Random projections for reduced dimension radar space-time adaptive processing

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 since the statistical properties vary significantly over range and azimuth. This precludes implementation of the full-dimension optimal 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. The Johnson-Lindenstrauss theorem provides theoretical guarantees which explicitly state that the low dimensional data after random projections is only very slightly perturbed when compared to the data from the original problem in an l 2 norm sense. Statistical analysis via probabilistic bounds is provided for a measure of whiteness of the random projected STAP. Random projections offers two advantages, first, it permits implementation of classical detectors in the small 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 clairvoyant output SINR for radar STAP. These trade-spaces also exist for other radar multisensor frameworks, not just limited to STAP. Hence we recommend exercising some caution and restraint when applying random sampling techniques such as random projections and compressive sensing for practical radar.