Signal Processing for Wireless Transceivers - Signal Processing Systems - page 182

data symbols. Orthogonality of the subchannels follows directly from the properties
of discrete Fourier transform (DFT). In the channel, each data symbols appears as a
square-windowed sinusoid, the frequency of which is determined by the subcarrier
index and amplitude and phase are determined by the transmitted complex symbol
value. Using continuous-time model, the transmitter and receiver OFDM waveform
processing can be formulated as follows.
An OFDM symbol with IFFT size of N and duration of T s is given by

N 1

k = 0 X ( k ) e j 2π f k t

−

x ( t )= , t ∈ [ 0 , T s ] (20)

where X ( k ) , k = 0 ,..., N − 1, are complex data symbols, typically from a QAM

alphabet,

f k = f 0 + k · Δ f (21)

are the subcarrier frequencies and

1
T s

Δ f = (22)

is the frequency separation between subcarriers. With this choice, the subcarriers
are orthogonal, i.e.,

1

T s

1
T s

, k = l

e j 2π f l t e − j 2π f k t dt

= δ kl =

(23)

0 , otherwise

0

Therefore in the absence of noise and other imperfections, the k th symbol is
demodulated as

T s T s

N 1

l = 0 X ( l ) e j 2π f l t e − j 2π f k t dt = X ( k ) .

−

1
T s

1
T s

e − j 2π f k t dt x ( t ) = (24)

0 0

In practical systems, guard-bands are introduced in the OFDM signal spectrum by
modulating zero-valued symbols to the subcarriers close to the band edges. The
images of the OFDM signal generated by the IFFT (centered at integer multiples
of the frequency N

· Δ

f ) need to be filtered away by the later stages in the
transmitter chain, and the filtering requirements depend essentially on the width
of the guard-band. Similarly, the guard-band width affects also the specifications of
the channelization filtering on the receiver side.
The signal path of an OFDM transmission link, as illustrated in Fig. 5 a , includes
on the transmitter side the IFFT for a block of data symbols and copying a number of
IFFT output samples in front of the produced OFDM symbol as a cyclic prefix, along
with the needed buffering and serial-parallel and parallel-serial operations. On the
receiver side, the core functions include extracting a block of N ISI-free samples
from the baseband sample sequence, FFT, and 1-tap subcarrier-wise equalizers.
Additionally, a channel estimation function, usually based on known subcarrier