Multiuser detection scheme based on canceling ... - IEEE Xplore

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 12, NO. 4, MAY 1994

593

Multiuser Detection Scheme Based on Canceling Cochannel Interference for MFSKFH-SSMA System Tetsuo Mabuchi, Ryuji Kohno, Member, IEEE, and Hideki Imai, Fellow, IEEE

Abstract- This paper proposes and investigates a multiuser detection scheme based on canceling cochannel interference (CCI) to improve spectral efficiency or to increase user capacity in an MFSK (multilevel frequency shift keying)/FH-SSMA (frequency hopping-spread spectrum multiple access) system. In the MFSK/FHSSMA system, an address code is employed as a hopping sequence to hop the carrier frequency in MFSK. In the proposed scheme, it is assumed that the address codes of all users in MFSK/FH-SSMA are known. Then, candidates of the transmitted vector which are regenerated from the timefrequency matrices decoded by all the users’ address codes are added with logical OR operation to produce candidates of the received matrix. The candidates of the received matrix are utilized in order to estimate a pattern of all users’ data symbols which has the most number of coincident entries with the received matrix. Its BER (bit error rate) performance is evaluated by theoretical analysis and computer simulation in order to show the improvement of user capacity. Moreover, we investigate a hybrid scheme combining a multiuser detection scheme and the decoding scheme of an errorcorrecting code for the coded MFSWFH-SSMA system.

I. INTRODUCTION

R

ECENTLY, much research and development of spread spectrum (SS) communication systems has been encouraged for commercial applications such as mobile communications, personal communications, and wireless LAN (local area network). To reduce the effect of selective fading, there has been much interest in frequency hopping-spread spectrum multiple access (FH-SSMA) systems because of their frequency diversity and resistance to the near-far problem. However, instead of near-far problems, FH-SSMA is hampered by collisions or hits among hopping frequencies of simultaneously accessing users, resulting in reduced user capacity. In order to reduce the hits, an MFSK (multilevel frequency shift keying)/FH-SSMA system was proposed by Goodman et al. [11. In this system, an address code was employed as a hopping sequence to hop the carrier frequency in MFSK. The MFSKFH-SSMA system is characterized by a logical OR channel. In decoding the address code, the time-frequency matrix which shows the state of frequency tones in each chip of each user is utilized. In this time-frequency matrix at the receiver, all entries which corresponds to not only the desired Manuscript received May 28, 1993; revised December 15, 1993. T. Mabuchi and R. Kohno are with Yokohama National University, Yokohama 240 Japan. H. Imai is with the Institute of Industrial Science, University of Tokyo, Tokyo 180 Japan. IEEE Log Number 9216786.

signal but also the undesired ones or cochannel interference (CCI) are detected. The entries due to the undesired signals or CCI result in decoding errors. Various schemes of canceling CCI have been proposed and investigated for DS (direct sequence)-SSMA [3]-[71, but it is not the case for FH-SSMA. The purpose of this study is to improve spectral efficiency or to increase user capacity by reducing the effect of undesired users or CCI in MFSK/FH-SSMA. In this paper, we propose and investigate a multiuser detection scheme based on canceling CCI for the MFSK/FH-SSMA system which utilizes the logical OR channel in order to improve spectral efficiency in MFSK/FH-SSMA. It is assumed that the address codes of all users are known. This is reasonable for a cell site in a cellular system. Candidates of each user’s correct data symbol are decoded by each user’s address code. Candidates of each user’s transmitted vector, which are regenerated by the encoding of each user’s address code, are added with the logical OR operation to produce a candidate of the received matrix. These operations are performed in the combination of all the candidates of each user’s correct symbol. We select a candidate of the received matrix which has the most number of coincident entries with the received matrix. Then, all the users’ data symbols can be decoded from the selected candidate of the received matrix. Its performance is evaluated by theoretical analysis and computer simulation in order to show the improvement of the user capacity. In the coded MFSKFH-SSMA system using an errorcorrecting code, a scheme which utilizes an error and erasure correction decoding was investigated [SI. In the scheme, if there are several rows having the largest number of entries in the time-frequency matrix decoded by the address code, then the received symbol which corresponds to that matrix is considered as an erasure and the error and erasure correction decoding is performed. We proposed a modified decoding scheme of the error-correcting code in order to improve user capacity [9], [lo]. In the proposed scheme, if there are several rows having the largest number of entries, each information of symbols corresponding to the rows is utilized to select candidates of the correct symbol for decoding of the errorcorrecting code. In this paper, we investigate a hybrid scheme combining the multiuser detection scheme and the modified decoding scheme of an error-correcting code, for the coded MFSKLFH-SSMA system. In the hybrid scheme, the manner of combining the multiuser detection scheme and the modified decoding scheme of the error-correcting code, with regard to each information

0733-8716/94$04.00 0 1994 IEEE

594


Transmitter

Reccivcr

v r

B8n.r"

rrn.rorm Synthesizer

Fig. 1. System model of a multiuser detection scheme based on canceling cochannel interference for the MFSK/FH-SSMA.

of symbols corresponding to rows having the largest number of entries, influences the performance and complexity. In consideration of the reduction of complexity, we investigate the hybrid scheme and evaluate its performance. The outline of this paper is as follows. In Section 11, the MFSWH-SSMA system is explained. In Section 111, a multiuser detection scheme based on canceling CCI for the MFSK/FH-SSMA system is investigated. In Section IV, the performance of a multiuser detection scheme for the MFSKFH-SSMA system is evaluated by theoretical analysis and computer simulation. In Section V, an address code assignment is investigated. In Section VI, we examine a modified scheme of the multiuser detection scheme based on canceling CCI. In Section VII, a hybrid scheme combining the multiuser detection scheme and the modified decoding scheme of an error-correcting code for the coded MFSKFH-SSMA system is investigated. Finally, in Section VIII, the main results of this paper are summarized.

