OFDM (Orthogonal Frequency Division Multiplexing) 서울대학교이동통신연구실 1
Contents Introduction Generation of subcarriers using the IFFT Guard time and cyclic extension Windowing Choice of OFDM parameters OFDM signal processing Implementation complexity of OFDM versus signal-carrier modulation Ref: OFDM for Wireless Multimedia Communications Richard Van Nee & Ramjee Prasad, Artech House 서울대학교이동통신연구실 2
Why OFDM? Freq 전송률증대필요 ( 음성, 데이터, ) 10 Kbps -> 100 usec/bit -> 10 KHz TX d1 10KHz RX d 1 Time d 1 100μsec Time 1 d 1 Time 10 Mbps -> 0.1 usec/bit -> 10 MHz Time Freq 10MHz TX d 1 Time d 1 d 2 d 3 d 4 d 9 d 10 RX d 1 Time 0.1μs 1μs Time d 1 Time 서울대학교이동통신연구실 3
10MHz d 1000 d 1000 d 999 cos2f 1000 t d 999 cos2f 999 t d 998 d 3 cos2f 998 t 10KHz d 2 d 1 100 μs d 1 cos2f 1 t 서울대학교이동통신연구실 4
Intruduction What is OFDM? High-rate data stream Number of lower rate streams < 그림 1. OFDM 전송방식의개념 > Parameters under consideration Number of subcarriers Guard time Symbol duration Subcarrier spacing Modulation type Error correction coding Sprint Nextel MIRS Channel spacing > 1/T < 그림 2. OFDM 방식의전송스펙트럼 > 서울대학교이동통신연구실 5
Orthogonality: subcarrier spacing = 1/T Baseband Mathematical Expression Transmitted signal N 1 i s t di exp j2 ( t ts ), ts t ts T i0 T s t 0, t t and t t T s s j2 0 t ts T e j2 N 1 t ts T e Frequencies: 0, 1/T, 2/T, (N-1)/T 서울대학교이동통신연구실 6
Orthogonality Each subcarrier has exactly an integer number of cycles Adjacent subcarriers exactly 1 cycle difference Integration integration over T desired output ts T N 1 t s l i exp j2 ( t ts ) di exp j2 ( t ts ) dt T i0 T t T N 1 s l i di exp j2 ( t ts ) dt dlt i0 T t s T j2 k t 0 0 서울대학교이동통신연구실 7 0 0 T e T e 2kt 2kt cos j sin dt T T j T 2 kt T dt dt T 2kt 2kt cos j sin dt 0 T T 0
Spectrum of One OFDM Signal - ICI (inter carrier interference) is avoided by having the maximum of one subcarrier spectrum occur at zero crossings of all the others. 서울대학교이동통신연구실 8
IDFT implementation. N i0 N 1 i0 j2i T t S t d e, 0 t T i S t 0, t 0, t T S n d e i j 2in N 0 T N 서울대학교이동통신연구실 9
0 S d d d 1 2 0 1 2 j2 j2 2 N N S d d e d e 0 1 2 j2 j2 22 2 N N S d d e d e 0 1 2 d0 S 0 d 1 IDFT S 1 P/S DN 1 S N 1 서울대학교이동통신연구실 10
IFFT OFDM signal generation = inverse Fourier Transform The number of multiplications in the IFFT can be reduced even further by using a radix-4 algorithm. This technique makes use of the fact that in a four-point IFFT, there are only multiplications by {1,-1,j,-j}. 서울대학교이동통신연구실 11
Guard time & Cyclic extension Guard Time The guard time is chosen larger than the expected delay spread, so that the delayed symbol cannot interfere with the next symbol. If the guard time consist of no signal (a) 0 신호삽입 (b) Cyclic prefix 의삽입 < 그림 4. 보호구간의삽입을위한두가지방식 > 서울대학교이동통신연구실 12
Single Carrier (ISI) Symbol 1 Symbol 2 S 1 (Delayed) S 2 (Delayed) (ISI) S 1 S 2 S 1 Guard time S 2 서울대학교이동통신연구실 13
Multiple Carrier (Inter carrier interference) Cyclic Extension 서울대학교이동통신연구실 14
Cyclic Extension OFDM signal should be extended in guard time Subcarriers should have integer number of cycle difference in FFT interval Orthogonality lost when multipath delay > guard time Fig 2.9 서울대학교이동통신연구실 15
Windowing Windowing: results in lower sidelobes Raised Cosine Window 0.5 0.5 cos t / Ts 0 t Ts wt 1.0 Ts t Ts 0.5 0.5 cos t T / T T t 1 T s s s s <OFDM 방식에서의전송스펙트럼 > 서울대학교이동통신연구실 16
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OFDM system design parameters Guard time >> Delay spread Symbol duration >> Guard time Number of subcarrier Subcarrier spacing 서울대학교이동통신연구실 18
OFDM system design System requirements Bit rate : 20Mbps Tolerable delay spread : 200ns Bandwidth : < 15MHz guard time = 800ns OFDM symbol duration = 6 * guard time = 4.8us FFT time = 4.8-0.8 = 4us (T s =T+T G ) subcarrier spacing = 1 / 4us = 250kHz symbol rate = 1 / T symbol duration =1/4.8us 서울대학교이동통신연구실 19
OFDM system design (cont d) No. of bits/ofdm symbol = Bit rate/ofdm symbol rate = 20Mbps 96 bits / OFDM symbol (1/ 4.8 us) (1) 16-QAM 4bits/subcarrier, 1/2rate coding -> 2 information bit/subcarrier number of subcarriers = 48 requiered Bandwidth = 48 * 250 khz = 12MHz < 15MHz (2) QPSK 2bits/symbol, 3/4rate coding -> 1.5information bits/subcarrier number of subcarrier = 96/1.5 = 64 required Bandwidth = 64 * 250kHz = 16MHz > 15MHz 서울대학교이동통신연구실 20
OFDM signal processing 서울대학교이동통신연구실 21
Implementation complexity of OFDM vs. Single-carrier modulation Complexity Single-carrier systems need equalizer when delay spread over 10% but OFDM systems don t FFT does not need full multiplication but rather phase rotation The complexity in OFDM grows slightly faster than linear Robustness Sigle-carrier system performance degrade abruptly when delay spread exceeds the value which equalizer is desiged OFDM systems are robust against delay spread 서울대학교이동통신연구실 22
OFDM 특징 구현용이 (FFT) 채널지연문제에강인 사용자에게다양한용량할당용이 주파수별전력할당과복조방법변화 사용자에게주파수할당방법 J. Jang and K. B. Lee, "Transmit Power Adaptation for Multiuser OFDM Systems," IEEE Journal on Selected Areas in Communications, vol. 21, no. 2, pp. 171-178, Feb. 2003. 서울대학교이동통신연구실 23