 Open Access
 Authors : J.Ravindrababu, Tata Balaji
 Paper ID : IJERTCONV9IS05053
 Volume & Issue : ICRADL – 2021 (Volume 09 – Issue 05)
 Published (First Online): 27032021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Ber Performance of Linear Multiuser Detectors in DSCDMA
J.Ravindrababu 1, Tata Balaji 2,
1 2 E.C.E.Dept. Prasad V. Potluri Siddhartha Institute of Technology, Vijayawada
Abstractthis paper examines the Bit Error Rate (BER) performance of Linear Multiuser Detectors in Direct Sequence Code Division Multiple Access (DSCDMA) system. Multiple access interference (MAI) limits the capacity of Direct Sequence Code Division Multiple Access (DSCDMA) systems. In CDMA systems MAI is considered as additive noise and a matched filter bank is employed. Multiuser detectors are classified as optimal and suboptimal. The main drawback of the
optimal multiuser detection is complexity so that suboptimal approaches are being sought. Much of the present research is aimed at finding an appropriate tradeoff between complexity and performance. These suboptimal techniques have linear and nonlinear algorithms. In this paper, introduce linear Multiuser Detectors in Direct Sequence Code Division Multiple Access (DSCDMA) system. Analysis is to be carried out and simulations to be done.
Keywords: DSCDMA, MF, Decorrelator, MMSE, ZF
1 INTRODUCTION
The Capacity of Frequency Division Multiple Access (FDMA) or Time Division Multiple Access (TDMA) or hybrids, common in the 2nd generation, is well defined when RF channels or time slots are no longer available no more customers can be accommodated. It is possible to include more users, although at the price of a slightly worse signalto interference ratio for everyone.
In DSCDMA communication system, users are multiplexed by distinct codes rather than by orthogonal frequency bands or by orthogonal time slots. A conventional DSCDMA detector follows a single user detection strategy in which each user is filter just treat the MAI as additive white Gaussian noise (AWGN). However, unlike AWGN, MAI has a nice correlative structure that is quantified treated separately as a signal, while the other users are considered as either interference or noise. Multiuser detection is a technology that spawned in the early 80s. It has now developed into an important, fullfledged field in multiaccess communications. Multiuser Detection (MUD) is the intelligent estimation /
Figure.1 A typical multiuser detector
The signal at the receiver is given by
K
demodulation of transmitted bits in the presence of Multiple Access Interference (MAI). MAI occurs in multiaccess communication systems (CDMA/ TDMA/FDMA) where simultaneously occurring digital streams of information interfere with each other. Conventional detectors based on the matched by the crosscorrelation matrix
of the signature sequences. Hence, detectors that take into account this correlation would perform better than the conventional matched filterbank [17].

SYSTEM MODEL
MUD is basically the design of signal processing algorithms that run in the black box shown in figure 1. These algorithms take into account the correlative structure of the MAI. The Kuser discrete time basic synchronous CDMA model has been used throughout the development of this paper. The case of antipodally modulated user information (BPSK modulation) spread using BPSK spreading is considered.
normalized to have unit energy) i.e.,
Where
. Ak is the received amplitude of the kth user
Bk is the input bit of the kth user, bk {1,1}.

n(t) is additive white Gaussian noise with PSD No .
Since synchronous CDMA is considered, it is assumed that the receiver has some means of achieving perfect chip synchronization.
The crosscorrelation of the signature sequences are defined as
y(t) AkBkSk (t) n(t) (1)
k 1
Where
ij SiSj
N
N
k 1
Si (k)Sj (k) (2)
Sk is the signature waveform of the kth user (Sk is
Where N is the length of the signature sequence The crosscorrelation matrix is then defined as
R ij
R is a symmetric, nonnegative definite, toeplitz matrix


MATCHED FILTER
Introduces and analyses the matched filter bank detector which was the conventional and simplest way of demodulating CDMA signals (or any other set of mutually interfering digital streams). The matched filter also forms the front end in most MUDs and hence understanding the operation is crucial in appreciating the evolution of MUD Technology. In conventional singleuser digital communication systems, the matched filter is used to generate sufficient statistics for signal detection. In the case of a multiuser system, the detector consists of a bank of matched filters (Each matched to the signature waveforms of different users in the case of CDMA). This is shown in figure 2. This type of detector is referred to as the conventional detector in MUD literature. It is worth mentioning that we need exact knowledge of the users
the category of linear multiuser detectors. As shown in figure 3, the decorrelating detector operates by processing the output of the matched filter bank with the R1 operator where R is the crosscorrelation matrix
Figure 3.Decorrelating Detector
signature sequences and the signal timing in order to implement this detector [8].
^
b sgn(R1
^
(RAb n)) (6)
1
Figure 2 A matched filter bank
The decision statistic the output of the Kth matched filter is given by
T
yk y(t)sk (t)dt (3)
0
Expanding this equation
T K
yk AjBjSj (t) n(t)Sk (t)dt (4)
b sgn( Ab R n) (7) Hence, we observe that in the absence of background noise the decorrelating detector achieves perfect demodulation
unlike the matched filter bank. One advantage of the
decorrelating detector is that it does not require knowledge of the received signal amplitudes. The decorrelating receiver performs only linear operations on the received statistic and hence it is indeed a linear detector. The decorrelating detector is proved to be optimal under 3 different criteria: least squares, nearfar resistance and MMSE receiver is another kind of linear multiuser receivers. The description of MMSE detector can be graphically represented in Figure 4. The MMSE implements the linear mapping which minimizes the mean squared error between the actual maximumlikelihood [8].
V MMSE LINEAR DETECTOR
The data and the soft output of the conventional detector, so the decision for the kth user is made based on in this approach where the mean squared error between the output and data is minimized. The detector resulting from the MMSE (minimum mean square error) criterion is a linear detector.
0 j1 ^ 2 1
y RAb n (5)
b R N0 A
(8)

