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  • 1. Multiuser Detection for CDMA Anders Høst-Madsen (with contributions from Yu Jaechon, Ph.D student) TR Labs & University of Calgary
  • 2. Overview <ul><li>Introduction </li></ul><ul><ul><li>Communications Signal Processing </li></ul></ul><ul><li>CDMA </li></ul><ul><ul><li>3G CDMA </li></ul></ul><ul><li>Multiuser Detection (MUD) </li></ul><ul><ul><li>Basics </li></ul></ul><ul><ul><li>Blind MUD </li></ul></ul><ul><ul><li>Group-blind MUD </li></ul></ul><ul><ul><li>Performance </li></ul></ul>
  • 3. Some Impression of a Changing Korea <ul><li>Compared with 2 years ago </li></ul><ul><ul><li>A lot has changed, fast </li></ul></ul><ul><li>Internet </li></ul><ul><ul><li>90% of subway ads about internet </li></ul></ul><ul><ul><li>All ads have internet address </li></ul></ul><ul><li>Cell phones </li></ul><ul><ul><li>Everyman’s </li></ul></ul><ul><ul><li>Fashion item </li></ul></ul><ul><ul><li>Small! </li></ul></ul>Even babies in Korea have mobile phones!
  • 4. The Demands <ul><li>“ The future of the internet is wireless,” Steve Balmer, CEO Microsoft </li></ul><ul><li>Now </li></ul><ul><ul><li>Internet through telephone </li></ul></ul><ul><ul><li>Wireless voice phones </li></ul></ul><ul><li>Emerging </li></ul><ul><ul><li>High-speed internet (ADSL, cable, satellite, fixed wireless) </li></ul></ul><ul><ul><li>Some wireless terminals (Nokia 9000, Palm VII, RIM Blackberry) </li></ul></ul><ul><ul><li>Web on wireless phones </li></ul></ul><ul><li>Future </li></ul><ul><ul><li>Wireless everything </li></ul></ul><ul><ul><ul><li>Internet terminals </li></ul></ul></ul><ul><ul><ul><li>LAN, home networks </li></ul></ul></ul><ul><ul><ul><li>Devices (Bluetooth) </li></ul></ul></ul><ul><ul><li>Wireless video phones? </li></ul></ul><ul><ul><li>More webphones than wired internet connections in 2004 (Ericsson, Nokia, Motorola) </li></ul></ul><ul><ul><li>All wireless phones web enabled from 2001 (Nokia) </li></ul></ul>
  • 5. The Constraints <ul><li>Limited spectrum </li></ul><ul><li>Limited power </li></ul><ul><li>Complex channels </li></ul><ul><ul><li>Multipath, shading </li></ul></ul><ul><ul><li>Interference: Other users, other electronics </li></ul></ul>
  • 6. Solutions <ul><li>Efficient compression </li></ul><ul><li>Coding </li></ul><ul><li>Channel signal processing </li></ul><ul><li>Efficient, cost-controlled media access </li></ul><ul><li>Software radio </li></ul><ul><li>New standards for mobile communications 3rd generation systems </li></ul><ul><ul><li>W-CDMA </li></ul></ul><ul><ul><li>cdma2000 </li></ul></ul><ul><li>4th generation by year 2010 </li></ul>
  • 7. The Communication Channel <ul><li>Channel Dispersion </li></ul><ul><ul><li>(Low pass) filter effect (wireline filters, frequency selective fading) </li></ul></ul><ul><ul><li>Intersymbol Interference (ISI) </li></ul></ul><ul><ul><li>Non-linear distortions (power amplifiers) </li></ul></ul>Com- pression Transmitter Receiver Unknown channel Source coding Channel coding Adaptive transmission Signal processing <ul><li>Multipath </li></ul><ul><ul><li>Slow fading </li></ul></ul><ul><ul><li>Time selective fading </li></ul></ul><ul><ul><li>Space-selective fading </li></ul></ul><ul><li>Interference </li></ul><ul><ul><li>External Interference (other electronics, communications, cars) </li></ul></ul><ul><ul><li>Multiple Access Interference (MAI) (other users using the same channel) </li></ul></ul><ul><ul><li>Echo (line hybrids, room microphones, hands-free mobiles) </li></ul></ul>Speech Data Video
  • 8. The Wireless Channel Frequency-selective fading: ISI Doppler spread: Time-varying channel Space-selective fading: Beamforming Path loss
  • 9. DS/CDMA † <ul><li>Applications </li></ul><ul><ul><li>US IS-95 standard </li></ul></ul><ul><ul><li>Korean cellular system </li></ul></ul><ul><ul><li>IMT-2000 (wide band (WB) CDMA) </li></ul></ul><ul><ul><li>Part of future European Frames standards </li></ul></ul><ul><li>Principle </li></ul><ul><ul><li>Users share frequency and time </li></ul></ul><ul><ul><li>Distinguished by unique code </li></ul></ul><ul><ul><li>Separated by correlation with code </li></ul></ul>† Direct Sequence Code Division Multiple Access
