Orthogonal Frequency Division Multiplexing - OFDM

Impact of fading S(f) High bit rate H(f) f r(t) s(t) f h(t) t t S(f) Low bit rate f t r(t) s(t) t t

Frequency Selective fading flat fading s(t) H(f) t r(t) f p1(t) h(t) t p2(t) t p3(t) p3(t) t p4(t) p4(t) t

FDM  OFDM Frequency Division Multiplexing OFDM GAIN IN SPECTRAL EFFICIENCY

OFDM DEFINITION OFDM = Orthogonal FDM Carrier centers are put on orthogonal frequencies ORTHOGONALITY - The peak of each signal coincides with zero crossing of other signals Subcarriers are spaced by 1/ Ts

A simplified view S-P + s(t) S-P P-S r(t) Cos 2f1t Input bits Output bits Cos 2f8t

OFDM THEORY s s s s s s The baseband OFDM signals can be written as where is the central frequency of the mth sub-channel and is the corresponding transmitted symbol. The signals are orthogonal over [0, T ] as illustrated below: s s s s s s s

Continuous Time: Orthogonal Time Signal Set

Discrete Time: Orthogonal Time Signal Set Ts = N T

k (t) OFDM Modulator

OFDM Demodulator

OFDM is a Block Process

Discrete Time Equivalent Inverse Discrete Fourier Transform  s(n) =  dk exp( j 2 k n/N) N-point IDFT  N2 complex multiplications Inverse Fast Fourier Transform Radix 2 N-point IFFT  (N/2). log2 N Radix 4 N-point IFFT  (3/8). N. ( log 2 N - 2) N -1 k=0

Generic OFDM Transmitter OFDM symbol bits Serial to Parallel Pulse shaper FEC IFFT Linear PA & DAC add cyclic extension fc view this as a time to frequency mapper Complexity (cost) is transferred back from the digital to the analog domain!

(of all tones sent in one OFDM symbol) Generic OFDM Receiver Slot & Timing AGC Sync. P/S and Detection Error Sampler FFT Recovery fc gross offset VCO Freq. Offset fine offset Estimation (of all tones sent in one OFDM symbol)

Complexity of OFDM versus Single Carrier Key difference between OFDM and single carrier transmission is FFT versus equalizer Complexity of 64 point radix-4 FFT in IEE 802.11a OFDM=96 million multiplications per second 16 taps OQPSK or GMSK Equalizer for same data rates above needs 768 million multiplications per second OFDM order of magnitude less complex

Salient features BASIC IDEA : Channel bandwidth is divided into multiple subchannels to reduce ISI and frequency-selective fading. Multicarrier transmission : Subcarriers are orthogonal each other in frequency domain. Time-domain spreading: Spreading is achieved in the time-domain by repeating the same information in an OFDM symbol on two different sub-bands => Frequency Diversity. Frequency-domain spreading: Spreading is achieved by choosing conjugate symmetric inputs for the input to the IFFT (real output) Exploits frequency diversity and helps reduce the transmitter complexity/power consumption.

OFDM ADVANTAGES OFDM is spectrally efficient IFFT/FFT operation ensures that sub-carriers do not interfere with each other. OFDM has an inherent robustness against narrowband interference. Narrowband interference will affect at most a couple of subchannels. Information from the affected subchannels can be erased and recovered via the forward error correction (FEC) codes. Equalization is very simple compared to Single-Carrier systems

OFDM ADVANTAGES OFDM has excellent robustness in multi-path environments. Cyclic prefix preserves orthogonality between sub- carriers. Cyclic prefix allows the receiver to capture multi- path energy more efficiently. Ability to comply with world-wide regulations: Bands and tones can be dynamically turned on/off to comply with changing regulations. Coexistence with current and future systems: for enhanced coexistence with the other devices.

OFDM DRAWBACKS High sensitivity inter-channel interference, ICI OFDM is sensitive to frequency, clock and phase offset The OFDM time-domain signal has a relatively large peak-to-average power ratio tends to reduce the power efficiency of the RF amplifier non-linear amplification destroys the orthogonality of the OFDM signal and introduced out-of-band radiation

Adjacent Symbol Interference (ASI) Symbol Smearing Due to Channel

Guard Interval Inserted Between Adjacent Symbols to Suppress ASI

Cyclic Prefix Inserted in Guard Interval to Suppress Adjacent Channel Interference (ACI) and retain orthogonality

Data Length Defines Sinc Width: Spectral Spacing Matches Width

Extended Data Length Reduces Sinc Width: Spectral Spacing Preserved

DFT (FFT) as Signal Generator for Complex Sinusoids

DFT (FFT) As Signal Analyzer for Complex Sinusoids

Radix-2 FFT Flow Diagrams

Input Vector FFT Mapped to Output Time Series, Up-Sampled, Converted Via DAC to Waveform, and I-Q Up-Converted

The FFT as Signal Generator and Interpolator

OFDM Modulation With IFFT and Interpolator

OFDM Demodulation With FFT

OFDM Transceiver