Future outdoor communication networks are expected to make use of the mmWave bands. In this context, this paper investigates the use of sparse signal processing for efficient angular frequency estimation. Compressive sensing (CS) and correlation-based method are shown to provide accurate estimates of the Power Angular Profile (PAP). The recovered PAP is used to perform analogue beamforming. When tracking mobile users it is shown that codebook based analogue beamforming, as used in IEEE 802.11ad, results in a large signalling overhead. This adversely affects net throughput. Our CS approach requires just 2% of the resources consumed by codebook-based beamforming while providing similar SNR performance.Interference cancellation is implemented by exploiting the accurate PAP recovered by CS. This method estimates the beamforming vector required to optimise the signal to leakage and noise ratio (SLNR), allowing the coexistence of both non-interfering and interfering links. To maximise user fairness the interference cancellation capabilities of CS beamforming are combined with a Space–Time Division Multiple Access (STDMA) scheduling scheme. Considerable network throughput enhancement is demonstrated when compared to the IEEE 802.11ad codebook based beamforming approach.