Performance Evaluation of Parallel Combinatory
`SSMA Systems in Rayleigh Fading Channel
`
`Shigenobu Sasaki t, Hisakazu Kikuchit, Hiromichi Watanabe', Jinkang Zhu" and Gen Marubayashittt
`
`t Faculty of Engineering, Niigata University, Ikarashi-2, Niigata, 950-21, JAPAN
`[E-mail: kojiro@ee.eng.niigata-u.ac.jp]
`tt University of Science and Technology of China, Hefei, Anhui, 230027, P. R. CHINA
`Faculty of Engineering, Soka University, Hachioji, Tokyo, 192, JAPAN
`
`Abstract The multiple access performance of parallel
`combinptory
`spread
`spectrum(PC/SS) communication
`aystems in Rayleigh fading channel is studied. The PC/SS
`system has the high-speed data transmission capability by
`transmitting multiple pseudo-noise sequences out of the pre-
`assigned sequence set. The performance is evaluated in terms
`of average bit error rate by numerical computation. Focus is
`put on the frequency-nonselective, slowly fading channel.
`It is found that the multiple access performance of the
`PUSS system including diversity is superior to that of
`conventional direct-sequence spread spectrum systems. Reed-
`Solomon coding to the PC/SS system improves of the multiple
`access performance.
`1. Introduction
`Recently, study on wireless information networks is an
`attractive area for future personal multimedia communication,
`mobile computing, and high-speed wireless local area
`networks, etc.[l] Spread spectrum (SS) technique is a
`promising way to provide efficient use of the frequency
`bandwidth in these area. In cellular mobile communication
`systems, SS techniques are expected to provide the high
`channel capacity over than conventional systems [2]. In Japan,
`since 2.4 GHz ISM band was assigned to the SS systems at
`thc end of 1992, many studies on SS wireless information
`networks have been initiated.
`In future wireless communication systems, high-speed
`data transmission capability is required. However, if we desire
`high-speed data transmission by the SS technique, a part of
`the advantage of the SS technique might be spoiled because
`of insufficient spectrum spreading owing to the limited
`bandwidth of a radio channel. To keep the performance merit
`offered by spectrum spreading, we need to develop another
`SS technique with high data rate transmission capability.
`For this purpose, parallel combinatory spread spectrum
`(PUSS) communication systems have k e n proposed [3]. In
`the PUSS system, multiple pseudo-noise (PN) sequences
`arc simultaneously transmitted out ofa pre-assigned spreading
`sequence set. The PN sequences for transmission depend on
`the state of aset of data bits. Direct sequence spread spectrum
`system using binary orthogonal signaling [6]-(81 is just a
`subset of the PUSS system. Up to now, a brief analysis was
`reported for the additive white gaussian noise (AWGN)
`environment [3]-[j].
`
`This paper addresses the error rate performance of pardel
`combitlatory spread spectrum multiple access (PC/SSMA)
`communication systems in Rayleigh fading channel. To
`simplify the analysis and discussions, focus is put on the
`case of frequency-nonselective, slowly fading channel.
`The diversity technique and the error-control codiiig are
`very effective to reduce the performance degradation caused
`by fading. Hence, the performance improvement by using
`these techniques is also studied.
`In the next section, a system model of the PC/SSMA
`systems and a channel model are described. In section 3, we
`analyzc the influence of the multiple access interference of
`the PC/SSMA systems and describe the error rate performance
`of the PC/SSMA systems in Rayleigh fading channel. The
`effect of Reed-Solomon coding for the PC/SS system to
`combat with the Rayleigh fading is also described in this
`section. Performance evaluation by numerical computation
`is presented in section 4, and we conclude our results in
`section 5.
`2. System and Channel Model
`2.1 PC/SS transmitter model
`In the transmitter, a set of M orthogonal sequences with
`chip duration T, are assigned. That is,
`a(n) = (a?), a t ) , a?), . . .,
`(1)
`a y ) = (a$), a$), ai";), . . ., a$),.l)) a$) E 1-1, t1)
`is the jth element of ith spreading sequence of the
`where $)
`rith user. N stands for the length of assigned sequence. An
`input data sequence with duration Td is written as
`d t ) = (dp', d$), . . ., 4)).
`d F ) E (0, 1)
`?he data in (2) is converted to the data of k parallel channels
`In the mapping circuit, r
`with duration T(=kT,%J.
`transmitting PN sequences are chosen from the Morthogonal
`PN sequences which an assigned for a particular user.
