Multi-channel noise suppression systems and methods are described that omit the traditional delay-and-sum fixed beamformer in devices that include a primary speech microphone and at least one noise reference microphone with the desired speech being in the near-field of the device. The multi-channel noise suppression systems and methods use a blocking matrix (BM) to remove desired speech in the input speech signal received by the noise reference microphone to get a “cleaner” background noise component. Then, an adaptive noise canceler (ANC) is used to remove the background noise in the input speech signal received by the primary speech microphone based on the “cleaner” background noise component to achieve noise suppression. The filters implemented by the BM and ANC are derived using closed-form solutions that require calculation of time-varying statistics of complex frequency domain signals in the noise suppression system.