Candidate of Initial Value in Lloyd Algorithm for Constructing Low-Coherence Matrix

The problem of constructing matrix with lowcoherence is arised in many applications, such as CDMA, compressive sensing (CS), beamforming, etc. Usually the design of low-coherence codebook can be modeled as vector quantization (VQ) problem, and generalized Lloyd algorithm is designed to solve it. Since Lloyd algorithm is a method of local optimization, its performance is influenced by initial value. In this paper, candidate of initial value of Lloyd algorithm is studied. A construction based on finite abelian group which can be used as candidate of initial value will be analyzed. Experimental results prove that using this construction as initial value in Lloyd algorithm can improve the performance significantly.