A Co-Channel Interference Cancellation Technique Using ...sndgw.snd.elec.keio.ac.jp/~sanada/TRANSACTION/1997IEEE_VTEC02.pdf · A Co-Channel Interference Cancellation Technique Using

114 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 46, NO. 1, FEBRUARY 1997

A Co-Channel Interference CancellationTechnique Using Orthogonal Convolutional

Codes on Multipath Rayleigh Fading ChannelYukitoshi Sanada,Student Member, IEEE, and Qiang Wang,Member, IEEE

Abstract—This paper proposes and evaluates a new co-channelinterference cancellation technique that utilizes orthogonal con-volutional codes on a multipath Rayleigh fading channel. In aspread spectrum multiple access environment, co-channel inter-ference (CCI) limits the performance of the communication link.To remove this interference, several CCI cancellation techniqueshave been proposed, including the technique that does not requirethe receiver to have knowledge of the cross-correlation betweenuser sequences. This method leaves residual interference afterthe cancellation caused by errors in the initial decisions. Toreduce the residual interference and improve the initial decisions,the proposed scheme utilizes the error-correcting capability oforthogonal convolutional codes. This paper evaluates the per-formance of this scheme. Our results show that the proposedCCI canceller offers an improvement in capacity by a factor of1.5� 3 as compared with a conventional canceller on a multipathRayleigh fading channel. The proposed canceller works in thepresence of residual interference due to imperfect cancellation.The proposed canceller also has a capacity improvement withthe use of soft handoff in a multicell configuration.

I. INTRODUCTION

RECENTLY, spread spectrum techniques have received alarge amount of attention in wireless and cellular com-

munication applications. This is in large part because spreadspectrum techniques have multiaccess capability, antimultipathfading capability, and antijamming capability [1].

There are three basic multiple access schemes: 1) frequencydivision multiple access (FDMA); 2) time division multipleaccess (TDMA); and 3) code division multiple access (CDMA)[2]. Unlike FDMA and TDMA capacities, which are primarilybandwidth limited, CDMA capacity is interference limited [3].This is one of the reasons that CDMA may be potentiallyspectral efficient for cellular communications for which theadditional spectrum will unlikely be allocated [2].

Multiuser detection has been developed to increase theCDMA system capacity for more than ten years. In [4],the other users’ interference can be minimized through theuse of maximum-likelihood sequence detection. Although this

Manuscript received August 22, 1994; revised February 22, 1995 andOctober 30, 1995. This work was supported by the Canadian Institute forTelecommunications Research, a Federal Network of Centres of Excellence.

Y. Sanada was with the Department of Electrical and Computer Engineer-ing, University of Victoria, Victoria, B.C., V8W 3P6 Canada. He is now withthe Department of Electrical Engineering, Faculty of Science and Technology,Keio University, Yokohama-shi 223, Japan.

Q. Wang is with the Department of Electrical and Computer Engineering,University of Victoria, Victoria, B.C., V8W 3P6 Canada.

Publisher Item Identifier S 0018-9545(97)00652-X.

scheme is optimum, the complexity of the detection is highand grows exponentially with the number of users. In [5]–[7],the interference is removed by utilizing matrix operations.These methods do not require complex receiver structures,and provide a cross-correlation free signal at the output.They are not useful, however, if the signature sequencesare used to separate the users’ channels, as these methodsrequire the receiver to have knowledge of the sequences’ cross-correlation, which varies with different relative phase of thesignature sequences. If these multiuser detectors are employedin the reverse link of the CDMA system specified by theIS-95 (North American Digital Cellular Standard), a receivermust calculate the cross-correlation and the computationalcomplexity increases exponentially with the number of users[8].

