Coherence Optimization and Best Complex Antipodal Spherical Codes

Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian line packing problem. Best Complex Antipodal Spherical Codes (BCASCs) are the best vector sets with respect to the coherence. By extending methods used to find best spherical codes in the real-valued Euclidean space, the proposed approach aims to find BCASCs, and thereby, a complex-valued vector set with minimal coherence. There are many applications demanding vector sets with low coherence. Examples are not limited to several techniques in wireless communication or to the field of compressed sensing. Within this contribution, existing analytical and numerical approaches for coherence optimization of complex-valued vector spaces are summarized and compared to the proposed approach. The numerically obtained coherence values improve previously reported results. The drawback of increased computational effort is addressed and a faster approximation is proposed which may be an alternative for time critical cases

Union bound minimization approach for designing grassmannian constellations

In this paper, we propose an algorithm for designing unstructured Grassmannian constellations for noncoherent multiple-input multiple-output (MIMO) communications over Rayleigh block-fading channels. Unlike the majority of existing unitary space-time or Grassmannian constellations, which are typically designed to maximize the minimum distance between codewords, in this work we employ the asymptotic pairwise error probability (PEP) union bound (UB) of the constellation as the design criterion. In addition, the proposed criterion allows the design of MIMO Grassmannian constellations specifically optimized for a given number of receiving antennas. A rigorous derivation of the gradient of the asymptotic UB on a Cartesian product of Grassmann manifolds, is the main technical ingredient of the proposed gradient descent algorithm. A simple modification of the proposed cost function, which weighs each pairwise error term in the UB according to the Hamming distance between the binary labels assigned to the respective codewords, allows us to jointly solve the constellation design and the bit labeling problem. Our simulation results show that the constellations designed with the proposed method outperform other structured and unstructured Grassmannian designs in terms of symbol error rate (SER) and bit error rate (BER), for a wide range of scenarios.This work was supported by Huawei Technologies, Sweden under the project GRASSCOM. The work of D. Cuevas was also partly supported under grant FPU20/03563 funded by Ministerio de Universidades (MIU), Spain. The work of Carlos Beltr´an was also partly supported under grant PID2020-113887GB-I00 funded by MCIN/ AEI /10.13039/501100011033. The work of I. Santamaria was also partly supported under grant PID2019-104958RB-C43 (ADELE) funded by MCIN/ AEI /10.13039/501100011033

A measure preserving mapping for structured Grassmannian constellations in SIMO channels

In this paper, we propose a new structured Grassmannian constellation for noncoherent communications over single-input multiple-output (SIMO) Rayleigh block-fading channels. The constellation, which we call Grass-Lattice, is based on a measure preserving mapping from the unit hypercube to the Grassmannian of lines. The constellation structure allows for on-the-fly symbol generation, low-complexity decoding, and simple bit-to-symbol Gray coding. Simulation results show that Grass-Lattice has symbol error rate performance close to that of a numerically optimized unstructured constellation, and is more power efficient than other structured constellations proposed in the literature.This work was supported by Huawei Technologies Sweden, under the project GRASSCOM. The work of D. Cuevas was also partly supported under grant FPU20/03563 funded by Ministerio de Universidades (MIU), Spain. The work of Carlos Beltr´an was also partly supported under grant PID2020-113887GB-I00 funded by MCIN/AEI /10.13039/501100011033. The work ofI. Santamaria was also partly supported under grant PID2019-104958RB-C43(ADELE) funded by MCIN/ AEI /10.13039/501100011033

Multi-user non-coherent detection for downlink MIMO communication

© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Current cellular technologies are based on the concept of coherent communication, in which the channel matrix used for demodulation is estimated via reference or pilot signals. Coherent systems, however, involve a significant increase of the signalling overhead, especially when the number of transmission points is increased or when the mobile channel changes rapidly, which motivates the use of non-coherent techniques. This letter extends the use of non-coherent communications to a multi-user (MU) multiple-input multiple-output (MIMO) framework by combining superposition coding with a reduced-complexity detection method. Numerical results confirm that our scheme achieves higher user rates than non-coherent MU transmission based on time multiplexing. In addition to the well-known sum-rate gain of MU systems, an extra performance gain given by downlink non-coherent MU communication is shown and qualitatively justified.This work was performed in the framework of the FP7 project ICT-317669 METIS, supported in part by the European Union. The authors would like to acknowledge the contributions of their colleagues in METIS, although the views expressed are those of the authors and do not necessarily represent the project. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Chandra Ramabhadra Murthy.Roger Varea, S.; Calabuig Soler, D.; Cabrejas Peñuelas, J.; Monserrat Del Río, JF. (2014). Multi-user non-coherent detection for downlink MIMO communication. IEEE Signal Processing Letters. 21(10):1225-1229. https://doi.org/10.1109/LSP.2014.2330854S12251229211

Quasi-Gray labelling for Grassmannian constellations

Abstract-This paper presents a technique for assigning binary labels to the points in an arbitrary Grassmannian constellation in a manner that approximates the Gray labelling. The idea behind this technique is to match the Grassmannian constellation of interest to the points in an auxiliary constellation that can be readily Gray labelled. In order to demonstrate the efficacy of the proposed technique, the labelled constellations are utilized in a BICM-encoded non-coherent MIMO communication system with iterative detection and decoding. Numerical simulations indicate that this labelling technique results in a non-coherent communication system that provides better bit error rate performance than systems that utilize the same constellation but employ labels that are generated either randomly or via a quasi-set-partitioning technique