmitted PN sequence correspond to the (ap-proximate) orthonormal-basis functions. In the OFDM/CDMAsystem, the narrow-band subcarrier signals arranged in the fre-quency axis take the role of the orthonormal-basis functions. Inthis context we may define theorthonormal-basis diversitytobe the diversity scheme that employs a set of orthonormal-basisfunctions to decompose the spread spectrum signal deformed bythe WSSUS channel into independent signal components (infor-mation). Then, it becomes a generalized spread-spectrum diver-sity technique that includes the existing path diversity and thefrequency diversity as two special cases.

In view of the orthonormal-basis diversity concept, a spreadspectrum diversity scheme can be entirely characterized by itsorthonormal bases. As the number of the orthonormal basesincreases, the diversity utilization also increases, and conse-quently the bit error performance gets improved. The diver-sity efficiency helps us to predict how much an additional basissignal will contribute to this performance improvement. For agiven number of bases, the diversity utilization, as well as thediversity efficiency, is supposed to be maximized for the K-L or-thonormal basis set. However, it is not practically feasible to de-termine such a K-L basis set for a time-varying channel as it re-quires complex adaptive filtering processes for each basis [20].Therefore, to construct a practical spread spectrum diversity re-ceiver, it is desirable to employ other fixed orthonormal-basissets(e.g., delayed PN sequence basis set, DFT or DCT basis set,etc.) instead. The performance will then be determined by thetype of basis set and the number of basis functions employed,with the primary performance criterion being the bit error rateand the system complexity.

III. T HE OCDD/CDMA SYSTEM

Throughout the discussions in the previous section, we havelearned that a spread spectrum diversity system is governedby its unique orthonormal-basis set. If put conversely, we maystate that for any given orthonormal-basis set, there can exist aCDMA system that is governed by the basis set. Apparently, indesigning such a diversity system, it is possible to employ anorthonormal-basis set that reflects the code division concept,rather than the time or frequency division concept. In thissection, we will introduce a new DS/CDMA system, called theorthonormal code diversity detection(OCDD)/CDMA system,that employs a code-division oriented orthonormal-basis set,taking the Walsh orthonormal-basis set as its target basis set.

A. OCDD/CDMA System Description

The OCDD/CDMA system has the structure shown in Fig. 3.The information bit signal is spread over a given time-band-width space by a user-specific PN sequence of period .The wideband signal reaches the receiver after traversing arandom multipath channel and being added by MAI and back-ground noise. In the receiver, a series of detection processingscomposed of PN multiplication, Walsh decomposition, andchannel compensation are done on the received signal, andthe original information bit signal is decided at the end. Thechannel compensator does the function of multiplying eachoutput with the corresponding optimal complex coefficients in


Fig. 3. The proposed OCDD/CDMA system employing Walsh orthonormal-basis diversity scheme.

compensation for the channel characteristics, thus achieving alowered BER. As far as the transmitter structure is concerned,this OCDD/CDMA system is nothing but the DS/CDMAsystem in Fig. 1, but in view of the receiver structure, it is closerto the OFDM/CDMA system in Fig. 2 as it can be obtainedby replacing the sinusoidal bases in Fig. 2 with the PN-con-catenated Walsh bases. Note, however, that the OCDD/CDMAsystem has the flexibility to choose the receiver basis functions,possibly including the delayed versions of the Walsh bases asin the rake reception of the DS/CDMA system.7

We consider the operation of the OCDD/CDMA system morerigorously. Let and respectively denote the informa-tion bit and user-specific PN sequence. We assume that

for all ’s and ’s and that the processing gain is equal tothe PN sequence period. Also we denote by a rectan-gular pulse function which is 1 in the interval and 0 else-where. Then, the user-specific PN signal , the informationbit signal , and the base-band equivalent transmitted signal

are respectively represented by

(3)

(4)

(5)

where , , and respectively denote the chip interval, thesymbol interval, and the power of the transmitted signal. We

7This delayed versions are especially useful when the delay spread of themultipath channel is too long to ignore the intersymbol interference (i.e., whenthe delay spreadLT is comparable to the symbol durationNT ).

assume that , (i.e., the BPSK modulation andspreading) in this paper.

