The waveform optimization problem for opportunistic communications is addressed, based on sensing the second-order statistics of the existing transmissions. We propose a minimum-norm waveform optimization that exhibits robustness to the worst-case subspace mismatch, minimizes the spectral overlapping with the existing transmissions, is rotationally invariant, and has maximally white spectrum. The derived solution can be seen as a different kind of signal dimension-based spreading. In addition, the effects of the residual interference caused to the existing transmissions are studied. Numerical results are provided to assess the performance of the proposed solution in the frequency domain for the asymptotic case. The level of induced interference is compared to traditional null space techniques.