A method comprises processing M subband communication signals and N target-cancelled signals in each subband with a set of beamformer coefficients to obtain an inverse target-cancelled covariance matrix of order N in each band; using a target absence signal to obtain an initial estimate of the noise power in a beamformer output signal averaged over recent frames with target absence in each subband; multiplying the initial noise estimate with a noise correction factor to obtain a refined estimate of the power of the beamformer output noise signal component in each subband; processing the refined estimate with the magnitude of the beamformer output to obtain a postfilter gain value in each subband; processing the beamformer output signal with the postfilter gain value to obtain a postfilter output signal in each subband; and processing the postfilter output subband signals to obtain an enhanced beamformed output signal.