Lecture 16

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E225C – Lecture 16 OFDM Introduction EE225C Introduction to OFDM l Basic idea » Using a large number of parallel narrow-band subcarriers instead of a single wide-band carrier to transport information l Advantages » Very easy and efficient in dealing with multi-path » Robust again narrow-band interference l Disadvantages » Sensitive to frequency offset and phase noise » Peak-to-average problem reduces the power efficiency of RF amplifier at the transmitter l Adopted for various standards – DSL, 802.11a, DAB, DVB 1 Multipath can be described in two domains: time and frequency Time domain: Impulse response time time time Impulse response Frequency domain: Frequency response time time time Sinusoidal signal as input f time Frequency response Sinusoidal signal as output Modulation techniques: monocarrier vs. multicarrier Channel N carriers Channelization Similar to FDM technique Guard bands B Pulse length ~1/B – Data are transmited over only one carrier Drawbacks B Pulse length ~ N/B – Data are shared among several carriers and simultaneously transmitted Advantages – Selective Fading Furthermore – Flat Fading per carrier – Very short pulses – N long pulses – ISI is compartively long – ISI is comparatively short – EQs are then very long – N short EQs needed – Poor spectral efficiency because of band guards – Poor spectral efficiency because of band guards – It is easy to exploit Frequency diversity – It allows to deploy 2D coding techniques – Dynamic signalling To improve the spectral efficiency: Eliminate band guards between carriers To use orthogonal carriers (allowing overlapping) 2 Orthogonal Frequency Division Modulation N carriers Symbol: 2 periods of f0 Transmit + f Symbol: 4 periods of f0 f B Symbol: 8 periods of f0 Channel frequency response Data coded in frequency domain Transformation to time domain: each frequency is a sine wave in time, all added up. Decode each frequency bin separately Receive time f B Time-domain signal Frequency-domain signal OFDM uses multiple carriers to modulate the data N carriers Frequency Time-frequency grid B Data Carrier f0 B Features – No intercarrier guard bands – Controlled overlapping of bands – Maximum spectral efficiency (Nyquist rate) – Easy implementation using IFFTs – Very sensitive to freq. synchronization T=1/f0 One OFDM symbol Time Intercarrier Separation = 1/(symbol duration) Modulation technique A user utilizes all carriers to transmit its data as coded quantity at each frequency carrier, which can be quadrature-amplitude modulated (QAM). 3 OFDM Modulation and Demodulation using FFTs d0 b0 d1 P/S IFFT b1 d2 d0, d1, d2, …., dN-1 b2 Inverse fast d3 Parallel to . Fourier transform . serial converter . Transmit time-domain . f . samples of one symbol . . . time bN-1 dN-1 Data coded in Data in time domain: frequency domain: one symbol at a time one symbol at a time d0’ d1’ d2’ . . . . dN-1’ S/P d0’, d1’, …., dN-1’ Receive time-domain samples of one symbol Serial to parallel converter time Decode each b0’ frequency bin b1’ independently b2’ . . f . . bN-1’ FFT Fast Fourier transform Loss of orthogonality (by frequency offset) ψ k (t) = exp( jk 2π t / T ) y ψ k +m ( t) = exp ( j2π (k + m )t / T ) Transmission pulses ψ k+ m (t) = exp ( j2π (k + m + δ ) / T ) con δ ≤ 1 / 2 δ Reception pulse with offset δ Interference between channels k and k+m I m (δ) = Summing up ∀m π m+δ ∑I m N −1 2 m (δ ) ≈ (Tδ)2 ∑ m =1 1 23 ≈ (Tδ )2 14 m2 -10 m=1 -20 m=3 m=5 m=7 -50 Asymetric -70 -0.4 -0.3 -0.2 0 -0.1 0.1 Frequency offset: ∂ j 2π(m + δ ) N >> 1 (N > 5 Is enough ) Total ICI due to loss of orthogonality -40 -60 for T (1 − exp(− j2πδ )) -10 -15 δ =0.05 -20 -25 δ =0.02 -30 δ =0.01 -35 δ =0.005 -40 Practical -45 δ =0.002 δ assumed r.v. -50 δ =0.001 Gaussian σ=δ -55 -60 2 4 6 8 10 12 14 16 Carrier position within the band (N=16) ICI in dB Interference: Im(? )/T en dB T 0 Loss for 8 carriers 0 -30 T sin πδ I m (δ ) = ∫ exp( jk2πt / T ) exp(− j(k + m + δ )2πt / T )dt = 0.2 0.3 0.4 limit 4 Loss of orthogonality (time) Let us assume a misadjustment τ Then if m=k-l Xi = c 0 ∫ − T /2+ τ −T /2 ψ k (t )ψ l (t − τ )dt + c 1 ∫ * τ  senmπ 2 T T , c ≠c 0 1 Xi =  mπ  0, c0 = c1  In average, the interfering power in any carrier is X 2 E i2  T T/ 2 independent on m τ  2  , τ << T  T Per carrier ICI ≈ 20log 2 2  1 τ 1 τ  = 4 T  2 + 0 2 = 2 T   ICI due to loss of orthogonaliy 45 Doubling N means 3 dB more ICI 40 m=1 35 ICI in dB Interference en dB τ Xi 2mπ T τ ≈ =2 T T mπ Or approximately, when τ< - Xem thêm -