Spectral Comb Shaping for Single Carrier Communication Signals by Polar Codes

Abstract

An approach to selecting information indices for polar codes is proposed to form signals with spectral comb shapes under BPSK modulation, whereby the signal could be separated from periodic interference in spectrum. By confining information indices to an index set termed comb-shaping index set (CIS) proposed in this paper, a spectral comb shape signal is formed, which has periodic nulls and notch bands in its spectrum. Furthermore, we propose a novel construction for polar coding under the CIS constraint. Numerical results are given under periodic interference and AWGN noise, indicating that a considerable signal-to-noise power ratio (SNR) gain is accomplished in comparison with conventional polar codes.

Figures (7)

• Figure 1: The system model.
• Figure 2: Rows of $G_8$ indexed in different $\Lambda_{r}$. (a)$\ r = 0$; (b) $r = 1$; (c) $r = 2$.
• Figure 3: Local-periodicity of $G_8$ rows indexed in different $\Lambda_{r}$. (a)$\ r = 0$; (b) $r = 1$; (c) $r = 2$.
• Figure 4: Power spectral density of the given example while $r = 3$. (a) -1.6kHz to 1.6kHz; (b) -100Hz to 100Hz.
• Figure 5: Mapping $g_{16,1}$.