## Figure 115 Naive implementation of guard time do not do this

Simplistic implementations of the guard time can destroy orthogonality in the presence of common delay spreads. OFDM depends on having an integer number of wavelengths between each of the carriers. When the guard time is perfectly quiet, it is easy to see how a delay can destroy this necessary precondition, as in Figure 11-5. When the two subcarriers are added together, the spectral analysis shows subcarrier 1 (two cycles/symbol) as a strong presence and a relatively smaller amount of subcarrier 2 (three cycles/symbol). In addition, the spectral analysis shows a large number of high-frequency components, muddying the waters further. These components are the consequence of suddenly turning a signal "on."

Solving the problems associated with a quiet guard time is quite simple. Each subcarrier is extended through the FFT integration period back through the preceding guard time. Extending each subcarrier (and hence the entire OFDM symbol) yields a Fourier transform that shows only the amplitudes of the subcarrier frequencies. This technique is commonly called cyclic extension, and it may be referred to as the "cyclic prefix extension." The guard time with the extended prefix is called the cyclic prefix.

In Figure 11-6, the cyclic prefix preserves the spectral analysis. Subcarrier 1 was not shifted and is not a problem. Subcarrier 2 is delayed, but the previous symbol appears only in the guard time and is not processed by the Fourier transform. Thanks to the cyclic prefix extension, when subcarrier 2 is processed by the Fourier transform, it is a pure wave at three cycles per integration time.

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