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Detection and avoidance (DAA) is a soft-spectrum-based adaptation scheme proposed for multi-band ultra-wideband (MB-UWB) radio as a measure of co-existence between UWB devices and existing radio systems in overlapped bands. However, the principle of DAA in the direct-sequence UWB (DS-UWB) is very different from that in MB-UWB method. In DS-UWB, re-design of transmission pulses is required each time a new set of allowed bandwidths is discovered, as opposed to the turning-off-carrier-tone way in MB-UWB. Therefore the re-design of DS-UWB pulses in a cognitive radio environment must be easily reconfigurable. The problem of synthesising DS-UWB pulses conforming to arbitrary spectrum masks is addressed. In the proposed method, the masks are expanded by orthonormal functions chosen to be Hermite-Gaussian functions (HGFs). As the HGFs are eigenfunctions to the fractional Fourier transform, of which the inverse Fourier transform is a particular case, the set of the HGFs constitutes both a time-domain and a frequency-domain basis, that is, a co-basis, and therefore the transmission pulses can be easily obtained from the expansion of the specified spectrum masks. The co-basis-expansion-based DAA scheme for DS-UWB is evaluated through computer simulations.