One-shot Linear Decorrelating Detector for Asynchronous CDMA

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One-shot Linear Decorrelating Detector for Asynchronous

CDMA

M.

Peng,

Y. J.

Guo and

S.

K. Bar ton

Telecommunication Research Group

Depar tment

of

Electronic and Electrical Engineering

Bradford University, UK

Abstract

A one-shot linear decorrelating detector(LDD) for the detec-

tion of asynchronous CDMA is presented. By treating every

user as two independent users and using maximal ra tio com-

bining, a bit-by-bit detection is obtained. By applying a

phase estimation algorithm on the output of the one-shot

LDD, it is shown that the proposed detector can be used for

the detection of asynchronous CDMA without the knowledge

of carrier phase of any user. Simulation results show th at the

performance of the proposed detector approaches that of the

optimum detector for single user transmission.

1 Introduction

The fundamental limitation of the DS/CDMA system is

the so-called near-far problem, which leads to severe per-

formance degradation for the conventional receiver. In 1986,

Verdu investigated the optimuni maximum-likelihood mul-

tiuser receiver for multiuser communication

[l].

Verdus re-

ceiver is near-far resistant, but its complexity is exponen-

tial in the number

of

active users. Recently much attention

has been given to suboptimal architectures with less com-

plexity. Among many suboptimal detectors proposed, Lupas

and Verdus linear decorrelating detector (LDD)

[2]

[3] has

attracted wide attention. The LDD achieves the same near-

far resistance as the optimum detector while its complexity

is linear in the number of users.

Although the LDD is much simpler than Verdus optimum

detector, it is still too complicated and will lead to unac-

ceptable detection delay while dealing with asynchronous

CDMA. With sacrifice of data transmission rate, Zheng and

Barton proposed an isolation bit insertion (IBI) LDD

[4]

o

simplify the implementation and reduce detection delay. An-

other scheme, also proposed by Verdu and Lupas,

is

called

one-shot LDD [ 5 ] [ 6 ] ,where the detection of data is based

on the signal observed in one bit length period, called one-

shot window, so the detection of an asynchronous CDMA

is transformed into that of synchronous one. According to

Verdu and Lupass scheme, the one-shot window is syn-

chronised with one of the users,

so

for

a

K-user asynchronous

CDMA, a (2K-l)-user synchronous CDMA problem must be

solved for the detection of one user, and a total of K different

0-7803-3336-5196

5.00

0 1996 IEEE

(2K-l)-user synchronous CDMA problems must be solved for

the detection of the total

K

users.

In this paper, an improved one-shot LDD scheme is pre-

sented, in which the one-shot window is not synchronised

with any user. By treating every user as two independent

users and using maximal ratio combining, a bit-by-bit de-

tection is obtained. With this approach, the multiuser de-

tection of a K-user asynchronous CDMA is converted into

that of

a

2K-user synchronous CDMA.

For

the LDD and

many other detection schemes, a knowledge of the time de-

lay, the carriers frequency and phase, is normally assumed.

Noncoherent detection has been reported

[7]

for unknown

carrier phase. In-this paper, by applying a single-user phase

estimation algorithm at each output of the one-shot LDD,

it is shown that the proposed detector can be used

for

the

coherent detection of asynchronous CDMA without the pre-

knowledge of user phase. Simulation results show that the

performance

of

the proposed detector approaches that of the

optimum detector for single user transmission.

2

One-shot

LDD

Consider a BPSK CDMA system. The received signal can

be expressed as:

N K

r t )= b k i ) ~ S k t - - i T b - - 7 ; E ) c o s 2 . r r f , t + 8 k ) + n t )

i = O k = l

(1)

where K is the number of total users, N the number of trans-

mitted information bits, Tb the duration of each information

bit,

fc

the carrier frequency,

Pk

and 8 k are power and initial

phase of user k , respectively, b k i ) is the ith bit of user I C

n t )

the AWGN with variance

a2

nd

s k t )

user

ks

signa-

ture waveform which satisfies:

and

S i t ) d t

= 1 3)

The idea of the one-shot LDD is to transform the detection

of asynchronous CDMA into the detection of synchronous


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CDMA. Consider the one-shot window as shown in Fig-

ure

1.

Each user can be treated a s the superposition of two

independent users. For example, user k can be treated as the

superposition of two new users k and k ?whose signatures

skf ( t ) and sk( t )are defined as:

The fact that Sk(t) has unit energy gives:

pk pk

=

1

All new signatures have unit energy. In this paper, it is

also assumed that all new signatures, sk ( t ) and sk(t) (k =

1 , 2 ,

..,

K), are linearly independent. Figure 2 shows an ex-

ample of the decomposition of signature waveforms.

(8)

- - - -

One shot

Window

- - - e- - -

Ooc-shot Window

- - - -

T h

...

Figure 1: One-shot window for

a

K-user asynchronous

CDMA.

