Hybrid Direction of Arrival Precoding for Multiple Unmanned Aerial Vehicles Aided Non-Orthogonal Multiple Access in 6G Networks

Unmanned aerial vehicles (UAV) have attracted increasing attention in acting as a relay for effectively improving the coverage and data rate of wireless systems, and according to this vision, they will be integrated in the future sixth generation (6G) cellular network. Non-orthogonal multiple access (NOMA) and mmWave band are planned to support ubiquitous connectivity towards a massive number of users in the 6G and Internet of Things (IOT) contexts. Unfortunately, the wireless terrestrial link between the end-users and the base station (BS) can suffer severe blockage conditions. Instead, UAV relaying can establish a line-of-sight (LoS) connection with high probability due to its flying height. The present paper focuses on a multi-UAV network which supports an uplink (UL) NOMA cellular system. In particular, by operating in the mmWave band, hybrid beamforming architecture is adopted. The MUltiple SIgnal Classification (MUSIC) spectral estimation method is considered at the hybrid beamforming to detect the different direction of arrival (DoA) of each UAV. We newly design the sum-rate maximization problem of the UAV-aided NOMA 6G network specifically for the uplink mmWave transmission. Numerical results point out the better behavior obtained by the use of UAV relays and the MUSIC DoA estimation in the Hybrid mmWave beamforming in terms of achievable sum-rate in comparison to UL NOMA connections without the help of a UAV network.

Stochastic optimal control with random coefficients and associated stochastic Hamilton–Jacobi–Bellman equations

We consider the optimal control problem for stochastic differential equations (SDEs) with random coefficients under the recursive-type objective functional captured by the backward SDE (BSDE). Due to the random coefficients, the associated Hamilton–Jacobi–Bellman (HJB) equation is a class of second-order stochastic PDEs (SPDEs) driven by Brownian motion, which we call the stochastic HJB (SHJB) equation. In addition, as we adopt the recursive-type objective functional, the drift term of the SHJB equation depends on the second component of its solution. These two generalizations cause several technical intricacies, which do not appear in the existing literature. We prove the dynamic programming principle (DPP) for the value function, for which unlike the existing literature we have to use the backward semigroup associated with the recursive-type objective functional. By the DPP, we are able to show the continuity of the value function. Using the Itô–Kunita’s formula, we prove the verification theorem, which constitutes a sufficient condition for optimality and characterizes the value function, provided that the smooth (classical) solution of the SHJB equation exists. In general, the smooth solution of the SHJB equation may not exist. Hence, we study the existence and uniqueness of the solution to the SHJB equation under two different weak solution concepts. First, we show, under appropriate assumptions, the existence and uniqueness of the weak solution via the Sobolev space technique, which requires converting the SHJB equation to a class of backward stochastic evolution equations. The second result is obtained under the notion of viscosity solutions, which is an extension of the classical one to the case for SPDEs. Using the DPP and the estimates of BSDEs, we prove that the value function is the viscosity solution to the SHJB equation. For applications, we consider the linear-quadratic problem, the utility maximization problem, and the European option pricing problem. Specifically, different from the existing literature, each problem is formulated by the generalized recursive-type objective functional and is subject to random coefficients. By applying the theoretical results of this paper, we obtain the explicit optimal solution for each problem in terms of the solution of the corresponding SHJB equation.

