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In wireless communication systems, the correlation among the antennas of diversity systems can hardly be neglected. To the best of our knowledge, no previous studies have attended to address, thoroughly, this problem for the cross-correlation-based detectors. This will be the topic of this paper. Namely, in this paper, we consider the performance assessment of a second-order decision metric that is based on the cross correlation of antenna's output. The detector performance analysis has been made concerning the receiver operating characteristic curves, the robustness to estimation uncertainty, and the design parameters. This last introduces the minimum required sample number that guarantees a given detection performance. To this end, the probability distribution of the inner product of two complex non-zero-mean partially correlated random vectors is investigated. Next, we exhibited the relevance of our results through the analytical performance derivation of the cross-correlation-assisted sensing approach in terms of design parameters, spectral efficiency, and decision reliability. Monte Carlo simulations are achieved to prove the tightness of our derived results. [ABSTRACT FROM AUTHOR]