cket-switched mobile communications system Narrowband modulator Narrowband fn Frequency modulator Narrowband modulator f1 f2 fn Frequency Figure 10.22 FDM and OFDM transmitters the first generation of standards described above. Both OFDM and FDM systems assign a number of frequency carriers for transmitting data in parallel, as shown in Figure 10.22. The difference is that in FDM systems, filters and guard band are used to ensure neighbouring car- riers do not interfere with each other. Carrier frequencies in an OFDM system overlap, and as a result do generally interfere with each other. However OFDM works in a way that at certain frequency sampling points, the interference is zero. If the received signal is sampled at these points, then a clear interference-free detection can be made. This "orthogonality" is very significant in interference-limited multiuser mobile telecommunications systems. The history of OFDM traces to the mid-1960s [13] and efforts to better utilise long-distance telephony lines. It was first used in the wireless local area network standards of IEEE, namely 802.11a and 802.11g (more details in Chapter 12). Frequency orthogonality arises from the fact that the frequency domain representation of a time-domain square waveform is a sinc function. For example a square waveform with a dura- tion of T and amplitude of 1 has a frequency representation of sinc(f) where f = 1/T as rep- resented in Figure 10.23. The square waveform may take any one of different values amplitude and phase as specified by a signal constellation. For example the square waveform may be one of 4 points in a QPSK signal constellation. As a result the frequency-domain rep- resentation will have corresponding different amplitude and phase value. Terrestrial Broadband Wireless Telecommunications Amplitude -0.5 Ts 0.5 Ts Amplitude Frequency fs=1/Ts Figure 10.23 A square waveform in the time domain and its frequency-domain representation Amplitude Frequency Figure 10.24 Three frequency domain orthogonal waveforms As can be seen f