This paper presents an overview and results from an ongoing research project to study parallel algorithms for the acquisition of Code Division Multiple Access (CDMA) communication signals. The goal of this research isto evaluate a class of related algorithms and architectures for the acquisition problem and map them onto parallel architectures containing DSPs. The algorithms used are generally termed subspace-based algorithms, since they involve computation of subspaces of the vector space spanned by certain observation vectors. This paper presents results from some preliminary implementations of such a subspace-based algorithm on the Texas Instruments TMS320C40 Parallel Processing Development System.