CCI cancellation methods, whose complexity grows onlylinearly with the number of users, have also been proposed[9]–[11]. In [10], users are detected jointly and the CCI isremoved. In this method, the receiver reconstructs the otherusers’ transmitted signals by using the initial decisions aboutthe other users’ signals. This receiver then uses the estimates(reconstructed signals) to remove the CCI from the compositereceived signal. This method does not require knowledgeof the cross-correlation between the spreading sequences.This method suffers from a significant amount of residualinterference, which is caused by symbol errors in the initialdecisions [12], [13]. Thus, the performance of the cancellerdepends on the error performance of the initial decision.Therefore, it is desirable to improve the accuracy of the initialdecisions.

To improve the accuracy of the initial decisions, we haveproposed a CCI cancellation technique that utilizes orthogonalconvolutional codes [14]. In this method, received signals areboth demodulated and decoded by a soft decision Viterbidecoder. The resulting bit streams are re-encoded and re-spread, and this reconstructed signal is then removed fromthe composite received signal. Due to the error-correctingcapability of orthogonal convolutional codes, the residualinterference is reduced since the decisions on the other users’signals are improved compared to a noncoded canceller. Thus,the BER performance of the receiver is improved. Since thedecoding of the orthogonal convolutional codes increases theprocessing delay, this system is most suitable for packet datacommunications. In [14], this CCI cancellation technique wasinvestigated on the AWGN channel. A similar technique pre-

0018–9545/97$10.00 1997 IEEE

SANADA AND WANG: A CO-CHANNEL INTERFERENCE CANCELLATION TECHNIQUE 115

Fig. 1. Transmitter structure.

sented at the same time as [14] utilizes cascaded combinationof cancelling CCI and hard decision decoding of aHamming code [15]. In this paper, we extend our resultsfor our cancellation technique to a multipath Rayleigh fadingchannel.

This paper is organized as follows. In Section II, the systemmodel is presented. In Section III, the conventional CCIcanceller is described. In Section IV, the new CCI cancelleris described and its performance is derived. In Section V, theeffects of imperfect cancellation are considered. In Section VI,a multicell configuration is assumed and intercell interferenceand soft handoff are considered. Simulation results and theo-retical performance results are shown in Section VII. SectionVIII presents our conclusions.

II. SYSTEM MODEL AND DEFINITIONS

The system model is of the same type as the CDMA systemspecified by IS-95. The receiver structure is based on that in[16] followed by a CCI canceller and a decoder for an orthog-onal convolutional code. There are active users in a cell.Each user encodes its data using an orthogonal convolutionalcode (Fig. 1). We define the code rate asand the constraint length as. Depending on the output ofthe convolutional code, one of orthogonal sequences ischosen. Then, the resulting orthogonal sequence is combinedwith long pseudo-noise (PN) sequences, which separate theusers’ channels, and is modulated using Offset-QPSK. Thetransmitted OQPSK signal of theth user during one symbolinterval is

(1)

where is the th -ary orthogonal symbol of equalenergy is the long PN sequence for theth user, , are the PN sequences for theand

channels, is the time offset, which is equal to , andis the chip interval. The processing gain where

is the symbol duration. is the signal power, thus theenergy per symbol is .

If the signal written in (1) is transmitted over a multipathchannel, the resulting signal at the receiver is the sumof delayed, phase-shifted, and attenuated versions of the input

signal. The received signal for theth user can be written as

(2)

where is the number of paths for theth user’s channel,and are the delay and complex gain coefficients,

respectively, for the th path for the th user, and the asteriskdenotes complex conjugation. The complex gain coefficientsare defined as

(3)

where and account for the attenuation and phaseshift, respectively. is Rayleigh distributed and is anuniform random variable in .

In a single-cell CDMA cellular system with users, thesignal arriving at the base station receiver is

(4)

where is additive white Gaussian noise with zero meanand two-side spectral density . At the output of thereceiver bandpass filter with a bandwidth ofbecomes narrowband noise that can be represented by

(5)

where and are independent lowpass Gaussianprocesses with zero mean and variance .

