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

694 DIGITAL COMMUNICATIONS UNDER LINEARLY DISTORTIVE CHANNELS
a vector of N output symbols can be written in matrix form as
z[N] h[O] h[ l] h[L]
z[N - 1] h[O] h[ l] h[L]
z[LJ h[O] h[l]
h[L]
z[l]
h[O]
h[l]
h[L]
SN
SN-1
w[N]
w[N - 1]
X
S J
so
+
w[L]
(12.63)
L(L-1 )
w[ l ]
The key step in OFDM is to introduce what is known as the cyclic prefix in the transmitted
data.* This step replaces the M leading elements
SQ , S- 1, ... , S- (L-1 )
of the (N + L)-dimensional data vector by the trailing symbols
{sN , SN-I , ... , SN-L+ d ---+ {so, LI, ... , L (L-IJ}
By inserting the cyclic prefix, we can then rewrite Eq. (12.63) as
z[N] h[O] h[ l] h[L]
z[N - 1] h[O] h[ I] h[L]
z[L] h[O] h[ l ] h[L]
z[ l] h[O] h[ l] h[L]
SN
SN-I
X s, +
SN
w[N]
w[N - ll
w[L]
(12.64a)
SN-L+ l
w [l]
* Besides the use cyclic prefix, zero padding is an alternative but equivalent approach.