Channel Estimation with Systematic Polar Codes in NS2

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. Construction of both systematic and nonsystematic polar codes is based on an information set and the known frozen bits. Efficient implementation of systematic and nonsystematic 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 are 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. The simulation results provided verify the performance of the proposed pilot selection schemes.