In this work, we investigate cooperative frequency-domain beamforming (FD-BF) for single-carrier frequency-domain equalization (SC-FDE) systems. In particular, we propose optimal and suboptimal FD-BF schemes for frequency-domain linear equalization (FD-LE) and an idealized matched filter receiver. For both receiver structures, we derive the optimal processing at the destination and develop corresponding expressions for the signal-to-interference-plus-noise ratio (SINR). For a given power allocation, the optimal FD-BF filters maximizing the SINR are obtained in closed form and the power allocation problem is shown to be convex. For computation of the optimal power allocation a numerical method is developed and two low-complexity suboptimal power allocations are provided. Simulation results confirm the excellent performance of all proposed FD-BF schemes.