The time-reversal technique re-interpreted: Subspace-based signal processing for multi-static target location

The time-reversal field processing technique for active remote sensing is re-interpreted in the conceptual framework of subspace-based signal processing. Although both of these subjects have a long and extensive history, we believe that our work is the first to relate these two rather different signal processing approaches. The concept at the heart of both approaches is the multi-static Frequency Response Matrix (FRM) of the active antenna array. It is a function of array/scatterer geometry (via a suitable Green function) and of the scatterers' reflection coefficients. The time-reversal technique locates the most reflective target by determining the largest singular value of the FRM and the corresponding (right) singular vector. Consequently, it performs well only when the scatterers are "well-resolved," i.e., when the Green function vectors used in forming the FRM are approximately orthogonal to each other. In contrast, we show that subspace based signal processing can be successfully used even when the targets are not "well-resolved.'' Moreover, the performance of our subspace-based schemes can be further enhanced by using wideband signals and combining FRM information from multiple frequencies. The coupling of time-reversal field. processing with subspace methods leads to a powerful approach for locating targets under arbitrary wave-propagation conditions (both near-field and far-field), including arbitrary non-homogeneous media and arbitrary geometries.