11. SYSTEM MODEL Fig. 1 shows the system model of a multiuser detection scheme based on canceling CCI for the MFSKFH-SSMA system. Fig. 2 shows an example of time-frequency matrices which represent the state of the frequency tones during each chip period corresponding to each part of Fig. 1 . In this section, the conventional scheme of the MFSKFH-SSMA system is explained. In this paper, it is assumed that synchronization between users is established. In the transmitter, K message bits are stored in a shift register and transformed to a symbol with 2K levels (the subscript m denotes the mth user among M ( 5 a K ) users). In Figs. 1 and 2, without loss of generality, it is assumed that

the 0th user is the desired one and the others are the undesired ones to CCI. We consider two systems: the uncoded system and the coded system. For the coded system, the data symbols with 2K levels are encoded by an error-correcting code. The symbol with symbol duration of T is divided into L chips . producing the vector X , = (X,,O, X m , l , . . . , X m , ~ - - l )For example, ( K = 3, L = 5 ) ,Xo = (4,4,4,4,4). The matrix A0 in Fig. 2 shows an example of the data matrix derived from the vector XO. The matrices A , in Figs. 1 and 2 have a relationship with the vector X , , such that:

Am = [ail]

(1)

where ail

= S ( i , Xm,l)

(2)

6 ( i , j ) is the Kronecker's delta. The different address codes R , (m = 0,1, . . . , M - 1) with 2K levels and L chips length are assigned to the mth users. Since M 2 2, it is named an MFSKFH-SSMA system. R, = (Rm,o,Rrn,~, . . . ,R ~ , L - I )

(3)

where R,,J E { 0 , 1 , . . . , 2 K - 1 ) . Forexample ( K = 3 , L = 5) = (1,2,4,3,6)

.. .

.. .

R5 = (6,7,5,1,2)

(4)

where R,,l E {0,1,...,7}(1 = 0 , 1 , . . . , 4 ). The address code R , is added to X, according to the rule of GF(2K) (the addition is operated in binary after R , and

MABUCHI et al.: MULTIUSER DETECTION SCHEME

Coded m a t r i x

Bn

ll.rclrcll

nlrlrlr

c

Decoded m a t r i x

Dg

6 S

4

3 2 I

0

7 6 S i

3 2

1 0

6 S

i 3

2 I

0

-

. . ..

..

I chip

Fig. 2. An example of the multiuser detection scheme based on canceling cochannel interference for the MFSK/FH-SSMA (2K=8. L=5, M=6 or five undesired users).

X, are transformed to binary digits, see Appendix A) to prod l l w the transmitted vector Y, = (Y,,o, y , , ~ ,. . ,Y , , L - ~ ) . Ym=Xm+R,

(5)

where Y,J, X,,J, and R,,J E { 0, 1, . . . , 2K - 1). For example ( K = 3 , L = 5),

.

.

Y5 = ( 1 , 1 , 1 , 1 , 1 )+ ( 6 , 7 , 5 , 1 , 2 ) =(7,6,4,0,3)

596


where Y m , l , X m , and R,J E { 0 , 1 , ~ ~ ~ ,The 7 } .matrix BO in Fig. 2 shows an example of the transmitted matrix derived Here, the matrices B, in Figs. 1 and 2 from the vector YO. are represented by the vector Y, in the same manner as (1). A tone signal selected from a set of 2K frequencies corresponding to the value of each entry Ym,lof the vector Y, is transmitted as an MFSK signal. Therefore, L frequency tones per data symbol are transmitted in serial. In the mth user’s receiver, all entries which correspond to not only the desired signal but also the undesired signal or CCI are detected. The matrix C in Figs. 1 and 2 shows an example of the received matrix derived from logical OR operation of the detected vectors Fn ( n = 0 , 1 , . . . ,M - 1). If m = n and there are not the effects of noise and fading, the detected vector Y, coincides with the transmitted vector Y,. The received matrix C can be expressed by:

c = [Cill

(7)

Before starting to describe the proposed scheme, its overview should be explained. In a conventional singleuser detection scheme, all users’ data symbols are decoded independently. However, the multiuser detection .scheme decodes all user’s data symbols interactively. From all users’ decoded matrices, every possible combination of all users’ data symbols can be estimated. Provided that the individual combination of all users’ data symbols is transmitted, the corresponded received matrix can be reconstructed. This received matrix indicates a candidate of all user’s data symbols. By means of comparing these candidate matrices with the actual received matrix, the proposed scheme can decode all users’ data symbols. We name the row having the largest number of entries as “the majority row.” A . Candidates of the Correct Data Symbol