Fig. 2 shows the receiver structure. At the output of thelow-pass filter (LPF) of the upper path (-channel)

(6)

where . Also for the lower path ( -channel)

(7)


Fig. 2. Receiver structure.

For the -channel, the output of the th correlator for the realpart of the th path of the th user is

(8)

where , and , which are given inAppendix A, represent the self path interference, interferencedue to the other paths, interference due to the other users,and thermal noise corresponding to the real part of thepath, respectively. Owing to the quadrature nature of the PNsequences, the self path interference is small compared tothe other interference (Appendix A). In this case,-channelcorrelator output becomes

(9)

where is the average attenuation of over the symbolperiod. Similarly the output of the th correlator for theimaginary part of the th path of the th user is

(10)

where , and are the interference due to theother paths, interference due to the other users, and thermal

noise corresponding to the imaginary part of the path,respectively. Also, the output of the -channel correlatorbecomes

(11)

where , and are the interference due tothe other paths, interference due to the other users, andthermal noise corresponding to the real part of the path,respectively, and

(12)

where , and are the interference due to theother paths, interference due to the other users, and thermalnoise corresponding to the imaginary part of the path,respectively. Due to the square-law combining, the decisionvariable for the th user will be

(13)

From [16], [17], and Appendix A, the average SNR for theth path of the th user after the correlation is

(14)


For simplicity, is set to for all . We assume all fadingpaths have equal mean strength, i.e.,is one for all and .With these assumptions, the SNR per path becomes

(15)

III. CONVENTIONAL CCI CANCELLER

A. System Model

Fig. 3 shows a receiver model using a conventional CCIcanceller with user 1 as a reference. Perfect chip synchro-nization for every user is assumed. In this method, as shownin Figs. 2 and 3, all of the user’s received signals are firstdemodulated and decorrelated with a bank of correlators.The output of the correlators for each path is squared andcombined. Then, the most probable orthogonal sequence isselected for each user. Utilizing these initial decisions, theselected sequences for each user are then re-spread and re-modulated with delay , attenuation , and phase shift(error in estimating these parameters is considered in SectionV). The re-modulated signals are removed from the compositereceived signal. Following this process, user 1’s signal isdemodulated, decorrelated, deinterleaved, and decoded basedon the orthogonal convolutional code employed.

B. Performance of the Conventional CCI Canceller

To emphasize the performance difference of the conven-tional and the proposed canceller, we consider the simplecase. To analyze the performance of the conventional CCIcanceller, we assume the interference from the other users isGaussian distributed, the chip pulse shape is rectangular, thechip synchronization is perfect, and the canceller can estimatethe phase shift, the attenuation, and the delay perfectly (if theparameters are not accurately estimated, performance of allcancellers will deteriorate [11], as will be shown in SectionV).

The error probability of the initial decision on the orthogonalsequence is given by [18, p. 745]

(16)

where is the signal-to-noise ratio after the first corre-lation given in (15) and is given by

(17)

When errors in the initial decisions arise, the CCI cancellerdoubles the interference power [12], [13]. The signal-to-noiseratio after the CCI cancellation is (Appendix B)

(18)

where

(19)

Here, we assume that the receiver can estimate the accuratevalue of received signal power. From the upper boundon the bit error rate using a soft decision Viterbi decoder canbe obtained as [18, p. 760]

(20)

where

probability of selecting the incorrect path (Ap-pendix C)

(21)

probability of error for square-law combiningbetween orthogonal sequences

(22)

weight spectra of the code which can be obtainedfrom [19];minimum free distance.

If the weight spectra is obtained from to in(20), the upper bound can be calculated. The bound becomeslooser, however, as the BER increases. Quite often, the firstfew terms in (20) are used to get a performance approximationof a Viterbi decoder. We use the first four terms as anapproximation for both the conventional and the new CCIcancellation techniques.