`The mapping method is carried out as follows. First, we
`split d t ) into two parts:
`
`(3
`
`(3)
`
`(4)
`d p ) represent the polarity of r transmitting PN sequences.
`n e state of d p ) specifies a particular set of r transmitting
`PN sequences among the M PN sequences.
`
`0-7803-1750-5/94/S3.00 8 1994 IEEE
`
`198
`
`ERIC-1002
`Ericsson v. IV
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`For choosing the PN sequences to be transmitted, d p ) is
`coded into a constant weight code of length M and weight r.
`This is referred to as (M, r ) constant weight code, and is
`written by
`
`C Y ) € {O, l}
`A set of r PN sequences for simultaneous transmission is
`determined by choosing ith PN sequence such that cy' = 1.
`The set of transmitting PN sequences is expressed by
`" (rz) = (Q), "p, . . ., "p),
`
`(6)
`
`The signature of the transmitted PN sequence is obtained
`from (3). It is written by
`b(") =(b?), $), b:),
`hi(") = (-1)4"'
`Ncxt, the state word of transmitting sequence is multiplied
`with the PN sequence set to form a transmitting signal.
`
`. . , b?').
`
`(7)
`
`A, refers to the magnitude of a transmitting PN sequence.
`PTc(t) represents the chip waveform. If the chip waveform is
`the rectangular pulse, it is given by
`
`(9)
`
`s,(n'(t) is a multi-level signal with ( r + l ) levels. Multiplying it
`with a carrier, the transmitter output is obtained as
`sn(r) = sp)(r)cos mr
`(10)
`where (I), is the carrier frequency. The carrier phase is assumed
`to Ix zero.
`2.2 Channel model
`In this papcr, slowly frcquency-nonselcctivc fading is
`assumcd. Let K be the number of simultaneous users in a
`channel, and transmission signals be faded independently.
`Then, by using a fading channel model in [9], the receiver
`input is of the form
`
`,I = I
`is the additive white gaussian noise (AWGN). p
`where
`is path gain, t is path delay, and e is path phase.
`It is assumed that
`has the Rayleigh distribution of
`which probability density function is given by
`
`In the decision part, the r-out-of-M combination of
`transmitted PN sequences is estimated from the matchcd
`filter outputs. Larger r elements in terms of the squared
`magnitude of yy)are decoded to '1,' and theothers are decoded
`to '0.' The estimate is transformed into a constant weight
`code
`. . ., .$If) .
`c(n)i = ( 1
`(17)
`# ) I ,
`$),,
`,(n)l,
`Passing c(")' through the (M, r ) constant weight decoder, the
`data are decoded into
`z p = (z;;, z;;, ZZi, ' ' ', 2,"') .
`(18)
`From the matched filter output in (14) and constant weight
`code c (")', we get the signature-dependent data
`zp = ($), zy, $1,
`. . ., $1)
`
`(19)
`
`Finally, the receiver output is obtained through parallel
`to serial conversion.
`In this paper, we assume the perfect synchronization of
`carrier and PN sequences between a transmitter of a desired
`user and a receiver.
`3. Performance Analysis
`3.1 Multiple access interference
`In the SSh4A environment, the output signal of a matched
`filter consists of a desired signal, interference signal, and
`thermal noise. Let us consider the receiver of the first uscr:
`y p ) in (15) is expressed by
`+ ldi) + r)i
`yi(l) = + ~ ~ ( i )
`Di = A l p l n i ( l )
`
`(22)
`
`(21)
`
`where U,? is the average power of faded signal. The pdf for
`the instantaneous signal-to-noise ratio (SNR) y is given by
`
`whcre Tis thc average SNR. It is also assumed that 0 has
`thc uniform distribution over (0, 2n].
`2.3 Receiver model
`At the rccciver, M matched filters are used to despread
`the receivedsignal. Amatched filter is matchcd to the assigned
`spreading sequence that is the same with the counterpart in a
`transmitter. The matched filter output is described as
`
`j.1
`r), is the AWGN component of which power spectral density
`is N&. Di represents the desired component. L(i) represents
`the selfiriterfererrce from other transmitted sequences of the
`desired user. One can avoid such interference by assigning
`different orthogonal codes to a user. In this case, as dcscrihcd
`above, r, and 0, are assumed to be 0. Hence, thc sclf-
`interference in (23) reduces to zero.