  • 10. 3G CDMA <ul><li>cdma2000 </li></ul><ul><ul><li>North America, Korea? </li></ul></ul><ul><ul><li>Compatible with IS-95 </li></ul></ul><ul><ul><li>Promoted by Qualcomm </li></ul></ul><ul><ul><li>Long codes, synchronous </li></ul></ul><ul><li>Wideband CDMA (WCDMA) </li></ul><ul><ul><li>Europe, Japan </li></ul></ul><ul><ul><li>Compatible with GSM </li></ul></ul><ul><ul><li>Promoted by Nokia, Ericsson </li></ul></ul><ul><ul><li>Long/short codes, asynchronous </li></ul></ul><ul><ul><li>FDD and TDD modes </li></ul></ul>
  • 11. Long versus Short Codes <ul><li>Principle </li></ul><ul><ul><li>Code “infinite” </li></ul></ul><ul><li>Applications </li></ul><ul><ul><li>IS-95 </li></ul></ul><ul><ul><li>cdma2000 </li></ul></ul><ul><li>Advantages </li></ul><ul><ul><li>Interference averaged out </li></ul></ul><ul><li>Disadvantages </li></ul><ul><ul><li>Limited signal processing options </li></ul></ul><ul><li>Principle </li></ul><ul><ul><li>Code repeats on every symbol </li></ul></ul><ul><li>Applications </li></ul><ul><ul><li>W-CDMA (FDD)? </li></ul></ul><ul><ul><li>W-CDMA (TDD) </li></ul></ul><ul><li>Advantages </li></ul><ul><ul><li>More signal processing options </li></ul></ul><ul><ul><li>Higher capacity </li></ul></ul><ul><li>Disadvantages </li></ul><ul><ul><li>Without advanced processing, high interference </li></ul></ul>Long Codes Short Codes
  • 12. Multi-user Detection <ul><li>Multiple-Access Interference (MAI) </li></ul><ul><ul><li>Due to non-orthogonality of codes </li></ul></ul><ul><ul><li>Caused by channel dispersion </li></ul></ul><ul><li>Multiuser detection </li></ul><ul><ul><li>reduction of MAI through interference cancellation </li></ul></ul><ul><ul><li>2-4 times capacity increase of cellular systems </li></ul></ul><ul><ul><li>Probably part of future wireless systems (cellular, satellite, WLAN) </li></ul></ul><ul><ul><ul><li>Included in WCDMA TDD standard </li></ul></ul></ul><ul><ul><ul><li>Several companies involved: Siemens, Nokia, Nortel </li></ul></ul></ul><ul><ul><ul><li>Some field trials [Siemens] </li></ul></ul></ul>
  • 13. History of Multi-user Detection Optimum Multi-user Detector Linear Multi-user Detector Subtractive Interference Cancellation Detector Decorrelating Detector Parallel IC Successive IC Blind MMSE Detector Blind Decorrelating Detector Minimum Mean Squared Error (MMSE) Detector Group-Blind MMSE
  • 14. Synchronous CDMA <ul><li>K users with no ISI. </li></ul><ul><li>Sufficient to consider signal in single symbol interval, i.e., [0,T] </li></ul><ul><li>Received signal </li></ul><ul><li>where </li></ul><ul><ul><li>b k  {-1,+1} is the k ’th user’s transmitted bit. </li></ul></ul><ul><ul><li>A k is the k ’th user’s amplitude </li></ul></ul><ul><ul><li>s k ( t ) is the k ’th user’s waveform (code or PN sequence) </li></ul></ul><ul><ul><li>n ( t ) is additive, white Gaussian noise. </li></ul></ul>
  • 15. Conventional detector Matched filter bank s 1 (t) s 2 (t) s K (t) t = i T t = i T t = i T y 1 y 2 y K ......... ......... r(t) Decision Decision Decision
  • 16. Detection of CDMA signals <ul><li>The signal is processed by cross correlation (or matched filtering): </li></ul><ul><li>In the conventional detector, the estimate of the k ’th bit is </li></ul><ul><li>If the MAI term is not small, the error probability will be large </li></ul><ul><li>MAI can be kept small by </li></ul><ul><ul><li>small cross correlation between codes ( small) </li></ul></ul><ul><ul><li>Power control (all A i same value) </li></ul></ul>Desired signal Multiple Access Interference (MAI) noise
  • 17. Signals on Vector Form <ul><li>The signal is processed by cross correlation (or matched filtering): </li></ul>
