Low-Rank Approximations for Spatial Channel Models

We analyze the problem of approximating vectors that are superpositions of many closely spaced steering vectors. Such vectors appear in realistic models for wireless communication channels and describe single clusters of scatterers. We question the practice of using a dictionary of steering vectors in order to find a sparse approximation. Alternative dictionaries can be obtained from the Karhunen-Loeve expansion of the channel vectors or they can be learned from observed channel realizations. Furthermore, it is possible to restrict the allowed combinations of dictionary elements, thereby reducing the complexity of algorithms that find an approximation. We provide simulation results and discuss the performance of the various approaches.