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

698 DIGITAL COMMUNICATIONS UNDER LINEARLY DISTORTIVE CHANNELS
then we can obtain the OFDM transmission symbols via
Despite the minor scalar I/ JN, we can call the matrix transformation of JNWN 1 the IDFT
(inverse DFT) operation. In other words, we apply IDFT on the information source data s at
the OFDM transmitter to obtain s before adding the cyclic prefix.
Similarly, we can also transform the channel output vector via
Corresponding to the IDFT, this operation can also be named the DPT: Finally, we note that
the noise vector at the channel output also undergoes the DFT:
We now can see the very simple relationship between the source data and the channel output
vector, which has undergone the DPT:
Because DH is diagonal, this matrix product is essentially element-wise multiplication:
(12.68a)
z[nJ = H[nJ sn + w[nl n = l, ...,N (12.68b)
This shows that we now equivalently have N parallel (sub)channels, each of which is just a
scalar channel with gain H[n] . Each vector of N data symbols in OFDM transmission is known
as an OFDMframe or an OFDM symbol. Each subchannel H[n] is also known as a subcarrier.
Thus, by applying the IDFT on the source data vector and the DPT on the channel output
vector, OFDM converts an ISi channel of order L into N parallel subchannels without ISL We
no longer have to deal with the complex convolution that involves the time domain channel
response. Instead, every subchannel is a non-frequency-selective gain only. There is no ISI
within each subchannel. The N parallel subchannels are independent of one another because
their noises are independent. This is why such a modulation is known as orthogonal frequency
division modulation (OFDM). The block diagram of an N-point OFDM system implementation
with a linear FIR channel of order Lis given in Fig. 12.10.
12.7.2 OFDM Channel Noise
According to Eq. (12.68b), each of the N channels acts like a separate carrier of frequency
f = n/NT with channel gain H[n]. Effectively, the original data symbols {sn} are split into N