The performance of a vertical array for source localization and for target detection (array gain) is studied in shallow water under a directional noise field. The acoustic environment consists of a downward refractive sound-speed profile. At mid (e.g., 500 Hz) frequencies the vertical directionality of the surface generated noise exhibits a notch near the signal arrival direction, i.e., which is close to horizontal for a submerged source. The ability of the beam filter in rejecting directional noise has been previously demonstrated using conventional beamforming. The same capability is carried over into full field processing by using matched-beam processing which is an equivalent of matched-field processing conducted in the beam domain. It is shown with simulated data that matched-beam processing incorporating a beam filter of 10 deg enhances the array output signal-to-noise ratio (array gain) by more than 5 dB compared with conventional beamforming and matched-field processing. For white noise, matched-field processing yields a higher peak-to-sidelobe ratio than matched-beam processing with a beam filter. For directional noise, matched-beam processing with a beam filter yields better results than matched beam processing using a minimum variance correlator. The noise field in the background ambiguity surface (the sidelobes) has been suppressed by the beam filter.