  Too high sampling rate is the bottleneck to wideband spectrum sensing for
cognitive radio in mobile communication. Compressed sensing (CS) is introduced
to transfer the sampling burden. The standard sparse signal recovery of CS does
not consider the distortion in the analogue-to-information converter (AIC). To
mitigate performance degeneration casued by the mismatch in least square
distortionless constraint which doesn't consider the AIC distortion, we define
the sparse signal with the sampling distortion as a bounded additive noise, and
An anti-sampling-distortion constraint (ASDC) is deduced. Then we combine the
\ell1 norm based sparse constraint with the ASDC to get a novel robust sparse
signal recovery operator with sampling distortion. Numerical simulations
demonstrate that the proposed method outperforms standard sparse wideband
spectrum sensing in accuracy, denoising ability, etc.
