Codificación para los sistemas de comunicaciones

Transcription

1 Codificación para los sistemas de comunicaciones (Coding and Modula,on for Wireless Networks) Robert H. Morelos- Zaragoza Department of Electrical Engineering San José State University Dia de Procesamiento de Señales Facultad de Ingeniería de la UNAM October 27, 2015

2 Outline Introduction: A simple two-path wireless channel Flat and frequency selective fading Fast and slow fading Diversity techniques for wireless channels IEEE 802 wireless network (PHY) standards Bit-interleaved coded modulation Modulations and codes used today Coding and Modulation for Wireless 2

3 A wireless two-path channel s(t) α 0, τ 0 Tx r(t) α 1, τ 1 Rx Figure 1: Awirelesstwo-pathchannel. Coding and Modulation for Wireless 3

4 Wireless two-path channel response to rectangular pulses Narrowband pulses, T > τ (Δτ = τ 1 - τ 0 ) T Input τ 0 T+ τ Output - Amplitude variation: Fading - Distorsion FLAT FADING Wideband pulses, T < τ Input Output τ 0 T+ τ - Amplitude variation: Fading (less) - No distorsion - Overlap to next pulse: Interference FREQUENCY-SELECTIVE FADING Coding and Modulation for Wireless 4

5 PSD of a wireless two-path channel Larger delay spread Larger frequency selectivity 4 3 H(f, τ) Frequency (Hz) 50 0 τ (sec) Figure 2: PSD of a wireless two-path channel. Coding and Modulation for Wireless 5

6 Fading and time variations Variations in received power due to movement (Doppler): T c = 1 B D B D : Doppler bandwidth B D = 2vf c / c Slow fading: T < T c Fast fading: T > T c T c Coherence time T is the symbol duration Coding and Modulation for Wireless 6

7 Multipath effects Reflections (paths) of the transmitted electromagnetic signal on objects L-path channel impulse response: h(t) α 0 (t) α 1 (t) Coherence bandwidth: B c = 1 T m τ 0 τ 1 τ L 1 T m Delay spread α L 1 (t) t Phase rotation: φ i (t) = 2π f c τ i (t) Coding and Modulation for Wireless 7

8 Flat fading: Basic types of fading B << B c or 2W << 1 T m Narrowband signaling B=2W is the signal bandwidth Frequency-selective fading: B >> B c or 2W >> 1 T m Wideband signaling Coding and Modulation for Wireless 8

9 Complex baseband frequency-selective multipath channel model s(t) τ τ τ τ : Time resolution c 0 (t) c 1 (t) c L-1 (t) Σ AWGN Note: L=1 and c 0 (t)=c 0 gives flat fading c i (t) = α i (t) e jφi(t) : i-th path (complex valued) gain, i=0,2,,l-1 r(t) QPSK Matlab demo Coding and Modulation for Wireless 9

10 Time diversity for multipath channels

11 Time-diversity techniques Time-diversity techniques can be classified according to the frequency selectivity of the multipath channel Flat fading channels Error correcting coding & interleaving Diversity order equal to the minimum Hamming distance of the code Frequency-selective channels RAKE demodulation Linear adaptive equalization Coding and Modulation for Wireless 11

12 Flat Rayleigh fading: ECC diversity with a Hamming (7,4,3) code Slope = -1 Slope = -3 Coding and Modulation for Wireless 12

13 RAKE demodulator: Assumptions Slow fading: T << T c c i (t) = c i, i = 0,, L 1 Frequency-selective fading: W >> B c (1) No intersymbol interference (ISI_: T >> T m (2) (1) and (2) are satisfied by wideband pulses, such as PPM or spread-spectrum Path gains and delays need to be known Need channel estimation techniques ( finger search ) Coding and Modulation for Wireless 13

14 RAKE demodulator: Structure (BPSK) r(t) τ τ τ Estimated path gains ψ(t) ψ(t) ψ(t) c* ^ L-1 c* ^ ^ L=2 c* 0 Σ L fingers (diversity branches) x(t) t 0 Integrator t=t Y Decision variable Coding and Modulation for Wireless 14

15 Maximal-ratio combining property s(t) τ τ τ Multipath Channel c 0 (t) c 1 (t) c L-1 (t) Σ r(t) τ τ RAKE demodulator τ AWGN ψ(t) ψ(t) ψ(t) ^ c* L-1 c* ^ ^ L-2 c* 0 Σ Signal delay on each RAKE finger: T m = (L-1) τ x(t) 0 Integrator t t=t Y Decision variable Coding and Modulation for Wireless 15

