A system for sensing a target in a region of interest (ROI) includes a coded compressive antenna (CCA) to generate an EM field codified in multiple dimensions. One or more receivers receives EM energy reflected by the target, and produces reflection information corresponding to the reflected energy. A compressive sensing imaging processor analyzes reflection information to generate an image representing the target. The CCA may use a distorted reflector, a vortex lens, and/or meta-materials to codify the EM field in multiple dimensions. The system may evaluate a sensing matrix that characterizes the transmission channel and the codified EM field. The system configures the CCA to produce a coded EM field enhances certain sensing matrix singular values, with respect to an EM field produced by a non-codified antenna. The sensing system provides increased target sensitivity while reducing false detections.