IV. Orthogonal Frequency Division Multiplexing (OFDM) Introduction Evolution of Wireless Communication Standards OFDM © Tallal Elshabrawy 2 Wireless Communication Channels From “Wireless Communications” Edfors, Molisch, Tufvesson Communications over wireless channels suffer from multi-path propagation Multi-path channels are usually frequency selective OFDM supports high data rate communications over frequency selective channels © Tallal Elshabrawy 3 Multi-Path Propagation Modeling Power Multi-Path Components τ0 τ1 τ2 Time Multi-path results from reflection, diffraction, and scattering off environment surroundings Note: The figure above demonstrates the roles of reflection and scattering only on multi-path © Tallal Elshabrawy 4 Multi-Path Propagation Modeling Power Multi-Path Components τ0 τ1 τ2 Time As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies © Tallal Elshabrawy 5 Multi-Path Propagation Modeling Power Multi-Path Components τ0 τ1 τ2 Time As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies © Tallal Elshabrawy 6 Multi-Path = Frequency-Selective! f=0 0.5 0.5 1 1 0.5 1 μs 1 μs f=1 MHz 1 0.5 -1 0.5 1 μs 1 0.5 -0.5 -1 1 μs 1 f=500 KHz -1 0.5 0.5 1 μs 1 0.5 -0.5 -1 1 μs © Tallal Elshabrawy 7 Multi-Path = Frequency-Selective! h(t) |H(f)| 0.5 0.5 1 f (MHz) 1 μs 0 0.5 1 1.5 2 A multi-path channel treats signals with different frequencies differently A signal composed of multiple frequencies would be distorted by passing through such channel © Tallal Elshabrawy 8 Frequency Division & Coherence Bandwidth Power Frequency Subdivide wideband bandwidth into multiple narrowband subcarriers Bandwidth of each channel is selected such that each sub-carrier approximately displays Flat Fading characteristics The bandwidth over which the wireless channel is assumed to display flat fading characteristics is called the coherence bandwidth © Tallal Elshabrawy 9 Example Frequency Response for 3G Channel Power Delay Profile (Vehicular A Channel Model) 10 Snapshot for Frequency Response 9 Resolv Relative able Delay Path (nsec) 0 8 7 6 0.0 H(f) 1 Average Power (dB) 5 2 310 -1.0 3 710 -9.0 3 4 1090 -10.0 2 5 1730 -15.0 1 6 2510 -20.0 0 0 4 0.5 1 Simulation Assumptions Rayleigh Fading for each resolvable path System Bandwidth = 5 MHz Coherence Bandwidth = 540 KHz Number of Sub-Carriers = 64 Sub-Carrier Bandwidth = 78.125 KHz © Tallal Elshabrawy 1.5 2 2.5 Frequency (Hz) 3 3.5 4 4.5 5 x 10 10 6 Example Frequency Response for 3G Channel Power Delay Profile (Vehicular A Channel Model) 10 Snapshot for Frequency Response 9 1 0 Average Power (dB) 8 7 0.0 6 H(f) Resolv Relative able Delay Path (nsec) 5 2 310 -1.0 3 710 -9.0 3 4 1090 -10.0 2 5 1730 -15.0 1 6 2510 -20.0 0 0 4 0.5 1 1.5 2 2.5 Frequency (Hz) Simulation Assumptions Rayleigh Fading for each resolvable path System Bandwidth = 5 MHz Coherence Bandwidth = 540 KHz Number of Sub-Carriers = 64 Sub-Carrier Bandwidth = 78.125 KHz © Tallal Elshabrawy 3 3.5 4 4.5 5 x 10 11 6 Frequency Division Multiplexing (FDM) Binary Encoder Transmitting Filter (f1) Modulation