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This paper studies the problem of waveform design for identification of communication channel parameters, when the waveform is to be embedded in a host signal. Applications of this study include watermarking and covert communications. We study a subspace-projection embedding method and a penalized nonlinear least-squares parameter estimator. The performance of the estimator is studied in an asymptotic regime. Conditions are given under which the estimator does as well as one that knows the host signal.