In the proposed scheme, we can consider various modified schemes of selecting candidates of the correct data symbol. M-1 First, the proposed scheme is investigated in an interference~ i= l b(i,Fn,l) (8) only channel. In this channel, decoding errors in the conn=O ventional MFSK/FH-SSMA system occur when there are S ( i , j ) is the Kronecker’s delta. several rows having the largest number of entries, L , in the The address code R,, which is equal to the address time-frequency matrix. This matrix does contain the correct code in transmitter, is subtracted from the detected vec- row consisting of desired user’s entries and rows consisttor Y,( n = 0 , 1 , . . . , M - 1) according to the rule ing of several undesired users’ entries or CCI. Therefore, of G F ( 2 K ) to produce the decoded vector Z,,, = even if only the symbols corresponding to several major(Zrn,n,O,Zm,n,l,...,Zrn,n,L-l)(n = 0 , 1 , . . . , M - 1). ity rows are considered as candidates of the correct data symbol, the data symbol of the desired user are certainly zm,n =Yn contained in the candidates, achieving a maximum likelihood - - R, = X, R, - R,. (9) scheme. Second, the proposed scheme is investigated in an additive When m = n, Z,,,(= = X,) shows the desired user’s white Gaussian noise (AWGN) channel and a Rayleigh fading vector. Thus, the desired user’s data can be decoded. For channel. In these channels, there are the effects of deletion example ( K = 3, L = 5), and false alarm. Deletion means that no entry is detected in some slot in the time-frequency matrix although it has z0,o = ( 5 , 6 , 0 , 7 , 2 )- (1,2 , 4 , 3 , 6 ) been transmitted. False alarm means that an entry is detected = (4,4,4,4,4) where none has been transmitted. Consequently, decoding errors in the conventional MFSKFH-SSMA system occur . . in two ways: one is when there are several majority rows 2 0 , 5 = (7,6,4,0,3) - (1,2,4,3,6) in the time-frequency matrix, which contain the correct row =(6,4,0,3,7) (10) consisting of the desired user’s entries, and rows consisting of several undesired users’ entries or CCI; another is when the where ZO,Oshows the desired user’s vector. The matrix DO in Fig. 2 shows an example of the decoded correct row has less entries than rows consisting of several undesired users’ entries or CCI. Therefore, in order to achieve matrix derived from the vectors a maximum likelihood scheme, all the symbols must be z m , n = (ZO,n,O,ZO,n,lr.‘ ‘ 1 ZO,n,4) ( n o,I, ’ ’ . 15). utilized as candidates of the correct data symbol. However, complexity increases considerably. The matrices D, in Figs. 1 and 2 are represented by the Since the probability that the correct row corresponding to vector Z m , , in the same manner as (7). the desired symbol has the largest number of entries is great, in most of this paper, we investigate a scheme which utilizes 111. A MULTIUSER DETECTION SCHEME BASEDON CANCELING symbols corresponding to the majority rows as candidates COCHANNEL INTERFERENCE FOR MFSKFH-SSMA SYSTEM of the correct data symbol. However, Section VI investigate In this section, a multiuser detection scheme based on schemes that utilize not only the symbols corresponding to canceling CCI which utilizes the logical OR channel for the majority rows but also the symbols corresponding to rows MFSKFH-SSMA systems is proposed in order to reduce the having a fewer number of entries than the majority rows as candidates of the correct data symbol. effect of CCI. where

U

+

x,

597


B . An Algorithm of Proposed Multiuser Detection Scheme We introduce an algorithm of the proposed multiuser detection scheme for the MFSK/FH-SSMA system, in which symbols corresponding to the majority rows are considered as candidates of the correct data symbol. 1) The matrices D, ( m= 0,1, . . ., 5 ) in Fig, 2 show each user's time-frequency matrices decoded by each user's address code &. Zm,n,~ ( m = O , l , . .. , 5) shows an entry of the vectors Z,,n decoded by the address codes or an entry of the matrices D,. The subscript n denotes entries of the nth user. When n = m, Zm,n,i shows a entry of the desired user

(y=F)-(" )

In this section, performance of the MFSK/FH-SSMA system using the conventional receiver and the proposed receiver for multiuser detection scheme is theoretically analyzed. Moreover, we investigate the reduction of complexity for the proposed multiuser detection scheme. It is assumed that an address code assigned to each user is arbitrarily selected from (2K)L different vectors which are all possible patterns of a vector with 2K levels and L chips. A . Conventional Receiver Let the deletion probability be p ~ The . probability that there is an entry in one slot of an incorrect symbol row in the time-frequency matrix, p , is represented by:

-

r)+(?-( Y,

ZM-l,n

IV. PERFORMANCE OF MULTIUSER DETECTIONSCHEME BASEDON CANCELING COCHANNEL bTERFERENCE

RM-1

p = [l - (1 - 2-K)M-'](1 - P o ) .

-

Xn

Let the probability that there is an entry due to the false alarm be p ~ The . overall insertion probability for one slot in the time-frequency matrix, P I , is written as:

").

-

R,

(n=O,l;..,M-l)

(13)

RM-1

(1 1)

2 ) Let ,i (1 5 ,i 5 a K ) be the number of the majority rows in the time-frequency matrix decoded by the address code. Symbols corresponding to the majority rows (1 5 ,i 5 a K ) in the matrices D, ( m = 0 , 1 , . . . , 5 ) in Fig. 2 are considered as candidates of the correct data symbol of each user, Xm,j ( j = 0 , 1 , . . . ,i, - 1). The matrices DL ( m = 0,1, . . . , 5 ) in Fig. 2 show examples of the symbol matrix derived from vector X,, respectively. 3) We regenerate replicas of all the users' transmitted vectors. Then, the encoding of the address code for every combination of candidates of all the user's correct data symbols is performed. Consequently, we c? derive candidates of the correct transmitted vectors W m , j = ( @ r n , j , O , @ m , j , l , . . .,@ r n , j , L - I ) ( j = 0 , 1 , . . . ,im - 1). matrices Em,j in Figs. 1 and 2 show examples of the canceling matrix derived from the vector ~ , , j , respectively

The probability that there are m entries in one row in the time-frequency matrix, Ps (m,P I ) , is described by:

Over the 2 K - 1 incorrect rows, the probability that n is the maximum number of entries and that exactly k unwanted rows contain n entries, P ( n ,k , p ~ )is, represented by:

(16) Now consider the correct symbol row. The probability that there is an entry in this row is 1- p~ and the probability that there are i entries in this row, P c ( i , p ~ )is, written as:

Thus, the word error probability P w ( M ) is described by:

( j = 0 , 1 , . . . ,i, - 1).

