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INTRODUCTION Orthogonal frequency-division multiplexing (OFDM) is a frequency- division multiplexing (FDM) scheme used as a digital multi-carrier modulation method. A large number of closely-spaced orthogonal sub-carriers are used to carry data. The data is divided into several parallel data streams or channels, one for each sub-carrier. Each sub-carrier is modulated with a conventional modulation scheme (such as QAM or PSK) at a low symbol rate, maintaining total data rates similar to conventional single-carrier modulation schemes in the same bandwidth. OFDM has developed into a popular scheme used in applications such as digital video and audio broadcasting, wireless networking and WIMAX.
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WHY OFDM? Can easily adapt to severe channel conditions without complex time- domain equalization. Robust against narrow-band co-channel interference. Robust against inter-symbol interference (ISI) and fading caused by multipath propagation. High spectral efficiency as compared to conventional modulation schemes, spread spectrum, etc. Efficient implementation using Fast Fourier Transform (FFT). Low sensitivity to time synchronization errors.
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HOW? Discrete Fourier transform (DFT) and inverse DFT (IDFT) processes are useful for implementing these orthogonal signals. Note that DFT and IDFT can be implemented efficiently by using fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT), respectively. In the OFDM transmission system, N-point IFFT is taken for the transmitted symbols , so as to generate , the samples for the sum of N orthogonal subcarrier signals. Let y[n] denote the received sample that corresponds to x[n] with the additive noise w[n] (i.e., y[n] =x[n]+w[n]). Taking the N-point FFT of the received samples, , the noisy version of transmitted symbols can be obtained in the receiver.
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ORTHOGONALITY Two conditions must be considered for the orthogonality between the subcarriers. Each subcarrier has exactly an integer number of cycles in the FFT interval. The number of cycles between adjacent subcarriers differs by exactly one.
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ORTHOGONALITY Time domain Frequency domainExample of four subcarriers within one OFDM symbol Spectra of individual subcarriers
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GUARD INTERVAL AND CYCLIC EXTENSION Two different sources of interference can be identified in the OFDM system. Intersymbol interference (ISI) is defined as the crosstalk between signals within the same sub-channel of consecutive FFT frames, which are separated in time by the signaling interval T. Inter-carrier interference (ICI) is the crosstalk between adjacent subchannels or frequency bands of the same FFT frame.
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GUARD INTERVAL AND CYCLIC EXTENSION Delay spread Environment Delay Spread Home < 50 ns Office ~ 100 ns Manufactures 200 ~ 300 ns Suburban < 10 us
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GUARD INTERVAL AND CYCLIC EXTENSION For the purpose to eliminate the effect of ISI, the guard interval could consist of no signals at all. Guard interval (or cyclic extension) is used in OFDM systems to combat against multipath fading. Tg :guard interval Tdelay-spread : multi path delay spread Tg > Tdelay-spread In that case, however, the problem of inter-carrier interference (ICI) would arise. The reason is that there is no integer number of cycles difference between subcarriers within the FFT interval.
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GUARD INTERVAL AND CYCLIC EXTENSION If T g < T dely-spread Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4 ﹒ ﹒ ﹒ ﹒ Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 ﹒ ﹒ ﹒ ﹒ Tdely-spread If T g > T dely-spread Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4 ﹒ ﹒ ﹒ ﹒ Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 ﹒ ﹒ ﹒ ﹒ Tdely-spread
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GUARD INTERVAL AND CYCLIC EXTENSION To eliminate ICI, the OFDM symbol is cyclically extended in the guard interval. This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard interval. Guard Interval (Cyclic Extension)
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GUARD INTERVAL AND CYCLIC EXTENSION Effect of multipath with zero signals in the guard interval, the delayed subcarrier 2 causes ICI on subcarrier 1 and vice versa.Part of subcarrier #2causing ICI onsubcarrier #1 Subcarrier #1 Delayed subcarrier #2 Guard time FFT integration time=1/carrier spacing Guard time FFT integration time=1/carrier spacing OFDM symbol time OFDM symbol time
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CFO The carrier frequency offset (CFO) is caused by Doppler frequency shift fd . We intend to generate exactly the same carrier frequencies in the transmitter and receiver, but ,there may be an unavoidable difference between them due to the physically inherent nature of the oscillators. Let fc and f ’c denote the carrier frequencies in the transmitter and receiver, respectively. Let foffset denote their difference (i.e., foffset = fc - f ’c). Doppler frequency fd is determined by the carrier frequency fc and the velocity v of the terminal (receiver) as fd = (v.fc)/c where c is the speed of light. Let us define the normalized CFO, Ɛ, as a ratio of the CFO to subcarrier spacing Δf , shown as Ɛ=(Foffset / Δf) Let Ɛi and Ɛf denote the integer part and fractional part of Ɛ, respectively, and therefore, Ɛ=Ɛi+Ɛf, where Ɛi= |Ɛ|.
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EFFECT OF INTEGER CARRIER FREQUENCYOFFSET(IFO) Due to the IFO, the transmit signal X(k) is cyclic shifted by Ɛi in the receiver, and thus producing X(k-Ɛi) in the kth subcarrier. Unless the cyclic shift is compensated, it will incur a significant degradation in the BER performance. However, we note that the orthogonality among the subcarrier frequency components is not destroyed and thus, ICI does not occur.
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EFFECT OF FRACTIONAL CARRIER FREQUENCYOFFSET(FFO) It is clear from this figure that amplitude and phase distortion becomes severe as FFO increases.
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CFO ESTIMATION TECHNIQUES CFO can be estimated in time domain and frequency domain. There are different techniques for both cases. The most popular being Moose for frequency domain and Schmidl for time domain. Moose’s Method If two identical training symbols are transmitted consecutively, the corresponding signals with CFO of ε are related with each other as follows: Using this relationship CFO can be estimated as: This is the well known Moose’s method. Although the range of CFO estimated is |ε|≤0.5
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Schmidl’s and the Improvement method is different in terms of the Pilot arrangement. In Schmidl method we use two repeated N/2 length long pilot sequences. While in the Improvement method we use four repeated N/4 length long pilot sequences.
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Schmidl Method Here CFO estimation is done with a single step. We use the correlation between the two PN sequences to determine an intermediate variable. In is the sum of all noise, which can be regarded as AWGN when N is larger enough. CFO estimated by taking the phase of ϕ.
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Improvement Method This estimation is done in two steps. First we do a coarse estimation to get the coarse CFO value. Then after correcting for this rough value we do a fine estimation on the corrected signal to get a better approximation to the true value. Coarse Estimation This estimation is done by the following iteration to get the intermediate value. Essentially we are correlating the first and fourth N/4 length pilot symbols. Coarse estimate is obtained by taking the phase of φ1.
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Correction The received signal is corrected by accounting for the CFO estimated. Fine Estimation This estimation is done by the following iteration to get a second intermediate value. Here we are correlating the second and third N/4 length pilot symbols. Where ε2=ε-ε1 the residual CFO. Fine estimate is obtained by taking the phase of φ2. The total CFO is the sum of the fine and coarse estimates.
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