  • 18. Signals on Vector Form <ul><li>The signal is processed by cross correlation (or matched filtering): </li></ul>
  • 19. Signals on Vector Form <ul><li>The signal is processed by cross correlation (or matched filtering): </li></ul>
  • 20. Signals on Vector Form <ul><li>The signal is processed by cross correlation (or matched filtering): </li></ul>
  • 21. Signals on Vector Form <ul><li>The signal is processed by cross correlation (or matched filtering): </li></ul>=1 =  12 =n 1 =1 =  12 =n 2 R A b n
  • 22. Detection of CDMA signals 2 <ul><li>The output y =[ y 1 , y 2 ,..., y K ] T is sufficient statistic for b =[ b 1 , b 2 ,..., b K ] T </li></ul>
  • 23. Optimum Multi-user Detector <ul><li>Too complex : 2 K Comparison </li></ul><ul><li>Impractical </li></ul><ul><li>S. Verdú, Optimum multiuser signal detection , PhD thesis, University of Illinois at Urbana-Champaign, Aug. 1984. </li></ul>Viterbi algorithm ... ... output correlator correlator correlator
  • 24. Linear Multi-User Detectors <ul><li>Decorrelating detector </li></ul><ul><li>General linear detector </li></ul><ul><li>Linear MMSE detector </li></ul><ul><ul><li>Minimizes </li></ul></ul><ul><ul><li>Gives </li></ul></ul><ul><ul><li>Lower bit error rate (BER) than decorrelating </li></ul></ul>
  • 25. Parallel Interference Canceller (PIC) <ul><li>Received signal </li></ul><ul><li>Suppose b known: </li></ul><ul><li>Use initial estimate of b </li></ul><ul><li>Advantages </li></ul><ul><ul><li>works for long codes </li></ul></ul><ul><ul><li>Each stage simple (no matrix inversion) </li></ul></ul><ul><li>Problems </li></ul><ul><ul><li>If bit wrong, magnifies MAI </li></ul></ul><ul><ul><li>Many stages needed </li></ul></ul>
  • 26. Blind Multiuser Detection <ul><li>Traditional, non-blind MUD </li></ul><ul><ul><li>Codes of all users known </li></ul></ul><ul><ul><li>Sufficient statistics </li></ul></ul><ul><li>Blind MUD </li></ul><ul><ul><li>Only code of desired user known </li></ul></ul><ul><ul><li>Similar to beam forming in antenna arrays </li></ul></ul><ul><ul><li>Works only for short codes </li></ul></ul><ul><ul><li>Mobile station </li></ul></ul>
  • 27. System Model - Synchroneous CDMA <ul><li>Signal is sampled at chip rate (from matched filter) </li></ul><ul><li>Received signal on vector form </li></ul><ul><li>b k (  1): transmitted bits </li></ul><ul><li>A k : received amplitude </li></ul><ul><li>s k : code waveforms </li></ul><ul><li>n : white, additive noise </li></ul>
  • 28. Linear Detectors <ul><li>Conventional detector </li></ul><ul><li>General linear detector: </li></ul>
  • 29. The Decorrelating Detector <ul><li>Choose w 1 so that </li></ul><ul><li>Detector: </li></ul>
  • 30. The MMSE Detector <ul><li>Choose w 1 to satisfy </li></ul><ul><li>Choose w 1 to satisfy </li></ul><ul><li>Solution </li></ul>
  • 31. The MMSE Detector <ul><li>Choose w 1 to satisfy </li></ul><ul><li>Solution </li></ul>=1 =0 =0
  • 32. The MMSE Detector <ul><li>Choose w 1 to satisfy </li></ul><ul><li>Solution </li></ul>R
  • 33. The Blind MMSE Detector <ul><li>Choose w 1 to satisfy </li></ul><ul><li>Solution </li></ul>Bit 1 Bit 2 Bit 3 Bit 4 Bit 5 Bit 6 Bit ... r 1 r 2 r 3 r 4 r 5 r 6 r... Chip rate sampling
  • 34. Subspace Methods <ul><li>Correlation matrix of received data </li></ul><ul><li>The correlation matrix for CDMA has EVD </li></ul><ul><li>The MMSE detector is given by: </li></ul>
  • 35. Subspace Tracking <ul><li>Computation of </li></ul><ul><li>Direct EVD </li></ul><ul><ul><li>Estimate R: </li></ul></ul><ul><ul><li>Calculate EVD of R </li></ul></ul><ul><ul><li>Find U s and  s from K largest eigenvalues </li></ul></ul><ul><li>Singular Value Decomposition </li></ul><ul><ul><li>Calculate SVD of [ r 0 r 1 ... r n-1 ] </li></ul></ul><ul><ul><li>Find U s and  s from K largest singular values </li></ul></ul><ul><li>Subspace tracking </li></ul><ul><ul><li>Low complexity methods of dynamically updating EVD/SVD </li></ul></ul><ul><ul><li>complexity O(MK 2 ) (e.g., F2) </li></ul></ul><ul><ul><li>or O(MK) (e.g., PASTd) </li></ul></ul>