Using the channel model in (2), and assuming the channel isslowly time-varying, we can represent the received signal as

(6)

where is a base-band equivalent complex gaussian channelnoise, and the channel coefficients’s have independent com-plex gaussian distributions according to the WSSUS assump-tion8 .

B. Detection Processing and Estimation of OptimalCompensation Coefficients

Fig. 4 details the receiver structure of the OCDD/CDMAsystem. The received signal 9 is projected into the signalspace spanned by the orthonormal basis functions and, option-ally, by their delayed replicas called theextended orthonormalbases. The extended orthonormal bases are generated by theWalsh orthogonal sequence in the following manner: ThethWalsh function for constructing the orthonormal basisfunctions is represented by

(7)

8Under the slowly time-varying channel assumption, the channel coefficientscan be regarded as constant for the duration of a number of bits, so the timeindex is omitted in the expression ofh .

9From now on we omit the subscriptp that used to represent thepth user,unless it is specifically needed.


Fig. 4. Receiver structure of the OCDD/CDMA system.

for the ( ) element of the Walsh-Hadamard matrix,, and the Walsh chip interval , where ,

, and for integers and .We take the first out of Walsh functions in (7) for the

elements of the orthonormal basis set (i.e., ), and definethe orthonormal basis function such that

(8)

Then, we can generate the extended orthonormal basesby taking the delayed replicas of , that is,

(9)

for the th signal acquisition position which is related to theinitial acquisition position by .

Employing these bases, we can represent the received signalin (6) by

(10)

where denotes the composite noise including the approxi-mation error and the channel noise (i.e.,

). In the equation denotes an optimal compensation co-

efficient in the MMSE sense which is obtained by minimizingthe mean noise power

(11)

for a large integer .On this basis, we now estimate the optimal coefficients. We

define the modulated bitstream for each basis and thecross-correlations such that

(12)

(13)

(14)

for , ; , , ,. In addition, we construct the correlation

matrix and the projection vector such that

(15)

(16)

Then, the rearranged vector of the optimal coefficients,, de-fined by

(17)

(18)


is determined by theWiener-HopfMMSE optimal solution [21]

(19)

Note that when the correlation matrix becomesidentity (with a proper scaling factor) due to the perfect or-thonormality between the basis fuctions and ( ,

).Once we get the optimal coefficients, we determine theth

transmitted information bit by choosing that minimizes theenergy of the residual error

(20)

If BPSK signaling is assumed, it is equivalent to determiningsuch that it takes the sign of thesufficient statistic for decision,

, defined by

(21)

Re (22)

since in (20) can be rearranged as

(23)

The two operations in (22), that is, first projecting the receivedsignal to each basis and then multiplying the conjugate of eachoptimal coefficient to the corresponding signal subcomponent,are executed respectively in the Walsh decomposer and thechannel compensator blocks in Fig. 3. The optimal coefficients

’s for the compensator block are computed by exploiting thetransmitted pilot symbol. The channel-compensated subcom-ponents are finally summed up to form the decision parameter

in (21).

IV. PERFORMANCEEVALUATIONS OF THE OCDD/CDMASYSTEM

Now, we evaluate the performance of the OCDD/CDMAsystem in the Rayleigh fading WSSUS environment, comparingits bit error performance with that of a conventional DS/CDMAsystem. We first carry out the SNR analysis to grasp the overallperformance improvement factors, and then examine computersimulation results.

A. SNR Analysis of OCDD/CDMA System

We begin the analysis by assuming, without loss of gener-ality, that the transmitted binary source bit is +1. In addition,

we assume that the delay spread is much smaller than thesymbol duration . Then, the intersymbol interference maybe ignored and the received signal in (10) can be rewritten as10

(24)

where is the sum of the MAI and the backgroud noise,and is the difference between the spread spectrum signaldeformed by the multipath channel and its approximation ob-tained by applying the estimated channel coefficients in (19).For simplicity, we assume that both the channel noise andthe approximation error are the zero mean complex whitegaussian random processes which are independent each other,i.e., and , whoseone-side power spectral densities areand respectively.