IV. NEW CCI CANCELLER

A. System Model

In this section, we present the new CCI canceller utilizingorthogonal convolutional codes. As mentioned before, the per-formance of the CCI canceller depends on the initial decisions.Therefore if the signal-to-noise ratio, , decreases, theprobability that the initial decisions are incorrect increases andthe canceller may increase the CCI seen by a user. To improvethe error performance of the initial decision, the proposedsystem utilizes the error-correcting capability of orthogonalconvolutional codes.

Fig. 4 is a model of the proposed system. After mak-ing a maximum likelihood decision on the received symbolsequence, the proposed canceller deinterleaves and decodesthe orthogonal convolutional code using a Viterbi decoder.The decoded data is then re-encoded, re-interleaved, assignedto an orthogonal sequence, combined with the long PN se-quences, and re-modulated to an OQPSK signal with delay

, attenuation , and phase shift . During this demodula-tion, decoding, re-encoding, re-interleaving, and re-modulation


Fig. 3. Model of a receiver using the conventional CCI canceller.

processes, the received signal is stored in the memory. Thememory size is dependent upon the interleaving size andthe delay caused by the decoding process. After the re-modulation, the new canceller follows the same steps as theconventional canceller. That is, the canceller removes the2 th users’ signals from the composite received signal,which is extracted from the memory, and user 1’s signal isdemodulated, decorrelated, deinterleaved, and decoded.

It is noted that Viterbi decoders needed in the proposedscheme are already utilized in the conventional CCI cancella-tion scheme where each user has a Viterbi decoder. If the reuseof the same Viterbi decoder after CCI cancellation creates anunacceptable delay (if we are dealing with the transmissionsof packets, they may tolerate a relatively long delay and thereceiver may not be busy for receiving consecutive packets),one can solve the problem by employing two Viterbi decodersper user. Later, we will show that, for the same performance,the complexity of each decoder may be reduced by more thana factor of 2 so that the overall decoding complexity is stillreduced.

B. Performance of the Proposed CCI Canceller

All the assumptions are the same as those for the con-ventional canceller, which were presented in Section III-B.The number of symbol errors caused by choosing a wrongpath after re-encoding is the same as the distance of thecoded sequence along the wrong path in the state diagram(for example, the number of symbol errors is four in Fig. 5)from the coded sequence along the correct path. Therefore, anapproximation of the expected number of interfering symbols

after the re-encoding is (Appendix B)

(23)where

(24)

(25)

(26)

coefficient of the weight enumerator function

of the orthogonal convolutional code [19]

Then, the signal-to-noise ratio after the cancellation is

(27)

From , the approximate error rate after the cancellationcan be obtained by the following equation, which is similarto (20):

(28)


Fig. 4. Model of a receiver using the proposed CCI canceller. (The Viterbi decoding just before the data output and the Viterbi decoding for CCIcancellation might be implemented by the same decoder.)

where the is obtained by substituting into(21) and (22) instead of

(29)

(30)

V. IMPERFECT CANCELLATION

In Sections III and IV, it is assumed that the cancellercan estimate the phase shift, the attenuation, and the delayperfectly. There are always errors in estimation of theseparameters, however, due to the noise and the co-channelinterference. Therefore, even though the canceller reconstructscorrect signals after the initial decisions, it might not re-move the co-channel interference completely; there is residualinterference caused by imperfect cancellation.

Suppose a fraction of cancelled signal power is left in thecomposite signal. For the conventional canceller, the expectednumber of cancelled symbols is ,

Fig. 5. Symbol errors caused by a wrong path.

so the SNR after the cancellation is

(31)


For the proposed canceller, the expected number of cancelledsymbols is given by , so the SNRafter the cancellation is

(32)

From and , the approximate error rateafter the cancellation can be obtained by equations similar to(20) and (28).

