1. 1 Multi-user Detection Gwo-Ruey Lee

2. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA Model/ Asynchronous CDMA Model Single-user Matched Filter Optimum Multi-user Detection Decorrelating Detector Non-Decorrelating Linear Multi-user Detection Decision-Driven Multi-user Detection

3. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 3 Multiple Access Communication Several transmitters share a common channel, e.g.,  mobile telephones transmitting to a base station  ground stations communicating with a satellite,...

4. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 4 Multiple Access Communication The receiver obtains the superposition of the signals sent by the active transmitters

5. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 5 Multiple Access Communication Frequency Division Multiple Access (FDMA)  FDMA assigns a different carrier frequency to each user so that the resulting spectra so not overlap

6. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 6 Multiple Access Communication Time Division Multiple Access (TDMA)  In TDMA, time is partitioned into slots assigned to each incoming digital stream in round-robin fashion. Synchronization is required.

7. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 7 Multiple Access Communication Code Division Multiple Access (CDMA)  Users are assigned different signature waveforms. Each transmitter send its data stream by modulating its own signature waveform as in a single-user digital communication system.

8. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 8 Multiple Access Communication Code Division Multiple Access (CDMA)  Direct Sequence Spread Spectrum (DS-SS)

9. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 9 Multiple Access Communication Code Division Multiple Access (CDMA)  Frequency Hopping Spread Spectrum (FH-SS)

10. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 10 Multiple Access Communication Near-far problem:  Any interferer that is sufficiently powerful receiver causes arbitrarily high performance degradation. The objective of multi-user detection is:  the design and analysis of digital demodulation in the presence of multi-access interference (MAI).

11. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 11 Synchronous CDMA Model Basic Synchronous CDMA Model where  is the inverse of the data rate.  is the deterministic signature waveform assigned to the k-th user. It is normalized such that  is the received amplitude of the k-th user's signal.  is the bit transimitted by the k-th user.  is the white Gaussian noise, which is uncorrelated with the transmitted signals, and has unit power spectral density.

12. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 12 Synchronous CDMA Model b1b1 A1A1 s1(t)s1(t) b2b2 A2A2 s2(t)s2(t) bKbK AKAK sK(t)sK(t)...... y(t)y(t) n(t)n(t)

13. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 13 Synchronous CDMA Model The crosscorrelation of two signature waveforms, and, is By Cauchy-Schwarz inequality, the crosscorrelation satisfies The cross correlation matrix, defined by has diagonal elements equal to 1 [see (29) and (30)], and is symmetric nonnegative definite, i.e.,

14. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 14 Asynchronous CDMA Model Basic Asynchronous CDMA Model  where are the time offsets that correspond to users  One special case happens when then asynchronous model reduces to synchronous model  Another special case happens when and (a single user undergoes multipaths), it becomes

15. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 15 CDMA Model Direct-sequence spread spectrum  Direct-sequence waveforms where  is the chip waveform that satisfies and  N is the number of chips per bit N, 

16. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 16 Single-user Matched Filter Consider the synchronous CDMA model, where only a single user exist: The signal listed above is passed through a linear filter, the output of which is then sampled at T

17. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 17 Single-user Matched Filter One problem is: Find the linear filter h(t) that maximize the signal-to-noise ratio at the filter output Y, i.e., By Cauchy-Schwarz inequality, we have

18. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 18 Single-user Matched Filter The objective function satisfies, where the equality holds when  Notice that in this derivation, we did not invoke the fact that noise is Gaussian. Note that is a Gaussian r.v. with zero- mean and unit variance.

19. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 19 Single-user Matched Filter The probability of error, in determining from, is

20. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 20 Single-user Matched Filter Single-user Matched Filter in Rayleigh Fading  single user model  Assuming that A and s(t) are given, we want to find the estimate of b,, that minimizes  The first and second terms on the RHS of above equation are irrelevant to b, and we can write the minimization problem as a maximization problem:

21. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 21 Single-user Matched Filter  The solution to

22. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 22 Single-user Matched Filter Discrete-time Synchronous Models  Multi-user detection commonly have a front-end, whose objective is to obtain a discrete-time process from the received continuous-time waveform y(t).  Matched filter outputs. Sync K. Sync 3. Sync 2. Sync 1 Matched Filter User 1 Matched Filter User 1 Matched Filter User 2 Matched Filter User 2 Matched Filter User 3 Matched Filter User 3 Matched Filter User K Matched Filter User K y(t) y1y1 y2y2 y3y3 yKyK............

23. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 23 Single-user Matched Filter  In the synchronous case, the outputs of the bank of matched filters are

24. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 24 Single-user Matched Filter  The vector form of above equation is where and n is a zero-mean Gaussian random vector with covariance matrix equal to, i.e.,

25. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 25 Maximum A Posteriori (MAP) and Maximum Likelihood (ML) Detectors The MAP-detector chooses the hypothesis that maximizes the a posteriori probability, and achieves the minimum probability of error. The ML-detector chooses the hypothesis that maximizes the likelihood function, it achieves the minimum probability of error, when the hypotheses are equally probable (P 0 = P 1 ).

26. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 26 Maximum Likelihood (ML) Detectors

27. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 27 Maximum Likelihood (ML) Detectors

28. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 28 Maximum Likelihood (ML) Detectors

29. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 29 Maximum Likelihood (ML) Detectors

30. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 30 Maximum Likelihood (ML) Detectors Are they the same?

31. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 31 Individual Optimum ML-Detector

32. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 32 Individual Optimum ML-Detector

33. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 33 Individual Optimum ML-Detector

34. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 34 Joint and Individual Optimum ML- Detector for the K-User Scenario Recall the discrete-time synchronous CDMA model that The joint optimum ML-detector is the solution to

35. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 35 Joint and Individual Optimum ML- Detector for the K-User Scenario The maximization problem is a combinatorial optimization one, which means that the set of possible arguments comprises a finite set. Combinatorial optimization problems can always be solved by exhaustive search, i.e., we evaluate the objective function at all possible arguments, and select our detected value to be the argument that produces the maximum. Joint optimum decisions would be preferable to minimum bit-error-rate decisions due to their complexity.

36. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 36 Decorrelation Detector Recall that the output vector of the bank of K matched filters is  Assume that R is invertible. Premultiplying by give In the absence of noise n, the k-th component of is The decorrelating detector detects through

37. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 37 Decorrelation Detector. Sync 3. Sync 2. Sync 1 Matched Filter User 1 Matched Filter User 1 Matched Filter User 2 Matched Filter User 2 Matched Filter User 3 Matched Filter User 3 Matched Filter User K Matched Filter User K y(t) R -1............. Sync K

38. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 38 Decorrelation Detector Note that the decorrelating detector is influenced by additive noise, and not by other interferers ( ). Two features of the decorrelating detectors are  1. It does not need to know the received amplitudes ( ).  2. Detection of each user can be implemented independently. Note that

39. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 39 Decorrelation Detector From the fact that We know that is orthogonal to any linear combination of. If is linearly independent, we can find from for all k, and can have the modified decorrelating detector.

40. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 40 Decorrelation Detector Modified decorrelating detector. Sync 3. Sync 2. Sync 1 Matched Filter y(t)............. Sync K

41. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 41 Decorrelation Detector In the two user scenario,

42. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 42 Decorrelating Detector and ML-Criterion

43. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 43 Non-Decorrelating Detector - LMMSE

44. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 44 Non-Decorrelating Detector - LMMSE. Sync 3. Sync 2. Sync 1 Matched Filter User 1 Matched Filter User 1 Matched Filter User 2 Matched Filter User 2 Matched Filter User 3 Matched Filter User 3 Matched Filter User K Matched Filter User K y(t) [R+  2 A -2 ] -1............. Sync K

45. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 45 Properties of the LMMSE Detector

46. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 46 LMMSE Detector for the Bank of Orthonormalized Filters

47. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 47 LMMSE Detector Maximizes Signal to Interference Ratio

48. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 48 Minimum Output Energy Detector

49. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 49 Successive Cancellation

50. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 50 Successive Cancellation

51. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 51 Successive Cancellation Equivalent implementation of successive cancellation for two synchronization users

52. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 52 Successive Interference Cancellation (SIC) It requires knowledge of the received amplitude. User weaker than the user (or users) of interest are neglected. In contrast to the (nonadaptive) multi-user linear detectors, successive cancellation require no arithmetic computations with the crosscorrelation beyond their product with the received amplitudes. The time complexity per bit is linear in the number of user It applies not only to the basic CDMA model (where signals are linearly modulated ) but to any multiple-access channel where the receiver observes the additive superposition of the transmitted signal. The demodulation delay in successive cancellation grows linearly with the number of user.

53. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 53 Partial Parallel Interference Cancellation (PPIC) Multistage PPIC detection scheme with the discrete-time equivalent complex baseband representation for synchronous CDMA systems.

54. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 54 Partial Parallel Interference Cancellation (PPIC) Discrete-time signal r (m) at the chip rate Decision statistic of the ith bit of the conventional receiver for the kth user

55. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 55 Adaptive NLMS-PPIC

56. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 56 Multi-user Detection Readings  SERGIO VERDU, Multi-user Detection, CAMBRIDGE, 1998.  Chapter 2 – 2..1, 2.2, 2.9  Chapter 4 – 4.1  Chapter 5 – 5.1  Chapter 6 – 6.1, 6.2  Chapter 7 – 7.1