Subspace detection for adaptive radar: Detectors and performance analysis

Coherent processing of various forms of multidimensional signals is commonplace in radar applications. Space-time adaptive processing in radars is a well-established example of coherent processing involving the domains of space (multiple receiving antenna elements separated spatially) and time (multiple pulse returns at each antenna element). The problem of detecting a subspace signal in a given test data vector can be formulated as a statistical hypothesis testing problem. An approach that has proven effective in dealing with nuisance parameters are invariant hypothesis tests. The general approach is to identify a set of matrices such that the linear transformation of the data by any member of the set leaves the original hypothesis testing problem unchanged, although the original nuisance parameters themselves are changed as a result. In this chapter, the author extended the three signal detectors above to a subspace signal model. Analytical expressions derived include results of signal mismatch errors. The analysis is applied to an example to illustrate the use of subspace detectors to mitigate detection loss resulting from signal mismatch errors.