  This paper considers the problem of detecting a high dimensional signal (not
necessarily sparse) based on compressed measurements with physical layer
secrecy guarantees. First, we propose a collaborative compressive detection
(CCD) framework to compensate for the performance loss due to compression with
a single sensor. We characterize the trade-off between dimensionality reduction
achieved by a universal compressive sensing (CS) based measurement scheme and
the achievable performance of CCD analytically. Next, we consider a scenario
where the network operates in the presence of an eavesdropper who wants to
discover the state of the nature being monitored by the system. To keep the
data secret from the eavesdropper, we propose to use cooperating trustworthy
nodes that assist the fusion center (FC) by injecting artificial noise to
deceive the eavesdropper. We seek the answers to the questions: Does CS help
improve the security performance in such a framework? What are the optimal
values of parameters which maximize the CS based collaborative detection
performance at the FC while ensuring perfect secrecy at the eavesdropper?
