On the relationship of the Cramer-Rao lower bound and channel capacity in an interfered binary channel through the log-likelihood ratio

This paper deals with the relationship of the Cramer-Rao lower bound (CRLB) and the channel capacity in a channel with interference. The former quantity is the representative of estimation theory and the latter is the envoy to information theory. CRLB is the lower bound on the variance of any unbiased estimator and channel capacity is the upper bound on the rate of reliable transmission. In the region that signal-to-interference ratio (SIR) is close to zero, the local minimum of the capacity of binary channel and local maximum of the CRLB happens. The log-likelihood ratio (LLR) is investigated to interpret the estimation and the capacity characteristics and plays a main role in this way.