Bandpass Filter (f1) Demod. Binary Encoder Transmitting Filter (f2) Modulation Bandpass Filter (f2) Demod. Bandpass Filter (fN) Demod. + Binary Encoder © Tallal Elshabrawy Transmitting Filter (fN) Modulation Wireless Channel Orthogonal FDM Is it possible to find carrier frequencies f1, f2 … fN such that TS cos 2πf t cos 2πf t dt 0 i j i j 0 T 1 S cos 2πf t cos 2πf t dt cos 2π f f t cos 2π f f t dt j i j i j 0 i 2 0 TS TS 1 sin2π fi fj t sin2π fi f j t 0 cos 2πfit cos 2πfjt dt 2 2π f f 2π f f i j i j 0 TS 1 sin2π fi fj TS sin2π fi f j TS 0 cos 2πfit cos 2πfjt dt 2 2π f f 2π f f i j i j TS © Tallal Elshabrawy 13 Orthogonal FDM Is it possible to find carrier frequencies f1, f2 … fN such that TS cos 2πf t cos 2πf t dt 0 i j i j 0 1 sin2π fi fj TS sin2π fi f j TS 0 cos 2πfit cos 2πfjt dt 2 2π f f 2π f f i j i j TS TS cos 2πf t cos 2πf t dt 0 i 0 j 2π fi f j TS nπ fi fj n 2TS © Tallal Elshabrawy n=1,2,3, .... & 2π fi f j TS mπ n=1,2,3, .... & m f f 2T i j m=1,2,3, .... m=1,2,3, .... S 14 Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts © Tallal Elshabrawy f1 1 2Ts f2 1 Ts f3 3 2Ts f4 2 Ts 15 Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts f1 1 2Ts f2 1 Ts πt 2πt sin sin T T s s s s πt 2πt πt 3πt sin sin dt cos dt cos 0 Ts Ts 0 Ts 0 Ts dt Ts T T sin πt Ts sin 3πt Ts πt 2πt sin sin dt 0 Ts Ts πt Ts 3πt Ts 0 0 Ts © Tallal Elshabrawy Ts 16 Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts f1 1 2Ts f3 3 2Ts πt 3πt sin sin T T s s s s πt 3πt 2πt 4πt sin sin dt cos dt cos 0 Ts Ts 0 Ts 0 Ts dt Ts T T sin 2πt Ts sin 4πt Ts πt 3πt sin sin dt 0 Ts Ts 2πt Ts 4πt Ts 0 0 Ts © Tallal Elshabrawy Ts Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts f1 1 2Ts f4 2 Ts πt 4πt sin sin T T s s s s πt 4πt 3πt 5πt sin sin dt cos dt cos 0 Ts Ts 0 Ts 0 Ts dt Ts T T sin 3πt Ts sin 5πt Ts πt 4πt sin sin dt 0 Ts Ts 3πt Ts 5πt Ts 0 0 Ts © Tallal Elshabrawy Ts Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts f2 1 Ts f3 3 2Ts 2πt 3πt sin sin T T s s s s 2πt 3πt πt 5πt sin sin dt cos dt cos 0 Ts Ts 0 Ts 0 Ts dt Ts T T sin πt Ts sin 5πt Ts 2πt 3πt sin sin dt 0 Ts Ts πt Ts 5πt Ts 0 0 Ts © Tallal Elshabrawy Ts Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts f2 1 Ts f4 2 Ts 2πt 4πt sin sin T T s s s s 2πt 4πt 2πt 6πt sin sin dt cos dt cos 0 Ts Ts 0 Ts 0 Ts dt Ts T T sin 2πt Ts sin 6πt Ts 2πt 4πt sin sin dt 0 Ts Ts 2πt Ts 6πt Ts 0 0 Ts © Tallal Elshabrawy Ts Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts f3 3 2Ts f4 2 Ts 3πt 4πt sin sin T T s s s s 3πt 4πt πt 7πt sin sin dt cos dt cos 0 Ts Ts 0 Ts 0 Ts dt Ts T T sin πt Ts sin 7πt Ts 3πt 4πt sin sin dt 0 Ts Ts πt Ts 7πt Ts 0 0 Ts © Tallal Elshabrawy Ts Orthogonal FDM Binary Encoder Transmitting Filter (f1) Modulation Correlate with (f1) Demod. Modulation Correlate with (f2) Demod. Correlate with (fN) Demod. f2=f1+1/2TS Binary Encoder Transmitting Filter (f2) + Wireless Channel fN=f1+1/2(N-1)TS Binary Encoder © Tallal Elshabrawy Transmitting Filter (fN) Modulation 22 Number of Subcarriers in OFDM For band-limited FDM if the system bandwidth