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

A Noncoherent Space-Time Code from Quantum Error Correction

In this work, we develop a space-time block code for noncoherent communication using techniques from the field of quantum error correction. We decompose the multiple-input multiple-output (MIMO) channel into operators from quantum mechanics, and design a non-coherent space time code using the quantum stabilizer formalism. We derive an optimal decoder, and analyze the former through a quantum mechanical lens. We compare our approach to a comparable coherent approach and a noncoherent differential approach, achieving comparable or better performance.Comment: 6 pages, one figure, accepted at the 53rd annual Conference on Information Sciences and System

Towards an enhanced noncoherent massive MU-MIMO system

PhD ThesisMany multiple-input multiple-output (MIMO) downlink transmission schemes assume channel state information (CSI) is available at the receiver/transmitter. In practice, knowledge of CSI is often obtained by using pilot symbols transmitted periodically. However, for some systems, due to high mobility and the cost of channel training and estimation, CSI acquisition is not always feasible. The problem becomes even more difficult when many antennas are used in the system and the channel is changing very rapidly before training is completed. Moreover, as the number of transmit/receive antennas grows large, the number of pilot symbols, system overheads, latency, and power consumption will grow proportionately and thereby the system becomes increasingly complex. As an alternative, a noncoherent system may be used wherein the transmitter/receiver does not need any knowledge of the CSI to perform precoding or detection. This thesis focuses on the design of a noncoherent downlink transmission system to jointly improve the performance and achieve a simple low complexity transmission scheme in three MIMO system scenarios: low rate differential spacetime block coding (STBC) in a downlink multiuser (MU-MIMO) system; high rate differential algebraic STBC in a downlink MU-MIMO system; and differential downlink transmission in a massive MU-MIMO system. Three novel design methods for each of these systems are proposed and analysed thoroughly. For the MIMO system with a low rate noncoherent scheme, a differential STBC MU-MIMO system with a downlink transmission scheme is considered. Specifically, downlink precoding combined with differential modulation (DM) is used to shift the complexity from the receivers to the transmitter. The block diagonalization (BD) precoding scheme is used to cancel co-channel interference (CCI) in addition to exploiting its advantage of enhancing diversity. Since the BD scheme requires channel knowledge at the transmitter, the downlink spreading technique along with DM is also proposed, which does not require channel knowledge neither at the transmitter nor at the receivers. The orthogonal spreading (OS) scheme is employed to have similar principle as code division multiple access (CDMA) multiplexing scheme in order to eliminate the interference between users. As a STBC scheme, the Alamouti code is used that can be encoded/decoded using DM thereby eliminating the need for channel knowledge at the receiver. The proposed schemes yield low complexity transceivers while providing good performance. For the MIMO system with a high rate noncoherent scheme, a differential STBC MU-MIMO system that operates at a high data rate is considered. In particular, a full-rate full-diversity downlink algebraic transmission scheme combined with a differential STBC systems is proposed. To achieve this, perfect algebraic space time codes and Cayley differential (CD) transforms are employed. Since CSI is not needed at the differential receiver, differential schemes are ideal for multiuser systems to shift the complexity from the receivers to the transmitter, thus simplifying user equipment. Furthermore, OS matrices are employed at the transmitter to separate the data streams of different users and enable simple single user decoding. In the OS scheme, the transmitter does not require any knowledge of the CSI to separate the data streams of multiple users; this results in a system which does not need CSI at either end. With this system, to limit the number of possible codewords, a sphere decoder (SD) is used to decode the signals at the receiving end. The proposed scheme yields low complexity transceivers while providing full-rate full-diversity system with good performance. Lastly, a differential downlink transmission scheme is proposed for a massive MIMO system without explicit channel estimation. In particular, a downlink precoding technique combined with a differential encoding scheme is used to simplify the overall system complexity. A novel precoder is designed which, with a large number of transmit antennas, can effectively precancel the multiple access interference (MAI) for each user, thus enhancing the system performance. Maximising the worst case signal-to-interference-plus-noise ratio (SINR) is adopted to optimise the precoder for the users in which full power space profile (PSP) knowledge is available to the base station (BS). Also, two suboptimal solutions based on the matched and the orthogonality approach of PSP are provided to separate the data streams of multiple users. The decision feedback differential detection (DFDD) technique is employed to further improve the performance. In summary, the proposed methods eliminate MAI, enhance system performance, and achieve a simple low complexity system. Moreover, transmission overheads are significantly reduced, the proposed methods avoid explicit channel estimation at both ends.King Fahad Security Collage at the Ministry of Interior - Saudi Arabia

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

Advanced wireless communications using large numbers of transmit antennas and receive nodes

The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD massive MIMO be used for training signal transmissions and channel state information (CSI) feedback. First, we propose practical open-loop and closed-loop training frameworks to reduce the overhead of the downlink training phase. We then discuss efficient CSI quantization techniques using a trellis search. The proposed CSI quantization techniques can be implemented with a complexity that only grows linearly with the number of transmit antennas while the performance is close to the optimal case. We also analyze distributed reception using a large number of geographically separated nodes, a scenario that may become popular with the emergence of the Internet of Things. For distributed reception, we first propose coded distributed diversity to minimize the symbol error probability at the fusion center when the transmitter is equipped with a single antenna. Then we develop efficient receivers at the fusion center using minimal processing overhead at the receive nodes when the transmitter with multiple transmit antennas sends multiple symbols simultaneously using spatial multiplexing

Signal design for Multiple-Antenna Systems and Wireless Networks

This dissertation is concerned with the signal design problems for Multiple Input and Multiple Output (MIMO) antenna systems and wireless networks. Three related but distinct problems are considered.The first problem considered is the design of space time codes for MIMO systems in the case when neither the transmitter nor the receiver knows the channel. We present the theoretical concept of communicating over block fading channel using Layered Unitary Space Time Codes (LUSTC), where the input signal is formed as a product of a series of unitary matrices with corresponding dimensionality. We show the channel capacity using isotropically distributed (i.d.) input signaling and optimal decoding can be achieved by layered i.d. signaling scheme along with a low complexity successive decoding. The closed form layered channel capacity is obtained, which serves as a design guideline for practical LUSTC. In the design of LUSTC, a successive design method is applied to leverage the problem of optimizing over lots of parameters.The feedback of channel state information (CSI) to the transmitter in MIMO systems is known to increase the forward channel capacity. A suboptimal power allocation scheme for MIMO systems is then proposed for limited rate feedback of CSI. We find that the capacity loss of this simple scheme is rather small compared to the optimal water-filling solution. This knowledge is applied for the design of the feedback codebook. In the codebook design, a generalized Lloyd algorithm is employed, in which the computation of the centroid is formulated as an optimization problem and solved optimally. Numerical results show that the proposed codebook design outperforms the existing algorithms in the literature.While it is not feasible to deploy multiple antennas in a wireless node due to the space limitation, user cooperation is an alternative to increase performance of the wireless networks. To this end, a coded user cooperation scheme is considered in the dissertation, which is shown to be equivalent to a coding scheme with the encoding done in a distributive manner. Utilizing the coding theoretic bound and simulation results, we show that the coded user cooperation scheme has great advantage over the non-cooperative scheme