  Study of polar codes in fading channels is of great importance when applying
polar codes in wireless communications. Channel estimation is a fundamental
step for communication to be possible in fading channels. For both systematic
and non-systematic polar codes, construction of them is based on an information
set and the known frozen bits. Efficient implementation of systematic and
non-systematic polar codes exists. When it comes to channel estimation or
channel tracking, additional pilot symbols are inserted in the codeword
traditionally. In this paper, to improve the performance of polar codes in the
finite domain, pilot symbols are selected from the coded symbols themselves. In
order to keep the existing efficient structure of polar code encoding, pilot
selection is critical since not all selections can reuse the existing
structure. In this paper, two pilot selections denoted as Uneven Pilot
Selection (UEPS) and Even Pilot Selection (EPS) are proposed, which do not
change the efficient polar encoding structure. The proposed UEPS and EPS is
proven to satisfy the efficient construction condition. The performance of EPS
is shown in this paper to outperform both the UEPS and the traditional pilot
insertion scheme. Simulation results are provided which verify the performance
of the proposed pilot selection schemes.
