Modeling of Digital Communication Systems using Simulink Chap10. Digital Communications BER Performance in AWGN (Block Coding and Fading) Chap11. Digital Communications BER Performance in AWGN and Fading (Convolution Coding)

목차 Chap10. Digital Communications BER Performance in AWGN (Block Coding and Fading) 10.1 Digital Communications with Block Coding in Fading 10.2 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code 10.3 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code 10.4 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code 10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code 10.6 BER Performance of 16-QAM in Rayleigh and Rician Fading with Interleaving and a Reed-Solomon(15,7) Block Code 10.7 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC 10.8 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC 10.9 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code and Alamouti STBC 10.10 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon (15,7) Block Code and Alamouti STBC

Chap11. Digital Communications BER Performance in AWGN and Fading (Convolutional Coding) 11.1 Digital Communications with Convolutional Coding 11.2 BER Performance of Convolutional Coding and BPSK in AWGN 11.3 BER Performance of Convolutional Coding and BPSK in AWGN and Rayleigh Fading with Interleaving (Soft- and Hard-Decision Decoding) 11.4 BER Performance of Convolutional Coding and BPSK and Alamouti STBC in Rayleigh Fading with Interleaving

10.4 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code 32-FSK in Rayleigh Fading with Interleaving and a RS (31,15) Block Code

10.4 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code BER 성능

10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code 16-QAM in Rayleigh Fading with Interleaving and a RS (15,7) Block Code

10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code BER 성능

10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code Rayleigh Fading Channel 의 Maximum Doppler shift 0.1 Hz 및 0.01 Hz 인 경우

10.6 BER Performance of 16-QAM in Rayleigh and Rician Fading with Interleaving and a Reed-Solomon(15,7) Block Code 16-QAM in Rayleigh and Rician Fading with Interleaving and a RS(15,7) Block Code

10.6 BER Performance of 16-QAM in Rayleigh and Rician Fading with Interleaving and a Reed-Solomon(15,7) Block Code BER 성능

10.7 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC

10.7 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC BER 성능

10.8 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC

10.8 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC BER 성능

10.9 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code and Alamouti STBC 32-FSK in Rayleigh Fading with Interleaving and a RS (31,15) Block Code and Alamouti STBC

10.9 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code and Alamouti STBC BER 성능

10.10 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon (15,7) Block Code and Alamouti STBC 16-QAM in Rayleigh Fading with Interleaving and a RS(15,7) Block Code and Alamouti STBC

10.10 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon (15,7) Block Code and Alamouti STBC BER 성능

11.1 Digital Communications with Convolutional Coding 11장의 내용은 AWGN 채널 및 Fading channel 에 convolutional error control coding 을 적용하는 방법을 소개한다. BPSK 의 BER 성능을 아래 세 가지 환경에서 알아본다. AWGN 에서 convolutional coding 을 적용한 경우 - Hard & Soft-decision decoding AWGN 및 Rayleigh fading channel 일 때 convolutional coding 을 적용한 경우 - Hard & Soft-decision decoding Rayleigh fading channel 일 때 convolutional coding 및 Alamouti STBC 적용한 경우 - Hard & Soft-decision decoding

11.2 BER Performance of Convolutional Coding and BPSK in AWGN Convolutional Code 란? Block code 방식에서는 데이터 비트에 패리티 비트를 추가하는 방식으로 code 를 생성하였으나 Convolutional Code 방식에서는 이전의 데이터와 현재의 데이터를 이용하여 패리티 비트를 생성. Block code 방식 (n, k) – memoryless - 코드 길이 n 비트 중 k 비트가 데이터이고 n-k 비트는 패리티 비트로 구성됨. Convolutional code 방식 (n, k, m) – contains memory - 입력 비트 수 k, 출력 비트 수 n, 메모리 레지스터 수 m

11.2.1 Hard-Decision Decoding Simulink 의 convolutional encoder 및 decoder 는 trellis (격자) 구조를 이용하여 8진수로 표현된 다항식 및 피드백 탭 정보를 구현함. 매트랩 함수 poly2trellis(7, [171, 133]) 7: shift register 에 저장되는 비트 수, 171 : 1111001, 133 : 1011011

State Diagram / Trellis Diagram

11.2.1 Hard-Decision Decoding (cont’d) Convolutional coding 을 적용한 BPSK 의 BER 특성을 보기 위한 시뮬링크 모델 ✔ ✔

11.2.1 Hard-Decision Decoding (cont’d) Convolutional Encoder

11.2.1 Hard-Decision Decoding (cont’d) Viterbi Decoder 복호 시 지연 : code rate ½ 인 경우 보통 constraint length의 다섯배 정도의 값을 씀.

Decode 원리 (에러가 없음, 현재 상태가 00 임을 가정할 때) If ip=0 If ip=1 Current state Next state (op) 00 00 (00) 10 (11) 01 00 (11) 10 (00) 10 01 (10) 11 (01) 11 01 (01) 11 (10) 00 00/2 00/X : op/hamming distance 11/0 10 11/2 10/2 10/2 00/0 01 01/0 01/0 01/0 11 10/2 Rx data 11 01 01 00 01 Tx data 1 1 1 1

Decode 절차 (에러가 있는 경우, Hard-decision) If ip=0 If ip=1 Current state Next state (op) 00 00 (00) 10 (11) 01 00 (11) 10 (00) 10 01 (10) 11 (01) 11 01 (01) 11 (10) 00 00/2 00/1 00/1 00/X : op/hamming distance 11/0 11/1 11/1 10 11/1 11/0 10/2 00/2 10/2 00/1 01 01/0 01/0 01/0 11 10/2 Rx data 11 01 01 10 01 Tx data 1 1 1 1 1

Decode 절차 Hard – decision decoding Hamming distance 를 계산하여 그 거리가 최소인 경로로 결정. ex.) 010→111 해밍거리: 2 100→011 해밍거리: 3 0110→1110 해밍거리: 1 0100→1001 해밍거리: 3

Soft – decision decoding Decode 절차 Soft – decision decoding Euclidean distance 를 계산하여 그 거리가 최소인 경로로 결정. ex.) (a) Hard-decision plane (b) 8-level by 8-level soft-decision plane (c) Example of soft code symbols (d) Encoding trellis section (e) Decoding trellis section.

11.2.1 Hard-Decision Decoding (cont’d) Viterbi Decoder – Decision Type - decoder 입력 데이터 타입이 달라짐. Unquantized: 실수를 받으며 양의 실수: logic 0, 음의 실수: logic 1 로 인식 Hard-Decision: 0, 1 을 받으며 0: logic 0, 1: logic 1로 인식 Soft-Decision: 0 ~ 2b-1 의 정수를 받으며 b 는 soft decision 비트의 개수. Input Value Interpretation Most confident zero 1 Second most confident zero 2 Third most confident zero 3 Least confident zero 4 Least confident one 5 Third most confident one 6 Second most confident one 7 Most confident one

11.2.1 Hard-Decision Decoding (cont’d) BER 성능

11.2.2 Soft-Decision Decoding Convolutional coding 을 적용한 BPSK 의 BER 특성을 보기 위한 시뮬링크 모델

11.2.2 Soft-Decision Decoding (cont’d) Scalar Quantizer Encoder boundary points 에 정해진 양자화 범위로 (index) 입력값을 대응시켜줌. partitioning ex.) Bounded: [0 0.5 3.7 5.8 6.0 11] Unbounded: 1 4 1 2 5 6

11.2.2 Soft-Decision Decoding (cont’d) BER 성능