Codebook Design for the Non-Coherent GLRT Receiver and Low SNR MIMO Block Fading Channel

We address the problem of codebook design for the low signal-to-noise ratio (SNR) fast non-coherent MIMO block fading channel. The channel matrix is assumed deterministic (no stochastic model attached) and unknown at both the receiver and the transmitter. To handle the unknown deterministic space-time channel, a generalized likelihood ratio test (GLRT) receiver is implemented. The case of single transmit antenna is considered and it is shown that the problem of finding good codes corresponds geometrically to a packing problem in the complex projective space. We provide new constellations and demonstrate that they perform substantially better than state-of-art known solutions which assume equal prior probabilities for the transmitted codewords. Our results are also of interest for Bayesian receivers which decode constellations with non-uniform priors