Blind multichannel estimation is classically done considering one of two constraints on the channel coefficients: (i) a quadratic constraint (i.e., unit-norm), or (ii) a linear constraint (i.e., fixed value for a particular coefficient). These constraints serve to remove the indeterminacy of the solution inherent to this estimation problem.
In this paper, we investigate the adequacy of both constraints in the particular case of sparse channels. For this purpose, we first conduct a Cramér-Rao Bound (CRB)-based performance comparison, then we support the obtained results with simulation experiments using a subspace method. The obtained results indicate that, contrary to common practice, the linear constraint should be favored over the quadratic constraint for the blind estimation of sparse channels.