Advanced Grassmannian Constellation Designs for Noncoherent MIMO Communications

In multiple-input multiple-output (MIMO) communications systems, the channel state information (CSI) is typically estimated at the receiver side by sending a few known pilots and then used for decoding at the receiver and/or for precoding at the transmitter. These are known as coherent schemes. However, in scenarios dominated by fast fading or massive MIMO systems dedicated to ultra-reliable low-latency communications (URLLC getting an accurate channel estimate would require pilots to occupy a disproportionate fraction of communication resources. This becomes also a problem in machine-to-machine (M2M) communications that arise in the so-called Internet of Things (IoT). The advent of 5G and beyond (B5G) systems has introduced these novel scenarios that underscore the need for noncoherent communications schemes in which neither the transmitter nor the receiver has any knowledge about the instantaneous CSI. The Grassmannian and Stiefel manifolds play a significant role in noncoherent multi-antenna communications, and in particular, Grassmannian signaling schemes appear to be a promising approach to this problem. The basic idea is to encode the messages to be transmitted into different subspaces. When the coherence time of the channel, understood as the time that the channel remains approximately constant, is greater than the number of transmit antennas, the transmitted subspaces (represented by a semi-unitary or Stiefel matrix) are invariant to the MIMO channel, allowing the receiver to decode the received signal without the need of knowing the channel. This thesis puts the spotlight on the design of Grassmannian constellations, aiming to achieve significant advances in this area. Our main goal is to improve error rates, enhance spectral efficiency, and develop low-complexity detection methods, making these designs suitable for the next generation of mobile communications. First, the work is focused on the single-user case, where three different optimization algorithms for Grassmannian constellation design are proposed. Since the computational complexity of the optimal maximum likelihood (ML) detector for these numerically optimized constellations grows exponentially with the constellation size, a new structured Grassmannian constellation is then developed. This new constellation facilitates low complexity detection, on-the-fly mapping and demapping and eliminates the need to store the whole constellation in the transmitter and receiver. After that, the analysis is then focused on multi-user scenarios. Specifically, Riemannian optimization techniques for designing multi-user noncoherent constellations for the MIMO Multiple Access Channel (MAC) in manifolds other than the complex Grassmannian are proposed. Furthermore, for the first time in the literature, closed-form formulas have been obtained for the gradients of cost functions previously proposed for the design of multi-user noncoherent constellations for the MAC, but whose optimization was so far considered to be intractable. Finally, this thesis transitions from theoretical models to practical application, culminating in experimental evaluations conducted in a laboratory setting. Specifically, we perform over-the-air (OTA) transmissions to assess the effectiveness of the proposed Grassmannian constellations. By implementing the previously studied transmission schemes on real hardware, the full scope of our analysis is completed, demonstrating the benefits that can be achieved when using Grassmannian noncoherent communications. Overall, this thesis provides advances in Grassmannian constellation design for both single-user and multi-user scenarios. Through a combination of theoretical analysis, simulations, and practical implementations, this study examines the potential performance advantages of Grassmannian constellations. These insights are crucial for future research focused on optimizing spectral efficiency for next-generation wireless communications.