VI. I NTERCELL INTERFERENCE ANDSOFT HANDOFF

In previous sections, we assumed a single-cell configuration.In this section we consider a multicell configuration, consistingof a cluster of seven cells as depicted in Fig. 6. Each cellis divided into three sectors. Due to the sectorization, theinterference at the base station comes from only two adjacentcells. Assuming perfect power control, wave propagationwith path loss proportional to the fourth power of distance,and uniformly distributed users in a sector, the intercellinterference energy from one of the adjacent cells is [20]

(33)

where is the distance between the base stations (in thiscase ), and is the total symbol energy defined as

. Therefore, in (15), the SNR per path becomes

(34)

If soft handoff is employed, mobiles close to cell boundariesmight transmit to two base stations. Suppose the handoffprobability is [21], the period of the soft handoff is short,and the mobiles that are in the soft handoff process transmittheir signals with energy to the base stations, the numberof users using the soft handoff can be considered as

(35)

where is the nearest integer less than or equal to. Alsothe intercell interference decreases to

(36)

The performance of the CCI cancellers can be calculated byadding the intercell interference term and replacingwith

. Therefore, the path SNR after the cancellation for theconventional canceller is

(37)

Fig. 6. Multicell configuration.

and for the proposed canceller the path after the can-cellation is

(38)

VII. RESULTS

The following results assume full interleaving. Results forfinite interleaving may also be readily obtained. Since theyare application specific, we omit them in this paper. We alsoassume that the processing gain is 128 and the coding rateis 1/3 (8-ary orthogonal convolutional code) with optimumgenerator polynomials given in [19] for the constraint lengthof 3 to 7 and in [8] for the constraint length of 9.

Fig. 7 shows the BER performance of the convolutionalorthogonal code on the multipath Rayleigh fading channel. Inthe figure, the points are the simulation results and the line isthe theoretical performance calculated from the approximationwith the first four terms in (20). For the results shown inFig. 7, the number of paths is assumed to be three. Asthe simulated points are close to the theoretical values with

, we assume that the approximation isappropriate.

From Figs. 8–24, the performances without a canceller, withthe conventional canceller, and with the proposed canceller arepresented for different conditions. The performance withouta canceller is calculated by (20)–(22) with replacing

. Figs. 8 and 9 show the system versus equivalentGaussian with the number of paths equal to 1 and 3,respectively. The system is the just before thefinal maximum likelihood decision (after the cancellation),defined as or . The equivalent GaussianSNR/symbol is the SNR without the CCI, which is defined as

. Thus the difference between these twois the CCI, which cannot be removed by the canceller,

shown in Figs. 10 and 11. From Figs. 10 and 11, it is clear thatthe proposed canceller cancels more CCI and provides betterSNR than the conventional canceller when the SNR/symbolis not too low. Especially when (the number of


Fig. 7. Performance of orthogonal convolutional code, number of paths= 3,code rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

Fig. 8. System SNR versus equivalent Gaussian SNR, number of paths= 1,code rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

users that transmit the signal at the same time), the proposedcanceller removes most of the CCI and provides a nearlyinterference free signal for the final maximum likelihooddecision. Also the proposed canceller works very well whenthere are multiple paths in the channel which cause more CCI.In Fig. 9, when , the system SNR of the conventionalcanceller does not improve in the high equivalent GaussianSNR area since the CCI dominates the accuracy of the initialdecision. On the other hand, the proposed canceller improvesthe system SNR as the equivalent Gaussian SNR becomes

Fig. 9. System SNR versus equivalent gaussian SNR, number of paths= 3,code rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

Fig. 10. Residual interference versus equivalent gaussian SNR, number ofpaths = 1, code rate= 1=3, constraint length= 9, 8-ary orthogonalsignalling.

larger. If is 40, however, there are three paths, and theequivalent Gaussian SNR is less than 12 dB, then the re-encoding process produces too much interference. Thus, inthis case, the proposed canceller is inferior to the conventionalcanceller.

Figs. 12 and 13 show the BER versus SNR with the numberof paths equal to one and three, respectively. SNR/symbolis defined as . When , the performance ofthe proposed canceller is very close to the performance with

and superior to the conventional canceller by 2 dB


Fig. 11. Residual interference versus equivalent gaussian SNR, number ofpaths= 3, code rate= 1=3, constraint length= 9, 8-ary orthogonalsignalling.

