Quadrature amplitude modulation (QAM) is one of the essential components of unmanned 1 aerial vehicle (UAV) communications. However, the output signal accuracy of QAM deteriorates dramatically and even collapses in the case of UAVs in a harsh channel environment. This is due to the fractionally spaced equalization based on the multi-modulus blind equalization algorithm being implemented prior to carrier synchronization in QAM-based UAV modulation systems. The carrier frequency offset from the harsh channel signal thus contributes to the significantly degraded performance of MMA by suffering the fractionally spaced equalization. Therefore, in this paper, a novel offset feedback fractionally spaced equalization architecture for UAVs to eliminate the carrier frequency offset is first proposed. In this architecture, the carrier frequency offset allows estimated and incorporation into the input signal of fractionally spaced equalization to compensate for the offset. Moreover, a new multi-modulus decision-directed algorithm is presented for the novel architecture to improve the received signal accuracy of UAVs further. It enables adaptive optimization of the convergence process in accordance with the dynamic UAV communication environment employing the multi-modulus blind equalization algorithm and decision-directed blind equalization algorithm (MDD). Simulation results demonstrate the effectiveness of the OF-FSE framework in enabling the QAM-based UAV modulation systems operation in harsh channel scenarios. Moreover, the performance of the presented new MDD algorithm compared with baseline approaches is also confirmed.