Channel estimation is challenging in multi-antenna communication systems, because of the large number of parameters to estimate. One way of facilitating this task is to use a physical model describing the multiple paths constituting the channel, in the hope of reducing the number of unknowns in the problem. The achievable performance of estimation using this kind of physical model is studied theoretically. It is found that adjusting the number of estimated paths leads to a bias-variance tradeoff which is characterized. Moreover, computing the Fisher information matrix of the model allows to identify orthogonal parameters, ultimately leading to fast and asymptotically optimal algorithms as a byproduct.