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We study the fundamental limits of matching pursuit, or the pure greedy algorithm, for approximating a target function by a sparse linear combination of elements from a dictionary. When the target function is contained in the variation space corresponding to the dictionary, many impressive works over the past few decades have obtained upper and lower bounds on the error of matching pursuit, but they do not match. The main contribution of this paper is to close this gap and obtain a sharp characterization of the decay rate of matching pursuit. Specifically, we construct a worst case dictionary which shows that the existing best upper bound cannot be significantly improved. It turns out that, unlike other greedy algorithm variants, the converge rate is suboptimal and is determined by the solution to a certain non-linear equation. This enables us to conclude that any amount of shrinkage improves matching pursuit in the worst case.

High data rates are one of the most prevalent requirements in current mobile communications. To cover this and other high standards regarding performance, increasing coverage, capacity, and reliability, numerous works have proposed the development of systems employing the combination of several techniques such as Multiple Input Multiple Output (MIMO) wireless technologies with Orthogonal Frequency Division Multiplexing (OFDM) in the evolving 4G wireless communications. Our proposed system is based on the 2x2 MIMO antenna technique, which is defined to enhance the performance of radio communication systems in terms of capacity and spectral efficiency, and the OFDM technique, which can be implemented using two types of sub-carrier mapping modes: Space-Time Block Coding and Space Frequency Block Code. SFBC has been considered in our developed model. The main advantage of SFBC over STBC is that SFBC encodes two modulated symbols over two subcarriers of the same OFDM symbol, whereas STBC encodes two modulated symbols over two subcarriers of the same OFDM symbol; thus, the coding is performed in the frequency domain. Our solution aims to demonstrate the performance analysis of the Space Frequency Block Codes scheme, increasing the Signal Noise Ratio (SNR) at the receiver and decreasing the Bit Error Rate (BER) through the use of 4 QAM, 16 QAM and 64QAM modulation over a 2x2 MIMO channel for an LTE downlink transmission, in different channel radio environments. In this work, an analytical tool to evaluate the performance of SFBC - Orthogonal Frequency Division Multiplexing, using two transmit antennas and two receive antennas has been implemented, and the analysis using the average SNR has been considered as a sufficient statistic to describe the performance of SFBC in the 3GPP Long Term Evolution system over Multiple Input Multiple Output channels.

Modern wireless cellular networks use massive multiple-input multiple-output (MIMO) technology. This technology involves operations with an antenna array at a base station that simultaneously serves multiple mobile devices which also use multiple antennas on their side. For this, various precoding and detection techniques are used, allowing each user to receive the signal intended for him from the base station. There is an important class of linear precoding called Regularized Zero-Forcing (RZF). In this work, we propose Adaptive RZF (ARZF) with a special kind of regularization matrix with different coefficients for each layer of multi-antenna users. These regularization coefficients are defined by explicit formulas based on Singular Value Decomposition (SVD) of user channel matrices. We study the optimization problem, which is solved by the proposed algorithm, with the connection to other possible problem statements. We prove theoretical estimates of the number of conditionality of the inverse covariance matrix of the ARZF method and the standard RZF method, which is important for systems with fixed computational accuracy. Finally, We compare the proposed algorithm with state-of-the-art linear precoding algorithms on simulations with the Quadriga channel model. The proposed approach provides a significant increase in quality with the same computation time as in the reference methods.

This paper discusses various types of constraints, difficulties and solutions to overcome the challenges regarding university course allocation problem. A hybrid evolutionary algorithm has been defined combining Local Repair Algorithm and Modified Genetic Algorithm to generate the best course assignment. After analyzing the collected dataset, all the necessary constraints were formulated. These constraints manage to cover the aspects needed to be kept in mind while preparing clash free and efficient class schedules for every faculty member. The goal is to generate an optimized solution which will fulfill those constraints while maintaining time efficiency and also reduce the workload of handling this task manually. The proposed algorithm was compared with some base level optimization algorithms to show the better efficiency in terms of accuracy and time.

