Performance of Parallel Combinatory Spread Spectrum
`Multiple Access Communication Systems
`Jinkang Zhu**
`
`Shigenobu Sasaki*
`(e-mail: kojiro @ voscc. nagaokaut. ac. jp)
`* Nagaoka University of Technology, Japan.
`1603- 1, Kamitomioka-cho, Nagaoka, Niigata, 940-21, JAPAN
`** University of Science and Technology of China,China
`Hefei, Anhui, 331134, Peoples republic of CHINA.
`
`Gen Marubayashi*
`
`Abstract
`In this paper, several results of study for
`our newly proposed parallel
`combinatory
`spread spectrum communication system are
`presented. The proposed system can transmit
`1.58N bits of
`information for a period of
`spreading
`sequence of
`length N
`in
`the
`maximum. For multiple access performance,
`more than 47% improvement of the spectral
`efficiency is achieved by the proposed system
`compared
`to conventional direct
`sequence
`spread spectrum system.
`1 .Introduction
`spread
`of
`application
`For commercial
`spectrum communication system, one of the
`most
`important problem
`the spectral
`is
`efficiency. Under band-limited condition, the
`higher the transmission rate is, the smaller
`the spreading
`factor gets, and performance
`merit obtained by spectrum spreading will be
`reduced.
`
`In this paper, several results of study for
`our newly
`proposed parallel combinatory
`spread
`spectrum
`(PC-SS)
`communication
`s y s t e m [ l ] are presented. The PC-SS system
`can transmit almost 1.58N information bits
`for a period of the pseudo-noise(PN) sequence
`length N. We discuss multiple access
`of
`performance,
`and
`show more
`than 47%
`
`data 1 data 2
`
`* - - - '
`
`PN PN
`
`- - - - a
`
`PN
`
`i n the spectral efficiency
`improvement
`is
`achieved by the PC-SS system compared t o
`conventional direct sequence spread spectrum
`(DS-SS) system at the same spreading factor,
`without error correction coding.
`
`In the following, fundamental principle
`PC-SS
`and
`system
`model
`of
`the
`communication
`system, average bit error
`probability
`of
`informations
`after
`the
`transmission i n
`additive white gaussian
`noise
`(AWGN) environment, and multiple
`access performance are shown.
`
`Spread
`2.Parallel Combinatory
`Spectrum Communication S y s t e m
`2 . 1 P r i n c i p l e s
`In conventional DS-SS system, one PN
`sequence
`i s assigned
`for one user,
`and
`transmit information by multiplying factor + 1
`o r -1 for each period of PN sequence. In the
`total of M orthogonal
`PC-SS system, a
`sequences are assigned for one user, and a
`total of r sequences(rch4) with multiplying
`factor + 1 o r -1
`are transmitted i n parallel
`correspond t o each state of every k data bits.
`Data format of conventional DS-SS system
`and the PC-SS system are shown i n Fig. 1.
`
`The amount of
`
`transmitting
`
`information
`
`ata 1 data2 ----. data k
`
`PN r
`
`(a) DS-SS system
`
`(b) Pc-ss system
`
`Fig.1 Data format of DS-SS and PC-SS system
`
`ERIC-1003
`Ericsson v. IV
`Page 1 of 5
`
`

