Frequency-domain and time-domain processing approaches to direction-of-arrival (DOA) estimation for multiple broadband far field signals using beamspace preprocessing structures are proposed. The technique is based on constant mainlobe response beamforming. A set of frequency-domain and time-domain beamformers with constant (frequency independent) mainlobe response and controlled sidelobes is designed to cover the spatial sector of interest using optimal array pattern synthesis technique and optimal FIR filters design technique. These techniques lead the resulting beampatterns higher mainlobe approximation accuracy and yet lower sidelobes. For the scenario of strong out-of-sector interfering sources, our approaches can form nulls or notches in the direction of them and yet guarantee that the mainlobe response of the beamformers is constant over the design band. Numerical results show that the proposed time-domain processing DOA estimator has comparable performance with the proposed frequency-domain processing method, and that both of them are able to resolve correlated source signals and provide better resolution at lower signal-to-noise ratio (SNR) and lower root-mean-square error (RMSE) of the DOA estimate compared with the existing method. Our beamspace DOA estimators maintain good DOA estimation and spatial resolution capability in the scenario of strong out-of-sector interfering sources.