The University of Nebraska has developed a coherent random noise radar technique that permits phase-coherent processing of random noise radar signals. This is achieved through a heterodyne correlation receiver that retains the phase of the reflected signal during the detection process. A simulation study was carried out to evaluate the system's expected performance during detection of objects buried under lossy dispersive media with different types of complex permittivity characteristics as a function of frequency. It was observed that system performance was degraded under dispersive media conditions. However, by suitably tailoring the random noise transmission characteristics to attain an inverse frequency relationship with respect to the attenuation characteristics of the media, a significant enhancement was observed in detecting obscured objects. This shows that adaptive matched illumination is useful in detecting objects buried under lossy coatings intentionally induced to inhibit detection.