We consider the term in (22), which is the signal compo-nent obtained by employing theth delayed version of the thorthogonal basis function. Applying (24) to (22), we get

(25)

for

(26)

(27)

where and respectively denote the phase angles ofand . If we assume that the user-specific PN sequence

randomly takes on the values +1 and1 and that the shapingpulse is rectangular as defined in (3), we can easily get the ex-pectations

(28)

(29)

The sufficient statistic in (21) then becomes

(30)

10In this section we focus on the 0th transmitted symbol, omitting the super-script (i).


for

(31)

(32)

Note that the term is involved due to the pseudo-orthogonalityof the extended orthogonal bases and thus becomes zero if theemployed basis signals are perfectly orthogonal (e.g., in the case

). Applying (28)–(29) to (31)–(32), we get

(33)

(34)

Applying the prorating approximation to (33) we can get

(35)

Finally, we obtain, by combining (30), (34), and (35), theoutputSNR

(36)

where is the energy of a symbol,is the total gain (i.e., total amount

of information) available in the receiver.11 The total gainitself is a random variable which depends mainly on the channelcharacteristic and the orthonormal-basis functions.

In general the output SNR is supposed to increase as thenumber of orthonormal-basis functions increases. In view of(36), this happens in the following manner: As increasesthe total gain increases while the approximation errordecreases, thus making the second term in the denominatorsmaller. According to the first term of the denominator, theoutput SNR is supposed to decrease as the number of thedelayed versions of the orthonormal Walsh basisincreases,but the decrease rate is insignificant in case the processinggain is large. Furthermore, the employment of the delayedversions may increase the total gain very efficiently (i.e., witha small number of bases) when the delay spread is long and

11This formula is also applicable to the output SNR of the conventionalDS/CDMA system employing MRC.

Fig. 5. Output SNR (SNRo) versus input SNR(Eb/No) (L = 3, N = R =M = 64, L = 1 for OCDD/CDMA).

sparsely distributed. If the K-L bases were employed in thereceiver, the average total gain would be maximized with theaverage approximation error power minimized, thus yielding amaximized output SNR.

B. Numerical Results

We now carry out computer simulations in order to mea-sure the SNR and bit error performance of the OCDD/CDMAsystem, confirming that its performace is much improved overthe conventional DS/CDMA system.

For the simulations, we set up the following environment:We take the Rayleigh fading WSSUS channel model in (2), andassume a uniform delay-power profile (except for the cases ofFigs. 10 and 11) for the interval so that the indepen-dent complex gaussian gains of ’s have the same variance

. This assumption is intended to make the normal-ized summation unity. In addition, we assume for simplicity theblockwise-constant channel in which each channel coefficient

remains constant for the duration of a block and changesto an independent coefficient in the next block. We take 100symbol transmission time as a block. Also we assume that pa-rameter estimation for coherent detection is perfectly done forboth the OCDD/CDMA and the DS/CDMA system (except forthe case of Fig. 11), and that the user-specific PN sequence israndomly generated with the number of +1’s being equal to thenumber of 1’s in a period .

Fig. 5 plots the output SNR of the OCDD/CDMA and theDS/CDMA systems with respect to the input SNR( ),which is based on the measurements of the average approxi-mation error power and the total gain.12 For the simulations,we took the values and , and employed the fullset of the length 64 Walsh codes (i.e., ), but nottheir delayed replicas, for the OCDD/CDMA basis functions.From Fig. 5, we can confirm that the output SNR is higher forthe OCDD/CDMA system than for the DS/CDMA system overall the input SNR ranges.

12In calculating the output SNR, we used the relationsN =(1=NS)Ej z(i)j = Ejz(i)j , N = (1=NS)Ej �(i)j ,andE = ju(i)j , respectively for the discrete-sampled versions ofthe channel noisez(t), the approximation error�(t), and the transmitted signalu(t).


Fig. 6. BER performance versus delay spread (LT ) (Eb/No = 12 dB,N =

R =M = 64,L = 1 for OCDD/CDMA;L = 0 means the flat fading case).

