Blind PARAFAC receivers for multiple access-multiple antenna systems

We present a new blind receiver for a multiple access channel with multiple transmit antennas per user and multiple receive antennas (MIMO channel). After being multiplied by a spreading sequence, each user´s data is split into N_t streams that are simultaneously transmitted using N_t transmit antennas. The received signal at each receive antenna is a linear superposition of the N_t transmitted signals of the N_u users perturbed by noise. We propose a new blind detection/identification algorithm under the assumption that the fading is slow and frequency non-selective. This algorithm relies on a generalization of parallel factor (PARAFAC) analysis (Kruskal, J., Linear Algebra Applications, vol.18, p.95-138, 1977; Sidiropoulos, N. et al., IEEE Trans. Sig. Process., vol.48, no.3, p.810-23, 2000). We show that a generalized canonical decomposition of the 3D data tensor is unique under mild assumptions without noise. Neither algebraic orthogonality nor independence between sources is needed for uniqueness of the decomposition. By performing this decomposition in rank (N_t, N_t, 1) terms, we are able to retrieve the three sets of parameters: the symbols; the channel fading coefficients (including the antenna gains); the spreading sequences. In a noisy context, we propose a simple algorithm of the alternating least squares (ALS) type, which yields a performance close to the linear minimum mean square error (LMMSE) receiver which requires knowledge of the channel and spreading sequences.