Interleave Division Multiple Access. Li Ping, Department of Electronic Engineering City University of Hong Kong

Transcription

1 Interleave Division Multiple Access Li Ping, Department of Electronic Engineering City University of Hong Kong 1

2 Outline! Introduction! IDMA! Chip-by-chip multiuser detection! Analysis and optimization! IDM space-time coding and IDM coded modulation! Conclusions 2

3 Outline! Introduction! IDMA! Chip-by-chip multiuser detection! Analysis and optimization! IDM space-time coding and IDM coded modulation! Conclusions 3

4 Bacground! Low-rate coded systems: Viterbi and Verdu! Iterative detectors (1998/1999): Moher, Reed, Schlegel, Alexander, Wang and Poor! TCMA (2002) Brannstrom, Aulin and Rasmussen! Graph-code based multiple access (2001): McEliece! Chip-interleaved CDMA (2002): Mahavadevappa and Proais! CDMA power control (2003/2004): Verdu, Shaimai, Caire and Muller 4

5 Some Requirements for Future Wireless Systems! low receiver cost! de-centralized (i.e., asynchronous) control,! simple treatment of ISI,! cross-cell interference mitigation,! diversity against fading,! power efficiency (long battery life),! multi-media services (e.g., mixed voice and IP),! high user number,! high throughput and high spectral efficiency, FDMA? TDMA? CDMA? OFDMA? 5

6 CDMA Spectrum Efficiency (per Dimension) Spectral efficiency (bits/chip) x x x Optimal Matched Filter Eb/N0 (db) 6

7 Outline! Introduction! IDMA! Chip-by-chip multiuser detection! Analysis and optimization! IDM space-time coding! Conclusions 7

8 Interleave Division Multiple Access (IDMA) User-1 C π 1 User- C π + User-K C π K AWGN Key: The interleavers π 1,, π Κ must be user-specific. 8

9 Outline! Introduction! IDMA! Chip-by-chip multiuser detection! Analysis and optimization! IDM space-time coding and IDM coded modulation! Conclusions 9

10 Interleave Division Multiple Access (IDMA) User-1 C π 1 User- C π + User-K C π K AWGN Key: The interleavers π 1,, π Κ must be user-specific. 10

11 Chip-by-Chip Multiuser Detection π π APP DEC-1 r(j) Chip-by-Chip Processing 1 π π APP DEC- 11

12 Chip-by-Chip Detection Gaussian Step 1. Chip-level path model: Step 2. Gaussian approximation: Step 3. Estimation: ( j ) e x r( j) r K = h x ( j) + = 1 Pr( x ( j) =+ 1) ( ) = log Pr( x ( j ) = 1) ( j) = h x ( j) + ζ ( j) ( r( j) E( ( j)) ) n( j) 2 ( r( j) E( ζ( j)) h) exp( ) 2Var( ζ ( j)) = log 2 ( r( j) E( ζ ( j)) + h) exp( ) 2Var( ζ ( j)) 2h = ζ Var( ζ ( j)) 12

13 The Single-Path Chip-by-Chip Detection Algorithm Step 1. Step 2. E ( r( j) ) = h E( x ( j) ) ( ζ ( j) ) = E( r( j ) h E( x ( j) ) E ) K = 1 Var K 2 ( r( j) ) = h Var( x ( j) ) = 1 2 ( ζ ( j) ) = Var( r( j ) h Var( x ( j) ) Var ) Step 3. 2h e x j r j j Var( ζ ( j)) ( ( )) = ( ( ) E( ζ ( ))) Notes: (1) This is an extremely simplified version of Wang-Poor Algorithm. (2) No matrix operations. 13

14 Chip-by-Chip Multiuser Detection Again r(j) Chip-by-Chip Processing e(x (j)) 1 π π E( x ( j)) APP DEC- 14

15 Complexity! 6 additions and 6 multiplications per chip per iteration per user.! Complexity (per user) is independent of user number K. Comparison: To achieve good performance, the cost for MMSE CDMA multi-user detection is O(K 2 ) due to matrix operations. 15

16 IDMA with Repetition Coding User-1 repeater π 1 User- repeater π + User-K repeater π K AWGN 16

17 Un-coded IDMA (with rate-1/8 repetition coding) 1.E+00 1.E-01 8 users 64 users 1.E-02 BER 1.E-03 single-user 1.E-04 1.E Average Eb/N 0 (db) 17

18 Rate 1/8 Convolutional-Repeat Coded IDMA 1.E+00 (b) (a) BER 1.E-01 1.E-02 1.E-03 CDMA 6 users matched filter 1.E-04 IDMA 8 users IDMA 16 users IDMA 32 users IDMA 64 users 1.E capacities Average Eb/N0 (db) 18