Fig. 6 plots the bit error performance of the OCDD/CDMAand the DS/CDMA systems with respect to the the delay spread

, with the input SNR fixed at 12 dB. For the DS/CDMAsystem we considered the two cases (i.e., single-rake)and (i.e., full-rake), and for the OCDD/CDMA systemswe took without using the delayed versions asbefore. The other parameters are set identical to the previouscase. From the figure, we observe that the BER performanceimproves as the number of rakes increase from single (i.e.,) to full (i.e., ) for the DS/CDMA system, which is a

very well known property. In addition, we can confirm that theBER performance of the OCDD/CDMA system is superior tothat of the DS/CDMA system for all , which means thatthe diversity utilization of the OCDD/CDMA system is higherthan that of the DS/CDMA system in the WSSUS multipathchannel. In the figure, represents the case of perfectly flatfading channel, for which the diversity potential itself becomes1 and thus no additional information is available out of the addedorthonormal bases.

Fig. 7 compares the bit error performances of theOCDD/CDMA system with respect to the number of or-thonormal bases. Considered are the two cases when thedelayed versions of the orthonormal bases are not employed(i.e., ) and employed (i.e., ). We set ,

dB, and set the other parameters identical tothe Fig. 5 case. From the figure, we observe that the BERperformance improves as the number of orthonormal basesincreases, but the improvement slows down ifincreases be-yond a certain number. We see the performance even degradingif the number of bases is larger than the spreading factor(=64). (see the case , .) The degradation originatesfrom the fact that the correlation matrix in (15) becomessingular when the number of bases exceeds the maximumpossible signal space dimension, which makes it impossibleto determine the optimal gain vector in (19). To make thecorrelation matrix nonsingular, we added small perturbationnoises to and thus got a suboptimal gain vector.13

13We may get an optimal gain vector by solving the Wiener-Hopf equationwithout applying the matrix inversion. The resulting performance becomes al-most the same as that of theN basis cases.

Fig. 7. BER performance versus number of Walsh basis signals (M ) (Eb/No= 12 dB,L = 3,N = R = 64).

Fig. 8. BER performance versus chip timing error (flat fading, Eb/No = 12 dB,N = R = M = 64, L = 1).

Aside from the performance in the multipath channel,we additionally investigated the performance robustness tothe timing misalignment in the receiver, as it can severelydegrade the performance of the DS/CDMA. Fig. 8 comparesthe bit error performance of the OCDD/CDMA system andthe DS/CDMA system with respect to the timing alignmenterror variation in the range of . We took the case of flatfading channel, in which the bit error performance is verysensitive to the timing recovery accuracy. According to thefigure, the performance degrades little for the OCDD/CDMAsystems even for the full chip misalignment, while it degradesseverely for the DS/CDMA system. Note that it is a big burdenfor a high-speed spread spectrum system to search and keepthe exact timing. Thus the overall hardware complexity of theDS/CDMA system having several rake fingers could be muchlarger in a high-speed system than is explicitly perceived fromthe small number of the receiver bases (i.e., rake fingers).

Fig. 9 compares the bit error performance of theOCDD/CDMA and the DS/CDMA systems with respect to theinput SNR. In Fig. 9(a), we took , ,

for the DS/CDMA system, and for theOCDD/CDMA system; and in Fig. 9(b), we took ,

, , , and for both the


Fig. 9. BER performance versus input SNR (Eb/No). (a)L = 3,N = R =

M = 64,L = 3 for DS/CDMA, andL = 1 for OCDD/CDMA; (b)L = 6,N = 32,R = 16,M = 4,L = 4 for both DS/CDMA and OCDD/CDMA.

DS/CDMA and the OCDD/CDMA system. We observe thatthe OCDD/CDMA system outperforms the DS/CDMA systememploying MRC, in general, and that the outperformancedominates in the low BER environment.

Differently from the above simulations in which we assumedthe uniform power-delay profile for the multipath channel, wenow compare the BER performance of the channel with theexponential power-delay profile, which is another importantmultipath channel prototype [13]. For simulations, we took theDS/CDMA system having three rake fingers ( ) whichare positioned at the optimal points within the information bitinterval and the OCDD/CDMA having only one finger( ). Fig. 10 exhibits the BER performance of the twosystems for various RMS delay spreads, with the average totalenergy of the multipath profile normalized to be unity as inthe uniform profile case. We observe that the OCDD/CDMAsystem exhibits superior bit error performance in all casesconsidered. We also observed that, as the RMS delay spreadincreases, the performance of the OCDD/CDMA systemimproves while that of the DS/CDMA system degrades. Wemay interpret this phenomenon as follows: As the multipath tailbecomes heavier, the DS/CDMA rake receiver loses more frac-

Fig. 10. BER performance versus input SNR (Eb/No): Expotentialpower-delay profile. (� denotes the RMS delay-spread;N = R = M = 64,L = 3 for DS/CDMA, andL = 1 for OCDD/CDMA.)