Fig. 12. BER versus SNR/symbol, number of paths= 1, code rate= 1=3,constraint length= 9, 8-ary orthogonal signalling.

with one path and by 1 dB with three paths at . If, the difference between the BER of the two methods is

much larger than the case. For example, for constraintlength 9, with one path, and at , the differenceis more than 6 dB as seen in Fig. 12.

Figs. 14 and 15 show the BER versus the number of usersfor one and three paths, respectively. It is shown that thenumber of simultaneous users at increases bya factor of 1.5 3 with the new canceller as compared with

Fig. 13. BER versus SNR/symbol, number of paths= 3, code rate= 1=3,constraint length= 9, 8-ary orthogonal signalling.

Fig. 14. BER versus number of users, number of paths= 1, code rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

the conventional canceller. It is also clear that up to about20 users the proposed canceller removes almost all CCI whenSNR/symbol equals to 10 dB as the error floor due to thermalnoise is observed.

Figs. 16 and 17 show the BER versus the constraint lengthof the convolutional code for one and three paths, respectively.From the figures, a significant performance improvement canbe obtained by using a longer constraint length, especiallywhen is large. As the constraint length becomes longer, theBER decreases linearly. Therefore the canceller should use


Fig. 15. BER versus number of users, number of paths= 3, code rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

Fig. 16. BER versus constraint length, number of paths= 1, SNR/symbol= 15 dB, code rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

a convolutional orthogonal code that has a large constraintlength.

The proposed cancellation scheme can also be viewedas an effective way of reducing the system implementationcomplexity as far as Viterbi decoding is concern. For example,for and required , from Fig. 16,the conventional canceller requires the code constraint lengthequal to 5, while the proposed canceller requires the constraintlength equal to 4. Thus the number of states in the trellis

Fig. 17. BER versus constraint length, number of paths= 3, SNR/symbol= 15 dB, code rate= 1=3, 8-ary orthogonal signalling.

diagram is reduced by a factor of four and the memory sizefor storing trellis paths is reduced by a factor ofas the decoding depth also reduces. This represents more thana factor of 4 reduction in Viterbi decoding complexity. Recallthat the number of Viterbi decoders could be doubled in orderto shorten the delay. Even with this taken into account, theoverall decoding complexity is reduced by more than a factorof 2.

Fig. 18 shows the BER versus number of paths that areavailable for the square-law combining. When is 20, theBER of both cancellers improves as the number of pathsincreases from one to two. If the number of paths fur-ther increases, however, the performance deteriorates and theproposed canceller is affected more than the conventionalcanceller. When is 40, as the number of paths increases, theBER becomes worse—as there is too much interference dueto too many paths—and the low SNR produces more symbolerrors in the decoding process.

Figs. 19 and 20 show the BER performance in the pres-ence of imperfect cancellation for one and three paths. Theestimation error is the fraction of cancelled signal powerthat is left in the composite signal. The estimation error hasalmost no affect on either the conventional or the proposedcanceller when , and both cancellers work welluntil . From these results, it is concluded that CCIcancellers are useful even with an estimation error.

Figs. 21 and 22 show the BER versus the number of userswith an estimation error for one and three paths, respectively.It is clear that the number of simultaneous users with anestimation error is almost the same as that withoutestimation error for both the conventional canceller and theproposed canceller. Therefore, the proposed canceller is ef-fective and better than the conventional canceller even in thepresence of the interference caused by imperfect cancellation.


Fig. 18. BER versus number of paths, SNR/symbol= 10 dB, code rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

Fig. 19. BER versus estimation error, number of users= 40, number ofpaths= 1, SNR/symbol= 10 dB, code rate= 1=3, constraint length= 9.

