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Physical Layer Challenges in Telecommunication Systems:
Optimum Multiuser Detection in CDMA System
Fatih AlagFatih Alagöözz
Department of Department of Computer Engineering Computer Engineering Bogazici Bogazici University University
CMPE300 Project CMPE300 Project Presentation Presentation
Outline
•Code Division Multiple Access (CDMA) Model
•Problem statement and motivation
•Optimum multiuser detection.
•The proposed algorithm for CDMA System: complexity and performance measures.•Conclusion
•Project Description!!!.
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:
(2) ,...,1 )()(10
KknbEbEdttstyy k
K
kii
iikikk
T
kk
T
kk
T
kiik dttntsndttsts00
)()( and )()(
ijjiiii
K
i
K
ijjiij
K
iii
EEyEA
bbBbAK
ij
1
1 11}1,1{
^
B and where
(3) max argb
b
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)
)sgn(,1
ii
K
ijj
iji yby
thenRule.1
Rule.2 )sgn(, ii
K
ijji ybyy
then
,11
K
Mjj
M
ii yy
Miyb ii ,...2,1)sgn(
if
elseif
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
WhatWhat can be C can be Cookookeded Next ? 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 200(end of 20055).).
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 Students: My Students: Haifa Abdulla, Muna Alawi, Amna Haifa Abdulla, Muna Alawi, Amna Rashid, Sally Asmar 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 … Department of Department of Computer Eng.Computer Eng.Bogazici UniversityBogazici University
(+)(+)66526652
falagoz@[email protected]://www.http://www.boun.edu.trboun.edu.tr/alagoz/alagoz
<<<<<< Any Questions >>>>>> <<<<<< Any Questions >>>>>>
(11)
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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]
b=[0 0 0]
Extra 2: Example of RCML Extra 2: Example of RCML detection for K=3 usersdetection for K=3 users