1. OFDM Each sub-carrier is modulated at a very low symbol rate, making the symbols much longer than the channel impulse response. Discrete Fourier transform (DFT) applied for multi- carrier modulation. The DFT exhibits the desired orthogonality and can be implemented efficiently through the fast fourier transform (FFT) algorithm.

2. Basic principles The orthogonality of the carriers means that each carrier has an integer number of cycles over a symbol period. Reception by integrate-and-dump-receiver Compact spectral utilization (with a high number of carriers spectra approaches rectangular-shape) OFDM systems are attractive for the way they handle ISI and ICI, which is usually introduced by frequency selective multipath fading in a wireless environment. (ICI in FDM)

3. Drawbacks of OFDM The large dynamic range of the signal, also known as the peak-to-average-power ratio (PAPR). Sensitivity to phase noise, timing and frequency offsets (reception) Efficiency gains reduced by guard interval. Can be compensated by multiuser receiver techniques (increased receiver complexity)

4. Examples of OFDM-systems OFDM is used (among others) in the following systems: IEEE 802.11a&g (WLAN) systems IEEE 802.16a (WiMAX) systems ADSL (DMT = Discrete MultiTone) systems DAB (Digital Audio Broadcasting) DVB-T (Digital Video Broadcasting) OFDM is spectral efficient, but not power efficient (due to linearity requirements of power amplifier= the PAPR-problem). OFDM is primarily a modulation method; OFDMA is the corresponding multiple access scheme.

6. OFDM Signal

7. Multiplexing techniques

9. OFDM signal in time domain OFDM TX signal = Sequence of OFDM symbols g k (t) consisting of serially converted complex data symbols The k:th OFDM symbol (in complex LPE form) is where N = number of subcarriers, T G + T S = symbol period with the guard interval, and a n,k is the complex data symbol modulating the n:th subcarrier during the k:th symbol period. In summary, the OFDM TX signal is serially converted IFFT of complex data symbols a n,k

10. Orthogonality of subcarriers Orthogonality over the FFT interval: Phase shift in any subcarrier - orthogonality over the FFT interval should still be retained: Definition: