IV. Orthogonal Frequency Division Multiplexing (OFDM)

Evolution of Wireless Communication Standards Introduction Evolution of Wireless Communication Standards OFDM

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

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

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

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

Multi-Path = Frequency-Selective! 0.5 0.5 1 1 0.5 1 μs 1 μs f=1 MHz 1 0.5 0.5 1 0.5 -0.5 -1 -1 1 μs 1 μs f=500 KHz 1 1 0.5 0.5 0.5 -0.5 -1 -1 1 μs 1 μs

Multi-Path = Frequency-Selective! h(t) |H(f)| 0.5 0.5 1 f (MHz) 0.5 1 1.5 2 1 μs A multi-path channel treats signals with different frequencies differently A signal composed of multiple frequencies would be distorted by passing through such channel

Frequency Division & Coherence Bandwidth Power Frequency Subdivide wideband bandwidth into multiple narrowband sub-carriers 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

Example Frequency Response for 3G Channel Power Delay Profile (Vehicular A Channel Model) Snapshot for Frequency Response Resolvable Path Relative Delay (nsec) Average Power (dB) 1 0.0 2 310 -1.0 3 710 -9.0 4 1090 -10.0 5 1730 -15.0 6 2510 -20.0 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

Example Frequency Response for 3G Channel Power Delay Profile (Vehicular A Channel Model) Snapshot for Frequency Response Resolvable Path Relative Delay (nsec) Average Power (dB) 1 0.0 2 310 -1.0 3 710 -9.0 4 1090 -10.0 5 1730 -15.0 6 2510 -20.0 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

Frequency Division Multiplexing (FDM) + Binary Encoder Transmitting Filter (f1) Modulation Filter (f2) Filter (fN) Wireless Channel Bandpass Demod.

Orthogonal FDM Is it possible to find carrier frequencies f1, f2 … fN such that

Orthogonal FDM Is it possible to find carrier frequencies f1, f2 … fN such that

Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

Orthogonality of Sub-Carriers Ts The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

Orthogonal FDM + Wireless Channel Binary Encoder Transmitting Filter (f1) Modulation Filter (f2) Filter (fN) Wireless Channel Correlate with (f1) Demod. with (f2) with (fN) f2=f1+1/2TS fN=f1+1/2(N-1)TS

Number of Subcarriers in OFDM For band-limited FDM if the system bandwidth is B, number of sub-carriers is given by: For OFDM if the system bandwidth is B, Number of sub-carriers is given by: OFDM has the potential to at least double the number of sub-carriers (i.e., double the total transmission rate over the system bandwidth)

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

OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriers Ts -f1 f1 -f2 f2 -f3 f3 -f4 f4 OFDM Signal: Time Domain OFDM Signal: Freq. Domain

OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriers 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

OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriers (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

OFDM & DFT (Discrete Fourier Transform) OFDM Signal over 4 Sub-carriers (Separated by 1/Ts) The separation between carriers guarantee that samples from individual spectrum of sub-carriers correspond to samples from the composite spectrum

Number of Subcarriers in OFDM with DFT For band-limited FDM if the system bandwidth is B, number of sub-carriers is given by: For OFDM if the system bandwidth is B, Number of sub-carriers is given by: OFDM with DFT has the potential to at increase the number of sub-carriers 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