In practical communication systems, the transmitter usually sends out training symbols to the receiver, based on which the channel can be estimated at the receiver. It is therefore reasonable to assume that the channel is known to the receiver. When the channel state information is also known to the transmitter, we can optimize the transmitter to better the system performance. Having this knowledge available to the transmitter requires the receiver to send back the information, which takes time. For wireless transmission, the channel varies rapidly. By the time the transmitter receives the channel profile, the channel may have changed. Therefore, for wireless applications it is often desirable to have a transmitter that is channel-independent. In such a channel-independent transmitter, there is no bit/power allocation. Having a channel-independent transmitter is also of vital importance for broadcasting applications, where there are many receivers with different transmission paths. The OFDM system has the much desired feature that the transmitter is channel-independent and furthermore the channel-dependent part of the transceiver is only a set of M scalars at the receiver. Moreover, the main processing at the transmitter (receiver) is M-point IDFT (DFT), which can be implemented efficiently using fast algorithms, and the complexity is in the order of M log2M instead of M2.

The discussion in Chapter 6 suggests that the OFDM system can be severely affected by channel spectral nulls. For high SNR the error rate is usually limited by those subchannels that have low SNRs. One method that prevents the performance being dominated by a few bad subchannels is to have a precoder. Figure 7.1 shows an OFDM transmission system with a precoder at the transmitter and a post-coder at the receiver. We have seen earlier that when the precoder is the DFT matrix, the precoder DFT matrix will cancel out the IDFT at the transmitter and the precoded system becomes the SC-CP system shown in Fig. 6.10. The SC-CP system illustrates that having a precoder can alter the BER behavior of the system, although the total output mean squared error is unchanged in this case.