Figs. 23 and 24 show the BER performance for the multicellsituation and the effects of the cancellation with soft handoffand one and three paths per channel. The number of users persector is the number of users that transmit in one sector atthe same time. Though the handoff probability dependson many parameters, is set to 0.087 following [21] asan example. It is shown that the combination of the softhandoff and the proposed canceller improves the capacity,while the conventional canceller does not make any significantdifference in the capacity. The reason is that if the number ofusers per sector is small, very few users utilize the soft handoff.

Fig. 20. BER versus estimation error, number of users= 40, number ofpaths= 3, SNR/symbol= 15 dB, code rate= 1=3, constraint length= 9.

Fig. 21. BER versus number of users with estimation error, number of paths= 1, coding rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

Therefore, the impact of the canceller is not significant as itdoes not cancel signals from mobiles in an adjacent cell thatare not in soft handoff to the reference cell. On the otherhand, if there are a large number of users per sector, theconventional canceller does not work well. In this case, eventhough some mobiles outside the cell transmit to the basestation during soft handoff, the conventional canceller mightnot cancel the interference from them. Since the proposedcanceller still works with a large number of users in the lowBER region, it shows the capacity improvement with the useof the soft handoff.


Fig. 22. BER versus number of users with estimation error, number of paths= 3, coding rate= 1=3, constraint length= 9, 8-ary orthogonal signalling.

Fig. 23. BER versus number of users/sector, number of paths= 1,SNR/symbol= 15 dB, code rate= 1=3, constraint length= 9, handoffprobability = 0:087.

VIII. C ONCLUSION

In this paper, we have proposed and evaluated a new co-channel interference cancellation technique on a multipathRayleigh fading channel that improves the accuracy of theinitial decision by utilizing the error correction capability oforthogonal convolutional codes. The performance of the pro-posed canceller has been computed on the multipath Rayleighfading channel and compared with the conventional canceller.It has been shown that the proposed canceller offers 1.53times higher user capacity than the conventional canceller.

Fig. 24. BER versus number of users/sector, number of paths= 3,SNR/symbol= 15 dB, code rate= 1=3, constraint length= 9, handoffprobability = 0:087.

We have also shown that the canceller significantly benefitsfrom the use of a large constraint length of an orthogonalconvolutional code. For the same performance, the proposedcanceller can effectively reduce the decoding complexity.The proposed canceller works even in the presence of theinterference due to imperfect cancellation. In the multicell con-figuration, the proposed canceller has been shown to improvethe user capacity in combination with soft handoff.

APPENDIX

A. Interference

The self interference on the output of the-channel’s thcorrelator is

(A1)

The interference due to the other paths of the same user is

(A2)


The interference due to the other users is

(A3)

The thermal noise is

(A4)Next we consider the statistics of the interference. It is

assumed that the PN sequences are independent and identicallydistributed binary sequences and the chip pulse shape isrectangular.

From [16] and [17], the variance of the interference due tothe other paths is (the variances of , and

are the same as that of )

(A5)

where is the average attenuation for theth path of theth user’s channel. Also the variance of the interference due

to the other users is (the variances of , and


(A6)

Due to the quadrature modulation, the variance of the self in-terference is half of the other interference in terms of the sameattenuation . Therefore (the variances of , and


(A7)

Since the self interference is small compared to the otherinterference, we assume that they are negligible [16].

The variance of the thermal noise is (the variances of, and are the same as that of )

(A8)

Then, assuming the thermal noise terms and the interferenceterms are uncorrelated,

is Gaussian-distributed with zero mean and variance

(A9)

Similarlyis Gaussian-distributed with zero mean and variance.Therefore, SNR per path is

(A10)