DECORRELATING DETECTOR
An optimal receiver must be capable of decoding the bits errorfree when the noise power is zero. The decorrelating detector is investigated. This detector makes use of the structure of MAI to improve the performance of the matched filter bank. The decorrelating detector falls into
0 Bit error probablity for decoralaor
10
1
10
dec=2 dec=5 dec=10
Bit Error Rate
Bit Error Rate
2
10
3
10
4
10
Figure 4 MMSE linear detector

ZEROFORCING DETECTOR
The zeroforcing receiver is a natural progression of the decorrelating detector. Now that we have removed the MAI, we want to eliminate the ISI as well. This can be done by taking into consideration each users channel impulse respose. The zero forcing equalizer is successful at eliminating MAI and ISI, but has some tradeoffs. Also, the zeroforcing equalizer suffers the noise enhancement problems as does the decorrelating detector. But In order to improved performance in the zero forcing detector in presence of noise[9].

SIMULATION RESULTS
Figure A, B, C and D show the error rate performance of the bank of matched filter. Decorralator , MMSE and ZF. The simulation scenario is observed that as the MAI increases (the number of users increases) the performance becomes poor. But the decorralator is better performanced than MF. Similarly the MMSE is better performed than decorralator and matched filter. Similarly like this the zero forcing detector is also well performed compared to other
0 1 2 3 4 5 6 7 8 9 10
Eb/No, dB
FigureB: performance of Decoralator
0 Bit error probability for MMSE
mmse=2
mmse=5
mmse=10
mmse=2
mmse=5
mmse=10
10
1
10
Bit Error Rate
Bit Error Rate
2
10
3
10
4
10
0 1 2 3 4 5 6 7 8 9 10
Eb/No, dB
FigureC: performance of MMSE
detectors. 0
Figure E, F, and G shows the comparison of error 10
performance of different detectors. The zero forcing detector is well performed compared to the other detector
Bit error probability for zero forcing
ZF=10 ZF=5 ZF=2
in all cases like 2user, 5user and also 10user case . 101
Bit Error Rate
Bit Error Rate
Bit error probability curve for matched filter
K=2 K=5
K=10
K=2 K=5
K=10
2
10
1
10
2
2
3
Bit Error Rate
Bit Error Rate
10 10
3
10
4
10
0 1 2 3 4 5 6 7 8
4
10
0 1 2 3 4 5 6 7 8 9 10
Eb/No, dB
FigureA: performance of Matched filter
Eb/No, dB
FigureD: performance of ZF
0 comparison of Bit error probability for different detectors for 2 users
10
ZF
MMSE

CONCLUSIONS
This Paper is a compilation of different approaches to linear multiuser detection. The requirement of this
1 DEC
10 MF
Bit Error Rate
Bit Error Rate
2
10
3
10
4
10
5
10
1 2 3 4 5 6 7 8 9 10
Eb/No, dB
FigureE: Comparison of Detectors for 2 user
comparison of Bit error probability for different detectors for 5users
0
MF DEC MMSE
ZF
MF DEC MMSE
ZF
10
1
Bit Error Rate
Bit Error Rate
10
2
10
3
10
0 1 2 3 4 5 6 7 8
Eb/No, dB
FigureF: Comparison of Detectors for 5 user
technology was motivated by studying the conventional detector. The matched filter bank just ignores the correlative structure of the MAI present in CDMA systems. Further, it was also shown that in the absence of noise, the conventional detector is a totally unreliable detector. This called for the need for better detectors. The decorrelating detector was then introduced which takes the conventional detector one step further by incorporating the correlative structure of the MAI in the detection. This implied that the decorrelating detector could be improved upon. The MMSE linear detector was then shown to take the decorrelating detector one step further by incorporating some SNR information along with the correlative structure of MAI. Thus, the performance was better than the decorrelating detector at high SNRs. It must also be noted that when the background noise is totally absent (infinite SNR). Finally the zero forcing detector is well performed. The choice of the MUD algorithm depends on a lot of factors like the application, channel information available, availability of training sequences, complexity cost and overhead involved.

REFERENCES


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Clark, George C., Jr., and J. Bibb Cain (1981), rrorCorrection Coding for Digital Communications, New York: Plenum Press.

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J. C. Liberti (1996), Spatial Processing for Higher Wireless Systems, Bellcore Pub. IM558.

J.G. Proakis (1995), Digital Communications,3rd Edition, New York: McGrawHilI.
0 comparision of MF, DEC, MMSE and ZF for 10 users
10
Bit Error Rate
Bit Error Rate
1
10
ZF MMSE DEC MF

Jochen Schiller (2003), Mobile Communications, 2nd Edition, Addison Wesley.

S. Verdu, Multiuser Detection Cambridge University Press, 1998.

D.R. Brown, D.L. Anair, C.R. Johnson, Jr.,'' Linear Detector Length Conditions for DSCDMA Perfect Symbol Recovery'' to appear in Proc. IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications, Mar. 1999.
2
10
0 1 2 3 4 5 6 7 8 9 10
. Eb/No, dB
FigureG: Comparison of Detectors for 10 user