We study regularity issues in finite impulse response (FIR) multi-input multi-output (MIMO) systems with additive noise, and with deterministic channel coefficients and sources. In the blind scenario, the model is rich with cross-related ambiguities, resulting in a singular Fisher information matrix (FIM). It is shown that the null space of the FIM has dimension of at least the number of sources squared, and necessary and sufficient conditions for the system to attain this minimum nullity are given. In addition, we show how the minimal set of known parameters must be specified to obtain a full rank FIM, and, thus, a valid and meaningful Crame/spl acute/r-Rao bound.