In one embodiment, a directional microphone array having (at least) two microphones generates forward and backward cardioid signals from two (e.g., omnidirectional) microphone signals. An adaptation factor is applied to the backward cardioid signal, and the resulting adjusted backward cardioid signal is subtracted from the forward cardioid signal to generate a (first-order) output audio signal corresponding to a beampattern having no nulls for negative values of the adaptation factor. After low-pass filtering, spatial noise suppression can be applied to the output audio signal. Microphone arrays having one (or more) additional microphones can be designed to generate second- (or higher-) order output audio signals.