Affine precoders for reliable communications

It is known that precoding a signal prior to its transmission through an unknown finite impulse response channel facilitates the equalisation of the channel. Moreover, since linear precoders spread the spectrum, the equalisation process mitigates the effects of channel spectral nulls caused by frequency selective fading. This paper argues that certain affine precoders are more efficient than linear precoders. Here, the efficiency of a precoder is a measure of its ability to enable the receiver to recover the source signal relative to the amount of redundancy introduced by the precoder. An efficient affine precoder is heuristically derived and simulations used to demonstrate that it is superior to both the traditional training sequence method and the more recent filter bank precoding scheme. This precoding and equalisation scheme naturally extends to time varying channels.