(12) The bit error probability Pb(M) is represented by:

These candidates of the transmitted vectors j,% are added with logical OR operation. Then, we can derive ,2 M-1 . candidates of the received matrix Ft (t = 0,1, . . . ,IIrnE0 2, 1). The matrices Ft in Figs. I and 2 show examples of the candidat: matrix derived from logical OR operation of the vector W , , j , respectively. 4) We select one among the candidate matrices Ft (t = 0 , l ) in Fig. 2, which has the most number of coincident entries with entries of the received matrix C in Fig. 2. Consequently, we can decode the data symbols of all the users from the selected candidate matrix.

nfzd

2K-1

Pb(M) =

~

2K -

PW(W

1

(19)

where p~ and p~ in an AWGN channel are, respectively, written as: pF = exp

(-$)


598

TABLE I PARAMETERS OF COMPUTER SIMULATION

7 Bit R a t e

1

Total Bandwidth and p~ and p~ in a Rayleigh fading channel are, respectively, written as:

16

T h e Length of Address Code, L

1 T h e Total Number of D a t a Bits P

-

(z(1+3)

(24)

where ,B denotes the actual threshold divided by the rms receiver noise.

j = 1 1=0

2K-1

-

The probability that data is incorrectly decoded in the undesired users’ matrix D, ( m = 1 , 2 , . . . , M - 1) because there are more than two majority rows, PWCCI,is described by:

The probability that in the matrix DO,s tones out of L tones of the desired user do not coincide with any tones of M - j undesired users and t tones out of L tones of false alarm is detected, P C O I N M ( ~ ,- j ) , is expressed by:

where

Moreover, the probability that CCI from M - j out of M users are canceled where only 1 out of the M - j users’ data - j , l ) , is represented by: are correct, PCAN(M

PCAN(M - j , 1) = M-j-1

PAcIPwCcI

. (1 - PCCI - PWcc1)j-l.

(29)

L

i=o 2K-1

B. Receiver with the Proposed Scheme of Multiuser Detection

L

5

1 100,000 I

Thus, the word error probability P w ( M ) can be described by: M M-.I

Equations (13)-(17) can be used as well as in the conventional receiver. The probability that data is correctly decoded in the undesired users’ matrix D , ( m = 1 , 2 , . . . , M - 1), PCCI,is represented by:

I

40kHz

One Slot Bandwidth T h e Number of Frequency Level, 2“

p~ = 1 - exp

32kbps 640kHz

-

where p c= ~ [1 - (1 - 2-K)m-1-1](1- P O ) .

(31)

Consequently, the bit error probability P b ( M ) can be represented by: 2K-1 Pb(M) = PW ( M ) (32) 2K - 1 where p~ and p~ are the same as (20) and (21) in an AWGN channel and (23) and (24) in a Rayleigh fading channel. Figs. 3 and 4 show BER versus the number of users which are derived by theoretical analysis and computer simulation for the conventional scheme and the proposed scheme. The P b ( M ) were numerically calculated with 2K = 16, L = 5, and ,!&/No = 00 in an interference-only channel in Fig. 3 and with 2K = 16, L = 5, and &/No = 16 dB in an AWGN channel in Fig. 4. Table I shows the parameters of computer simulation. Since the number of data bits per subset of the address codes is 20,000 bits and five subsets of the address codes are utilized, the total number of all the users’ data is 100,000 bits. Each subset consists of the address codes Ro N R15 dependent on the number of users. The address code assigned to each user is arbitrarily selected from 165 different vectors, which are all possible patterns of a vector with 16 levels and five chips. Figs. 5 and 6 show BER of all users versus the number of users which are derived by theoretical analysis for the conventional scheme and the proposed scheme. The Pb(M) were numerically calculated with 2K = 256, L = 10, and & , / N o = 00 in an interference-only channel in Fig. 5 and with 2K = 256,L = 10, and &/No = 25 dB in a Rayleigh fading channel in Fig. 6. From Figs. 3-6, it has been shown that BER performance of the proposed scheme is better than that of the conventional scheme. In P b ( M ) = as a standard level for comparison, it has been shown that the number of users simultaneously accessing the channel in the proposed scheme is about two times as large as that of the conventional scheme, in particular Fig. 6. ~

MABUCHI

el

599

al.: MULTIUSER DETECTION SCHEME

BER 0 10

1

BER 0 10 10-l 102

Coilwilt ionid

Scliciiir Tlirorg

107

-9

10

0 Nll1lll)rr

Fig. 3. BER versus number of users in MFSK/FH-SSMA system for conventional scheme and proposed scheme in an interference-only channel with random address code.

BER 0 10

50

of 11scrs

100

150 200 N~uul,rrof users

300

250

Fig. 5. BER versus number of users in MFSK/FH-SSMA system for conventional scheme and proposed scheme in an interference-only channel.

BER 0 10

E

I 7 li

10-l

101

1G

L

-2

10

-3

10

-4

10

1i3 -4 10

4

10

-7

Coiivciit ioiiid Scliciire

10

-----

-

Proposctl S C l l C l l l C

-8 10

10B

1i9

0

5

10 Nll1lll)rr

15

20

of 1iscrs

Fig. 4. BER versus number of users in MFSK/FH-SSMA system for conventional scheme and proposed scheme in an AWGN channel with random address code.

C . Reduction of Complexityfor Multiuser Detection Scheme

In the proposed scheme of multiuser detection, there are

M-1 . 5 2 K ) candidate matrices of the received nm=o am (1 5 ,i

matrix. If the total number of users, M , increases implying also in more number of the majority rows, ,i (1 5 i, 5 2 K ) , the complexity of calculation in the proposed scheme will greatly augment. We should investigate reduction of the amount of calculation. If there is no false alarm, the number of entries in candidate matrices is not longer than that of the received matrix. Therefore, in order to reduce complexity of the proposed scheme, when candidate matrices are compared with the received matrix, if the number of entries in the candidates matrices is equal to that of the received matrix we had better finish comparing with the received matrix and select the candidate matrix as a correct candidate of the received matrix.

Fig. 6. BER versus number of users in MFSIVFH-SSMA system for conventional scheme and proposed scheme in a Rayleigh fading channel.

Tables I1 and I11 show the number of the candidate matrices normalized by the number of symbols per user, N,, which are compared with the received matrix.

