This work focuses on the study of a heterogeneous wireless-powered communication (H-WPCN) system, where a device-to-device (D2D) communication pair is overlaid with a downlink (DL) communication pair. In DL communications, the access point keeps spreading radio frequency (RF) signals to serve the DL user equipment (UE). In addition to being the data source of the UE, DL RF signals are also utilized by the D2D transmitter as the only energy source supporting D2D communications. To capture the impact of limited spectrum resource on the proposed H-WPCN system, co-channel interference is considered. Assuming the Rayleigh block fading channel for signal propagation, a tight lower bound as well as its closed-form approximation are provided for the outage probability of the DL communication link, and an exact expression is derived for the outage probability of the D2D communication link. After that, the throughput of the H-WPCN system is optimized via joint power control and time allocation, where the throughput of the D2D communication link is maximized subject to a required throughput for DL communications. Finally, our theoretical analysis is verified by numerical simulations. The simulation results show that the throughput of the H-WPCN system may not benefit from a high energy conversion efficiency.

Compared to the successive cancellation (SC)-based decoding algorithms, the sphere decoding (SD) algorithm can achieve better performance with reduced computational complexity, especially for short polar codes. In this paper, we propose a new method to construct the binary polar codes with the modified multiplicative repetition (MR)-based matrix. Different from the original construction, we first design a $2\times 2q$-ary kernel to guarantee the single-level polarization effect. Then, by replacing the new-designed binary companion matrix, a novel strategy is further developed to enhance the polarization in the bit level, resulting in a better distance property. Finally, the SD-based Monte-Carlo (SDMC) method is used to construct MR-based binary polar codes, while the resulting codes without the butterfly pattern are decoded by the SD algorithm. Simulation results show that the proposed method with the SD algorithm can achieve a maximum performance gain of 0.27 dB compared to the original method with slightly lower complexity.