`Ic(i) is the multiple access interference (MAI) from
`undesired users. b/';n'! and b:;) are the previous and present
`199
`
`Page 2 of 5
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`

`

`Pci = [ xz(u;l,p). [[ ,&;I)
`
`(34)
` du
`d v r
`where the SNR per information bit becomes yb = (r/k)yo.
`The- average SNR per transmitted PN sequence at the
`output of a matched filter ro is written by
`r -L A 2 ~ 2 E(p ')
`.
`(35)
`a -
`%f
`In a fading environment, the received power varies over
`an extremely wide range. If M, r and k are fixed in (30) and
`(31), error rate is written as a function of y. Generally, the
`error rate performance in fading channel is given by
`
`Pe' =
`
`Pe(y)P(y)dy
`
`(36)
`
`l
`
`bit of j th signature in itth user, respectively. They are. assumed
`to be +1 or -1 with equal probability. z. and q5" are the
`difference of arrival time and phase between the path of the
`first user and the path of the irth user, respectively. q and
`arc 0. It is also assumed that
`is uniformly distributed over
`10, 2111. /jn is the path gain which has the Rayleigh distribution.
`Rio"), j ( n j ( r ) and R i ( m A j(n,(r) are the partial crosscorrelation
`functions (see Ref.[lO][ll]).
`Since a PC/SS system transmits r PN sequences
`simultaneously for one user, any matched filter output at a
`specific user is interfered by r PN sequences of every other
`user. MAI in auser hasthe same path gainand phase difference,
`and thus the variance of MAI term is expressed by
`
`(3)
`Sincc the PN sequence used here is random, the variance of
`thc crosscorrelation term is calculated approximately as
`I IO][ 111:
`
`From thc dcfinition of (13),
`
`If the power control is ideal, (25) is expressed as
`
`In this paper, the interference term is approximated by a
`zcro mean gaussian random variable. The total variance of
`intcrfcrcncc and thcrmal noise is expressed by
`= &W,(i) t vi) .
`(299)
`3.2 Symbol and bit error rate of the PC/SSMA system
`The performance of the PC/SSMA systems described
`above is evaluated in terms of error rate characteristics.
`The symbol error rate (SER) of the PUSS system with
`complete coherent detection in an AWGNchannelis described
`in 141. That is written approximately by
`
`where p(y) is the pdf of input energy-to-noise ratio at a
`receiver. Substituting (14) and (31) into (36), one gets the
`bit error rate in Rayleigh fading channel.
`33Error rate ofthe PC/SS systems with selection diversity
`Diversity technique gives a gain against the influence of
`large channel attenuation. Our interest is in frequency-
`nonselective fading. Thus, we consider in the case of explicit
`diversity. We study the case of selective combining method
`among a few combining methods as it is easy to implement.
`The diversity by selective combining method (we call this
`selecriori diversiry) is to select the strongest signal from a set
`of signals carrying the same information.
`The received signal on every branch is assumed to be
`equally distributed and mutually independent. The pdf of y
`with selection diversity is described as
`
`(37)
`where J is the number of branches and Tis average SNR of
`a single branch. The error rate is obtained by substituting
`(37) into p(y) of (36).
`3.4 Reed-Solomon coding for PC/SS systems
`It is advantageous to combine the error control coding
`with the FWSS technique for improving the emor rate
`performance. Since the PC/SS system transmits k bits of
`data during a PN period, Z k - q Reed-Solomon coding brings
`about a considerable improvement of error rate performances
`in AWGN channel (See Ref@]). So, we study the effect of
`RS coding in the PC/SS system in the fading channels.
`Applying bounded distance decoding, the SER is given
`
`(30)
`where y(u;/n,,l) and ,&u;in)
`are. the probability density
`functions (pdf) of U : they have noncentral and central chi-
`square distribution with in degrees of freedom and noncentral
`parameter
`respectively. yo represents the signal to noise
`ratio (SNR) per transmitted PN sequence. Hence, the SNR
`per symbol becomes ys = r p .
`The bit error rate (BER) of the PC/SS system is given by
`(31)
`
`pcb = i p c h + yP&
`
`where
`
`ifxSjitdy2isinteger mid
`'n-iGs mirt pi-j. i tjl d b-4
`otherwise
`
`. (39)
`
`P, and P,, are written as
`Pc = 1 - P e
`
`(40)
`
`- 1)
`(41)
`Pel =Pe/@
`respectively. A, is the number of codes with weight j . it
`stands for the length of codeword. It means error correction
`200
`
`Page 3 of 5
`
`

`

`( 4 3
`
`capability ofthc RS codc. Thc nuinbcr of information symbols
`p is exprcsscd by it-2h. In the rest of thc paper, this RS code
`(11, p)-RS codc. The BER is calculatcd
`is dcnotcd by
`approximately from the SER in (38),
`P,.h = fP,?