Fig. 11. BER performance versus number of accumulated pilot symbols:Expotential power-delay profile. (RMS delay-spread:2T , Eb/No = 12dB, N = R = M = 64, L = 3 for DS/CDMA, andL = 1 forOCDD/CDMA.).

tion of the total useful energy, and consequently the multipathdiversity effect is overwhelmed by this energy leakage effect.On the contrary, the performance of the OCDD/CDMA receiverimproves even under the heavy tail owing to the enhanceddiversity effect which always gathers most signal energy unlessthe delay spread becomes exceedingly large (i.e., comparableto the information bit duration ). In terms of the diversitydefinitions given in Section II, we may state that, as the multi-path tail becomes heavier (i.e., as the channel becomes morefrequency-selective), the diversity utilization of the DS/CDMArake receiver decreases, while the diversity potential increases,thus resulting in a little degraded overall performance as wecan see in the figure. As for the OCDD/CDMA system, sincethe diversity utilization changes little with the variation of themultipath profile, its performance improves with the increaseof the RMS delay spread owing to the increased diversitypotential.

As the OCDD/CDMA system employs multiple basis func-tions each of which has a weak signal component, it is moresensitive to the channel estimation accuracy than the DS/CDMArake receiver. Fig. 11 exhibits the performance variation of thetwo systems as the number of pilot symbols for channel estima-


tion varies from 10 to 50. The figure shows that the performanceof the OCDD/CDMA system degrades seriously when the reli-able channel gain is not provided. Therefore, the OCDD/CDMAsystem will not be so effective in the fast fading channel wherethe channel estimation results are not accurate. However, in theslowly fading channel, the OCDD/CDMA system can improvethe BER performance a lot by utilizing the reliable channel es-timation results.

V. CONCLUDING REMARKS

The concept of diversity potential we have newly introducedin this paper helps to quantify the maximum effective diversitygain of a spread spectrum signal in a given WSSUS channel.Likewise, the concepts of diversity utilization and diversity ef-ficiency respectively help to quantify the utilization of the di-versity potential by a spread spectrum diversity receiver and thediversity gain per receiver basis function. These quantified ap-proaches enable us to establish the concept of orthonormal-basisdiversity as a means of generalizing the frequency and path di-versities. With the introduction of the orthonormal-basis diver-sity, we can interpret the spread-spectrum diversity detectionscheme of the existing DS/CDMA and OFDM/CDMA systemsas a technique that decomposes the received signal based ona set of orthonormal-basis functions (i.e., the time-delayed PNsequence bases and the frequency-shifted sinusoidal bases, re-spectively).

The OCDD/CDMA system is a spread spectrum systemwhich is basically a DS/CDMA system but employs code divi-sion-oriented orthonormal-basis diversity detection technique,differently from the conventional rake receiver technique. Ittransmits the data symbol over a given time-bandwidth byusing a spreading sequence, and estimates and combines eachsignal component using a set of orthonormal PN-concatenatedWalsh codes and, optionally, their time-delayed replicas.The OCDD/CDMA system, as we have confirmed throughsimulations, exhibits much improved bit error performanceover the conventional DS/CDMA system in the slowly-varyingmultipath channel. This happens because the conventionalDS/CDMA rake systems cannot effectively resolve the mul-tipath components within a chip interval, nor can catch allthe signal components in a heavy-tailed multipath channel,thus under-utilizing the signal information. In contrast, theOCDD/CDMA system can fully utilize the signal informationby employing multiple simple bases.

