A wideband signal occupies a finite bandwidth that is significant compared to its carrier frequency. As a result when transmitted, its returns cause bandwidth dispersion across the antenna. It is shown here that the effect of the finite bandwidth is to introduce a set of uncorrelated return signals for every physical scatter in the field. Further, each such uncorrelated return contains a set of coherent signals with different directional and Doppler components that result from a jittering effect both in angle and Doppler domain. As a result, adaptive clutter cancellation using traditional processing schemes does not work well. Although in principle it is possible to correct these decorrelating effects by 3D spacetime adaptive processing (STAP), the present day methods are quite costly and difficult to implement. In addition to the new wideband signal modeling framework mentioned above, we outline a hierarchical processing scheme which has the potential for dramatically reducing both processing and sample support burdens.