A describing function study of saturated quantization and its application to the stability analysis of multi-bit sigma delta modulators

Just as their single-bit counterparts, multi-bit sigma delta modulators exhibit nonlinear behavior due to the presence of the quantizer in the loop. In the multi-bit case this is caused by the fact that any quantizer has a limited output range and hence gives an implicit saturation effect. Due to this, any multi-bit modulator is prone to modulator overloading. Unfortunately, until now, designers had to rely on extensive time-domain simulations to predict the overloading level, because there is no adequate analytical theory to model this effect. In this work, we have developed such an analytical theory based on multiple input describing function analysis. This way, we obtained expressions for the signal gain, the noise gain and the variance of the quantization noise. Here, both the case of DC as well as sinusoidal signals was considered. These results were used for the stability analysis of multi-bit Sigma Delta modulators, which allows to predict the overloading level. Code implementing the proposed expressions is available for download at http://cas1.elis.ugent. be/cas/en/download

TEMPORAL CONNECTIVITY AS A MEASURE OF ROBUSTNESS IN NONORTHOGONAL MULTIPLE ACCESS WIRELESS NETWORKS

Supplementary Material has been provided, but is not yet published.Nonorthogonal multiple access (NOMA) is recognized as an important technology to meet the performance requirements of fifth generation (5G) and beyond 5G (B5G) wireless networks. Through the technique of overloading, NOMA has the potential to support higher connection densities, increased spectral efficiency, and lower latency than orthogonal multiple access. The role of NOMA in 5G/B5G wireless networks necessitates a clear understanding of how overloading variability affects network robustness. This dissertation considers the relationship between variable overloading and network robustness through the lens of temporal network theory, where robustness is measured through the evolution of temporal connectivity between network devices (ND). We develop a NOMA temporal graph model and stochastic temporal component framework to characterize time-varying network connectivity as a function of NOMA overloading. The analysis is extended to derive stochastic expressions and probability mass functions for unidirectional connectivity, bidirectional connectivity, the inter-event time between unidirectional connectivity, and the minimum time required for bidirectional connectivity between all NDs. We test the accuracy of our analytical results through numerical simulations. Our results provide an overloading-based characterization of time-varying network robustness that is generalizable to any underlying NOMA implementation.National Security Agency, Fort George G. Meade, MD 20775Major, United States Marine CorpsApproved for public release. Distribution is unlimited

Elaboration in Dependent Type Theory

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean's elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved

Sub-graph based joint sparse graph for sparse code multiple access systems

Sparse code multiple access (SCMA) is a promising air interface candidate technique for next generation mobile networks, especially for massive machine type communications (mMTC). In this paper, we design a LDPC coded SCMA detector by combining the sparse graphs of LDPC and SCMA into one joint sparse graph (JSG). In our proposed scheme, SCMA sparse graph (SSG) defined by small size indicator matrix is utilized to construct the JSG, which is termed as sub-graph based joint sparse graph of SCMA (SG-JSG-SCMA). In this paper, we first study the binary-LDPC (B-LDPC) coded SGJSG- SCMA system. To combine the SCMA variable node (SVN) and LDPC variable node (LVN) into one joint variable node (JVN), a non-binary LDPC (NB-LDPC) coded SG-JSG-SCMA is also proposed. Furthermore, to reduce the complexity of NBLDPC coded SG-JSG-SCMA, a joint trellis representation (JTR) is introduced to represent the search space of NB-LDPC coded SG-JSG-SCMA. Based on JTR, a low complexity joint trellis based detection and decoding (JTDD) algorithm is proposed to reduce the computational complexity of NB-LDPC coded SGJSG- SCMA system. According to the simulation results, SG-JSGSCMA brings significant performance improvement compare to the conventional receiver using the disjoint approach, and it can also outperform a Turbo-structured receiver with comparable complexity. Moreover, the joint approach also has advantages in terms of processing latency compare to the Turbo approaches

Modelling Planner-Carrier Interactions in Road Freight Transport: Optimization of Road Maintenance Costs Via Overloading Control

A bi-level modelling approach is proposed to represent the interaction between the vehicle loading practices of road freight transport carriers, and the decisions of a road planning authority responsible both for road maintenance and for the enforcement of overloading control. At the lower (reactive) level, the overloading decisions of the carriers impact on road maintenance expenditure, while at the upper (anticipatory) level the planner decides fine and enforcement levels by anticipating the responses of the carriers. A case study using data from Mexico is used to illustrate the method