16 Frequency diversity for frequencyselective multipath channels: OFDM

17 Frequency-domain approach Divide and conquer: Create K subchannels with frequency responses that are relatively constant (flat): C(f) B=KΔf Δf f f c Subcarrier frequencies: f k = f c K 1 2T + k T, k = 0,1,, K 1. Coding and Modulation for Wireless 17

18 Complex baseband spectrum C(f) Δf 0 KΔf=W f Each baseband channel has an associated basis signal ψ k (t) = e j # " 2π! k T t $ % &, k = 0,1,, K 1. Frequency separation and symbol duration (sinc pulses): Δf = W K, T = 1 Δf = K W Symbol duration is proportional to K Coding and Modulation for Wireless 18

19 OFDM signal A large value of K results in T >> T m and fading becomes flat Constant subchannel gains: Each subcarrier is typically M-QAM mapped so that the signal transmitted over each subchannel is: u k (t) =! C 2π k $ # & = C k = A k e jφ k, k = 0,1,, K 1. " T % 2 T S! Ik cos# 2π k " T t $ &+ j % where S k =S Ik +js Qk represent the modulation symbols. 2 T S! Qk sin# 2π k " T t $ &, 0 t T, % Complex baseband OFDM signal: s(t) = K 1 k=0 u k (t) Coding and Modulation for Wireless 19

20 OFDM receiver processing For each subchannel, k=0,1,, K-1, the received signal is r k (t) = 2 T A S cos! 2π k k k1 T t +φ $ 2 # k &+ j " % T A S sin! 2π k k k 2 T t +φ $ # k & + N k (t), 0 t T, " % AWGN with A k the amplitude response and φ k the phase response. Basis functions: ψ k1 (t) = 2 T cos! # 2π k " T t $ % &, ψ (t) = 2 k 2 T sin! # 2π k " T t $ &, 0 t T. % Corresponding matched filter outputs: Y k1 = A k cos( φ k ) S k1 +W k1, Y k 2 = A k sin( φ k ) S k 2 +W k 2, or Y k = C k S k +W k, as a complex number. Coding and Modulation for Wireless 20

21 One-tap equalization The receiver estimates the subchannel gains using pilot symbols known to both transmitter and receiver Based on these estimates Ĉ k, the scaling of the transmitted symbols is removed by a process known in the literature as one-tap equalization : Y k! = Ĉk * Y 2 k = Ĉ k Ĉ k * Ĉ k 2 ( C k S k +W k ) S k +W k!, k = 0,1,, K 1 Coding and Modulation for Wireless 21

22 ISI removal Effects of delay spread T m can be removed using a prefix Two choices Zero prefix (or time guardband) OFDM SIGNAL No signal Cyclic prefix T data Copy and paste OFDM SIGNAL SAMPLES T p >T m T data T p >T m The choice of a cyclic prefix offers the additional advantage that the discrete Fourier transform (implemented via the FFT algorithm) can be used Coding and Modulation for Wireless 22

23 OFDM transmitter S 1 { B k } K BITS K mappers (QAM/PSK) M = 2 S 2 IFFT x Add cyclic prefix D/A Up-converter S K x : Vector of K signal samples f c K 1 2T Copy and paste OFDM SIGNAL SAMPLES N v Coding and Modulation for Wireless 23

24 OFDM receiver Y 1 { ˆB k } K BITS K decision devices (QAM/PSK) M = 2 Y 2 Y K FFT and EQ r Remove cyclic prefix A/D Downconverter { Ĉ k } f c K 1 2T Subchannel gain estimation Pilot symbols r : Vector of K received signal samples EQ : Array of K one-tap equalizers Coding and Modulation for Wireless 24

25 Error floors in OFDM Subchannels (say K b out of K) with high attenuation (low amplitude A k ) will experience large number of errors ( 1/ 2) C(f) P b K b /2K Error floor 0 f All subchannels low attenuation E b /N 0 Solution (e.g., all IEEE physical layer specifications): Scramble the symbols: Interleaving Use error correcting coding Coding and Modulation for Wireless 25

26 Time-Frequency Interleaving Goal: Spread those subchannel symbols affected by frequency nulls (low energy) in channel response Without interleaving: With interleaving: Frequency Frequency KT Time OFDM symbol Time Coding and Modulation for Wireless 26