  • 36. Group-Blind MUD <ul><li>Multiple-Access Interference (MAI) </li></ul><ul><ul><li>Intra-cell interference: users in same cell as desired user </li></ul></ul><ul><ul><li>Inter-cell interference: users from other cells </li></ul></ul><ul><ul><li>Inter-cell interference 1/3 of total interference </li></ul></ul>
  • 37. Blind Multi-User Detection <ul><li>Non-Blind multi-user detection </li></ul><ul><ul><li>Codes of all users known </li></ul></ul><ul><ul><li>Cancels only intracell interference </li></ul></ul><ul><li>Blind multi-user detection </li></ul><ul><ul><li>Only code of desired user known </li></ul></ul><ul><ul><li>Cancels both intra- and inter-cell interference </li></ul></ul>
  • 38. Group-blind MUD <ul><li>Codes of some, but not all, users known </li></ul><ul><li>Cancels both intra- and inter-cell interference </li></ul><ul><li>Uses all information available to receiver </li></ul><ul><li>Decreases estimation error </li></ul><ul><ul><li>Decreases BER </li></ul></ul><ul><li>Potentially less computationally complex </li></ul><ul><ul><li>Only one adaptive IC common to all users. </li></ul></ul><ul><ul><li>Adaptive IC can have lower complexity than pure blind IC </li></ul></ul>
  • 39. Group-Blind Hybrid Detector <ul><li>Hybrid detector </li></ul><ul><ul><li>Decorrelating among known users </li></ul></ul><ul><ul><li>MMSE with respect to unknown users </li></ul></ul><ul><ul><li>Has convenient, simple expression </li></ul></ul><ul><li>Algorithm </li></ul><ul><ul><li>Projection onto subspace of known codes </li></ul></ul><ul><ul><li>Orthogonal Projection </li></ul></ul><ul><ul><li>EVD </li></ul></ul><ul><ul><li>Detector </li></ul></ul>
  • 40. Group-Blind Detector
  • 41. Performance Simulations <ul><li>K=7 users with known codes </li></ul><ul><li>Variable number (4 or 10) of users with unknown codes </li></ul><ul><li>Purely random codes of length M=31 </li></ul><ul><li>SNR=20 dB </li></ul><ul><li>Ensemble of 50 different random code assignments is generated </li></ul><ul><li>Median signal to inference and noise ratio (SINR) </li></ul><ul><ul><li>Over all code choices and known users </li></ul></ul><ul><ul><li>total ensemble of 350 </li></ul></ul>
  • 42. Simulation Results <ul><li>7 Known users </li></ul><ul><li>4 Unknown users </li></ul><ul><li>All same power </li></ul>50 100 150 200 250 300 350 400 -2 0 2 4 6 8 10 12 14 16 18 20 SINR(dB) Bits Full Group-blind Blind Direct Non-blind Single user 1 2
  • 43. Simulation Results <ul><li>7 Known users </li></ul><ul><li>10 Unknown users </li></ul><ul><ul><li>4 Unknown users with power 0dB </li></ul></ul><ul><ul><li>6 unknown users with power -6dB </li></ul></ul>50 100 150 200 250 300 350 400 -2 0 2 4 6 8 10 12 14 16 18 20 SINR(dB) Bits Full Group-blind Blind Direct Non-blind Single user 2 1
  • 44. Simulation Results, BER <ul><li>7 Known users </li></ul><ul><li>4 Unknown users </li></ul><ul><li>Blocksize fixed at 200 </li></ul><ul><li>20 different code matrices </li></ul><ul><ul><li>Ensemble of 140 for each SNR value </li></ul></ul><ul><li>Upper curve: 90-percentile </li></ul><ul><li>Lower curve: median </li></ul>0 2 4 6 8 10 12 14 16 18 20 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB) BER Group-blind Blind Non-blind
  • 45. Summary <ul><li>Multiuser Detection </li></ul><ul><ul><li>Gives considerably performance improvement </li></ul></ul><ul><ul><li>Most useful for short codes </li></ul></ul><ul><ul><li>PIC also useful for long codes </li></ul></ul><ul><li>(Group) blind MUD </li></ul><ul><ul><li>For short code MUD </li></ul></ul><ul><ul><li>More useful in real environments </li></ul></ul><ul><li>Future Developments </li></ul><ul><ul><li>Further development of PIC </li></ul></ul><ul><ul><li>Practical, real-time implementation of MUD </li></ul></ul><ul><ul><li>Complexity reduction of (group-) blind MUD </li></ul></ul>

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