  An asymptotically optimal blind calibration scheme of uniform linear arrays
for narrowband Gaussian signals is proposed. Rather than taking the direct
Maximum Likelihood (ML) approach for joint estimation of all the unknown model
parameters, which leads to a multi-dimensional optimization problem with no
closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical
approach in exploiting the special (Toeplitz) structure of the observations'
covariance. However, we offer a substantial improvement over P-K's ordinary
Least Squares (LS) estimates by using asymptotic approximations in order to
obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS)
estimates of the sensors gains and phases offsets with asymptotically optimal
weighting, based only on the empirical covariance matrix of the measurements.
Moreover, we prove that our resulting estimates are also asymptotically optimal
w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates
(MLE), which are otherwise obtained by joint ML estimation of all the unknown
model parameters. After deriving computationally convenient expressions of the
respective Cram\'er-Rao lower bounds, we also show that our estimates offer
improved performance when applied to non-Gaussian signals (and/or noise) as
quasi-MLE in a similar setting. The optimal performance of our estimates is
demonstrated in simulation experiments, with a considerable improvement
(reaching an order of magnitude and more) in the resulting mean squared errors
w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy
in a multiple-sources directions-of-arrivals estimation task.