`4. Numerical Results
`The performance of the PC/SSfvl+ system in Rayleigh
`channel is evaluated through the BER performanceand is
`compared with conventional DS/SSMA system.
`Figure 1 displays the BER versus number of simultaneous
`users of the PC/SSMA system in the Rayleigh fading channel.
`The parameters of the PCiSS system are. set as k=8, M=12,
`r=2, N=84 and k=12, M=16, r=3, N=128, respectively. The
`spreading factor of the PCiSS system without error control
`coding is expressed as Nlk. In this case, the spreading factor
`is set from 10 to 11 for lMbps data transmission in the
`7.4GHz ISM band under the Japanese regulation [14]. The
`BER of conventional DS/SSMA systcm with N = l l is also
`plotted in this figure. In the case of the PC/SSMA system in
`fading channel without diversity, the BER performance of
`the PC/SSMA system is slightly worse than conventional
`DS/SSMA system. This
`is because
`the performance
`dcgradation in low, SNR is much largcr than that of DS/SSMA
`systems. However, the BER reduction by diversity techniques
`in PC/SSMA systems is larger than that of conventional
`DS/SSMA systems without error-control coding technique.
`Fig. 2 displays the BER versus the number of diversity
`branches of the PC/SSMA system with selection diversity.
`Thc average SNR per information bit on a diversity branch
`is set to 30dB. The number of simultaneous users is set to 2.
`The BER improvement of PC/SSMA system is larger than
`that of DSiSSMA systems. In the case of k=8, M=12, r=2,
`"84,
`the BER performance is better than conventional
`DSiSSMA systems when the number of diversity branches
`is more than five.
`Fig. 3 displays the BER with (16, 8)-RS coding and that
`with the combination of (16, 8)-RS coding and selection
`diversity. The parameters of the PC/SS system are k=12,
`M=16, r=3. Here, the length of the PN sequences N is set as
`64, yielding the same total ratio of spectrum spreading. It is
`found that the RS coding elevatcs the multiple access
`performance of the PC/SSMA system considerably. In the
`case of J=3, the RS coded PC/SSMA system allows 3
`simultaneous users with keeping the 10' BER.
`The BER plot versus the number of diversity branches
`of the PC/SSMA system with the (16, 8)-RS coding is shown
`in Fig. 4. There are 2 simultaneous users in this case. When
`Jz2, the BER is lower than 10' at 20 dB of the average SNR
`per information bit.
`5. Conclusion
`The performance of parallel combinatory SSMA
`communication systems over slowly, frequency- nonselective
`Rayleigh fading channel is obtained.
`On the contrary to the performance in AWGN channel,
`the BER of the PC/SSMA system is a little bit worse than
`that of conventional DS/SSMA systems. However, the BER
`performance of the PC/SSMA system including diversity
`technique is better than that of conventional DS/SSMA
`systcms. This
`result
`implies
`that more
`significant
`improvement in error rate performance will be achievable
`by PC/SS technique with RAKE receiver in frequency-
`selcctive fading channel.
`
`Applying Reed-Solomon coding to the PC/SSMA systcm,
`significant improvement in bit error rate performancc is
`achievable.
`in frequency selective fading
`Performance analysis
`channel and more effective error control coding arc left as
`further research.
`
`Acknowledgment lhis work is partially supported by lhe Grant-iil-Aid
`for Scientific Research, 05750334, the Miuistry of Education, Science
`and Culture of Japan, and the Support Center for Advanced
`Telecomniunication Technology Research of Japan.
`
`References
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`IEEE Commun Mag., Vol. 30, No. 12, pp. %115, Dec. 1997,.
`[ZIW. C Y. Lee, "Overview of Cellular CDMA," IEEE Trois. on Vrh.
`Teclr. VT40.2, pp.291-302, May 1991
`[3] J. Zhu, S . Sasakl and G. Marubayashi, "Proposal of parallel
`combinatory spread s p e c " conununication system," Train. of IEICE.,
`J74-B-11. No. 5. pp.207-214, May 1991 (In Japanese).
