Closed-form Optimal Solution Research Articles

Legitimate eavesdropping of wireless powered suspicious communication networks with a monitoring power station

This paper investigates the legitimate eavesdropping of a wireless powered suspicious communication network. The considered network consists of a wireless powered suspicious transmitter, a suspicious receiver, and a power station. The power station is assumed to be also a monitor to legitimately eavesdrop the suspicious communication with the help from a wireless powered jammer. The problem for maximizing the average eavesdropping rate under the minimum suspicious communication rate constraint and the transmit power constraint at the monitor is investigated, where the time allocation for energy transferring and information transmission, and the power controls of the monitoring power station and the jammer are jointly optimized. By using the Lagrange duality method and exploring the particular problem structure, the closed-form optimal solution is derived. Some valuable insights are also obtained from the optimal solution. Extensive simulations are provided to confirm the superiority of the proposed optimal solution compared to various benchmark algorithms.

Green Product Design Considering Consumer’s Income and Environmental Awareness

With the enhancement of consumer environmental awareness, many companies are paying more attention to developing green products with higher environmental quality. In this paper, we study how the consumer’s valuation towards product’s qualities and consumer demand affect manufacturer’s product design and pricing regimes. Assuming there is a monopolist who manufacture products with traditional and environmental qualities and the market is divided into four segments according to consumer’s income level and environmental awareness, we give the optimal closed form solutions of the qualities and prices of products in mass-market and segment-market strategies. Additionally, we discuss the impacts of consumers’ valuation towards products’ qualities and market segments’ size on the total environmental qualities. We find that (i) various parameters, especially consumers’ valuation towards products’ qualities and market share of each segment affect the firm’s choice on market strategies and consequent environmental performance; (ii) green product development does not always increase and may decrease the degree of environmentally friendliness.

Automatic Kinematic Calibration of Multiaxis Gimbal Systems

This article presents an automatic and efficient calibration method for multiaxis gimbal systems. The calibrated kinematic parameters consist of the axis orientation, the joint encoder nonlinearity map, and the endpoint gyro bias. The calibration of these parameters is conducted simultaneously by sequentially and independently moving one gimbal joint back and forth. With such straightforward intuition, the algorithm is formulated based on the product-of-exponential formula with an analytically derived error model. The key and unique contribution of this algorithm is that it produces a closed-form optimal solution, which is computation efficient and easy for embedded implementation. Both numerical and experimental tests are performed to validate the effectiveness of the proposed algorithm in calibrating the kinematic parameters of gimbal systems and compensating the gyro bias.

Design of single and dual-mode companding scalar quantizers based on piecewise linear approximation of the Gaussian PDF

This paper proposes a novel companding quantizer design for Gaussian source by using piecewise linear approximation of the probability density function. As the optimal companding technique represents very effective tool for quantizing signals with non-linear distribution, such as speech, the lack of optimal closed-form solution for Gaussian source represents an issue that motivated us to provide an approximation model, supported with closed-form designing expressions, suitable for applications requiring low processing delays. We provide the derivation of closed-form expressions for approximate compressor and inverse compressor functions, which are used to define representation levels and boundary segments, as the optimal compandor design requires integral equations solving. Also, we analyze how the probability density function within a dual-mode framework behaves and we propose a novel model of probability density function. System performances are analyzed for various values of configuration parameters and estimated theoretical performances are compared with appropriate simulations. Moreover, the results are compared with performance of the optimal compandor to justify the usefulness of dual-mode technique and it is demonstrated that the model we propose outperforms it, making the model competitive for speech applications where the system complexity is significant or critical aspect alongside achieved performances.

