Spectrum sensing for cognitive radio requires a high linearity to handle strong signals, and at the same time a low noise figure (NF) to enable detection of much weaker signals. Often there is a trade-off between linearity and noise: improving one of them degrades the other. Cross-correlation can break this trade-off by reducing noise at the cost of measurement time. An existing RF front-end in CMOS-technology with IIP3=+11dBm and NF<6.5dB is duplicated and attenuators are put in front to increase linearity (IIP3=+24dBm). The attenuation degrades NF, but by using cross-correlation of the outputs of the two frontends, the NF is reduced to below 4dB. In total this results in a spurious-free dynamic range (SFDR) of 89dB in 1MHz resolution bandwidth (RBW).