This chapter gives a brief introduction to the recent work on the exploitation of signals’ properties, including the non circularity, the cyclostationarity, the conjugate symmetry in array signal processing. Besides in DoA estimation, the non circularity is exploited in signal detection/demodulation in MIMO communication system; and this property is further utilized in the MIMO-NOMA downlink system to jointly eliminate or control the intra/inter-cluster interferences. The cyclostationarity is used for filtering out the interferences with cycle frequencies distinct from the desired signals to enhance the performance of DoA estimation or beamforming. The non circularity can be considered as a special case of the conjugate symmetry, which exhibits in the general linearly modulated digital signals. Therefore, the non circularity exploiting method can be extended to the exploitation of conjugate symmetry, which can be equally applied in DoA estimation and signal detection/demodulation.