Fiber-based quantum key distribution (QKD) networks are currently limited without quantum repeaters. Satellite-based QKD links have been proposed to extend the network domain. We have developed a quantum communication system, suitable for realistic satellite-to-ground communication. With this system, we have executed an entanglement-based QKD protocol developed by Bennett, Brassard, and Mermin in 1992 (BBM92), achieving quantum bit error rates (QBER) below 2$\%$. More importantly, we demonstrate low QBER execution of a higher dimensional hyperentanglement-based QKD protocol, using photons simultaneously entangled in polarization and time-bin, which has a distinct advantage over BBM92. We show that our protocol is suitable for a space-to-ground link, after incorporating Doppler shift compensation, and verify its security using a rigorous finite-key analysis.