is B, number of sub-carriers is given by: BTS B NC 1 α / TS 1 α 0 α 1 Rolloff Factor For OFDM if the system bandwidth is B, Number of sub-carriers is given by: NC B 2BTS 1/ 2TS OFDM has the potential to at least double the number of sub-carriers (i.e., double the total transmission rate over the system bandwidth) © Tallal Elshabrawy 23 OFDM a New Idea? The idea of OFDM has been out there since the 1950s OFDM was first used in military HF radios in late 1950s and early 1960s Early use of OFDM has been limited in commercial communication systems due to the high costs associated with the requirements for hundreds/thousands of oscillators The use of OFDM has experienced a breakthrough in the 1990s with advancements in DSP hardware Currently, OFDM has been adopted in numerous wire-line and wireless communications systems, such as: Digital audio and video broadcasting Digital subscriber lines (DSL) Wireless LAN 802.11 WiMAX 802.16 LTE (Long term Evolution), 4G Cellular Networks © Tallal Elshabrawy 24 OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriers f1 cos πt Ts f2 cos 2 πt Ts f3 cos 3πt Ts f4 cos 4πt Ts Ts f1 1 2Ts f2 1 Ts f3 -f1 -f2 f2 3 2Ts -f3 f4 f1 f3 2 Ts -f4 OFDM Signal: Time Domain © Tallal Elshabrawy f4 OFDM Signal: Freq. Domain 25 OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriers f1 cos πt Ts f2 cos 2 πt Ts f3 cos 3πt Ts f4 cos 4πt Ts OFDM Signal: Time Domain OFDM Signal: Freq. Domain DFT is means to generate samples of the OFDM signal in the frequency and time domain without the use of oscillators At the transmitter OFDM uses IDFT to convert samples of the spectrum of the OFDM signal into a corresponding equal number of samples from the OFDM signal at the time domain At the receiver OFDM uses DFT to restore the signal representation in the frequency domain and proceed with symbols detection © Tallal Elshabrawy 26 OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriers f1 cos πt Ts f2 cos 2 πt Ts f3 cos 3πt Ts f4 cos 4πt Ts (Separated by 1/2Ts) We need to compute the composite spectrum in the frequency domain to be able to compute the 4 samples used by the IDFT f1 © Tallal Elshabrawy 1 1 3 2 f2 f3 f4 2Ts Ts 2Ts Ts 27 OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriersf1 cos 2πt Ts f2 cos 4 πt Ts f3 cos 6πt Ts f4 cos 8πt Ts (Separated by 1/Ts) The separation between carriers guarantee that samples from individual spectrum of sub-carriers correspond to samples from the composite spectrum f1 © Tallal Elshabrawy 1 Ts f2 2 Ts f3 3 Ts f4 4 Ts 28 Number of Subcarriers in OFDM with DFT For band-limited FDM if the system bandwidth is B, number of sub-carriers is given by: BTS B NC 1 α / TS 1 α 0 α 1 Rolloff Factor For OFDM if the system bandwidth is B, Number of sub-carriers is given by: B NC BTS 1/ TS OFDM with DFT has the potential to at increase the number of subcarriers compared to FDM for α>0 (remember that α=0 filter is not physically realizable ) DFT implementation of OFDM avoids the needs for oscillators to generate the OFDM signal © Tallal Elshabrawy 29