Bayesian Foundations of Channel Estimation for Smart Radios

In this paper, we revisit the philosophical foundations of the field of channel estimation. Our main intention is to come up with a partial answer to the question: “given some available sensed signals, how should cognitive radios ideally perform channel estimation?”.We specifically introduce a general framework to provide optimal channel estimates under any prior knowledge at the sensing device. Our discussion is articulated as a top-down approach, introducing successively (i) a discussion on the philosophical foundations of channel estimation as a simplification means for the general problem of wireless detection, (ii) an information theoretically optimal approach to channel detection assuming the sensing device has infinite memory, and (iii) a derived optimal approach when limited memory size is accounted for. The key mathematical tools used in this discussion emerge from Bayesian probability theory and are known as the maximum entropy principle and the minimum update principle. Derivations are carried out for the particular case of channel estimation in orthogonal frequency division multiplexing (OFDM) systems. While some theoretical results will be proven to match already known techniques, such as Kalman filters, another set of novel results will be shown by simulations to perform better than known channel estimation schemes.