Statistics of a Blind Channel Estimator based on 'Logic Strings'

Abstract:
We derive the mean squared error (variance) of a blind channel estimator that exploits constraints imposed on valid combinations of code bits (also called ’logic strings’) and the respective receive symbols by the parity check equations of a channel code. The dependence of the estimation error on the length of the logic strings, their available number as well as on the channel impulse response is quantified for a finite number of observations, i.e. logic strings that are available within one data block. The result explains, why short logic strings perform significantly better than longer ones. This provides a guideline to choose appropriate codes and allows for given typical channel conditions to select the appropriate code or block length to achieve the desired accuracy of the channel estimate.