  In spectrum sensing for cognitive radio, the presence of a primary user can
be detected by making use of the cyclostationarity property of digital
communication signals. For the general scenario of a cyclostationary signal in
temporally colored and spatially correlated noise, it has previously been shown
that an asymptotic generalized likelihood ratio test (GLRT) and locally most
powerful invariant test (LMPIT) exist. In this paper, we derive detectors for
the presence of a cyclostationary signal in various scenarios with structured
noise. In particular, we consider noise that is temporally white and/or
spatially uncorrelated. Detectors that make use of this additional information
about the noise process have enhanced performance. We have previously derived
GLRTs for these specific scenarios; here, we examine the existence of LMPITs.
We show that these exist only for detecting the presence of a cyclostationary
signal in spatially uncorrelated noise. For white noise, an LMPIT does not
exist. Instead, we propose tests that approximate the LMPIT, and they are shown
to perform well in simulations. Finally, if the noise structure is not known in
advance, we also present hypothesis tests using our framework.