27 Error Control Coding (ECC) Correct errors in symbols with low energy OFDM MODULATOR Message Bits ECC Encoding Interleaving Π and Mapping IFFT Insert cyclic prefix D/A and Quadrature Modulation OFDM DEMODULATOR Recovered Bits ECC Decoding Demapping (metrics) and Deinterleaving Π -1 FFT Remove cyclic prefix Quadrature Demodulation and A/D Coding and Modulation for Wireless 27

28 Coding and Modulation in IEEE 802 Wireless Network Standards

29 Bit-interleaved coded modulation Gray mapping of bits to modulation symbols Demapping to produce binary metrics (LLR values) Practically all IEEE 802 standards use it Coding and Modulation for Wireless 29

30 IEEE Major specifications for the OFDM PHY are listed in Table FEC Coder Interleaving+ IFFT GI Mapping Addition Symbol Wave Shaping I/Q Mod. HPA AGC Amp I/Q Det. Remove GI FFT Demapping+ Deinterleaving FEC Decoder LNA Rx Lev. Det. AFC Clock Recovery Coding and Modulation for Wireless 30

31 IEEE : Constellations (1) BPSK Q I 16-QAM b Q b 0 b 1 b 2 b QPSK 01 1 Q b 0 b I I Coding and Modulation for Wireless 31

32 IEEE : Constellations (2) 64-QAM Q b 0 b 1 b 2 b 3 b 4 b I Coding and Modulation for Wireless 32

33 IEEE : OFDM and Rates Table 17-3 Modulation-dependent parameters Modulation Coding rate (R) Coded bits per subcarrier (N BPSC ) Coded bits per OFDM symbol (N CBPS ) Data bits per OFDM symbol (N DBPS ) Data rate (Mb/s) (20 MHz channel spacing) Data rate (Mb/s) (10 MHz channel spacing) Data rate (Mb/s) (5 MHz channel spacing) BPSK 1/ BPSK 3/ QPSK 1/ QPSK 3/ QAM 1/ QAM 3/ QAM 2/ QAM 3/ Coding and Modulation for Wireless 33

34 Table F-1 Matrix prototypes for codeword block length n=648 bits, subblock size is Z = 27 bits Permutation matrix (a) Coding rate R = 1/ (b) Coding rate R = 2/ Matrices de paridad (c) Coding rate R = 3/ (d) Coding rate R = 5/ Coding and Modulation for Wireless 34

35 Permutation matrix example Z=27, p=22 Coding and Modulation for Wireless 35

36 Table F-2 Matrix prototypes for codeword block length n=1296 bits, subblock size is Z= 54 bits (a) Coding rate R = 1/ (b) Coding rate R = 2/ (c) Coding rate R = 3/ (d) Coding rate R = 5/ Coding and Modulation for Wireless 36

37 Table F-3 Matrix prototypes for codeword block length n=1944 bits, subblock size is Z = 81 bits (a) Coding rate R = 1/ (b) Coding rate R = 2/ (c) Coding rate R = 3/ (d) Coding rate R = 5/ Coding and Modulation for Wireless 37

38 The parity-check matrix interpreted as the incidence matrix of a graph Example: Hamming (7,4,3) code H = Parity-check matrix Parity-check equations (syndromes) z 1 =x 1 +x 2 +x 3 +x 5 z 2 =x 2 +x 3 +x 4 +x 6 z 3 =x 1 +x 2 +x 4 +x 7 Variable nodes (Bit nodes) Incidence matrix x 1 x 2 x 3 x 4 x 5 x 6 x 7 Parity nodes z 1 z 2 z 3 Tanner graph (Bayesian network) ECC techniques 38

39 Iterative decoding of LDPC codes using Tanner graph Hard-decision Preliminary ( hard ) decisions: bit-flip Soft-decision Channel outputs (matched filter): belief propagation ECC techniques 39

40 More constellations: Illustration using binary (273,191,17) EG code LDPC BER QPSK 8-QAM 16-QAM 32-QAM 64-QAM 128-QAM BER 10-2 Add 8-, 32- and 128-QAM to the mix!! Es/No (db) Coding and Modulation for Wireless 40

41 IEEE n-2009: Code rates Table Allowed relative constellation error versus constellation size and coding rate Modulation Coding rate Relative constellation error (db) BPSK 1/2 5 QPSK 1/2 10 QPSK 3/ QAM 1/ QAM 3/ QAM 2/ QAM 3/ QAM 5/6 28 Coding and Modulation for Wireless 41

