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An adaptive degrees of freedom (DOFs) selection principle for notch-widening a partially adaptive beamformer is proposed. This principle indicates the relationship between the desired width of the notch and the required number of adaptive DOFs. The principle implies that a sufficient number of adaptive DOFs are required to produce a notch with the desired width at the direction of a nonstationary interference. That is to say, the number of adaptive DOFs should match the nonstationarity of the interference. The principle is validated by computer simulations that use a wide- notch beam space adaptive multiple sidelobe canceller (MSLC). According to the principle the nonstationary high-frequency (HF) interference cancellation performance is mainly affected by factors such as the number of adaptive DOFs and the nonstationarity of the interference. The effects of the number of adaptive DOFs and adaptive weights update interval on the nonstationary HF interference suppression performance are investigated by using beam space adaptive MSLC to process the experimental data collected by a trial HF over-the-horizon radar (OTHR). Experimental data processing results suggest that the principle will be very helpful in designing nonstationary interference cancellation schemes for practical implementation.