Energy-efficient channel estimation

We investigate the energy-efficient channel estimation in wireless networks, where one pilot is inserted for every several data slots to estimate the channel coefficients. Both the channel state information estimation error and the time-varying model are considered. We first formulate the energy-efficient channel estimation problem into a mixed integer nonlinear programming (MINLP) problem, where the variables include the transmitted power and the number of data slots. Due to the NP-hard nature, we degenerate the MINLP problem into a series of non-concave optimization problems without integer variables. Then we solve these problems using successive convex approximation, geometric programming, and the Dinkelbach algorithm to obtain a point satisfying the Karush-Kuhn-Tucker (KKT) conditions. Furthermore, we develop a low-complexity sub-optimal scheme through binary variable relaxation to obtain a solution, and the convergence point satisfies the KKT conditions of the relaxed non-concave problem. Simulation results demonstrate the convergence and effectiveness of our proposed schemes.