42 IEEE n: Space-Time Block Coding Table Constellation mapper output to spatial mapper input for STBC N STS HT-SIG MCS field (bits 0 6 in HT-SIG 1 ) N SS HT-SIG STBC field (bits 4 5 in HT-SIG 2 ) i STS d ki,, 2m d ki,, 2m , d k, 12m, d k, 12m, + 1 * d k, 12m, + 1 d k, 12m, d k, 12m, d k, 12m, + 1 * d k, 12m, + 1 d k, 12m, d k, 22m, d k, 22m, + 1 d k, 12m, d k, 12m, + 1 * d k, 12m, + 1 d k, 12m, d k, 22m, d k, 22m, + 1 * d k, 22m, + 1 d k, 22m, d k, 12m, d k, 12m, + 1 * * * * , 39, 41, 43, 46, 48, * d k, 12m, + 1 d k, 12m, d k, 22m, d k, 22m, + 1 * 4 d k, 32m, d k, 32m, + 1 Coding and Modulation for Wireless 42

43 802.11ad-2012: OFDM Coding and Modulation for Wireless 43

44 802.11ad-2012: LDPC codes (1) Rate 1/2: N = 16x42 = 672 N-K = 8x42 = 336 K = Rate-1/2 LDPC code matrix H = 336 rows x 672 columns, Z = 42 Table 21-6 Rate 1/2 LDPC code matrix (Each nonblank element i in the table is the cyclic permutation matrix P i of size Z Z; blank entries represent the zero matrix of size Z Z) Coding and Modulation for Wireless 44

45 802.11ad-2012: LDPC codes (2) Rate 5/8: N = 16x42 = 672 N-K = 6x42 = 252 K = Rate-5/8 LDPC code matrix H = 252 rows x 672 columns, Z = 42 Table 21-7 Rate 5/8 LDPC code matrix (Each nonblank element i in the table is the cyclic permutation matrix P i of size Z Z; blank entries represent the zero matrix of size Z Z) Coding and Modulation for Wireless 45

46 802.11ad-2012: LDPC codes (3) Rate 3/4: N = 16x42 = 672 N-K = 4x42 = 168 K = Rate-3/4 LDPC code matrix H = 168 rows x 672 columns, Z = 42 Table 21-8 Rate 3/4 LPDC code matrix (Each nonblank element i in the table is the cyclic permutation matrix P i of size Z Z; blank entries represent the zero matrix of size Z Z) Coding and Modulation for Wireless 46

47 802.11ad-2012: LDPC codes (4) Rate 13/16: N = 16x42 = 672 N-K = 3x42 = 126 K = Rate-13/16 LDPC code matrix H = 126 rows x 672 columns, Z = 42 Table 21-9 Rate 13/16 LDPC code matrix (Each nonblank element i in the table is the cyclic permutation matrix P i of size Z Z; blank entries represent the zero matrix of size Z Z) Coding and Modulation for Wireless 47

48 802.11ad-2012: Single-Carrier (1) Coding and Modulation for Wireless 48

49 802.11ad-2012: Single-Carrier (2) Coding and Modulation for Wireless 49

50 IEEE c-2009: Code Rates Table 103 MCS dependent parameters MCS class MCS identifier Data rate (Mb/s) with pilot word length = 0 Data rate (Mb/s) with pilot word length = 64 Modulation Spreading factor, L SF FEC type Class (CMS) π/2 BPSK/(G)MSK a RS(255,239) (MPR) π/2 BPSK/(G)MSK 1 LDPC(672,504) π/2 BPSK/(G)MSK LDPC(672,336) Class π/2 QPSK 1 LDPC(672,336) π/2 QPSK 1 LDPC(672,504) π/2 QPSK 1 LDPC(672,588) π/2 QPSK 1 LDPC(1440,1344) π/2 QPSK 1 RS(255,239) Class π/2 8-PSK 1 LDPC(672,504) π/2 16-QAM 1 LDPC(672,504) a Coding and Modulation for Wireless 50

51 IEEE c-2009: Unequal Error Protection!! 12.4 Audio/Visual mode of mmwave PHY The Audio/Visual (AV) PHY is implemented with two PHY modes, the high-rate PHY (HRP) and low-rate PHY (LRP), both of which use orthogonal frequency domain multiplexing (OFDM). The data rates supported by the HRP are defined in Table 134. Table 134 HRP data rates and coding Inner code rate HRP mode index Coding mode Modulation MSB LSB [7] [6] [5] [4] [3] [2] [1] [0] Data rate (Gb/s) 0 QPSK 1/ EEP QPSK 2/ QAM 2/ QPSK 4/7 4/ UEP 4 16-QAM 4/7 4/ MSB-only QPSK 1/3 N/A retransmission QPSK 2/3 N/A Coding and Modulation for Wireless 51

