In 2018 26th European Signal Processing Conference (EUSIPCO), pages 1102-1106, Sep., 2018. Paper doi abstract bibtex
We address the detection of a low rank n×n matrix X0 from the noisy observation X0+Z when n → ∞, where Z is a complex Gaussian random matrix with independent identically distributed ℕc (0, [1/n]) entries. Thanks to large random matrix theory results, it is now well-known that if the largest singular value λ1(X0) of X0 verifies λ1(X0) > 1, then it is possible to exhibit consistent tests. In this contribution, we prove a contrario that under the condition λ1(X0) <; 1, there are no consistent tests. Our proof is inspired by previous works devoted to the case of rank 1 matrices X0.