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

12.7 OFDM (Multicarrier) Communications 70 1
The rest of the OFDM transmission steps remain unchanged. At the receiver end, we can stack
up the received symbols in
y =
z[N] 0
z[N - 1]
z[LJ
0
+ z[N + L]
z[l ] z[N + l ]
We then can show (Prob. 12.7-4) that
(12.70)
would achieve the same multichannel relationship of Eq. ( 12.68b ).
12.7.4 Cyclic Prefix Redundancy in OFDM
The two critical steps of OFDM at the transmitter are the insertion of the cyclic prefix and the
use of N -point TDFT. The necessary length of cyclic prefix L depends on the order of the FIR
channel. Since the channel order may vary in practical systems, the OFDM transmitter must
be aware of the maximum channel order information a priori.
Although it is acceptable for OFDM transmitters to use an overestimated channel order, the
major disadvantage of inserting a longer-than-necessary cyclic prefix is the waste of channel
bandwidth. To understand this drawback, notice that in OFDM, the cyclic prefix makes possible
the successful transmission of N data symbols {s1 , ...• s N } with time duration (N + L) T. The
L cyclic prefix symbols are introduced by OFDM as redundancy to remove the ISi in the
original frequency-selective channel H (z). Because (N + L) symbol periods are now being
used to transmit the N information data, the effective data rate of OFDM equals
N
-- -
N+LT
If Lis overestimated, the effective data rate is reduced, and the transmission of the unnecessarily
long cyclic prefix wastes some channel bandwidth. For this reason, OFDM transmitters require
accurate knowledge about the channel delay spread to achieve good bandwidth efficiency. If
the cyclic prefix is shorter than L, then the receiver is required to include a time domain
filter known as the channel-shortening filter to reduce the effective channel-filter response to
within LT.
12.7.5 OFDM Equalization
We have shown that OFDM converts an ISi channel into N parallel AWGN subchannels as
shown in Fig. I 2.11. Each of the N subchannels has an additive white Gaussian noise of
zero mean and variance N /2. The subchannel gain equals H[k], which is the FIR frequency
response at k / NT Hz. Strictly speaking, these N parallel channels do not have any ISi. Hence,