Optimum Multiuser Detection in CDMA System

Fatih AlagozFatih Alagoz

Outline

• Code Division Multiple Access (CDMA) System Model

• Problem statement and motivation

• Optimum multiuser detection.

• The proposed algorithm for CDMA System: complexity and performance measures in AWGN Channel.

• Conclusion & future work.

Multiple Access Communication Systems

• Frequency Division Multiple Access- (FDMA) • Time Division Multiple Access- (TDMA) • Code Division Multiple Access (CDMA)

FDMA …. Fj Fj+1 ...

TDMA

...

Tj

Tj+1

...CD

MA

CDMA System ModelCDMA System Model

1

K

1

P

Multi-paths

Multi-paths

1 billion mobile users !!!1 billion mobile users !!! $ US 100 billion/year !!!$ US 100 billion/year !!!

• Optimum multiuser detection: (find optimum using exhaustive search algorithm) i.e., 2K computational complexity in the # of users, K.

• Exceptions with polynomial complexity: stringent requirements on the signature waveforms design.

• These requirements limit the system capacity.• Motivation: Design optimum/suboptimum detectors

with acceptable complexity and performance.

Problem statement & motivation

CDMA in AWGN Channel (1)

The received signal employing antipodal signaling:

where: K: number of users, Ek: Energy/bit for user k, sk(t): unit-energy signature waveform for user k, bk{1,-1}: bit value for user k, T: bit interval, n(t): Additive White Gaussian Noise (AWGN) with one-sided power spectral density No.

(1) 0 ),()()(1

TttnbtsEtyK

kkkk

CDMA in AWGN Channel (2)• The output of K filters matched to the users signature

waveform and sampled at T are:

where

• The output of the matched filters are sufficient statistics for the optimum detector:

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The IdeaThe Idea

View the coefficients of the optimum metric as weightsView the coefficients of the optimum metric as weights indicating the order in which the bits are estimatedindicating the order in which the bits are estimated

Achieve decision regions to reduce the complexity Achieve decision regions to reduce the complexity while providing optimum detectionwhile providing optimum detection

Aim is to reduce computational complexity while Aim is to reduce computational complexity while maintaining the optimum detectionmaintaining the optimum detection

No-need to compute the insignificant terms !!!No-need to compute the insignificant terms !!!

Reduced Complexity MaximumLikelohood (RCML) Algorithm (1)

• It is based on the Maximum Likelihood (ML) metric:

• It views the coefficients of the bits in the ML metric {Ai, Bij, i{1,…K}and j>i} as weights that indicate the order in which bits can be estimated.

• Large values of the coefficients have more effect on deciding the bit value than smaller values, i.e. Order of their contribution to the ML metric.

(4) 1

1 11

K

i

K

ijjiij

K

iii bbBbA

)6(,2....3,2,1 nmm Kmbnb

= y1b1 + y2b2 + y3b3 - 12b1b2 - 13b1b3 - 23b2b3.

RCML Algorithm (2)bn is optimum solution iff

Example: K=3,

Compare bn versus bmi Resulting Inequality

bn =[+ + +] > bm1 = [+ + -] y3>13+

23

bn =[+ + +] > bm2 = [+ - +] y2>12+

23

bn =[+ + +] > bm3 = [- + +] y1>12+

13

bn =[+ + +] > bm4 = [+ - -] y2+y3>12+

13

bn =[+ + +] > bm5 = [- - +] y1+y2>13+

23

bn =[+ + +] > bm6 = [- + -] y1+y3>12+

23

bn =[+ + +] > bm7 = [- - -] y1+y2+y3>0

Table 1. ML metric comparisons for K=3 users.

RCML Algorithm (3)

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iji yby

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Rule.2 )sgn(, ii

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ijji ybyy

then

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if

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PRUNEend

Rule.3 Once User i is optimally detected, apply the rules to K-1 user system.

if

A Few Results: Complexity …A Few Results: Complexity …

4 6 8 10 12 14 16 18 20 22 24

10-2

10-1

100

101

102

103

104

Number of Active Users

Ave

rage

Com

puta

tiona

l Tim

e/s

ML RCMLSDPB

Blue: Blue: OptimumOptimumRed:Red: SDP SDPGreen:Green: RCML RCML

CCoommpplleexxiittyy

Number of Users (K)Number of Users (K)

0 1 2 3 4 5 6 7 8 9

10-5

10-4

10-3

10-2

10-1

100

Eb/No (dB)

Ave

rage

Bit

Err

or P

roba

bilit

y

ML(K=10) RCML(K=10)SDPB(K=10)Singleuser

A Few Results: A Few Results: Average Bit Error Rate (BER) Average Bit Error Rate (BER)

in lightly loaded CDMA Systemsin lightly loaded CDMA Systems

BBEERR

Signal to Noise Ratio (ESignal to Noise Ratio (Ebb/N/Noo) in (dB)) in (dB)

