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Methods to mitigate interference from ultra wide band (UWB) radio devices into other communication services whose spectra lie within the major frequency band allowed for UWB, 3.1 to 10.6 GHz, can be classified as non-adaptive and adaptive. Adaptive methods began to emerge in about 2002, and a publication on UWB cognitive radio appeared in 2004. The non-adaptive methods for mitigation of interference by UWB first appeared in publications in the middle 1980's, and were mainly on pulse shaping, modulation and randomization methods that will be summarized, with their advantages and shortcomings, in the paper. Examples are pulse position modulation (PPM), which was replaced in about 2002 by bi-phase modulation (BPM), hybrid modulation combining PPM and BPM, DS-CDMA, pulse shapes obtained by constrained optimization methods, forming notches or eliminating a subband in a pulse spectrum, use of spreading codes, etc. Motivated by the urgent need to utilize spectrum more efficiently and maintain the most effective form of communications in changing conditions, adaptive methods, proposed in about 2003 for more flexible and efficient use of the spectrum and minimization of interference by UWB than possible with non-adaptive methods, have evolved to R & D on UWB cognitive radio (UWBCR). UWBCR builds on software defined radio technology, by building intelligence into a radio, to adapt to spectrum availability, activity and detection of clear spectrum, to learn and adapt to waveforms and protocols, and current user needs, thus enabling the choice of the best current form of communication. The paper will summarize how cognitive UWB may be used for dynamic interference cancellation, and enable interference cancellation by producing spectral notches. A number of functions that could be performed by cognitive UWB radio will be described.