N, =

(Number of total candidate matrices) (Number of total symbols per user)

'

(33)

In the Tables I1 and 111, (A)represents N, of a scheme where all candidate matrices are compared with the received matrix. (B) represents N , of a scheme where we select a candidate matrix, in which the number of entries is equal to that of entries in the received matrix. The rate refers to the normalized candidate number of (B) divided by that of (A). From Tables I1 and 111, it can be seen that the number of the compared candidate matrices in (B) is fewer than that of (A).

600


TABLE I1 THENUMBER OF THE COMPARED CANDIDATE MATRICES NORMALIZED BY THE NUMBER OF SYMBOLS P E R USER (2K=16, k 5 , Eh/No=m).

BER 0

10

0

0

0

-4 10

10

10

20.85

11.462 55.0%

11

67.508

38.363 56.8%

12

384.000

222.355 57.9%

10

0

1

I

13 3149.943 1756.938 155.8%

1

4

(B)

(A)

Number of users I1

1.025 I

I

Rate

1.014 I 98.9% 1

I

1

9.097 5.989 65.8% 9 28.242 18.204 64.5% 10 11 I1 115.774 I 78.804 I 68.1%1 I 12 605.806 419.137 69.2% 13 3706.558 2674.496 72.2% V. ADDRESSCODEASSIGNMENT

In the previous section, it is assumed that an address code is arbitrarily selected from ( 2 K ) L different vectors which are all possible patterns of a vector with 2K levels and L chips length. To improve the discrimination between the desired signal and the undesired ones in the MFSK/FH-SSMA or to increase the user capacity, we must consider an address code assignment. In this section, an address code assignment for the proposed scheme of multiuser detection for the MFSK/FH-SSMA system is investigated. An address code assignment was proposed by Einarsson [ 2 ] , where two transmitted vectors with different address codes will coincide in, at most, one chip in a synchronous system, which means that the signals from all users are aligned in time.

5

10 of

Nllllll,c.r

15

20

IlSrrS

Fig. 7. BER versus number of users in MFSK/FH-SSMA system for conventional scheme and proposed scheme in an interference-only channel with optimized address code.

where ym is an element of G F ( 2 K )assigned to user m and /3 is a fixed primitive element of G F ( 2 K ) . In the proposed scheme of multiuser detection, if there are not the effects of deletion and false alarm, decoding errors occur when there are several candidates of the received matrix, which have the most number of coincident entries with the received matrix or when all the entries of a certain user coincide with the entries of other users. According to this address code assignment, since a complex row which consists of L entries arises when there are at least L undesired users, it is possible to reduce the effects of undesired entries. Therefore, we can consider that this address code assignment is suitable to the proposed scheme of multiuser detection. We investigate the performance of the proposed scheme using this address code. Fig. 7 shows BER versus the number of users which are derived by computer simulation for the conventional scheme and the proposed scheme using the address codes of (34). The BER's were numerically calculated with 2K = 16, L = 5 , and Eb/NO = 00 in an interference-only channel. The parameters of computer simulation is showed in Table I. The total number of all users' data bits is 100,000 bits and a subset of the address code of (34) is utilized. From Figs. 3 and 7, it can be seen that the BER performance of the scheme using the address code of (34) is improved. VI. MODIFIEDSCHEMES OF MULTIUSER DETECTION In this section, reduction of decoding errors in the proposed scheme is investigated when there are the effects of deletion and false alarm. If the correct row has less entries than rows consisting of several undesired users' entries, decoding errors occur in the proposed scheme based on Section 111, in which only the symbols corresponding to the majority rows are utilized as candidates of the correct data symbol. Instead, if the symbols corresponding to rows having fewer number of entries than the majority rows are utilized as candidates of the correct data symbol, we may improve the BER performance.


Number of Users 4

(A)

(B)

1.300e-4

0.000 1.100e-4 5.196e-4 1.469e-3 3.640e-3 6.005e-3

5 6.800e-4 6 1.689e-3 7 3.926e-3 8 6.740e-3 9

Number of Users

1.115e-2

(A)

(B)

60 1

(C) 0.000 1.400e-4 5.296e-4 1.459e-3 3.690e-3 6.675e-3

4

1.014

5

1.062

1.214 2.352

6 7

1.229 1.620

8.147 45.752

(C) 1.210 2.227 6.596 29.976

8

2.814

9

5.989

475.021 5901.360

203.315 1481.371

However, complexity increases considerably because there will be more candidates of the received matrix. If we would like to obtain more improved performance, all symbols corresponding to rows having at least an entry should be utilized as candidates of the correct data symbol. However, as we discuss, complexity increases considerably. Using the fact that the probability that a row corresponding to the correct data symbol has close to L entries is high, by the distinction of the manner of selecting candidates of the correct data symbol in the time-frequency matrix, the performance of Schemes (A), (B), and (C) described as follows is investigated. Scheme (A): The symbols corresponding to rows having the largest number of entries are considered as the candidates. Scheme (B): The symbols corresponding to rows having the first and second largest number of entries are considered as candidates. Scheme (C): The symbols corresponding to rows having the largest number of entries are considered as candidates. Moreover, only when there is one row having the largest number of entries, the symbols corresponding to rows having the second largest number of entries are considered as candidates. Table IV shows the BER performance in Schemes (A), (B), and (C). Table V shows the number of compared candidate matrices normalized by the number of symbols per user in Schemes (A), (B), and (C). From Table V, it has been shown that the BER performance of Scheme (B) is superior to that of Schemes (A) and (C).From Table V, it has been shown that the complexity of Schemes (B) and (C) is greater than that of Scheme (A). Consequently, even if the symbols corresponding to the majority rows and the symbols corresponding to rows having fewer number of

entries than the majority rows are utilized as candidates of the correct data symbol, the improvement of BER performance is small in quantity for the increase in complexity. Therefore, one can consider that it is necessary to select the suitable scheme depending upon the criteria of BER performance and complexity.