An optimal Islamic investment decision in two-region economy: The case of Indonesia and Malaysia

In this work, the possibility of cross-border activities between two regions in the framework of the investment contract is viewed as optimal allocation problems. The problems of determining the optimal proportion of funds to be invested in liquidity and technology are analyzed in two different environments. In the first case, we consider a two-region and two-technology economy in which both regions possess the same productive technology or project, but a different stream of return. While in the second case, we examine an economy where two regions (i.e., Indonesia and Malaysia) hold different Islamic productive projects with identical returns. Allocation models are formulated in terms of investors’ expected utility maximization problem under budget constraints with respect to regional and sectoral shocks. It is revealed that optimal parameters for liquidity ratio, technological investment profile, and bank repayment are analytically characterized by the return of a more productive project and the proportion of impatient and patient investors in the region. Even though both cases employ different assumptions, they provide the same expressions of optimal parameters. The model suggests that cross-border Islamic investment activities between two regions might be realized, provided both regions hold productive projects with an identical stream of return. This paper also shows that by increasing the lower return of the project approaching the higher return, a room for inter-region investment can be created. An analytical framework of an investment contract in terms of optimal allocation model is provided.

Downlink Transmission And Channel Estimation For Cell-Free Massive MIMO-OFDM With Symbol Time Offset

In a cell-free massive MIMO system, multiple users arrive at multiple access points at separate times, while in an OFDM system, different delays can be equivalent to symbol timing offsets (STOs). Since symbol timing offsets are not all the same, in the downlink transmission process, it is necessary to consider its impact on transmission techniques, such as channel estimation and downlink precoding. In this paper, aiming at the performance loss caused by STO in cell-free massive MIMO-OFDM system, we propose a multi-RB precoding optimization algorithm that maximizes the downlink sum rate. We derive the sum rate maximization problem into an iterative second-order cone programming (SOCP) form to achieve convex approximation. Then, considering the impact of STO on the accuracy of cell-free massive MIMO-OFDM channel estimation, we propose a downlink channel estimation method, which jointly uses channel state information reference signal (CSI-RS) and demodulation reference signal (DMRS). Simulation results show that the proposed multi-RB optimal precoding can effectively improve the downlink sum rate, and the proposed downlink channel estimation can obtain accurate multi-RB frequency domain channel parameters.

Nonsubmodular Constrained Profit Maximization in Attribute Networks

The number of social individuals who interact with their friends through social networks is increasing, leading to an undeniable fact that word-of-mouth marketing has become one of the useful ways to promote sale of products. The Constrained Profit Maximization in Attribute network (CPMA) problem, as an extension of the classical influence maximization problem, is the main focus of this paper. We propose the profit maximization in attribute network problem under a cardinality constraint which is closer to the actual situation. The profit spread metric of CPMA calculates the total benefit and cost generated by all the active nodes. Different from the classical Influence Maximization problem, the influence strength should be recalculated according to the emotional tendency and classification label of nodes in attribute networks. The profit spread metric is no longer monotone and submodular in general. Given that the profit spread metric can be expressed as the difference between two submodular functions and admits a DS decomposition, a three-phase algorithm named as Marginal increment and Community-based Prune and Search(MCPS) Algorithm frame is proposed which is based on Louvain algorithm and logistic function. Due to the method of marginal increment, MPCS algorithm can compute profit spread more directly and accurately. Experiments demonstrate the effectiveness of MCPS algorithm.

A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility

The mixing process of liquid products is a crucial activity in the industry of essential commodities like, medicine, pesticide, detergent, and so on. So, the mathematical study of the mixing problem is very much important to formulate a production inventory model of such type of items. In this work, the concept of the mixing problem is studied in the branch of production inventory. Here, a production model of mixed liquids with price-dependent demand and a stock-dependent production rate is formulated under preservation technology. In the formulation, first of all, the mixing process is presented mathematically with the help of simultaneous differential equations. Then, the mixed liquid produced in the mixing process is taken as a raw material of a manufacturing system. Then, all the cost components and average profit of the system are calculated. Now, the objective is to maximize the corresponding profit maximization problem along with the highly nonlinear objective function. Because of this, the mentioned maximization problem is solved numerically using MATHEMATICA software. In order to justify the validity of the model, two numerical examples are worked out. Finally, to show the impact of inventory parameters on the optimal policy, sensitivity analyses are performed and the obtained results are presented graphically.