The conventional DS/CDMA system employs much smallernumber of basis functions, but it requires exact PN-codesynchronization (i.e., acquisition and tracking) for each path,instead. This imposes a big burden on realizing the timingcircuits in the receiver and consequently increases hardwarecomplexity. A little timing-misalignment could bring abouta disastrous performance degradation, thus requiring newtime-consuming synchronization processes. This problemwill become even more critical in the future CDMA systemshaving a higher data rate and smaller chip interval. In contrast,according to the simulation results, the OCDD/CDMA systemexhibits little BER degradation in the chip misaligned situation.Instead, the OCDD/CDMA system is more sensitive to the

inaccurate channel estimation than the DS/CDMA system.Therefore, we may conclude that the OCDD/CDMA system isan effective wideband communication solution to achieving avery low BER in the slowly fading channel environment.

On the other hand, the OFDM/CDMA system can alsoeffectively resolve the multipath components by using manynarrowband sinusoidal bases, but it requires complex hardwarefor both the transmitter and receiver implementation and hasthe high peak-to-average ratio (PAR) problem. As far as theimplementation complexity is concerned, the OCDD/CDMAsystem is much simpler than the OFDM/CDMA systembecause its transmitter has the simplicity of the DS/CDMAsystem, and the Fast-Hadamard transformer (Green machine)required in the OCDD/CDMA receiver is simpler than theFFT circuit for the OFDM/CDMA system. Furthermore, theOCDD/CDMA system is free from the high PAR problem,as well as the accompanying inefficient amplifier utilizationproblem, which troubles the OFDM/CDMA system andobstructs its employment for portable terminals.

REFERENCES

[1] A. Baier, U.-C. Fiebig, W. Granzow, W. Koch, P. Teder, and J. Thi-elecke, “Design study for a CDMA-based third-generation mobile radiosystem,”IEEE J. Select. Areas Commun., pp. 733–743, May 1994.

[2] M. K. Varanasi and B. Aazhang, “Multistage detection in asynchronouscode division multiple access communications,”IEEE Trans. Commun.,vol. 38, pp. 509–519, 1990.

[3] R. Lupas and S. Verdu, “Near-far resistance of multiuser detectors inasynchronous channels,”IEEE Trans. Commun., vol. 38, pp. 496–508,1990.

[4] P. Rapajic and B. Vucetic, “Adaptive receiver structures for asyn-chronous CDMA systems,”IEEE J. Select. Areas Commun., vol. 12,pp. 685–697, May 1994.

[5] N. Yee, J.-H. Linnartz, and G. Fettweis, “Multi-carrier CDMA in indoorwireless radio networks,” inProc. PIMRC’93, 1993, pp. 109–113.

[6] S. Kaiser, “OFDM-CDMA versus DS-CDMA: Performance evaluationfor fading channels,” inProc. ICC’95, 1995, pp. 1722–1726.

[7] , “On the performance of different detection techniques forOFDM-CDMA in fading channels,” inProc. GLOBECOM’95, 1995,pp. 2059–2063.

[8] T. A. Wilkison and A. E. Jones, “Minimization of the peak to mean enve-lope power ratio of multicarrier transmission schemes by block coding,”in Proc. VTC’95, 1995, pp. 825–829.

[9] S. Kondo and L. B. Milstein, “Performance of multicarrier DS CDMAsystems,”IEEE Trans. Commun., vol. 44, pp. 238–246, Feb. 1996.

[10] J. G. Proakis,Digital Communications. New York: McGraw-Hill,1989.

[11] K. W. Yip and T.-S Ng, “Karhunen-Loeve expansion of the USSUSchannel output and its applications to efficient simulation,”IEEE J. Se-lect. Areas Commun., vol. 15, pp. 640–646, May 1997.

[12] M. Kavehrad and B. Ramamurthi, “Direct-sequence spread spectrumwith DPSK modulation and diversity for indoor wireless communica-tions,” IEEE Trans. Commun., vol. COM-35, pp. 224–236, 1987.

[13] J. M. Bargallo and J. A. Roberts, “Performance of BPSK and TCMusing the exponential multipath profile model for spread-spectrumindoor radio channels,”IEEE Trans. Commun., vol. 43, pp. 615–623,Feb./Mar./Apr. 1995.

[14] K. Pahlavan and A. H. Levesque,Wireless Information Networks. NewYork: Wiley, 1995.

