We focus on the Multi-Rate Sampling (MRS) Compressed Sensing (CS) scheme, in which several Analog-to-Digital Converters (ADC) sample in parallel at different sub-Nyquist rates. In this paper, we postulate that a good signal recovery requires the measurement matrix rank (MMR) to be as high as possible. We also present an upper-bound for the MMR. Choosing pairwise coprime sampling rates allows to reach this upper-bound.