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Physical Layer Challenges in Telecommunication Systems: Optimum Multiuser Detection in CDMA System Fatih Alagöz Department of Computer Engineering Bogazici

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  • Physical Layer Challenges in Telecommunication Systems:

    Optimum Multiuser Detection in CDMA SystemFatih Alagz Department of Computer Engineering Bogazici UniversityCMPE300 Project Presentation

  • OutlineCode Division Multiple Access (CDMA) ModelProblem statement and motivationOptimum multiuser detection.The proposed algorithm for CDMA System: complexity and performance measures.Conclusion Project Description!!!.

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

  • CDMA System Model 1KMulti-pathsMulti-paths1 billion mobile users !!! $ 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.

  • CDMA in AWGN Channel (2)The output of K filters matched to the users signature waveform and sampled at T are:


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

  • The Idea View the coefficients of the optimum metric as weights indicating the order in which the bits are estimatedAchieve decision regions to reduce the complexity while providing optimum detectionAim is to reduce computational complexity while maintaining the optimum detection 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.

  • RCML Algorithm (2)bn is optimum solution iff Example: K=3,

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

    Compare bn versus bmi

    Resulting Inequality

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


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


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


    bn =[+ + +] > bm4 = [+ - -]


    bn =[+ + +] > bm5 = [- - +]


    bn =[+ + +] > bm6 = [- + -]


    bn =[+ + +] > bm7 = [- - -]


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

  • RCML Algorithm (3)Rule.1Rule.2ifelseifPRUNEendRule.3Once User i is optimally detected, apply the rules to K-1 user system.if

  • A Few Results: Complexity Blue: OptimumRed: SDPGreen: RCMLComplexity

    Number of Users (K)

  • A Few Results: Average Bit Error Rate (BER) in lightly loaded CDMA SystemsBER

    Signal to Noise Ratio (Eb/No) in (dB)

  • A Few Results: Average Bit Error Rate (BER) in highly loaded CDMA SystemsBER

    Signal to Noise Ratio (Eb/No) in (dB)

  • Expert Comments... for the Proposed RCML Algorithm

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

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

  • What can be Cooked Next ? Test the performance of algorithms for Asynchronous CDMA systems Extend the RCML algorithm for Devising a New 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 channels

  • Please Read F. Alagoz, A New Algorithm for Optimum Multiuser Detection in Synchronous CDMA Systems, Int. J. of Electronics & Commun., vol. 57, 2003.F. Alagoz, and A. Al-Rustamani A new branch andbound algorithm for multiuser detection, Proc. of Int. GAP Conference, Turkey, June, 2002.F. Alagoz, and M. Abdel-Hafez RCML Algorithm for Suboptimum Multiuser Detection in CDMA Systems, in prep. IEEE Trans. on Commun. (end of 2005).

  • Acknowledgements.Dr. P. Tan of Chalmers University, Sweden, for providing the material on SDBP algorithm

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

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

    My Students: Haifa Abdulla, Muna Alawi, Amna Rashid, Sally Asmar and Dina Nasr.

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

  • Feel Free to Contact Me Department of Computer Eng.Bogazici University (+)[email protected]://>

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

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