B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

12.7 OFDM (Multicarrier) Communications 693
the frequency.{ is sampled at
1
Jo = 0·-=0
NT
1 1
NT NT
f1 =l·- = -
I (N - 1)
fN- 1 = (N - l) .
NT
=
NT
We can use a simpler notation to denote the DFT sequence by letting Wn = 2nn/ NT
H[n] = H(Jwn T )
L
= L h[k] exp(-jw n Tk)
k=O
L
= Lh[k] exp (-j2n ;.kT)
k=O
= t h[k] exp (-j2n ; )
k=O
n = 0, 1, ... , (N - 1) (12.61)
From Eq. (12.61), it is useful to notice that H[n] is periodic with period N (Fig. 12.9). Hence,
L
( nk
)
H[-n] = L h[k] exp j2n N
k=O
(12.62a)
( nk Nk
= L h[k] exp j2n - j2n )
N N
k=O
L
°"' [ (N - n)k
= L, h[k] exp -j2n ]
N
k=O
= H[N - n]
(12.62b)
Based on the linear convolutional relationship between the channel input {sk } and output
L
z[k] = L h[i]sk-i + w[k]
i=O
Figure 12.9
(a) Discrete time
domain channel
response and (b)
its corresponding
periodic DFT.
h[O]
h[l] h[L]
0 L 0
(a)
(b)