In this paper, we study a federated learning system at the wireless edge that uses over-the-air computation (AirComp). In such a system, users transmit their messages over a multi-access channel concurrently to achieve fast model aggregation. Recently, an AirComp scheme based on digital modulation has been proposed featuring one-bit gradient quantization and truncated channel inversion at users and a majority-voting based decoder at the fusion center (FC). We propose an improved digital AirComp scheme to relax its requirements on the transmitters, where users perform phase correction and transmit with full power. To characterize the decoding failure probability at the FC, we introduce the normalized detection signal-to-noise ratio (SNR), which can be interpreted as the effective participation rate of users. To mitigate wireless fading, we further propose a cluster-based system and design the relay selection scheme based on the normalized detection SNR. By local data fusion within each cluster and relay selection, our scheme can fully exploit spatial diversity to increase the effective number of voting users and accelerate model convergence.