Wireless federated learning (FL) is an emerging machine learning paradigm that trains a global parametric model from distributed datasets via wireless communications. This paper proposes a unit-modulus wireless FL (UMWFL) framework, which simultaneously uploads local model parameters and computes global model parameters via optimized phase shifting. The proposed framework avoids sophisticated baseband signal processing, leading to both low communication delays and implementation costs. A training loss bound is derived and a penalty alternating minimization (PAM) algorithm is proposed to minimize the nonconvex nonsmooth loss bound. Experimental results in the Car Learning to Act (CARLA) platform show that the proposed UMWFL framework with PAM algorithm achieves smaller training losses and testing errors than those of the benchmark scheme.