Abstract : Consider the matrix Σn = n −1/2 XnD 1/2 n + Pn where the matrix Xn ∈ C N×n has Gaussian standard independent elements, Dn is a deter-ministic diagonal nonnegative matrix, and Pn is a deterministic matrix with fixed rank. Under some known conditions, the spectral measures of ΣnΣ * n and n −1 XnDnX * n both converge towards a compactly supported probability measure µ as N, n → ∞ with N/n → c > 0. In this paper, it is proved that finitely many eigenvalues of ΣnΣ * n may stay away from the support of µ in the large dimensional regime. The existence and locations of these outliers in any connected component of R − supp(µ) are studied. The fluctuations of the largest outliers of ΣnΣ * n are also analyzed. The results find applications in the fields of signal processing and radio communications.