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OFDM_CP

# OFDM_CP - 400 Orthogonal frequency division...

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19.2 Principle of orthogonal frequency division multiplexing OFDM splits the information into N parallel streams, which are then transmitted by modulating N distinct carriers (henceforth called subcarriers or tones ). Symbol duration on each subcarrier thus becomes larger by a factor of N . In order for the receiver to be able to separate signals carried by different subcarriers, they have to be orthogonal. Conventional Frequency Division Multiple Access (FDMA), as described in Section 17.1 and depicted again in Fig. 19.1, can achieve this by having large (frequency) spacing between carriers. This, however, wastes precious spectrum. A much narrower spacing of subcarriers can be achieved. Specifically, let subcarriers be at the frequencies f n ¼ nW = N , where n is an integer, and W the total available bandwidth; in the most simple case, W ¼ N = T S . We furthermore assume for the moment that modulation on each of the subcarriers is Pulse Amplitude Modulation (PAM) with rectangular basis pulses. We can then easily see that subcarriers are mutually orthogonal, since the relationship Z ð i þ 1 Þ T S iT S exp ð j 2 % f k t Þ exp ð± j 2 % f n t Þ dt ¼ ± nk ð 19 : 1 Þ holds. Figure 19.1 shows this principle in the frequency domain. Due to the rectangular shape of pulses in the time domain, the spectrum of each modulated carrier has a sin ð x Þ = x shape. The spectra of different modulated carriers overlap, but each carrier is in the spectral nulls of all other carriers. Therefore, as long as the receiver does the appropriate demodulation (multiplying by exp ð± j 2 % f n t Þ and integrating over symbol duration), the datastreams of any two subcarriers will not interfere. 19.3 Implementation of transceivers OFDM can be interpreted in two ways: one is an ‘‘analog’’ interpretation, following from the picture of Fig. 19.2a. As discussed in Section 19.2, we first split our original datastream into N parallel datastreams, each of which has a lower data rate. We furthermore have a number of local oscillators available, each of which oscillates at a frequency f n ¼ nW = N , where n ¼ 0 ; 1 ; . . . ; N ± 1. Each of the parallel datastreams then modulates one of the carriers. This picture allows an easy understanding of the principle, but is ill-suited for actual implementation – the hardware effort of multiple local oscillators is too high. An alternative implementation 400 Orthogonal frequency division multiplexing (OFDM) Figure 19.1 Principle behind orthogonal frequency division multiplexing: N carriers within a bandwidth of W :

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