Non-Coherent Codes over the Grassmannian

Abstract

We construct a new family of space-time codes suited for multiple-antenna non-coherent communications over Rayleigh flat fading channels. These codes use all the complex degrees of freedom of the system, i.e. (M times(1-M/T)) symbols per channel use, where T is the code length and M is the number of transmit antennas. Their codewords belong to the Grassmann manifold G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TldrM</sub> (C), the set of the M-dimensional vector subspaces of C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> . Our codes are built from space-time codes for coherent systems via a non linear map (parameterization) called the exponential map. The relationships between some properties of the non-coherent space-time codes and their corresponding coherent codes are investigated. We also propose a simplified decoding for these classes of unitary space-time codes. We analyse the performance of these codes in terms of complexity and error probability and we compare them with some current best propositions, in particular training-based codes. The performance of our codes is substantially equivalent or slightly better than the one of training-based codes, under GLRT (Generalized Likelihood Ratio Test) decoding. When a simplified decoder is applied at the receiver, the error probability curves of the two propositions seem to be basically equivalent in the SIMO case with small block size, high spectral efficiency and high number of receive antennas, and in the 2times2 MIMO case with low spectral efficiency. In the other cases the training codes with simplified decoding seem to outperform our proposition.