The rapid expansion of the Internet of Vehicles (IoV) necessitates high-capacity backhaul connectivity, yet the deployment of such networks under strict hardware and power constraints poses significant computational challenges for network optimization. To address this challenge, this paper investigates a joint transmit–receive beamforming optimization problem for narrowband wireless backhaul in IoV networks under constant-modulus constraints. Unlike ideal digital architectures, we focus on cost-effective analog phase shifters, which introduce strictly non-convex constant-modulus constraints, rendering the optimization problem mathematically intractable for standard solvers. Since the resulting problem is highly non-convex, we develop two structured numerical methods: an iterative alternating optimization (AO) method and a joint optimization (JO) method, where AO employs auxiliary WMMSE-guided alternating updates together with constant-modulus projection, while JO jointly updates both beamformers over the constant-modulus feasible set. We compare their achievable sum-rate performance with that of a CDO-based benchmark and analyze their dominant computational costs through representative Big-O complexity expressions. Furthermore, we examine the effect of SVD-based and random feasible initializations on empirical convergence behavior, runtime, and final achievable performance. Simulation results demonstrate that the proposed computational methods significantly improve achievable sum-rate performance compared with the CDO benchmark. Moreover, SVD-based initialization provides a more structured starting point and generally leads to better convergence behavior and lower runtime than random feasible initialization. The empirical timing results further show that AO exhibits faster empirical convergence and requires lower runtime, whereas JO achieves better final sum-rate performance after more iterations.
Zheng et al. (Sun,) studied this question.