Blind SDMA with a signal space geometry matched algorithm

We address the problem of the blind reconstruction of binary sequences transmitted by P sources, sharing simultaneously the same frequency channel. This is the situation in space division multiple access (SDMA) systems, where an array receiver is used to discriminate the spatial signatures of the sources. We exploit the geometry induced by the finite nature of the sources alphabet in order to derive a blind multichannel inversion algorithm. This algorithm minimizes a generalized constant modulus (GCM) cost function, subject to the constraints imposed by the signal space geometry (geometric priors). We define the GCM cost function for the case of additive Gaussian noise channels. We show that, except for a sign ambiguity, the minimization of the GCM criterion has a unique solution. Therefore, convergence to the global minimum is guaranteed. Computer simulations illustrate the performance achieved with the proposed method.