  The problem of optimum watermark embedding and detection was addressed in a
recent paper by Merhav and Sabbag, where the optimality criterion was the
maximum false-negative error exponent subject to a guaranteed false-positive
error exponent. In particular, Merhav and Sabbag derived universal
asymptotically optimum embedding and detection rules under the assumption that
the detector relies solely on second order joint empirical statistics of the
received signal and the watermark. In the case of a Gaussian host signal and a
Gaussian attack, however, closed-form expressions for the optimum embedding
strategy and the false-negative error exponent were not obtained in that work.
In this paper, we derive such expressions, again, under the universality
assumption that neither the host variance nor the attack power are known to
either the embedder or the detector. The optimum embedding rule turns out to be
very simple and with an intuitively-appealing geometrical interpretation. The
improvement with respect to existing sub-optimum schemes is demonstrated by
displaying the optimum false-negative error exponent as a function of the
guaranteed false-positive error exponent.
