Compressed channel sensing: Is the Restricted Isometry Property the right metric?

In this paper we are concerned with the estimation of doubly-selective multi-path communication channels trough methods referred to as compressed channel sensing. Many authors have used the Restricted Isometry Property (RIP) as a guiding principle to select training to ensure good estimation performance. In this paper we discuss why this approach can be restrictive and why its entanglement with modeling aspects can be misleading. More importantly, we provide an alternative approach to classify inputs based on a new metric that we call localized coherence.