This paper investigates the signal detection problem in colored noise with an unknown covariance matrix. To be specific, we consider a scenario in which the number of signal bearing samples $(n)$ is strictly smaller than the dimensionality of the signal space $(m)$. Our test statistic is the leading generalized eigenvalue of the whitened sample covariance matrix (a.k.a. $F- \mathbf{matrix}$ ) which is constructed by whitening the signal bearing sample covariance matrix with noise-only sample covariance matrix. The sample deficiency (i.e., $m > n)$ in turn makes this $F$-matrix rank deficient, thereby singular. Therefore, an exact statistical characterization of the leading generalized eigenvalue (l.g.e.) of a singular $F-\mathbf{matrix}$ is of paramount importance to assess the performance of the detector (i.e., the receiver operating characteristics (ROC)). To this end, we employ the powerful orthogonal polynomial approach to derive a new finite dimensional c.d.f. expression for the l.g.e. of a singular F-matrix. It turns out that when the noise only sample covariance matrix is nearly rank deficient and the signal-to-noise ratio is $O(m)$, the ROC profile converges to a limit.