Computational Complexity of Multiuser Receivers in DS-CDMA Systems Digital Signal Processing (DSP)-I Fall 2004 By Syed Rizvi Department of Electrical & Computer Engineering Old Dominion University
Outline Overview of FDMA & TDMA Systems Overview of DS-CDMA Systems Multiuser receivers Optimal SE Advantages Problems Simulation Results
Overview of FDMA & TDMA FDMA is a fixed assigned protocol Channel bandwidth is divided into non-overlapping frequency bands Transmission time is divided into frames Frames are divided into number of slots Time slots have equal duration User can only transmit in its own time slot Still waste system resources Synchronization is not required Problem Wastage of bandwidth
Overview of DS-CDMA systems Each user has its own code sequence Every channel uses the full available spectrum Need to transform the original signal before actual transmission Code is used to perform transformation Original signal changes to wideband signal Not capacity limited
Overview of DS-CDMA systems User Data [s 1 (t)] X Digital Modulator r 1 (t) X Wideband Signal User s PN code Code f c Generator Data transmission in DS-CDMA systems
Overview of DS-CDMA systems Received signal [r x (t)] Demodulator r (t) X r 1 (t) Decoder S 1 (t) C 1 (t) Data reception in DS-CDMA systems
Multiuser Receivers Multiuser receivers Optimal SE Sub-optimal SE Linear Non-Linear Zero Forcing MMSE SIC PIC
Optimal SE First proposed by Verdu s Consists of a match filter with maximum likelihood detector Choose a good sequence code with good correlation properties Use a maximum likelihood detection instead of linear transformation Give optimal performance
Optimal SE [Problems] Increases receiver complexity Complexity is a linear function of K Knowledge is required Receiver knows signature waveform for each user Receiver knows time delay, phase shift, and amplitudes Computational complexity is O(2 k )
approach Reduces computational complexity Transformation matrix technique Inverse matrix algorithms Combined computational complexity at the receiving end is O(5/4) K
Computational Complexity (Part-I) 10 4 10 3 10 2 Asymptotic Complexity 10 1 10 0 0 1 2 3 4 5 6 7 8 9 10 U s e r s The asymptotic computational complexities versus small number of users
Computational Complexity (Part-II) 10 35 10 30 10 25 10 20 10 15 10 10 Asymptotic Complexity 10 5 10 0 0 10 20 30 40 50 60 70 80 90 100 U s e r s The asymptotic computational complexities versus intermediate number of users
Computational Complexity (Part-III) 10 160 10 140 10 120 10 100 10 80 10 60 Asymptotic Complexity 10 40 10 20 10 0 0 50 100 150 200 250 300 350 400 450 500 U s e r s The asymptotic computational complexities versus large number of users
Signal to Noise Ratio (SNR) for Lightly-loaded network (Part I) 22 20 18 16 14 S N R 18 16 14 12 10 8 6 12 10 8 6 2 4 6 8 10 12 14 16 18 20 22 U S E R S 2 5 8 11 14 17 20 23 26 29 32 U S E R S Approximate value of SNR (db) versus number of users (K=22 and 32) with a random amount of variance for a synchronous DS-CDMA system in a Gaussian channel. S N R
26 24 22 20 18 16 14 12 10 8 6 Multiuser Detection For DS-CDMA Signal to Noise Ratio (SNR) for Lightly-loaded network (Part I) 30 25 20 15 10 5 2 6 10 14 18 22 26 30 34 38 42 U S E R S 2 7 12 17 22 27 32 37 42 47 52 U S E R S Approximate value of SNR (db) versus number of users (K=42 and 52) with a random amount of variance for a synchronous DS-CDMA system in a Gaussian channel. S N R S N R
35 30 25 20 15 10 5 Multiuser Detection For DS-CDMA Signal to Noise Ratio (SNR) for Highly-loaded network (Part I) 45 40 35 30 25 20 15 10 5 2 12 22 32 42 52 62 U S E R S 2 12 22 32 42 52 62 72 82 U S E R S Approximate value of SNR (db) versus number of users (K=62 and 82) with a random amount of variance for a synchronous DS-CDMA system in a Gaussian channel. S N R S N R
50 45 40 35 30 25 S N R 45 40 35 30 25 20 15 10 5 Signal to Noise Ratio (SNR) for Highly-loaded network (Part I) 20 15 10 2 11 20 29 38 47 56 65 74 83 92 U S E R S 5 2 12 22 32 42 52 62 72 82 92 102 U S E R S Approximate value of SNR (db) versus number of users (K=92 and 102) with a random amount of variance for a synchronous DS-CDMA system in a Gaussian channel. S N R
Bit Error Rate (BER) for Lightly-loaded network (Part I) 10 0 10 0 10-1 10-1 BER 10-2 10-2 10-3 10-3 10-4 10-5 Original Algorithm Reduced Algorithm Algorithm 10-4 10-5 0 1 2 3 4 5 6 7 8 9 10 11 Number of users 10
Conclusion We described Optimal SE and the associated problem Too complex for practical implementation Transformation technique can be used to reduce computational complexity Useful for better processing gain