On the relationship between minimum norm and linear prediction for spatial spectrum estimation

Abstract

When teaching high-resolution spatial spectrum estimation, there is a simple progression from the minimum variance method to the MUSIC method, while the linear prediction and minimum norm methods seem to be more or less independent methods based on their own unique criteria of optimality. In this paper, the minimum norm method is derived from the linear prediction method in exactly the same way as the MUSIC method is derived from the minimum variance method. The derivation consists of replacing the correlation with its noise subspace component and setting all noise eigenvalues to unity. This makes it simpler to understand the methods and their properties. This relationship also brings out the meaning of setting the first element to unity in the minimum norm method—it corresponds to the predicted element in linear prediction.