In a digital communications system, the symbols that arrive at the receiver have been convolved with the time-domain channel impulse response of length L subscript C samples. Thus, the effect of the channel is convolutional. In order to undo the effects of the channel, another convolution must be performed at the receiver using a time-domain filter known as an equalizer. The length of the equalizer needs to be on the order of the time span of the channel. The equalizer processes symbols in order to adapt its response in an attempt to remove the effects of the channel. Such an equalizer can be expensive to implement in hardware and often requires a large number of symbols in order to adapt its response to a good setting.

In OFDM, the time-domain signal is still convolved with the channel response. However, the data will ultimately be transformed back into the frequency-domain by the FFT in the receiver. Because of the periodic nature of the cyclically-extended OFDM symbol, this time-domain convolution will result in the multiplication of the spectrum of the OFDM signal (i.e., the frequency-domain constellation points) with the frequency response of the channel. The result is that each subcarrier's symbol will be multiplied by a complex number equal to the channel's frequency response at that subcarrier's frequency. Each received subcarrier experiences a complex gain (amplitude and phase distortion) due to the channel. In order to undo these effects, a frequency-domain equalizer is employed. Such an equalizer is much simpler than a time-domain equalizer. The frequency-domain equalizer consists of a single complex multiplication for each subcarrier. For the simple case of no noise, the ideal value of the equalizer's response is the inverse of the channel's frequency response. An example is shown in Figure 7. With such a setting, the frequency-domain equalizer would cancel out the multiplicative effect of the channel.

Coded OFDM, or COFDM, is a term used for a system in which the error control coding and OFDM modulation processes work closely together. An important step in a COFDM system is to interleave and code the bits prior to the IFFT. This step serves the purpose of taking adjacent bits in the source data and spreading them out across multiple subcarriers. One or more subcarriers may be lost or impaired due to a frequency null, and this loss would cause a contiguous stream of bit errors. Such a burst of errors would typically be hard to correct. The interleaving at the transmitter spreads out the contiguous bits such that the bit errors become spaced far apart in time. This spacing makes it easier for the decoder to correct the errors. Another important step in a COFDM system is to use channel information from the equalizer to determine the reliability of the received bits. The values of the equalizer response are used to infer the strength of the received subcarriers. For example, if the equalizer response had a large value at a certain frequency, it would correspond to a frequency null at that point in the channel. The equalizer response would have a large value at that point because it is trying to compensate for the weak received signal. This reliability information is passed on to the decoding blocks so that they can properly weight the bits when making decoding decisions. In the case of a frequency null, the bits would be marked as "low confidence" and those bits would not be weighted as heavily as bits from a strong subcarrier. COFDM systems are able to achieve excellent performance on frequency-selective channels because of the combined benefits of multicarrier modulation and coding.

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