[15] F. Ling, E. Bruckert, and T. A. Sexton, “Analysis of performance andcapacity of coherent DS-CDMA reverse link communications,” inProc.VTC’95, 1995, pp. 912–916.

[16] G. L. Turin, “The effects of multipath and fading on the performance ofdirect-sequence CDMA systems,”IEEE J. Select. Areas Commun., vol.SAC-2, pp. 597–603, July 1984.

[17] C. W. Helstrom, Elements of Signal Detection and Estima-tion. Englewood Cliffs, NJ: Prentice-Hall, 1995.

[18] N. Hess-Nielsen and M. V. Wickerhauser, “Wavelets and time-frequencyanalysis,”Proc. IEEE, vol. 84, pp. 523–540, Apr. 1996.


[19] H. J. Landau and H. O. Pollak, “Prolate spheroidal wave functions,fourier analysis and uncertainty—III: The dimension of the space ofessentially time- and band-limited signals,”B.S.T.J., pp. 1295–1336,July 1962.

[20] M. V. Clark, L. J. Greenstein, W. K. Kennedy, and M. Shafi, “Optimumlinear diversity receivers for mobile communications,”IEEE Trans. Veh.Technol., vol. 43, pp. 47–56, Feb. 1994.

[21] S. Haykin,Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1991.

Byoung-Hoon Kim received the B.S. and M.E.degrees in electronics engineering, and the Ph.D.degree in electrical engineering and computerscience from Seoul National University, Seoul,Korea, in 1994, 1996, and 2000, respectively.

He has been with GCT Semiconductor TechnologyR&D Center, Seoul, Korea, since 2000, respon-sible for implementation of IMT-2000 W-CDMAtechnologies. His current research interests includeCDMA, channel coding, digital communications,and signal processing for telecommunications.

Dr. Kim received the Best Paper Award (on Communications) of SamsungHumantech Paper Contest in 1999, an Excellent Paper Award from APCC’99,and the Best Paper Award from EW2000.

Byeong Gi Lee(S’80–M’82–SM’89–F’97) receivedthe B.S. and M.E. degrees in 1974 and 1978,respectively, from Seoul National University, Seoul,Korea, and Kyungpook National University, Taegu,Korea, both in electronics engineering. He receivedthe Ph.D. degree in 1982 from the University ofCalifornia, Los Angeles, in electrical engineering.

He was with Electronics Engineering Departmentof ROK Naval Academy as an Instructor and NavalOfficer in active service from 1974 to 1979. Heworked for Granger Associates, Santa Clara, CA,

from 1982 to 1984 as a Senior Engineer responsible for applications of digitalsignal processing to digital transmission, and for AT&T Bell Laboratories,North Andover, MA, from 1984 to 1986, as a Member of Technical Staffresponsible for optical transmission system development along with relatedstandard works. He joined the faculty of Seoul National University, in 1986,where he is a Professor and Vice Chancellor for Research Affairs. He is aco-author of Broadband Telecommunication Technology, 2nd ed., (ArtechHouse, 1996) and Scrambling Techniques for Digital Transmission (SpringerVerlag, 1994). He holds six U.S. patents with five more patents pending.His current fields of interest include communication systems, integratedtelecommunication networks, and signal processing.

Dr. Lee is the Associate Editor-in-Chief of theJournal of Communicationsand Networks, the past Editor of the IEEE GLOBAL COMMUNICATIONS

NEWSLETTER, and a past Associate Editor of the IEEE TRANSACTIONS ON

CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY. He is the Director forMembership Programs Development, the past Director of Asia Pacific Region,and a Member-at-Large of IEEE Communications Society (ComSoc). Hewas the Chair of the APCC (Asia Pacific Conference on Communications)Steering Committee, and the Chair of the ABEEK (Accreditation Board forEngineering Education of Korea) Founding Committee. He is a member ofNational Academy of Engineering of Korea, a member of Board of Governorsof IEEE ComSoc, and a member of Sigma Xi. He received the 1984 Myril B.Reed Best Paper Award from the Midwest Symposium on Circuits and Systemsand Exceptional Contribution Awards from AT&T Bell Laboratories.

Documents

OCDD/CDMA: a new DS/CDMA with orthonormal code diversity detection