Equalization of Time-Varying Channels

As discussed in Chapter 1, the wireless communication channel can be modeled as a timevarying (TV) linear1 system whose output is corrupted by additive noise. To reliably recover the transmitted information from the channel output, the receiver must address the effects of both linear distortion and additive noise. While, in theory, the mitigation of linear distortion and additive noise should be done jointly, in practice the task is often partitioned into two tasks, equalization and decoding, in order to reduce implementation complexity. Roughly speaking, equalization leverages knowledge of channel structure to mitigate the effects of the linear distortion while decoding leverages knowledge of code structure to mitigate the channel’s additive noise component. The equalizer might be well informed about the channel (e.g., knowing the complete channel impulse response) or relatively uninformed (e.g., knowing only the maximum channel length). In some cases, knowledge of symbol structure (e.g., the symbol alphabet or, if applicable, the fact that the symbols have a constant modulus) is assumed to be in the domain of the equalizer, while in other cases it is assumed to be in the domain of the decoder; since the equalizer and decoder work together to infer the transmitted information from the channel output, the role of equalization versus decoding is somewhat a matter of definition. For this chapter, however, we assume that exploitation of code structure is not in the domain of the equalizer. Generally speaking, the output of the equalizer is a sequence of symbol (or bit) estimates which have been, to the best of the equalizer’s ability, freed of channel corruption. These estimates are then passed to the decoder for further refinement and final decision making. In so called turbo equalization schemes [DJB+95, KST04], the decoder passes