Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

134 Implementation IssuesFrom the above expression we note that the transmitted OFDM symbol can be generatedby using an inverse complex FFT operation (IFFT), where the de-multiplexing is done byan FFT operation. In the complex digital domain this operation leads to an IDFT operationwith N c points at the transmitter side and a DFT with N c points at the receiver side (seeFigure 4-4). Note that for the guard time and pre-/post-fix L g samples are inserted afterthe IDFT operation at the transmitter side and removed before the DFT at the receiverside.Highly repetitive structures based on elementary operations such as butterflies for theFFT operation can be applied if N c is of the power of 2 [1]. Depending on the transmissionmedia and the carrier frequency f c , the actual OFDM transmission systems employ from64 up to 2048 (2k) sub-carriers. In the DVB-T standard [19], up to 8192 (8k) sub-carriersare chosen to combat long echoes in a single frequency network operation.The complexity of the FFT operation (multiplications and additions) depends on thenumber of FFT points N c . It can be approximated by (N c /2)log N c operations [1]. Furthermore,large numbers of FFT points, resulting in long OFDM symbol durations T s ′,make the system more sensitive to the time variance of the channel (Doppler effect) andmore vulnerable to the oscillator phase noise (technological limitation). However, on theother hand, a large symbol duration increases the spectral efficiency due to a decrease ofthe guard interval loss.Therefore, for any OFDM realization a tradeoff between the number of FFT points, thesensitivity to the Doppler and phase noise effects, and the loss due to the guard intervalhas to be found.4.1.3 Virtual Sub-Carriers and DC Sub-CarrierBy employing large numbers of sub-carriers in OFDM transmission, a high frequencyresolution in the channel bandwidth can be achieved. This enables a much easier0101L g −10101N c -PointIFFTP/SD/AA/DS/PN c -PointFFTN c − 1N c − 1 N c − 1Guard time/post/prefixinsertionN c + L g − 1TransmitterFigure 4-4Digital implementation of OFDMGuard time/post/prefixremovalN c + L g − 1Receiver