`[4] S. Sasaki, J. Zhu and G. Marubayashi. "Perfomlance of parallel
`conibinatory spread spectrum niultiple access communication systems,"
`Proc ofPIMRC 91, pp.204-209, Sep. 1991.
`[5] S. Sasaki. J. Zhu and G. Marubayashi, "Perfomlance of parallel
`conibinatory spread spearuni niultiple access conlniunicalion sysleni
`with the error coiitrol technique," Proc oflSSSTA 92, pp.159-162, k c .
`1992.
`[6] P.K. Enge aid D.V. Sarwate, "Spread spectrunt niultiple access
`performance of orthogonal codes: Linear receivers," IEEE Tram
`Commuir , COM-35, pp.1309-1319, Dec. 1987.
`[7] K. Pahlavan and M. Chase, "Spread-Spectruni niultiple-access
`perfomiance of orthogonal codes for indoor radio conwiunications," lEEE
`Tram. Commuir , COM-38, pp.574-577, May 1990.
`[SI S. Tachikawa and G. Marubayashi, "Performance of M-aryhpread
`spectrum multiple access communication systems." Roc. of lEEE
`hiterilotwrlol Conference of Communicotioii Sysrems. Singapore, pp.78-
`82, Nov. 1988.
`[9] J. G. Proakis, "Digital CoBmuiucatiois, 2nd Ed. ))I McCraw-Hill,
`1989.
`[lo] M. B. Pursley, "Performance evaluation of phase-coded spread
`spec" multiple access mmmunication -part I: system analysis," IEEE
`Tram. on Commuir COM-25, pp.795-799, Aug. 1977.
`[ll] M. B. Pursley and D. V. b a t e , "Performance evaluation of phase-
`parr 11: code
`coded spread spectnun multiple access communication
`sequelice analysis." IEEE Tram. on Commuir COM-25, pp.SO0-SO3,
`Aug. 1977.
`[12] G. L. Turin, " n i e effeas of multipath and fading on the perforniaoce
`of direct-sequence CDMA syslems." IEEE J. Select. Areas Com~~i~rii.
`SAC-2, pp.597-603, Jul. 1984
`[13] M. Kavehrad, "Performance of noitdivenity receivers for spread
`speei" in indoor wireless communications," AT&T Teclriiical Joiiriinl ,
`Vol. 64, No. 6, pp.1181-1210, Jul-Aug. 1985
`[14] RCR Standard Radio equipment for low power data commuiiicatioii
`system radio station. RCR SlD-33, Research & Developmat Center
`for Radio Systems, JAPAN, Mar. 1993.
`
`~
`
`20 I
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`

`BER
`i o o r
`10 '
`10
`
`10
`
`10
`
`10
`
`l o 6
`
`10
`
`10-8'
`1
`
`'! '
`2
`
`5
`4
`# of users
`Fig. 1 BER pcrformancc of the PC/SSMA system in Rayleigh
`fading channel
`
`solid line DSiSSMA
`bold line PCISSMA
`(W-12 '=2, k=8, N=84)
`
`L
`
`3
`
`6
`
`I
`7
`
`+ DSISSMA
`PCISSMA
`(M=i2, r=2. k=8, N=84)
`--)- PCISSMA
`(M=16, r=3, k.12, N=128)
`
`BER
`
`-
`
`l o 3
`
`-
`1 0 . ~
`
`-
`
`K=2
`
`i n 6
`1
`
`I "
`
`2
`
`3
`4
`# of branches
`Fig. 2 BER versus numbcr of diversity branches in the
`PCiSSMA system with evplicit diversity
`
`5
`
`6
`
`BER
`ioo r
`
`J=l
`
`I " 1
`
`
`
`2
`
`3
`
`5
`
`6
`
`7
`
`
`
`4
`# of users
`solid 1ine:DSISSMA
`bold line: PWSSMA
`(M=16, r=3,k=l?, N=63,(16,8) RS coding)
`Fig. 3 BER of the PC/SSMA system with (16, 8)-RS coding
`
`BER
`i o " r
`
`lo-*
`
`IO3
`
`10
`
`10
`
`( M 1 6 , r=3, k=12, N=64, (16,8) RS coding)
`
`/SSMA (without coding)
`
`# of branches
`Fig. 4 BER versus number of diversity branches in the
`PCBSMA system with explicit diversity and RS coding
`(2 users)
`
`202
`
`Page 5 of 5
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