Non-reconstruction Compressive Detection of Random Signal using Maximum Likelihood Criterion and its Analysis

Compressive sampling theory can effectively maintain structures and information of the original signal，so detection tasks of the original signal could be solved by directly processing the samples without reconstructing the original signal. The existing signal detection theory based on CS is directed at the deterministic signal；however，most practice signal is random signal. This paper firstly set up a model of signal detection based on compressive sampling without signal recovery，and then derives the maximum likelihood detection algorithm of random signal in detail，and analysis the performance of this detection algorithm lastly. Theoretical analysis and simulation show that detection probability is increased logarithmic progression with the decrease of the compression ratio for given false alarm probability，in addition, it can achieve very high detection rates while simultaneously keeping the false alarm rate very low. Lastly, the applicability of broadband signal detection is verified.