COMBINING MULTIUSERDETECTION VII. HYBRIDSCHEME SCHEME AND DECODING OF ERROR-CORRECTING CODEFOR CODEDMFSWFH-SSMA SYSTEM In this section, we investigate a hybrid scheme combining the multiuser detection scheme based on canceling CCI and the modified decoding scheme of an error-correcting code for the coded MFSK/FH-SSMA system. Moreover, its performance is evaluated by computer simulation.

A. Modified Decoding Scheme of Error-Correcting Code

In conventional decoding [8], if there are several majority rows in one time-frequency matrix decoded by the address code, then the received symbol which corresponds to that matrix was considered as an erasure and decoded by the conventional error-and-erasure correction decoding. In our proposed decoding scheme [9], [lo], if there are several majority rows, each information of symbols corresponding to the rows was utilized in the decoding of the error-correcting code. Then, we select a codeword which is closest to the words which are derived from the possible combination of candidates of the correct symbol. However, since decoding complexity increases considerably, we investigate a scheme as follows. We classify candidates of the correct symbol corresponding to each matrix into decoding candidates and check candidates. The decoding candidates are defined as candidates of the correct symbol, which are utilized to perform the error-anderasure correction decoding. The check candidates are defined as candidates of the correct symbol, which are utilized to compare with candidates of the correct codeword. The symbols corresponding to the matrices containing the check candidates are considered erasures, and the error-anderasure correction decoding is performed by utilizing each possible combination of several decoding candidates. Consequently, several candidates of the correct codeword is derived. Then, the conventional error-and-erasure correction decoding is repeatedly performed. A codeword closest to each possible combination of candidates of the correct symbol from several candidates of the decoded codeword is selected as the correct codeword. However, one can consider that decoding errors in the proposed decoding scheme occur in two ways: one is when a word derived from a combination of several candidates coincides with another codeword; another is when the number of matrices containing a correct row which have less entries than rows consisting of several undesired users’ entries, is larger than the error-correcting capability. In this paper, we made use of the ( n ,k) Reed-Solomon (RS) error-correcting code. However, this scheme can be applied with other codes.

~

602


where the underlined symbols show symbols coincided with candidates of the correct symbol. Therefore, the codeword (4, 1, 7, 3, 2, 5, 6) is selected as the correct codeword.

B. Hybrid Scheme Combining Multiuser Detection Scheme and Decodingof Error-Correcting Code for Coded MFSKIFH-SSMA System In either the multiuser detection scheme or the modified decoding scheme of an error-correcting code, we utilize each information of symbols corresponding to the majority rows in order to restrict candidates of the correct data symbol. Therefore, the manner of combining the multiuser detection 1 ) An Example of Modified Decoding Scheme: We show scheme and the decoding scheme of an error-correcting code an example of the modified decoding scheme using (7, 2 ) RS with regard to each information of symbols corresponding to code for the coded MFSK/FH-SSMA system in Fig. 8. The error-and-erasure correcting capability of the (7, 2 ) RS code the majority rows influences the performance and complexity in the hybrid scheme. is expressed by: If we would like to obtain more improved performance, 2s + e 1 5 6 (35) we should perform the multiuser detection scheme for all the where s and e denote the number of errors and erasures, users' matrices. Then, if there are several candidates of the received matrix, which have the most number of coincident respectively. entries with the received matrix, we had better select a In Fig. 8, each time-frequency matrix decoded by the correct candidate of the received matrix from the candidates address code corresponds to one data symbol, and the seven of the received matrix by utilizing an error-correcting code. time-frequency matrices correspond to a block of RS code. 1) In this example, there are two matrices containing two However, complexity increases considerably. In this paper, in consideration of reduction of complexity, majority rows and five matrices containing three majority the hybrid scheme is investigated. Fig. 9 shows the BER rows. 2 ) Each information of symbols corresponding to the ma- versus the number of users for Schemes (1) and ( 2 ) of jority rows are registered as candidates of the correct symbol the multiuser detection in the MFSK/FH-SSMA system: in Scheme (l), all the users' matrices are utilized in order to such as Fig. 8. estimate candidates of the received matrix; in Scheme (2), 3) When s = 0, the erasure-correcting capability is five. Symbols which correspond to the matrices containing the first only the user's matrices containing less than two majority rows to fifth largest number of the majority rows are considered is utilized. The numerical results are calculated by computer erasures. In the matrices containing two majority rows, pos- simulation in an interference-only channel with 2 K = 16, L = sible combinations of candidates of the correct symbol are 5, and &/NO = CO. In Scheme ( 2 ) ,however, we demodulated indicated by (4, 5), (4, l), (2, 5), and (2, 1). The erasure only the data symbols of the users' matrices containing less correction decoding is repeatedly performed by decoding each than two majority rows. Consequently, even if we utilize combination of the candidates such as (4, 5), (4, l), (2, 5), Scheme (2), we will be able to decode correctly to some degree and (2, 1). Consequently, we can respectively obtain four in the case that there is a large number of matrices containing less than two majority rows. candidates of the correct codeword as shown in the table. Therefore, in this section, we utilize only the users' matrices 4 5 4 0 5 1 1 containing less than two majority rows in order to estimate 4 1 7 3 2 5 6 candidates of the received matrix. Then, if there are several 2 5 6 4 1 7 3 candidates of the received matrix, which have the most num2 1 5 7 6 3 4 ber of coincident entries with the received matrix, symbols where the underlined symbols show candidates of the correct corresponding to several candidates of the received matrix are symbol. also considered as candidates for the decoding of an error4) By utilizing the matrices containing two and three ma- correcting code. Afterward, we perform the decoding of the jority rows, 2' x 35 vectors are derived as each possible error-correcting code by utilizing each information of symbols combination of candidates of the correct symbol. We calculate corresponding to more than three majority rows and candidates the number of coincident symbols with the vectors for each of the correct data symbol which are restricted by the multiuser codeword decoded by operation (3). We select a codeword detection scheme. which has the most coincidence with the vectors among the By the distinction of the decoding of the error-correcting decoded codewords as the correct codeword. code, the performance of Schemes (A), (B), (C), and (D) as 4 5 4 0 5 1 1 follows is investigated. However, Scheme (D) is the scheme 4 1 1 3 2 5 6 without the multiuser detection. 2 5 6 4 1 / 3 Scheme (A): The symbols corresponding to matrices con2 1 5 7 6 3 4 taining several majority rows in the candidates of the correct Fig. 8. An example of the proposed decoding scheme using the (7,2) RS code.

