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Sec. 5–12 Orthogonal Frequency Division Multiplexing 385
TABLE 5–9
SPECTRAL EFFICIENCY OF DIGITAL SIGNALS
Spectral Efficiency, = R B T
a bit>s
Hz b
Type of Signal
Null-to-Null Bandwidth
30-dB Bandwidth
OOK and BPSK 0.500 0.052
QPSK, OQPSK, and p4> QPSK
1.00 0.104
MSK 0.667 0.438
16 QAM 2.00 0.208
64 QAM 3.00 0.313
5–12 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
Orthogonal frequency division multiplexing (OFDM) is a technique for transmitting data in
parallel by using a large number of modulated carriers with sufficient frequency spacing so
that the carriers are orthogonal. As we shall see, OFDM provides resistance to data errors
caused by multipath channels.
Over a T-sec interval, the complex envelope for the OFDM signal is
N-1
g(t) = A c a w n w n (t), 0 7 t 7 T
n=0
(5–117a)
where A c is the carrier amplitude, wn is the element of the N-element parallel data vector
w = [w 0 , w 1 , Á , w N-1 ], and the orthogonal carriers are
w n (t) = e j2pf nt
where f n = 1 T an - N - 1 b
2
(5–117b)
The duration of the data symbol on each carrier is T seconds, and the carriers are spaced 1T Hz
apart. This assures that the carriers are orthogonal, since the w n (t) satisfy the orthogonality
condition of Eq. (2–77) over the T-sec interval (as shown in Example 2–12). Because the
carriers are orthogonal, data can be detected on each of these closely spaced carriers without
interference from the other carriers.
A key advantage of OFDM is that it can be generated by using FFT digital signalprocessing
techniques. For example, if we suppress the frequency offset (N - 1)2T of
Eq. (5–117b) and substitute Eq. (5–117b) into Eq. (5–117a), where t = kTN, then the elements
of the IFFT vector, as defined by Eq. (2–117), are obtained. Thus, the OFDM signal
may be generated by using the IFFT algorithm as shown in Fig. 5–37. In that figure, the complex
envelope, g(t), is described by the I and Q components x(t) and y(t), where g(t) = x(t) and
jy(t). (This is an application of the generalized transmitter of Fig. 4–28b.)