Ber Performance of Linear Multiuser Detectors in DS-CDMA

Ber Performance of Linear Multiuser Detectors in DS-CDMA

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 Multi-user Detectors in Direct Sequence Code Division Multiple Access (DS-CDMA) system. Multiple access interference (MAI) limits the capacity of Direct Sequence Code Division Multiple Access (DS-CDMA) systems. In CDMA systems MAI is considered as additive noise and a matched filter bank is employed. Multi-user detectors are classified as optimal and suboptimal. The main drawback of the

optimal multi-user 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 non-linear algorithms. In this paper, introduce linear Multi-user Detectors in Direct Sequence Code Division Multiple Access (DS-CDMA) system. Analysis is to be carried out and simulations to be done.

Keywords: DS-CDMA, 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 signal-to- interference ratio for everyone.

In DS-CDMA communication system, users are multiplexed by distinct codes rather than by orthogonal frequency bands or by orthogonal time slots. A conventional DS-CDMA 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. Multi-user detection is a technology that spawned in the early 80s. It has now developed into an important, full-fledged field in multi-access communications. Multi-user Detection (MUD) is the intelligent estimation /

Figure.1 A typical multi-user 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 multi-access communication systems (CDMA/ TDMA/FDMA) where simultaneously occurring digital streams of information interfere with each other. Conventional detectors based on the matched by the cross-correlation matrix

of the signature sequences. Hence, detectors that take into account this correlation would perform better than the conventional matched filter-bank [1-7].

1. 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 K-user 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 cross-correlation 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 cross-correlation matrix is then defined as

   R ij

   R is a symmetric, non-negative definite, toeplitz matrix

2. 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 single-user digital communication systems, the matched filter is used to generate sufficient statistics for signal detection. In the case of a multi-user 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 multi-user detectors. As shown in figure 3, the decorrelating detector operates by processing the output of the matched filter bank with the R-1 operator where R is the cross-correlation 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, near-far resistance and MMSE receiver is another kind of linear multi-user 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 maximum-likelihood [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)

3. DECORRELATING DETECTOR

   An optimal receiver must be capable of decoding the bits error-free 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

   1. ZERO-FORCING DETECTOR

      The zero-forcing 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 zero-forcing 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].

   2. 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

      Figure-B: 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

      Figure-C: 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 2-user, 5-user and also 10-user case . 10-1

      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

      Figure-A: performance of Matched filter

      Eb/No, dB

      Figure-D: performance of ZF

      0 comparison of Bit error probability for different detectors for 2 users

      10

      ZF

      MMSE

   3. CONCLUSIONS

      This Paper is a compilation of different approaches to linear multi-user 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

      Figure-E: Comparison of Detectors for 2 -user

      comparison of Bit error probability for different detectors for 5-users

      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

      Figure-F: 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.

   4. REFERENCES

1. A J. Viterbi (1994), The Orthogonal-Random Waveform Dichotomy for Digital Mobile Personal Communications, IEEE Pers. Commun, 1st qtr., pp. 18-24.

2. C. Kchao and G. Stuber (1993), Performance Analysis of a Single Cell Direct Sequence Mobile Radio System, IEEE Trans. on Commun., vol . COM-41, no 10, pp. 1507-1516.

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

4. D. V. Sarwate and M. B. Pursley (1980), Cross correlation Properties of Pseudorandom and Related Sequences, Proc. IEEE, vol. 68, no. 5, pp. 593-619.

5. J. C. Liberti (1996), Spatial Processing for Higher Wireless Systems, Bellcore Pub. IM-558.

6. J.G. Proakis (1995), Digital Communications,3rd Edition, New York: McGraw-HilI.

   0 comparision of MF, DEC, MMSE and ZF for 10 users

   10

   Bit Error Rate

   Bit Error Rate

   -1

   10

   ZF MMSE DEC MF

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

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

9. D.R. Brown, D.L. Anair, C.R. Johnson, Jr.,'' Linear Detector Length Conditions for DS-CDMA 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

Figure-G: Comparison of Detectors for 10 -user