Defining

b k - 1 ) =

0

(k = 1 , 2 ,

...,

K ) ,

equation

(1)

can be

rewritten as:

T t )

=

xzo

xf= i[bk( i ) d m s k f ( t

T b )

f

b k ( i ) d m s k t Tb)] o s ( 2 ~ f ~ t6,) + n ( t )

9)

Thus the original K-user asynchronous CDMA problem can

be treated as

a

2K-user synchronous CDMA problem, on

which a synchronous LDD can be applied.

Let y ( i )

= [y l t

i ) ,

l

i ) ,

.., K t i), y K i)]

represent the

matched filters output at time iTb, where

n

Figure 2: Decomposition of signature waveforms for the o

shot LDD.

with p

=

1, 1 ,..,

K,

K . Let R represent the correlat

matrix with its element given by:

(

n

where

p ,

q

=

1 , l ,2 ,

..,

K ,K

and b( i )

= [ b l (

1),

b1

i ) , 2 i ) , b2 i), ..

,

b~ i ) ,

b~

i)] represent the d

vector, then we have

(

( i )=

RWb(i) +

n( i )

where W e d i a g [ , / n , d f l ,

...,

/SI

and

n(i)

is a zero-mean Gaussian K-vector with covaria

matrix equal to

a2R.

With z ( i )

=

[zl/ i), zl i ) , ..,zK

i),

z ~ i)] represen

the LDD output, equation

(12)

gives

~ ( i )

R - l y ( i )

a

=

Wb(i)

+

n,(i)

(

where n,(i)

=

[ n 1 / ( i ) , n 1 ( i ) ,. . ,nK ( i ) ,nK , , ( i ) ]s a n

vector, whose elements nk and nk-3 are zero-mean Gaus

noise with variance

a 2 < k 1

and a 2 < k k , respectively, wh

< k l k : and < k k are the corresponding diagonal elements

matrix

R-l.

From equation (9) , it can be seen that users

k

and

in the synchronous CDMA share the power of user k in

original asynchronous system. Therefore, any detection a

rithm based on one single bit period will suffer from the


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of signal-noise-ratio (SNR). On the other hand, it can also

be seen that for any two consecutive one-shot windows, user

k in the first carries the same da ta information as user k' in

the following. Therefore, by combining the outputs of LDD

in two consecutive windows, the SNR loss can be recovered.

. ( i l

lI

A

Figure 3: One-shot LDD for asynchronous CDMA.

Define Z k ( 2 ) as:

(14)

A

z k ( i ) ZZ x ; z k i 1)+ x ; z k l i)

where A and

A

are weighting coefficients to be determined.

From equation (13), we have:

Zk i )

= [A;

s d z ] b k 2

1)

+ nkt

i )

+ & n k x , i 1)

(15)

As

nkl i )

and

n k

i

1)

are independent zero-mean Gaus-

sian noise with variances

c r c k l t

and

a 2 < k k ,

respectively,

the above two noise items can be represented as one noise

n k ( i ) ,

which is also zero-mean Gaussian but with variance

By solving an optimization problem, the maximum SNR

C2

[

ck' k' ( xk ) 2 ; e 1

in equation (15) is achieved with A and A given by:

Accordingly, equation (15) leads to:

where n k has variance 02 [ *

+

e]nd the maximal

SNR is:

k r k

The above SNR is the efficient SNR for the one-shot LDD to

detect the information bits of user k under a CDMA scenario.

The maximum SNR, which can be obtained in the absence

of multiuser interference, is 9 . he ratio

of

the two

S N Rs

characterises the near-far resistance of the one-shot LDD,

which is:

With the statistic z k ( i ) , the estimate of the dat a bit b k ( i

1)

can be obtained:

& k ( i 1)

=

s g n [ z k ( i ) ]

(20)

This means that the above detector has one bit detection

delay.

From (19), it can be seen th at the near-far resistance of

the one-shot LDD is determined by the diagonal elements of

the inverse of the cross-correlation matrix, k / and

< k k ,

as well as the energy p k f and

p k

defined by (6). Generally

speaking, both

c k l k ~

and


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Phase Delay '7-k

user 1

0 . 1 ~

0.12Tb

user

2

0 . 3 ~ 0.25Tb

user 3 - 0 . 1 5 ~

0.3Tb

user 4

0 . 2 3 ~

0.76Tb

user 5 -0 . 35 ~

0.8Th

Let c 'k~,k ,nd

c'k,.kj,

epresent the diagonal elements Of

matrix

R

- , and let represent the output of the LDD.

Similar to equation (17), we have:

z k i )

=a[ F ] b k i 1)eJek+ 6 k

(23)

e kt Ck

,

where Re{fik} and Im{6k} are independent zero-mean

Gaussian noise with variance

c2[$k -

+

1

From statistics

z k ,

the estimation

of

data

b k

and phase

0k can be carried out on

a

single user basis. It is seen that

by using the one-shot LDD, the problem of multiuser phase

estimation has been simplified into that of single user one,

on which many techniques can be employed [8].

