OFDM Communication System
Figure 10.1 is a block
diagram of an OFDM communication system. A serial-to-parallel buffer segments
the information sequence into frames of Q
symbols. An OFDM word at time i consists of Q data symbols X0[i], X1[i], ...,
XQ-1[i]. An inverse
discrete Fourier transform (IDFT) is first applied to the OFDM word, to
obtain
Equation 10.1
A guard interval with cyclic prefix is then inserted to prevent
possible intersymbol interference between OFDM words. After pulse shaping and
parallel-to-serial conversion, the signals are then transmitted through a
frequency-selective fading channel. The time-domain channel impulse response can
be modeled as a tapped-delay line, given by
Equation 10.2
where 
denotes the maximum number of
resolvable channel taps, with tm being the maximum multipath spread and Df being the
carrier spacing. Assume that the channel taps remain constant over the interval
of one OFDM word [i.e., al(t) 
al[(i-1)T] for (i-1)T 
t < iT, where T is the duration of one OFDM word]. At the receiver
end, after matched filtering and removing the cyclic prefix, the sampled
received signal corresponding to the nth OFDM
word becomes
Equation 10.3
Equation 10.4
where * denotes the convolution, 
, and
{nm[i]}m are
i.i.d. complex white Gaussian noise samples. A DFT is then applied to the
received signals {ym[i]}m to
demultiplex the multicarrier signals:
Equation 10.5
For OFDM systems with proper cyclic extensions and proper
sample timing, with tolerable leakage, the received signal after demultiplexing
at the kth subcarrier can be expressed as
Equation 10.6
where {Nk[i]}k contains
the DFT of the noise samples {nm[i]}m, and
; and {Hk[i]}k contains
the DFT of channel impulse response {hm[i]}m:
Equation 10.7
Assume that for each l, 0 l < L, {hl[i]}i is a
complex Gaussian process with an autocorrelation following the Jakes model:
Equation 10.8
where Pl is the
average power of the lth tap and fd is the Doppler spread. Assume further
that the L fading processes are mutually
independent. Since {Hk[i]}k are
linear transformations of {hl[i]}l, then
for each k, 0 k < Q, {Hk[i]}i is also
a complex Gaussian process with autocorrelation
Equation 10.9
Hence from (10.6) and
(10.9) it is seen that the received
frequency-domain signal at each subcarrier k
follows a flat-fading model with the same fading autocorrelation function as
that in the time domain. Hence the OFDM system effectively transforms a
frequency-selective fading channel into a set of parallel flat-fading channels.
However, note that the frequency-domain channel responses of different carriers
are correlated. In fact, we have
Equation 10.10
Sections