52 IEEE : OOK and PPM (1) Table 73 PHY I operating modes Modulation RLL code Optical clock rate Outer code (RS) FEC Inner code (CC) Data rate (15,7) 1/ kb/s (15,11) 1/ kb/s OOK Manchester 200 khz (15,11) 2/ kb/s (15,11) none 73.3 kb/s none none 100 kb/s (15,2) none kb/s VPPM 4B6B 400 khz (15,4) none kb/s (15,7) none kb/s none none kb/s Coding and Modulation for Wireless 52

53 IEEE : OOK and PPM (2) Table 74 PHY II operating modes Modulation RLL code Optical clock rate FEC Data rate 3.75 MHz RS(64,32) RS(160,128) 1.25 Mb/s 2 Mb/s VPPM 4B6B RS(64,32) 2.5 Mb/s 7.5 MHz RS(160,128) 4 Mb/s none 5 Mb/s 15 MHz RS(64,32) RS(160,128) 6 Mb/s 9.6 Mb/s 30 MHz RS(64,32) RS(160,128) 12 Mb/s 19.2 Mb/s OOK 8B10B 60 MHz RS(64,32) RS(160,128) 24 Mb/s 38.4 Mb/s RS(64,32) 48 Mb/s 120 MHz RS(160,128) 76.8 Mb/s none 96 Mb/s Coding and Modulation for Wireless 53

54 IEEE : CSK (Color-Shift Keying) Table 75 PHY III operating modes Modulation Optical clock rate FEC Data rate 4-CSK RS(64,32) 12 Mb/s 12 MHz 8-CSK RS(64,32) 18 Mb/s 4-CSK RS(64,32) 24 Mb/s 8-CSK RS(64,32) 36 Mb/s 16-CSK 24 MHz RS(64,32) 48 Mb/s 8-CSK none 72 Mb/s 16-CSK none 96 Mb/s Coding and Modulation for Wireless 54

55 IEEE : Colors Table 106 xy color coordinates Band (nm) Code Center (nm) (x, y) (0.169, 0.007) 001 y (0.011, 0.733) (0.402, 0.597) (0.669, 0.331) (0.729, 0.271) (0.734, 0.265) (0.734, 0.265) x Figure 137 Center of color bands on xy color coordinates Coding and Modulation for Wireless 55

56 IEEE : Alamouti (STBC) Subchannel Modulation IFFT Input Packing Tx Diversity Encoder IFFT IFFT Filter Filter DAC DAC RF RF BS RF ADC Filter FFT SS Diversity Combiner Sub- Logchannel likelihood decoder Demod. Ratios Figure 259 Illustration of STC Coding and Modulation for Wireless 56

57 IEEE : Modulations Table 434 Modulation and coding rates ModClass Bits/Sym Signal Set Puncture Shaper Block Code π/2 BPSK Repeat π/2 BPSK 1 of QPSK QPSK 2 of PSK (64,57) PSK (64,57) QAM 2 of 6 3/4 (48,47) QAM 2 of 6 4/4 (64,63) QAM 2 of 6 5/4 (80,79) QAM 2 of 6 5/5 (80,79) QAM 2 of 5 6/6 (80,79) RESERVED Coding and Modulation for Wireless 57

58 References [1] IEEE 802 Part 3: Carrier sense multiple access with Collision Detection (CSMA/CD) Access Method and Physical Layer Specifications, IEEE Computer Society, [2] IEEE 802 Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, IEEE Computer Society, [3] IEEE 802 Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications Amendment 5: Enhancements for Higher Throughput, IEEE Computer Society, [4] IEEE 802 Part 15.3: Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for High Rate Wireless Personal Area Networks (WPANs) Amendment 2: Millimeter-wave-based Alternative Physical Layer Extension, 2009 [5] IEEE 802 Part 15.7: Short-Range Wireless Optical Communication Using Visible Light, IEEE Computer Society, [6] IEEE 802 Part 16: Air Interface for Broadband Wireless Access Systems, IEEE Computer Society, [7] IEEE 802 Part 20: Air Interface for Mobile Broadband Wireless Access Systems Supporting Vehicular Mobility Physical and Media Access Control Layer Specification, IEEE Computer Society, [8] IEEE 802 Part 22: Cognitive Wireless RAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: Policies and Procedures for Operation in the TV Bands, IEEE Computer Society, Coding and Modulation for Wireless 58

59 GRACIAS! Contact Information Coding and Modulation for Wireless 59