الفهرس 
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Abstract
This thesis considers the design of multi-antenna unitary space-time constellations.Particularly, we focus on the scenario in which the channel state information is unknown at both the transmitter and the receiver. This scenario encompasses two main directions: the design of non-coherent unitary space-time constellations, and the design of differential unitary space-time constellations. Constellation designs for both unitary and non-coherent space-time scenarios are provided in this thesis. In the first part of the thesis, we focus on the so-called non-coherent constellation design. In particular, we develop a geometry-inspired, multi-layer methodology for generating systematic and structured Grassmannian constellations with large cardinalities. In the proposed methodology we begin with a small close-to-optimal “parent” Grassmann constellation. Each point in this constellation is augmented with a number of “children” points, which are generated along a set of geodesics emanating from that point. These geodesics are chosen to ensure close-to-maximal spacing. In particular, the directions of the geodesics and the distance that each “children” point is moved are chosen to maximize the pairwise chordal distance between the resulting constellation points. Although finding these directions directly seems difficult, by embedding the Grassmann manifold on a sphere of larger dimension, we were able to develop structures that are not only simple to generate but that also yield constellations that, under certain conditions, satisfy the maximum distance criterion and lie within a decaying gap from a tight upper bound. Moreover, we employ the same multi-layer design in multi-resolution systems that enable Unequal Error Protection (UEP). Specifically, the proposed methodology yields multi-layer constellations that are amenable to a natural set partitioning strategy. The resulting subsets from such partitioning are used to encode the more protected symbols. On the other hand, the less protected symbols are mapped to points within these subsets. Finally, we exploit the underlying structure to develop a sequential decoding approach. Numerical results suggest that the performance of the new constellations is comparable to that of the ones generated directly and significantly better than the performance of the ones generated using the so-called exponential map. On top of that, numerical evaluations of the simplified decoding strategy indicate computational savings with respect to the optimal decoding while maintaining comparable performance. The second part of this thesis is devoted to differential multi-antenna constellation design. In particular, we construct a new class of unitary space-time constellations that is suitable for multi-antenna differential signaling. This class of constellations follows a certain structure that is inspired by the so-called biorthogonal spherical codes. As a consequence of this, we show that the proposed class achieves optimal diversity sum in some cases, and close-to-optimal diversity sum in other cases. Furthermore, we demonstrate how such constellations are altered in order to improve the diversity product while maintaining the same diversity sum, thereby yielding constellations with favorable diversity sum and product. Numerical evaluations against some of the best-known constellation designs typically reveal performance gains in terms of error rate probability.