`

`transmitter
`
`channel
`
`1"' .
`
`serial to
`parallel
`
`k
`i n p u t +b
`
`I
`
`weight
`
`state
`
`* of transmitted +
`
`decide state
`
`sequence
`r
`
`square
`law
`
`decoder
`
`receiver
`
`Fig.:! PC-SS communication system model
`
`serial
`
`o u t p u t
`
`per period of PN sequence are
`( 1 )
`( b i t s )
`k = r + [ l o g 2 ( M C r ) ]
`where [XI indicates the maximal integer which
`i s less than or equal to x . In the special case,
`when r = l , this system is the same as the M -
`ary S S system[2] with multiplying factor + 1
`o r -1, and r=M, i t i s simple S S parallel
`transmission
`system
`(i.e.
`code division
`multiplexing by one user). When M i s equal
`t o PN length N, an# r=M/4, k = N is obtained
`after short calculations. And when M i s equal
`i s
`to PN length N, and r=2M/3, kw1.58N
`obtained for large N.
`
`2 . 2 S y s t e m M o d e l
`The system model of the PC-SS system for
`baseband transmission i s shown i n Fig.2.
`
`that number of
`implies
`(1)
`Equation
`t o represent all
`information bits necessary
`combinations of sign k l for a selected r
`sequences i s r, and number of information bits
`necessary
`t o represent all combinations of
`from M
`choosing
`r
`is
`(k-r). Considering
`these, we
`find a
`reasonable method of
`constructing circuit as follows.
`
`First, k serial data bits with information
`rate Rb is converted to k parallel data with
`rate Rb/k. Next, we take particularly settled r
`parallel channels for attaching + o r - sign to a
`
`r
`
`
`
`( 2 )
`
`S = ( S I 9 ~ 2
`
`,
`S i € { + 1 , - 1 }
`Then, remaining k-r bits are used for the
`representation of a combination of sequences.
`This can be represented by constant weight
`code of length M and weight r
`c = ( c i , c 2 , c 3 , . . . ! CM).
`C i E ( 0 9 1 )
`Using C of eq.(3), r transmitting sequences
`are selected from the orthogonal sequence set
`PN(t)=(PN, (t),PNZ(t), . . . ,PNM(t)).
`(4)
`And multiplying each selected sequence with
`each element of S, we
`finally get
`a
`transmitting signal. Output signal of
`the
`transmitter appears as (r+ 1) level signal.
`
`state of
`sequences. A
`combination of
`transmitted sequences i s represented by
`..., ~ r ) .
`
`~
`
`3
`
`1
`
`
`
`( 3 )
`
`In the receiver, received signal is correlated
`with each of M orthogonal sequences which is
`the same as used i n the transmitter. To make
`estimation of r transmitted sequences, each
`output of
`the correlator
`i s squared
`and
`compared, and r sequences which has larger
`values than others are selected. The sign of
`these sequences can be obtained by zero-level
`decision as shown
`i n Fig.2. And from r
`combination of M , (k-r) bits of information
`are decoded by constant weight decoding.
`Finally we get the receiver output through
`parallel to serial conversion.
`
`Page 2 of 5
`
`

`

`2 . 3 B i t E r r o r P r o b a b i l i t y
`The average bit error probability of PC-SS
`system can be calculated similarly as M-ary
`system with orthogonal signals[3]. It i s given
`by
`
`the probability
`Here, X2(u;n,h) indicates
`density function of noncentral X2-distribution
`freedom n and noncentral
`with degrees of
`parameter h . And X2(u;n)
`indicates
`the
`x2-
`probability
`density
`function
`of
`distribution with degrees of freedom n. Q(x)
`i s
`the distribution
`function
`of
`normal
`distribution expresced as
`X
`
`Q, (x)=- 1
`
`,(exp(-$ciu. 6m
`
`results of average bit error
`Calculated
`vs
`signal-to-noise
`ratio
`per
`probability
`information bit of
`the PC-SS
`system
`is
`shown in Fig.3. As an example, for N = 32
`and information rate is nearly equal t o PN
`chip rate, necessary E d N o of
`the PC-SS
`system i s 1dB better than that of conventional
`bipolar NRZ system for bit error probability
`of 10-5.
`3.Multiple Access Performance
`3 . 1 S S M A S y s t e m M o d e l and R e q u i r e d
`Eb/NO
`is
`System model of PC-SSMA system
`shown in Fig.4. ~i is time delay of i-th user.
`In the spread spectrum multiple access
`(SSMA) communication, most serious noise
`i s the interference from other users. Average
`signal-to-noise ratio of the DS-SSMA system
`has been analyzed by Pursley[4]. Using
`similar
`calculations,
`assuming
`baseband
`signal, signal-to-noise ratio per information
`bit can be obtained approximately
`
`I 0-'
`
`lo"
`P
`ob
`
`1 o - ~
`
`i oe5
`0
`
`2
`
`4
`
`6
`
`8
`
`1
`
`0
`
`E,/N*
`Fig. 3 Average bit error probability
`
`2
`
`
`
`1
`(dB)
`
`-
`
`i
`
`PC-ss
`
`Fig.4 PC-SSMA system model
`
`Page 3 of 5
`
`