19 Multiuser Detection in Multipath Channels Step 1. Chip-level path model r( j) L 1 l= 0 = 1 Step 2. Gaussian approximation, l x ( j l) n( j) 2 hl, e x( j l) = r( j) E( ζ, l( j)) l Var( ζl, ( j)) Step 4. Rae combining: K = h + r( j) = h, l x ( j l) + ζ, l ( j) Step 3. Estimation: ( ) ( ) e( x L 1 ( j)) = l= 0 e( x ( j)) Note: Still no matrix operations here. l 19

20 Rae Detector in Multipath Channels (rate 1/2 convolutional & length-8 repetition, 32 users) BER 1.E+00 1.E-01 1.E-02 1.E-03 single user in AWGN quasi-static fading 1 tap 2 taps 4 taps 8 taps 1.E E b /N 0 (db) 20

21 Multipath Performance (rate-1/2 convolutional & length-8 repetition) 1.E+00 multi-user single-user 1.E-01 K =48 BER 1.E-02 K =96 K =48 (L, M ) = (1, 1) 1.E-03 K =96 (L, M ) = (2, 1) 1.E-04 (L, M ) = (2, 2) (L, M ) = (1, 2) E b /N 0 per receive antenna (db) L= the number of taps. M = the number of receive antennas. K=the number of users 21

22 Chip-by-Chip Joint Channel Estimation and Multi-User Detection ˆd 1 Decoder (DEC) π 1 1 π 1 { ( x1 ( j))} e ESE { ( x1 ( j))} e DEC dˆ dˆk... Decoder (DEC)... Decoder (DEC) 1 π π... 1 π K π K { e ( x ( j))} ESE { e ( x ( j))} DEC { e ( x ( j))} ESE K { e ( x ( j))} DEC K Elementary Signal Estimator (ESE) π 1 { ( x1 ( j))} l DEC { hˆ } π π K { l ( x ( j))} DEC { l ( x ( j))} DEC K Channel Estimator (CE) r 22

23 Performance with Joint Channel Estimation and Multi-user Detection BER 1.E+00 1.E-01 1.E-02 Ideal CSI ρ=0.2 ρ=0.24 ρ= users 1.E-03 1.E E b /N 0 (db) E b includes the pilot overhead. 23

24 Outline! Introduction! IDMA! Chip-by-chip multi-user detection! Analysis and optimization! IDM space-time coding and IDM coded modulation! Conclusions 24

25 Chip-by-Chip Multiuser Detection Again r(j) Chip-by-Chip Processing e(x (j)) 1 π π E( x ( j)) APP DEC- 25

26 SNR Evolution in the Chip-by-Chip Algorithm Chip-by-Chip Processing SNR _ new = ' h ' 2 ( SNR ) _ old 2 2 f h + σ f( ) DEC- 26

27 Number of Iterations Required by IDMA (24 users, 1/2 convolutional + 1/8 repetition coding) BER 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 Evolution Simulation 1 iteration 2 iterations E b /N 0 (db) 3 iterations 15 iterations 4 iterations 27

28 Power Allocation for Non-ideal Coding Optimization: Find {h } to maximize {SNR } after certain iterations. SNR _ new = ' h 2 ( ) _ 2 2 ' old + h f SNR σ Constraint: 2 h = fixed 28

29 Power Allocation for Different Users h 2 29

30 Un-coded IDMA (with rate-1/8 repetition coding) 1.E+00 1.E-01 8 users 64 users 1.E-02 BER 1.E-03 single-user 1.E-04 1.E Average Eb/N 0 (db) 30

31 Rate 1/8 Convolutional-Repeat Coded IDMA 1.E+00 (b) (a) BER 1.E-01 1.E-02 1.E-03 CDMA 6 users matched filter 1.E-04 IDMA 8 users IDMA 16 users IDMA 32 users IDMA 64 users 1.E capacities Average Eb/N0 (db) 31

32 Impact of FEC Coding on IDMA 10 capacity Rate 1 Turbo Hadamard Turbo Super-orthonoga-rate-1/32 Convolutional uncoded Capacity Eb/N0(dB) 32

33 Spectral Efficiency 1/8 repeating with 64 users, spectral efficiency = 8bits/chip. Equivalent to single-user 256-QAM. Comparison: IS-95 CDMA efficiency? 33

34 with ideal coding 34

35 with ideal coding User-1 FEC π 1 Ε 1 Power control + User-2 FEC π 2 Ε 2 N(0, σ 2 ) Achieving overall capacity Onion-peeling capacity C E1+ E2 E1 E2 = log(1 + ) = log(1 + ) + log(1 + ) σ σ σ + E Single-user capacity 1 35

36 with ideal coding E1+ E2 + E3 log(1 + ) 2 σ E E E = log(1 + ) + log(1 + ) + log(1 + ) σ σ σ E1+ E2 + E1 We can achieve multi-user capacity provided that an ideal code is used for every user. 36

37 Outline! Introduction! IDMA! Chip-by-chip multi-user detection! Analysis and optimization! IDM space-time coding and IDM coded modulation! Conclusions 37