+

MABUCHI

er al.: MULTIUSER

DETECTION SCHEME

603

BER 0

10

I

TABLE VI BER PERFORMANCE OF THE HYBRIDSCHEME IN AN INTERFERENCE-ONLY CHANNEL BY COMPUTER SIMULATION (2K=16, k 5 , Eb/No=cO AND (15, 2 ) RS CODE)

(A) (B) (C) (D) 13 9.964e-6 0.000 0.000 2.100e-4 14 4.589e-4 3.392e-4 9.976e-5 8.300e-4 15 1.152e-2 2.964e-3 1.257e-3 2.100e-3

Number ofusers

1

TABLE VI1 BER PERFORMANCE OF THE HYBRIDSCHEME IN AN AWGN CHANNEL BY COMPUTER SIMULATION (2K=6, L=5, Eb/No=l6 dB, AND (15, 2 ) RS CODE)

[Number of Users

Fig. 9. BER versus number of users in MFSIVFH-SSMA system with multiuser detection scheme using all the users’ matrices and the users’ matrices containing less than two rows having the largest number of entries in an interference-only channel.

12 13 14 15

,1

(A) 9.968e-6 2.989e-4 3.093e-3 2.328e-2

(B) 0.000 2.092e-4 2.554e-3 1.239e-2

TABLE VI11

data symbol, which are restricted by the multiuser detection scheme, are considered as erasures. The error and erasure correction decoding is performed by utilizing the erasures. Scheme (B): The symbols corresponding to one and two majority rows in the candidates of the correct data symbol, which are restricted by the multiuser detection scheme, are considered as the decoding candidates. The modified decoding scheme is performed by utilizing the decoding candidates. Scheme (C): The symbols corresponding to one, two, and three majority rows in the candidates of the correct data symbol, which are restricted by the multiuser detection scheme, are considered as the decoding candidates. The modified decoding scheme is performed by utilizing the decoding candidates. Scheme (D): The symbols corresponding to one and two majority rows are considered the decoding candidates. The modified decoding scheme is performed by utilizing the decoding candidates.

THENUMBER OF THE COMPARED CANDIDATE MATRICES NORMALIZED BY THE NUMBER OF SYMBOLS P E R USER IN THE MULTIUSER DETECTION SCHEME CODE (2K=16, 1=5, AND EhlNo=m) WITHOUT AN ERROR-CORRECTING

Number of Users

&/NO = 00 Eb/N0=16dB

12

384.000

605.806

13

3149.943

3706.558

TABLE IX THENUMBER OF THE COMPARED CANDIDATE MATRICES NORMALIZED BY THE NUMBER OF SYMBOLS P E R USER IN THEMULTIUSER DETECTION SCHEME WITH CODE (2K=16, L=5, Eb/No=cO AND (15, 2 ) RS CODE) AN ERROR-CORRECTING

Number of Users

E b / N o= 00

Eb/N0=16dB

12

37.695

31.898

13

70.281

58.808

14

119.706

100.199

15

178.834

156.988

C . Performance of Hybrid Scheme We investigate performance of the hybrid scheme combining the multiuser detection scheme and decoding of an errorcorrecting code for the coded MFSKFH-SSMA system. Tables VI and VI1 show the BER performance of Schemes (A), (B), (C), and (D) with (15, 2) RS code obtained by computer simulation. The BER’s were numerically calculated with 2K = 1 6 , L = 5, and Et,/No = 00 in an interferenceonly channel in Table VI and with 2K = 16, L = 5, and &,/No = 16 dB in an additive white Gaussian noise (AWGN) channel in Table VII. The parameters of computer simulation is shown in Table I. Tables VI11 and IX show the number of candidate matrices normalized by the number of symbols per user,. N,, which is compared with the received matrix for the multiuser detection

scheme without an error-correcting code in Table VI11 and with an error-correcting code in Table IX. From Tables VI and VII, it has been shown that BER performance of Scheme (C) is better than that of Schemes (A), (B), and (D). In operation of the multiuser detection scheme, only the users’ matrices containing less than two majority rows number of entries are utilized in order to estimate candidates of the received matrix. Therefore, at 15 users in Table VII, the performance of Scheme (D) is greater than that of Schemes (A) and (B) because of increasing the decoding errors of the multiuser detection scheme. From Tables VI11 and IX, it has been shown that the number of compared candidate matrices normalized by the number of symbols per user in the hybrid scheme is reduced.


604

Tetsuo Mabuchi was born in Hiroshima, Japan on May 18, 1967. He received the B.E. and M.E. degrees in electrical and computer engineering from Yokohama National University in 1991 and 1993, respectively. He joined the NEC Corporation in 1993. While at the university, his research interests were in the areas of spread spectrum communication systems and coding theory.

Therefore, we should select the suitable scheme depending upon the criteria of performance and complexity.