Efficient Targeted Influence Maximization Based on Multidimensional Selection in Social Networks

The influence maximization problem over social networks has become a popular research problem, since it has many important practical applications such as online advertising, virtual market, and so on. General influence maximization problem is defined over the whole network, whose intuitive aim is to find a seed node set with size at most k in order to affect as many as nodes in the network. However, in real applications, it is commonly required that only special nodes (target) in the network are expected to be influenced, which can use the same cost of placing seed nodes but influence more targeted nodes really needed. Some research efforts have provided solutions for the corresponding targeted influence maximization problem (TIM for short). However, there are two main drawbacks of previous works focusing on the TIM problem. First, some works focusing on the case the targets are given arbitrarily make it hard to achieve efficient performance guarantee required by real applications. Second, some previous works studying the TIM problems by specifying the target set in a probabilistic way is not proper for the case that only exact target set is required. In this paper, we study the Multidimensional Selection based Targeted Influence Maximization problem, MSTIM for short. First, the formal definition of the problem is given based on a brief and expressive fragment of general multi-dimensional queries. Then, a formal theoretical analysis about the computational hardness of the MSTIM problem shows that even for a very simple case that the target set specified is 1 larger than the seed node set, the MSTIM problem is still NP-hard. Then, the basic framework of RIS (short for Reverse Influence Sampling) is extended and shown to have a 1 − 1/e − ϵ approximation ratio when a sampling size is satisfied. To satisfy the efficiency requirements, an index-based method for the MSTIM problem is proposed, which utilizes the ideas of reusing previous results, exploits the covering relationship between queries and achieves an efficient solution for MSTIM. Finally, the experimental results on real datasets show that the proposed method is indeed rather efficient.

Community-based framework for influence maximization problem in social networks

<p>Given a social graph, the influence maximization problem (IMP) is the act of selecting a group of nodes that cause maximum influence if they are considered as seed nodes of a diffusion process. IMP is an active research area in social network analysis due to its practical need in applications like viral marketing, target advertisement, and recommendation system. In this work, we propose an efficient solution for IMP based on the social network structure. The community structure is a property of real-world graphs. In fact, communities are often overlapping because of the involvement of users in many groups (family, workplace, and friends). These users are represented by overlapped nodes in the social graphs and they play a special role in the information diffusion process. This fact prompts us to propose a solution framework consisting of three phases: firstly, the community structure is discovered, secondly, the candidate seeds are generated, then lastly the set of final seed nodes are selected. The aim is to maximize the influence with the community diversity of influenced users. The study was validated using synthetic as well as real social network datasets. The experimental results show improvement over baseline methods and some important conclusions were reported.</p>

Energy Efficiency Analysis in Modified GoF Spectrum Sensing-Based AF Relay Cooperative Cognitive Sensor Network with Energy Harvesting

In this paper, we propose a joint sensing duration and transmission power allocation scheme to maximize the energy efficiency (EE) of the secondary user (SU) in a cooperative cognitive sensor network (CSN). At the initial time slot of the frame, the secondary transmitter (ST) performs energy harvesting (EH) and spectrum sensing simultaneously using power splitting (PS) protocol. The modified goodness of fit (GoF) spectrum sensing algorithm is employed to detect the licensed spectrum, which is not sensitive to an inaccurate noise power estimate. Based on the imperfect sensing results, the ST will act as an amplify-and-forward (AF) relay and assist in transmission of the primary user (PU) or transmit its own data. The SU’s EE maximization problem is constructed under the constraints of meeting energy causality, sensing reliability, and PU’s quality of service (QoS) requirement. Since the SU’s EE function is a nonconvex problem and difficult to solve, we transform the original problem into a tractable convex one with the aid of Dinkelbach’s method and convex optimization technique by applying a nonlinear fractional programming. The closed-form expression of the ST’s transmission power is also derived through Karush-Kuhn-Tucker (KKT) and gradient method. Simulation results show that our scheme is superior to the existing schemes.