Random and localized random projections for radar: Statistical and performance analysis

Abstract

Multisensor radar data is high-dimensional and suffers from the curse of dimensionality. For example, in radar space time adaptive processing (STAP), training data from neighboring range cells is limited. This precludes implementation of the full-dimension adaptive detectors, i.e. the minimum variance distortionless response (MVDR) filter. In this paper we reduce the dimension of the problem by random sampling, i.e. by projecting the data into a random d-dimensional subspace. Random projections offers two advantages, first, it permits implementation of classical detectors in the limited sample size regime. Second, it offers significant computational savings permitting possible real time solutions. Both these advantages are however at the cost of reducing the output SINR for radar STAP. To ameliorate over this SINR loss, we propose another technique which is localized random projections for radar. In this technique, the lower dimension subspace is not entirely random, but is broken down into both a random and a deterministic part.