VIII. CONCLUSIONS In this paper, we have proposed a multiuser detection scheme based on canceling CCI for the MFSK/FH-SSMA system and have evaluated its performance by theoretical analysis and computer simulation. It has been shown that the proposed scheme based on canceling CCI can increase the number of users simultaneously accessing a channel. Moreover, we have investigated a hybrid scheme combining the proposed multiuser detection scheme and the proposed decoding scheme of the error-correcting code. It has been shown that we should select the suitable scheme depending upon the criteria of performance and complexity. As one of the remaining problems, an address code assignment which is more suitable for the various schemes for the MFSK/FH-SSMA system should be investigated. APPENDIX

Ryuji Kohno was born in Kyoto, Japan, on March 30, 1956. He received the B.E. and M.E. degrees in computer engineenng from Yokohama National University in 1979 and 1981, respectively, and the Ph.D. degree in electncal engineering from the University of Tokyo in 1984. He joined the Department of Electncal Engineering of Tokyo University in 1984 and became an Associate Professor in 1986. Since 1988, he has been an Associate Professor in the Division of Electncal and Computer Engineering, Yokohama National University. From 1984 to 1985, he was a Visiting Scientist in the Department of Electncal Engineenng University of Toronto. Currently, he is a Vice-chairman of the Society of Spread-Spectrum Technology of the IEICE (Institute of Electronics, Information, Communications Engineers) and a Chairman of the Program Committee of the 1992 IEEE International Symposium on Spread-Spectrum Techniques and Applications. His current research interests lie in the areas of adaptive signal processing, coding theory, spread spectrum system, and various kinds of communication systems. Dr. Kohno is a member of EURASIP, IEICE, IEE of Japan, and IPS of

The rule of addition in G F ( 2 K ) is defined. The symbol finite field ( ~ ~field) l of ~ 2 Ki elements. ~ The Of the are represented as binary numbers or vector of length K . As an example, for 23 = 8 the elements are expressed as thee+$ binary 0 = 000, 1 = 001, 2 = = O1 = loo, = lol, 6 = lo, 7 = 111. Addition is now defined as componentwise mod 2 addition. For example, 3 + 1 = 0 1 1 + 0 0 1 = 0 1 0 = 2 , 5 + 4 = 1 0 1 + 1 0 0 = 0 0 1 = 1 , e t c . Japan. G F ( ~ K )denotes the

O1O3

1t

REFERENCES [ I ] D. J. Goodman, P. S. Henry, and V. K. Prabhu, “Frequency-hopped multilevel FSK for mobile radio,” Bell Syst. Tech. J., vol. 59, no. 7, pp, 1257-1275, Sept. 1980. [2] G. Einarsson, “Address assignment for a time-frequency-coded, spreadspectrum system,” Bell Syst. Tech. J . , vol. 59, no. 7, pp. 1241-1255, Sept. 1980. [3] R. Kohno, H. Imai, and M. Hatori, “Cancellation technique of cochannel interference in asynchronous spread spectrum multiple access system,” Trans. IEICE Japan, vol. J65-A, no. 5, pp. 4 1 f 9 2 3 , May 1983. [4] S. Verdu, “Optimum multiuser asymptotic efficiency,” IEEE Trans. Commun., vol. COM-34, pp. 890-897, Sept. 1986. [5] R. Kohno, H. Imai, M. Hatori, and S. Pasupathy, “Combination of an adaptive array antenna and a canceller of interference for directsequence spread-spectrum multiple-access system,” IEEE J . Select. Areas Commun., vol. SAC-8, pp. 675-682, May 1990. [6] R. Kohno, H. Imai, M. Hatori, and S. Pasupathy, “An adpative canceller of cochannel interference for spread-spectrum multiple-access communication networks in a power line,” IEEE J. Select. Areas Commun., vol. SAC-8, pp. 691-4199, May 1990. [7] R. Kohno, “Pseudo-noise sequences and interference cancellation techniques for spread spectrum systems-Spread spectrum theory and techniques in Japan,” Trans. IEICE Japan, vol. J74-B-II, no. 5, pp. 1083-1092, May 1991. [8] T. Kawahara and T. Matsumoto, “Forward link capacity of coded W C D M A mobile radios,” in Proc. 14th Symp. Inform. Theory and Its Applicat. (SITA ’91), Ibusuki, Japan, Dec. 1991. [9] T. Mabuchi, R. Kohno, and H. Imai, “Multihopping and decoding of error-correcting code for MFSK/FH-SSMA systems,” in Proc. IEEE Int. Symp. Spread Spectrum Tech. and Appl., Yokohama, Japan, Nov. 1992. [IO] T. Mabuchi, R. Kohno, and H. Imai, “Multihopping and decoding of error-correcting code for MFSK/FH-SSMA systems,” IEICE Trans. Commun., vol. E76-B, No. 8, pp. 87+885, Aug. 1993.

Hideki Imai (M’67-SM’88-F’92) was born in Shimane, Japan on May 31, 1943. He received the B.E., M.E., and Ph.D. degrees in electncal engineering from the University of Tokyo in 1966, 1968, and 1971, respectively. Since 1971, he has been on the faculty of Yokohama National University (Lecturer 1971; Associate Professor 1972; Full Professor 1984), where he is presently a part-time Professor in the Division of Electncal and Computer Engineenng. In 1992, he joined the faculty of the University of Tokyo, where he is currently a Full Professor in the Institute of Industnal Science. His current research interests include information theory, coding theory, cryptography, spread spectrum systems, and their applications. He is the author of three books, the editor of four books, and coauthor of seven books. He received Excellent Book Awards from the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan in 1976 and 1991 He also received the Best Paper Award (Yonezawa Memonal Award) from IEICE in 1992. He chaired several committees of scientific societies such as the IEICE Professional Group on Information Theory and the IEICE Professional Group on Information Security. He served as the editor of several scientific journals such as the IEICE Transactions on Engineering Sczence He chaired the 8th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-8) in 1990, and the Program Committees of the International Symposium on Information Theory and Its Applications (ISITA ‘90) and of the Asiacrypt ‘91. He will chair the IEEE Information Theory Workshop in 1993. He IS on the board of the IEEE IT Society, IEICE, International Association for Cryptologic Research (IACR), anhd the Japan Society of Secunty Management (JSSM) Dr. Imai is a member of IEE of Japan, IPS of Japan, and ITE of Japan