B. Path SNR After the Cancellation

The path SNR after the cancellation can be written as

(B1)

where the first term of the denominator represents the interfer-ence due to the other users, the second term is the interferencedue to the other paths, and the third term is the thermal noise.Also is the number of paths and is the expected numberof interfering symbols after the cancellation process. Considerinterference from theth path of the th user to the th path ofthe th user after the cancellation. We assume that two adjacentsymbols of the th user overlap the reference symbol of the

th user and they make independent errors with probability. If the first interfering symbol overlaps with the reference

symbol with time duration , the expected number ofinterfering symbols is . Then, the secondinterfering symbol overlaps with time durationand the expected number of interfering symbols is

. Therefore, the expected number of symbolscorresponding to interference from theth path of the th userto the reference symbol of theth user is

(B2)

There are interfering users and there arepaths for eachuser. Thus, the total expected number of interfering symbolsis given by

(B3)

For the proposed canceller, supposeis the distance ofthe coded sequence along the wrong path in the state diagramfrom the coded sequence along the correct path, is thecoefficient of the weight enumerator function, andis the probability that the Viterbi decoder chooses the wrongpath with the distance and the number of paths. Thewrong path, which has the distance, causes symbol errors.Also, there are wrong paths whose distance is. Theprobability of symbol errors increases by times.Therefore, summing from to , the total expectednumber of interfering symbols created by the cancellationprocess is

(B4)


C. Probability of Selecting the Incorrect Path

From (13), the decision variable for theth user at the thcorrelator is

(C1)

Thus has a chi-square probability distribution withdegrees of freedom. Assuming there are paths andis the distance of the coded sequence along the wrong path inthe state diagram from the coded sequence along the correctpath, the decision variable between paths has a chi-squareprobability distribution with degrees of freedom

(C2)

Therefore, the probability of choosing a wrong path is

(C3)

where is the output of a matched filter corresponding to thecorrect path while corresponds to the wrong path. Therefore

and are statistically independent zero-mean Gaussianrandom variables with variance

(C4)

(C5)

where is the noise and is the co-channel interference.The density function of a chi-square distribution withdegrees of freedom is [22, p. 542]

(C6)

(C7)

The probability of selecting the wrong path is

(C8)

Carrying out the integrations of (C8) by parts, we obtain first

(C9)

and then

(C10)

The error probability depends on the average received signalenergy through

(C11)

and

(C12)

Therefore

(C13)

ACKNOWLEDGMENT

The authors would like to express their deep gratitude to themembers of CITR Lab, especially to M. Wang and R. Kerr fortheir help in preparing this paper.

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Yukitoshi Sanada (S’94) was born in Tokyo in1969. He received the B.E. degree in electrical en-gineering from Keio University, Yokohama, Japan,and the M.A.Sc. degree in electrical engineeringfrom the University of Victoria, Victoria, B.C.,Canada, in 1992 and 1995, respectively. He iscurrently pursuing the Ph.D. degree at Keio Uni-versity. His research interest is in spread spectrumcommunications.

Qiang Wang (S’87–M’88) received the B.Sc. andM.Sc. degrees from the Nanjing CommunicationsEngineering Institute, Nanjing, China, in 1982 and1985, respectively, and the Ph.D. degree from theUniversity of Victoria, Victoria, B.C., Canada, in1988, all in electrical engineering.

From 1987 to 1990, he was a Member of Tech-nical Staff in the Division of Radio and SatelliteNetworks, Microtel Pacific Research (now MPRTeltech), Burnaby, B.C., Canada. He was involvedin designs and implementation of various error-

correction coding and modulation schemes and spread spectrum systems usingDSP and VLSI technology. Since 1990, he has been on the faculty in theDepartment of Electrical and Computer Engineering at the University ofVictoria, where he is an Associate Professor. He has been a consultant toseveral Canadian companies and Government agencies on spread spectrumand wireless communications. During 1995, he was a Visiting Professor inthe Department of Information and Computer Sciences, Saitama University,Japan, as a Research Fellow of Telecommunications Advancement Organ-ization of Japan. Since April of 1993, he has been a Fellow of BritishColumbia Advanced Systems Institute. His current research interests includespread spectrum communications, personal wireless communications, anderror-control coding.

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