An optimum radar signal detector using orthogonal projection

In a general radar operation environment, there exist various kinds of undesired signals which include ground and weather clutter, interferences, background noise, etc.. These noise should be eliminated for the detection of weak target signals. For optimal detection, there are two different methods. One is to maximize the SNR (signal to noise ratio) and the other is to maximize the probability of detection. These two are shown to be same if the assumption of Gaussian probability density is valid. However, the noise covariance matrix should be known or estimated previously to apply these methods. The SMI (sample matrix inversion) method uses the sample covariance matrix as the estimate of the unknown noise covariance matrix and then optimal weight parameters are obtained through matrix inversion. Although this method converges very fast, it has inherent problems related with matrix inversion such as computational complexity and instability. The paper describes the unconstrained minimum variance method obtained by the projection of the signal onto the constrained orthogonal subspace. The suggested algorithm is also optimal in terms of maximum SNR output. Applying Gram-Schmidt orthogonalization to this method, a fast convergence can be achieved without matrix inversion problems.