In this paper,

a

decision-feedback algorithm, similar to

that given in

[8],

is employed for phase estimation. The

estimate of the phase is updated in every bit period and is

based on all the statistics 2, and the estimate of data i&

before:

k l k'

c

k , l

2 1

e k ( i ) =

arg xk(j )zk(j)]

(24)

,3=1

For the first bit period, the estimate of the phase is carried

out as:

m = arg [ (O)l (25)

(26)

The estimate of data bit is given as:

g k ( i 1)= Sgn[Rte(zk(i)e-3sk(2))]

Power (9/ 20 2)( dB)

5

50

10

20

Similar to other phase estimation techniques, the above

method results in

an

ambiguity of T, but this problem can

be solved by using differentially encoded PSK transmission

(DEPSK)

[8].

4

Computer simulation

511-chip Gold codes have been chosen as signatures in the

simulation. The first example is on the one-shot LDD with

known phases. A 5-user CDMA system is simulated. The

parameters of the 5 users are shown in Table 1. Fixing the

powers of noise and users

2,

3, 4 and 5, Figure

4

shows the

bit-error-ratio (BER) curve of user 1 with the change of its

SNR. For comparision, the theoretical BER curve of opti-

mum coherent detection for single user transmission is also

shown in Figure

4

(The two curves are very closely located.).

It

can be seen that the performance of the one-shot LDD

is very close to that of the optimum detection with single

user transmission, which is the upper bound of any detec-

tion scheme for CDMA.

The second example is on the near-far resistance of the

proposed detector. Fixing the SNRs of user 1, 2, 4 and 5

and changing the SNR of user 3, the BER of user 1 s tested.

Figure

5

clearly shows the near-far resistance of the proposed

detector.

The third example is on the one-shot LDD without the

knowledge of phases. The parameters of users are the same

Table

1:

Parameters of 5 users in the simulation system. T

power of user 1 will be changed during simulations.

0

1 2

3 4 5

6

7

8

9

SNRl = 1010g(Pl /2i~~)dB)

Figure

4:

User 1's BER with the change of its own pow

as that shown in Table 1. Differential coding is employ

Fixing the powers of noise and users 2, 3,

4

and 5, the B

curve of the user

1

with the change of its SNR is obtain

based on the phase estimation and one-shot detection te

niques described in section 3. The estimates of phases

updated in every bit period. The converging speed of

estimate of

a

phase to its real value depends on the SNR

the corresponding user. Simulation shows that the esti

tion error is less than 5O after about 200 bit period time

SNR=OdB, and about 10 bit period time for SNR=5dB.

BER curve of user 1 is also shown in Figure 4. From Fig

4, it is observed that the BER for DEPSK approxima

doubles that for BPSK with the same SNR. This is a re

similar to that of single user transmission [8].

5

Conclusion

A one-shot LDD for the detection of asynchronous CD

has been investigated. By treating every user as two indep

dent users and using maximal ratio combining,

a

bit-by

detection is obtained. Then by making use

of

the outpu

the one-shot LDD and employing a phase estimation te

nique,

a

one-shot LDD without the knowledge of user ph

has been obtained. Computer simulation showed the

formance of the proposed detector approaches that of

optimum detector for single user transmission, which is


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SNRl

=

8dB

0 10 20 30 40 50 60

S N R3

= 1010g(P~/20~)

dB)

Figure

5 :

User 1s BER with the change of user 3s power.

upper bound of any detection schemes for CDMA. As the

proposed detector has very good performance but simple ar-

chitecture, it is

a

promising scheme for practical application.

References

S. Verdu. Minimum probability of error for asynchronous

gaussian multiple-access channels.

IEEE Trans. Informa-

tion Theory,

IT-3235-96, Jan. 1986.

R. Lupas and

S.

Verdu. Linear multuser detectors for syn-

chronous code-division multiple-access channels.

IEEE

Trans. Inform. Theory,

IT-35:123-136, Ja n. 1989.

R.

Lupas and S. Verdu. Near-far resistance of multiuser

detectors in asynchronous code-division multiple-access

communications.

IEEE Trans. Communications,

COM-

38:496-508, April 1990.

F-C. Zheng and S. K. Barton. Near-far resistant

detection of CDMA signals via isolation bit inser-

tion.

IEEE Trans. Communications,

COM-43:1313-1317,

Feb./ March/April 1995.

S. Verdu.

Recent progress an multiyser detection: Ad-

vances in Communication and Consystem, CornCon

88

and Lecture Notes in Control and Information Sciences

Seraes.

Springer Verlag, 1988.

Lupas.

Near-far resistant linear multiuser detection.

Ph.

D. thesis, Dept. Elec. Eng., Princeton Univ., Princeton,

N J , 1989.

M. Varanasi. Noncoherent detection in asynchronous

multiuser channels.

IEEE 13.ans. Inform. Theory,

IT-

39:157-176, Jan. 1993.

J.G. Proakis.

Digital Communications.

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ternational Edition, third edition, 1995.

One-shot Linear Decorrelating Detector for Asynchronous CDMA

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