In this paper, AlGaN/GaN heterostructure high electron mobility transistors (HEMTs) have been fabricated on GaN-on-Si substrate. These devices were studied for the application of the 5^th generation (5G) wireless communication. The geometric parameters such as gate length (L_g), cap length (L_cap) and gate-to-source distance (L_gs) are optimized so that the cut-off frequency reaches 38.8 GHz. It is found that decreasing L_g and L_gs can both improve drain current and peak transconductance (G_mmax). Highest drain current of 1 A/mm at V_g=2V and biggest G_mmax of 240 mS/mm was achieved. A fabricated device with L_g of 100 nm, L_cap of 300 nm and L_gs of 800 nm showed a f_T of 38.8 GHz and a f_MAX of 60 GHz at V_ds=5V which can meet the requirement of the 5G application.