38 Some Requirements for Future Wireless Systems! low receiver cost! de-centralized (i.e., asynchronous) control,! simple treatment of ISI,! cross-cell interference mitigation,! diversity against fading,! power efficiency (long battery life), IDMA! multi-media services (e.g., mixed voice and IP),! high user number,! high throughput and spectral efficiency, 38

39 Outline! Introduction! IDMA! Chip-by-chip multi-user detection! Analysis and optimization! IDM space-time coding and IDM coded modulation! Conclusions 39

40 Application 1: IDM Space-Time Coding 40

41 IDM Space-Time Coding π 1 antenna-1 data C π N antenna-n The interleavers π 1,, π Ν are randomly chosen. 41

42 Multi Layer IDM Space-Time Coding d 1 layer-1 C c 1 c 1 c 1 (1) π 1 π! ( N ) 1 (1) x 1 x ( N ) 1 p 1! p 1 antenna-1 Σ!!!! d K layer- C K c K c K c K (1) π K ( N ) π K (1) x K (N ) x K p K!! p K antenna- Σ N 42

43 Performance of IDM Space-Time Codes (overall rate R = 2 bits/symbol) 1.E-01 1.E-02 FER SFER Outage FER 1.E-03 1.E-04 4x1 2x Eb/N0 (db) 43

44 Performance of IDM Space-Time Codes (overall rate R = 4 bits/symbol) FER 1.E-01 1.E-02 1.E-03 4x1 2x1 FER SFER Outage 1.E E b /N 0 (db) 44

45 Performance Analysis of Space-Time Codes For performance analysis of space-time codes, we have to consider all possible fading coefficients {h n }. This is usually very difficult, involving multidimensional integration over the distribution of {h n }. 45

46 Performance Bounds of IDM Space-Time Codes Theorem 1: Worst performance at: h 1 = h 2 = = h N Theorem 2: Best performance at: h 1 = 1, h 2 = = h N = 0 46

47 Performance Bounds (overall rate R = 4 bits/symbol) FER 1.E-01 1.E-02 1.E-03 4x1 Simulated FER FER Upper Bound FER Lower Bound 2x1 1.E E b /N 0 (db) 47

48 Performance in Multi-Path Channels (R = 2 bits/symbol, 2 2 system) 1.E+00 1.E-01 FER 1.E-02 1.E-03 1.E-04 L = 4 L = 2 1.E E b /N 0 (db) 48

49 The Capacity Achieving Property An IDM-ST code can achieve capacity if C is low-rate and achieves capacity in AWGN. 49

50 Multi Layer IDM Space-Time Coding d 1 layer-1 C c 1 c 1 c 1 (1) π 1 π! ( N ) 1 (1) x 1 x ( N ) 1 p 1! p 1 antenna-1 Σ!!!! d K layer- C K c K c K c K (1) π K ( N ) π K (1) x K (N ) x K p K!! p K antenna- Σ N 50

51 Summary: Properties of IDM ST Codes Conceptually simple. Potentially capacity achieving. Low decoding complexity. Multi-path resolution. 51

52 Application 2: IDM Coded Modulation 52

53 IDM Coded Modulation " Sigma mapping: Duan Rimoldi and Urbane. " Multi-level codes: Imai and Hiraawa 53

54 IDM Coded Modulation layer-1 C π 1 S/P layer- C π + layer-k C π K 54

55 Advantages of IDM Coded Modulation - Simplicity - Flexibility - High performance - Low-decoding cost - Easy treatments for ISI 55

56 Rate-1/8-Repeating IDMA 1.E+00 1.E-01 8 users 64 users 1.E-02 BER 1.E-03 single-user 1.E-04 1.E Average Eb/N 0 (db) 56

57 Performance of IDM Coded Modulation (per real dimension) 57

58 Conclusions Again What maes IDMA wor? Randomness. 58

59 A Comparison between Un-coded IDMA and CDMA 1.E+00 CDMA BER 1.E-01 1.E-02 1.E-03 1.E-04 IDMA K =1, 16, E-05 IDMA CDMA K =16 1.E E b /N 0 (db) 59

60 For Details 60

61 Chip-by-Chip Detection Step 1. Chip-level path model: Step 2. Gaussian approximation: Step 3. Estimation: r( j) r K = h x ( j) + = 1 ( j) = h x ( j) + ζ ( j) n( j) Gaussian 2h e x j r j j Var( ζ ( j)) ( ( )) = ( ( ) E( ζ ( ))) For a chip, not much can be done. It must be simple. 61

62 Analysis of the Chip-by-Chip Algorithm 2h e x j r j j Var( ζ ( j)) ( ( )) = ( ( ) E( ζ ( ))) 2h = Var( ζ ( j) ) ( h x ( j) + ζ ( j) E( ζ ( j) )) signal noise SNR = ' ' h Var( ' ( )) + σ h x j 62