`

`Eb
`
`4(Ks-I)
`
`- 1
`
`(7)
`
`In which, Eb is energy per information bit,
`NO and NO' represent
`respectively noise
`spectral density without o r with interference
`from other users. K, is the number of users,
`and N is the length of PN sequence (equal to
`spreading factor).
`
`This analysis can be easily extended to the
`PC-SSMA
`system. Since an orthogonal
`sequence set are used for each user, there i s no
`interlerence from the other channels of
`the
`same user. From
`the other users,
`all
`transmitted r sequences interfere with desired
`signal. Taking
`into
`these considerations,
`assuming random sequences are used, average
`signal-to-noise ratio for correlation output
`can be obtained as
`
`P I T
`NO
`
`4r(Ks-1)
`3N
`
`(8)
`
`the power of
`represents
`where P1
`transmitted sequence, and T
`represents
`period of the sequence. Since
`
`each
`the
`
`(9)
`r P l T = kEb,
`we get signal-to-noise ratio per information
`bit as
`
`For DS-SS system, spreading factor Fs i s
`the same as N. But, for the PC-SS system,
`apparentspreading factor Fs is given by Nlk.
`Noting this, eq.(7) and eq.(10) represent as
`
`3 . 2 T h e S p e c t r a l E f f i c i e n c y
`The spectral efficiency is defined as
`v=-.
`KsRb
`WS
`In which, Ks is the number of users, Rb i s
`information data, and Ws i s
`the rate of
`channel bandwidth. And, Ws/Rb i s equal to
`the spreading factor Fs. From eq(lO),
`the
`number of users Ks is obtained as
`
`Substituting (13) into (12), the spectral
`efficiency can be represented as
`
`'p,
`- y * I.
`
`Eb
`
`Eb
`
`Fs
`
`q =
`
`is
`When Fs
`approximated as
`
`large, q can be closely
`
`the spectral efficiency vs.
`Fig.4 shows
`i n several case of M , when the bit
`Eb/NO
`error probability is l o m 5 . For example, Eb/NO
`is equal to 2O(dB), in the case of M = 3 2 , the
`spectral efficiency of PC-SSMA system
`i s
`almost double compared to conventional DS-
`SSMA system.
`
`the
`the comparison of
`Table 1 shows
`spectral efficiency of the DS-SSMA and the
`PC-SSMA
`system when
`the
`bit
`error
`For example, when Fs i s
`probability i s
`improvement
`i n the
`the same, some 4 7 %
`spectral efficiency i s achieved by the PC-
`S S M A system with M=16, r=2 and k=8
`compared to conventional DS-SSMA system,
`without error-correction coding. The more the
`sequences
`for one user,
`the more
`the
`improvement i n the spectral efficiency can be
`achieved.
`
`F
`
`Oq4
`
`--tDS-SS
`M= 1 6, k=8
`--bM=32, k= I 0
`0-3 j t M = 6 4 , k = 1 2
`rl
`-t-M=256,
`k=l6
`0.2
`
`0.1
`
`0
`5
`
`10 E L N O
`Fig.4 The spectral efficiency vs. Eb/NO
`(baseband, r=2, BER=10-5)
`
`l5
`
`(dB)
`
`20
`
`Page 4 of 5
`
`

`

`SSMA system
`DS-SSMA
`
`PC-SSMA
`
`M
`
`16
`32
`64
`256
`1024
`
`E@o'[dB]
`9.55
`7.89
`7.15
`6.55
`5.7
`5.12
`
`tl
`0.083
`0.122
`0.144
`0.166
`0.202
`0.230
`
`4. Conclusion
`spread
`combinatory
`Proposed
`parallel
`spectrum communication
`system has
`the
`following advantages.
`(1) High-speed
`avail able.
`(2) Multiple access performance can be
`DS-SSMA
`improved
`from
`conventional
`system with
`the
`same
`spreading
`factor,
`without error correction coding.
`
`is
`
`data
`
`transmission
`
`JL&xxms
`"Parallel
`and G.Marubayashi:
`J.Zhu
`[ 11
`SS communication",
`IEICE
`combinatory
`Technical Report, SSTA90-23, Jun. 1990.(In
`Japanese)
`:"Spread
`[2] P.K. Enge and D.V. Sarwate
`spectrum multiple access performance of
`orthogonal codes : Linear
`receivers",
`IEEE
`Trans. Commun., COM-35, 12, pp.1309-
`1319(Dec.1987).
`[3] A. J . Viterbi : "Principles of coherent
`communication ", McGraw-Hill Book, 1966.
`141 M.B.Pursley:"Performance evaluation of
`phase-coded spread spectrum multiple access
`- part I: system analysis",
`communication
`IEEE Trans. on Commun. COM-25,
`8,
`pp.795-799, Aug. 1977.
`
`Page 5 of 5
`
`