Detection of unknown signals with constant modulus (CM) using multiple antennas in additive white Gaussian noise of unknown variance is considered. The channels from the source to each antenna are assumed frequency-flat and unknown. This problem is of interest for spectrum sensing in cognitive radio systems in which primary signals are known to have the CM property. Examples include analog frequency modulated signals such as those transmitted by wireless microphones in the TV bands and Gaussian Minimum Shift Keying modulated signals as in the GSM cellular standard. The proposed detector, derived from a Generalized Likelihood Ratio (GLR) approach, exploits both the CM property and the spatial independence of noise, outperforming the GLR test for Gaussian signals as shown by simulation.