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments.

In Mobile Edge Computing (MEC), Internet of Things (IoT) devices offload computationally-intensive tasks to edge nodes, where they are executed within containers, reducing the reliance on centralized cloud infrastructure. Frequent upgrades are essential to maintain the efficient and secure operation of edge clusters. However, traditional cloud cluster upgrade strategies are ill-suited for edge clusters due to their geographically distributed nature and resource limitations. Therefore, it is crucial to properly schedule containers and upgrade edge clusters to minimize the impact on running tasks. In this paper, we propose a low-latency container scheduling algorithm for edge cluster upgrades. Specifically: 1) We formulate the online container scheduling problem for edge cluster upgrade to minimize the total task latency. 2) We propose a policy gradient-based reinforcement learning algorithm to address this problem, considering the unique characteristics of MEC. 3) Experimental results demonstrate that our algorithm reduces total task latency by approximately 27\% compared to baseline algorithms.

In this paper, we consider the one-bit precoding problem for the multiuser downlink massive multiple-input multiple-output (MIMO) system with phase shift keying (PSK) modulation. We focus on the celebrated constructive interference (CI)-based problem formulation. We first establish the NP-hardness of the problem (even in the single-user case), which reveals the intrinsic difficulty of globally solving the problem. Then, we propose a novel negative $\ell_1$ penalty model for the considered problem, which penalizes the one-bit constraint into the objective by a negative $\ell_1$-norm term, and show the equivalence between (global and local) solutions of the original problem and the penalty problem when the penalty parameter is sufficiently large. We further transform the penalty model into an equivalent min-max problem and propose an efficient alternating proximal/projection gradient descent ascent (APGDA) algorithm for solving it, which performs a proximal gradient decent over one block of variables and a projection gradient ascent over the other block of variables alternately. The APGDA algorithm enjoys a low per-iteration complexity and is guaranteed to converge to a stationary point of the min-max problem and a local minimizer of the penalty problem. To further reduce the computational cost, we also propose a low-complexity implementation of the APGDA algorithm, where the values of the variables will be fixed in later iterations once they satisfy the one-bit constraint. Numerical results show that, compared to the state-of-the-art CI-based algorithms, both of the proposed algorithms generally achieve better bit-error-rate (BER) performance with lower computational cost.

This paper focuses on advancing outdoor wireless systems to better support ubiquitous extended reality (XR) applications, and close the gap with current indoor wireless transmission capabilities. We propose a hybrid knowledge-data driven method for channel semantic acquisition and multi-user beamforming in cell-free massive multiple-input multiple-output (MIMO) systems. Specifically, we firstly propose a data-driven multiple layer perceptron (MLP)-Mixer-based auto-encoder for channel semantic acquisition, where the pilot signals, CSI quantizer for channel semantic embedding, and CSI reconstruction for channel semantic extraction are jointly optimized in an end-to-end manner. Moreover, based on the acquired channel semantic, we further propose a knowledge-driven deep-unfolding multi-user beamformer, which is capable of achieving good spectral efficiency with robustness to imperfect CSI in outdoor XR scenarios. By unfolding conventional successive over-relaxation (SOR)-based linear beamforming scheme with deep learning, the proposed beamforming scheme is capable of adaptively learning the optimal parameters to accelerate convergence and improve the robustness to imperfect CSI. The proposed deep unfolding beamforming scheme can be used for access points (APs) with fully-digital array and APs with hybrid analog-digital array. Simulation results demonstrate the effectiveness of our proposed scheme in improving the accuracy of channel acquisition, as well as reducing complexity in both CSI acquisition and beamformer design. The proposed beamforming method achieves approximately 96% of the converged spectrum efficiency performance after only three iterations in downlink transmission, demonstrating its efficacy and potential to improve outdoor XR applications.

This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.