Noncoherent MIMO Communication: Grassmannian Constellations and Efficient Detection

This paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency-flat, richly scattered multiple-input multiple-output (MIMO) channel. The design is guided by the fact that at high signal-to-noise ratios (SNRs), the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the (compact) Grassmann manifold. The first part of the paper considers the design of Grassmannian constellations that mimic the isotropic distribution. A subspace perturbation analysis is used to determine an appropriate metric for the distance between Grassmannian constellation points, and using this metric, greedy, direct and rotation-based techniques for designing constellations are proposed. These techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity. In addition, the rotation-based technique results in constellations that have lower storage requirements and admit a natural “quasi-set-partitioning” binary labeling. In the second part of the paper, a reduced search suboptimum detector is proposed. The development of this detector relies on the subspace perturbation analysis and exploits the geometric properties of the Grassmann manifold and the isotropic distribution of the constellation points and the noise realizations. The performance of this detector is comparable to that of the maximum likelihood detector, but it requires considerably less computational effort. Finally, in order to assess the performance of a given constellation, an exact expression is provided for the pairwise error probability of the ML detector. In comparison to existing pairwise error probability expressions, the proposed expression is numerically stable and does not require the evaluation of residues at poles with high multiplicities.