0 1 2 3 4 5 6 7 8 910

-5

10-4

10-3

10-2

10-1

100

Eb/No (dB)

Ave

rage

Bit

Err

or P

roba

bilit

y

ML(K=24) RCML(K=24)SDPB(K=24)Singleuser

A Few Results: A Few Results: Average Bit Error Rate (BER) Average Bit Error Rate (BER)

in highly loaded CDMA Systemsin highly loaded CDMA Systems

BBEERR

Signal to Noise Ratio (ESignal to Noise Ratio (Ebb/N/Noo) in (dB)) in (dB)

Expert Comments... Expert Comments... for the Proposed RCML for the Proposed RCML

Algorithm Algorithm

Complexity is lower than that of Complexity is lower than that of SDP Algorithm and significantly SDP Algorithm and significantly lower than ML (Optimum) Algorithmlower than ML (Optimum) Algorithm

BER performance is better than SDP BER performance is better than SDP algorithm and similar to ML algorithm and similar to ML algorithmalgorithm

Complexity is lower than that of Complexity is lower than that of SDP Algorithm and significantly SDP Algorithm and significantly lower than ML (Optimum) Algorithmlower than ML (Optimum) Algorithm

BER performance is better than SDP BER performance is better than SDP algorithm and similar to ML algorithm and similar to ML algorithmalgorithm

What’s Cooking Next ?What’s Cooking Next ?

Test the performance of algorithms for Asynchronous Test the performance of algorithms for Asynchronous CDMA systems CDMA systems

Extend the RCML algorithm for Devising a New Extend the RCML algorithm for Devising a New Suboptimum Multiuser Detector :Suboptimum Multiuser Detector :

•Consider coefficients that are greater than some certain value Z (eg. mean).

•Terminate the algorithm if the largest value does not change after P stages.

Extend the RCML algorithm for fading channelsExtend the RCML algorithm for fading channels

Please Read Please Read ……

F. Alagoz, F. Alagoz, ““A New Algorithm for Optimum Multiuser Detection in Synchronous CDMA Systems”, ”, Int. J. of Int. J. of Electronics & Commun.Electronics & Commun., vol. 57, 2003., vol. 57, 2003.

F. Alagoz, and A. Al-Rustamani F. Alagoz, and A. Al-Rustamani ““A new branch andbound algorithm for multiuser detection”, , Proc. of Int. Proc. of Int. GAP ConferenceGAP Conference, , Turkey, June, 2002.Turkey, June, 2002.

F. Alagoz, and M. Abdel-Hafez F. Alagoz, and M. Abdel-Hafez ““RCML Algorithm for Suboptimum Multiuser Detection in CDMA Systems”, ”, in prep. in prep. IEEE Trans. on Commun.IEEE Trans. on Commun. (end of 2003).(end of 2003).

AcknowledgementsAcknowledgements….….•Dr. P. TanDr. P. Tan of Chalmers University, Sweden, for of Chalmers University, Sweden, for

providing the material on SDBP algorithmproviding the material on SDBP algorithm

• Dr. A. AlRustamaniDr. A. AlRustamani of Dubai Internet City, UAE, for of Dubai Internet City, UAE, for her collaboration in Algorithm 1 and 2.her collaboration in Algorithm 1 and 2.

•My colleague My colleague Dr. M. Abdel-HafezDr. M. Abdel-Hafez of Electrical Eng. of Electrical Eng. Dept., UAEU, for his constructive criticism.Dept., UAEU, for his constructive criticism.

•My Dear Students: My Dear Students: Haifa Abdulla, Muna Alawi, Haifa Abdulla, Muna Alawi, Amna Rashid, Sally Asmar Amna Rashid, Sally Asmar andand Dina Nasr Dina Nasr..

•Finally, Finally, The UAE University Research AffairsThe UAE University Research Affairs for for their trust at the proposal stage of this work... their trust at the proposal stage of this work... and off course, their financial support during the and off course, their financial support during the course of the research....course of the research....

Feel Free to Contact Me …Feel Free to Contact Me …

<<<<<< Any Questions >>>>>> <<<<<< Any Questions >>>>>>

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Extra1: Simplified form of the Extra1: Simplified form of the metric for Asynchronous CDMA metric for Asynchronous CDMA

SystemSystem

n=1 n=2 n=3 n=4 n=5 n=6

b=[1 0 0]

b=[-1 0 0]

b=[1 1 1]

b=[1 -1 1]

b=[1 1 -1]

b=[1 -1 -1]

b=[-1 1 1]

b=[-1 -1 1]

b=[1 1 1]

b=[-1 -1 -1]

b=[-1 1 -1]

b=[1 -1 1]

b=[-1 -1 1]

b=[1 -1 -1]

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Extra 2: Example of RCML Extra 2: Example of RCML detection for K=3 usersdetection for K=3 users