A Statistical Approach to Subspace Based Estimation with Applications in Telecommunications

Subspace based estimation using decomposition techniques such as the SVD is a powerful tool in many signal processing applications where low rank signals in noise are observed. Examples of which include, sensor array signal processing, harmonic analysis, factor analysis, system identification, and blind channel equalization. By appropriately making use of eigenvalue or singular value decompositions, low rank approximations of the data may be obtained. From these approximations, subspace based, computationally efficient estimation techniques may be formulated. Also, the performance of subspace based methods is in many cases optimal or near optimal. This paper presents a systematic approach for formulating subspace based estimation techniques based on statistical considerations of the data. This approach may be applied to a wide range of problems where low rank signals are observed in noise. Some special cases are shown to result in well known estimators and examples of subspace based te..