Transpose domain filtering: Dual algorithms in adaptive filtering

In this paper, we describe a new parameter estimation methodology called transpose domain filtering (TDF). TDF is a processing formulation that that is different from conventional processing (e.g., beamscan processing) in that the weight vector is applied in the domain that lies transpose to the signal model. For a typical radar array processing problem, this means TDF would apply the weight vector in the snapshot domain as opposed to the element domain. We provide two examples of TDF applied to minimum variance distortionless response (MVDR) beam scan and code division multiple access (CDMA) synchronization. We later show that rank reduction techniques can be used in TDF, and then prove that when principal components rank reduction is applied to TDF, the result is mathematically equivalent to the better-known multiple signal characterization (MUSIC) algorithm.