On energy efficiency of pilot assisted modulation schemes

In this paper we investigate energy efficiency of basic modulation techniques in systems with partial channel state information (CSI) at the receiver, obtained via channel estimation. Both in-band and superimposed pilot aided channel estimation schemes are considered. Efficiency is defined as amount of energy per bit of information delivered. The efficiency is optimized with respect to the number and/or power of pilots for a given modulation. It is shown that there is an optimal power allocation for every modulation scheme and channel estimation scheme.