Geometric properties of the blind digital co-channel communications problem

Due to the rapid growth of wireless cellular communications, an important problem in cellular radio today is increasing the frequency re-use factor of the cells. One way to achieve this increase is through smart antenna arrays at the cell base sites. We examine a space division multiple access (SDMA) problem arising from the demodulation of multiple co-channel digital signals arriving at an antenna array. In the absence of noise, the problem can be completely described by the equation X=AS, where A is an unknown array response matrix and S is the unknown digital signal matrix. We show that the matrix A is completely described by the facets of the convex hull of X. We then give an algorithm that solves exactly for A and S (up to a simple matrix factor T). We conclude with a description of how the algorithm can be extended to solve the noisy problem X=AS+V