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Sec. 5–12 Orthogonal Frequency Division Multiplexing 387
Referring to Fig. 5–37, let the input serial data symbols have a duration of T s sec each.
These data can be binary (;1) to produce BPSK modulated carriers or can be multilevel
complex-valued serial data to produce (as appropriate) QPSK, MPSK, or QAM carriers.
D s = 1T s , is the input symbol (baud) rate. The serial-to-parallel converter reads in N input
serial symbols at a time and holds their values (elements of w) on the parallel output lines for
T = NT s seconds, where T is the time span of the IFFT. The IFFT uses w to evaluate output
IFFT vector g, which contains elements representing samples of the complex envelope. The
parallel-to-serial converter shifts out the element values of g. These are the samples of the
complex envelope for the OFDM signal described by Eq. (5–117), where x(t) and y(t) are
the I and Q components of the complex envelope. The OFDM signal is produced by the IQ
modulators as shown in the figure.
At the receiver, the serial data are recovered from the received OFDM signal by (1)
demodulating the signal to produce serial I and Q data, (2) converting the serial data to
parallel data, (3) evaluating the FTT, and (4) converting the FFT vector (parallel data) to
serial output data.
The length-of-the-FFT vector determines the resistance of OFDM to errors caused by
multipath channels. N is chosen so that T = NT s is much larger than the maximum delay time
of echo components in the received multipath signal.
The PSD of the OFDM signal can be obtained relatively easily, since the OFDM signal
of Eq. (5–117) consists of orthogonal carriers modulated by data with rectangular pulse
shapes that have a duration of T sec. Consequently, the PSD of each carrier is of the form
|Sa[p(f - f n )T] |
2 , and the overall PSD for the complex envelope of the OFDM signal is
g (f) = C a
N-1
n=0
` sin [p(f - f n)T]
p(f - f n )T
2
`
(5–118)
where C = A 2 c ƒ w n ƒ 2 T and w n = 0. The spectrum is shown in Fig. 5–38 for the case of
N = 32. Since the spacing between the carriers is 1T Hz and there are N carriers, the null
bandwidth of the OFDM signal is
B T = N + 1
T
= N + 1
NT s
L 1 T s
= D s Hz
(5–119)
where the approximation is reasonable for N 7 10 and D s is the symbol (baud) rate of the
input serial data for the OFDM transmitter. In more advanced OFDM systems, rounded
(nonrectangular) pulse shapes can be used to reduce the PSD sidelobes outside the B T = D s
band.
Example 5–15 PSD FOR AN OFDM SIGNAL
Compute and plot the PSD for the complex envelope of an OFDM signal. See Example5_15.m
for the solution. Compare this result with that shown in Figure 5–38.