Localized random projections for space-time adaptive processing

Abstract

High-dimensional multi-sensor radar data suffers from the well known 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. Therefore, precluding straightforward implementation of standard detectors, for example, the whitening minimum variance distortionless response filter. Using random projections, we can reduce the dimension of the radar problem by random sampling, i.e. by projecting the data into a random d-dimensional subspace. The Johnson-Lindenstrauss (JL) theorem provides theoretical guarantees which explicitly states 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. Random projections offers significant computational savings permitting possible real time solutions, however, at the cost of reducing the clairvoyant SINR for radar STAP. To alleviate this issue of SINR loss, we use localized random projections where the random projection matrix incorporates the look angle information, thereby minimizing the noise and interference effects from other angles, and increasing the SINR. We show that the resulting detector is CFAR, and the transformation matrix satisfies all the necessary conditions for the the JL theorem to hold.