Optimal Collaborative Spectrum Sharing for a Cognitive Multi-Antenna Relay With Full-Duplex Capability and Stability Constraint

Collaborative spectrum sharing (CSS) between primary and secondary users (PU and SU) is an effective way of utilizing limited radio spectrum. In CSS, cognitive SU acts as a relay for PU, which facilitates the PU to send its packet with a lower error probability by the help of the SU, and consequently, the SU has more chances to find a vacant spectrum. When SU is equipped with multiple antennas, it can further efficiently utilize the radio spectrum by adopting a growing self-interference cancellation technique for full-duplex (FD) transmission. In this paper, both an aggressive and a passive secondary usage of the spectrum are proposed, the operational principles of which are defined using spectrum-sharing probability φ in FD CSS environments. For the spectrum-sharing probability φ, SU for each of the methods sends its own signal and the PU's (relayed) signal together by using superposition transmission. For the remaining probability 1 - φ, the two methods work differently: SU sends its own signal only in the aggressive mode while it sends only the relaying signal for PU in the passive mode. We formulate an FD CSS problem with various physical-layer parameters and the proposed operating modes as a function of the spectrum-sharing probability. Our goal is to maximize the secondary stable throughput while keeping a primary traffic constraint. Closed-form optimal solutions on φ are provided in the paper, the value of which heavily depends on the primary traffic volume, the operating modes, the relative locations of the collaborative nodes and the transmit power budget at SU. The analytical results in the paper are verified with numerical investigation, and the performance enhancement by the proposed methods is evaluated in comparison with benchmark systems. The results show that the aggressive mode is promising if SU has a relatively small transmit power and the primary traffic load is low, while the passive mode is suitable when the primary traffic load is high.

End-to-End Energy-Efficiency and Reliability of UAV-Assisted Wireless Data Ferrying

We analyze the end-to-end performance of an unmanned-aerial-vehicle (UAV)-assisted data ferrying network where the UAV serves as a data ferry between the source base station (BS) and multiple destination receivers. We evaluate the end-to-end reliability both with and without packet retransmission technique called automatic repeat request (ARQ), bit error probability (BEP), energy-efficiency, and transmission outage probability. We consider line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions in both the data loading and delivering links and model them with the Rician and Rayleigh fading channels, respectively. We derive tractable approximations for the derived SNR outage results and demonstrate their application in optimizing the distance that a UAV should travel in order to balance the energy-coverage trade-offs. We formulate two different optimization problems and convexify them to solve for the optimal ferrying distance, i.e. (i) outage-constrained energy minimization and (ii) energy-constrained SNR outage minimization. Closed-form optimal solutions are obtained for the second problem. In addition, we formulate a bi-objective optimization problem in order to minimize SNR outage and energy consumption with desired SNR outage probability constraints. The objective function is then reformulated using difference of convex functions (DC) and solved using a DC algorithm. Numerical results validate the derived expressions and show a comparison of the obtained solutions with the solutions obtained from exhaustive search. Insights related to the impact of LoS Rician and NLoS Rayleigh fading channels as well as the optimal ferrying distance are obtained considering a variety of objective functions.

Optimal and Sub-Optimal Uplink NOMA: Joint User Grouping, Decoding Order, and Power Control

In this letter we explore the user grouping, decoding order and power control in an uplink non-orthogonal multiple access (NOMA) system. We formulate a joint optimization problem to maximize the achievable sum rate (ASR) of the multiple users, where each user has a minimum rate requirement. The problem is a combinatorial integer programming problem, due to the discreteness and coupling of the decoding order and user grouping. We then first derive the closed-form optimal solution of the decoding order and power control. By exhaustively searching the user grouping variables, we can obtain the globally optimal solution of the formulated problem. To achieve the tradeoff between the computational complexity and performance, we propose a sub-optimal user grouping algorithm with a linear complexity. Simulation results show that the proposed sub-optimal solution can achieve a near-optimal performance in terms of ASR.

Total Throughput Maximization of Cooperative Cognitive Radio Networks With Energy Harvesting

Cognitive radio and energy harvesting techniques have provided significant benefits in terms of spectrum reuse and lifetime prolongation for conventional wireless networks. We are thus motivated to consider the energy harvesting cognitive radio networks (CRNs) consisting of multiple primary users (PUs) and secondary users (SUs). We introduce two cooperation modes: the energy cooperation mode and joint cooperation mode. In the energy cooperation mode, there only exists energy cooperation between PUs and SUs, i.e., the SU transmits its own packets by using the energy harvested from primary signals. In the joint cooperation mode, the SU relays primary packets by using the energy harvested from primary signals. In each cooperation mode of three representational scenarios (the CRN with one pair of PUs and one pair of SUs, the CRN with two pairs of PUs and one pair of SUs, and the CRN with one pair of PUs and two pairs of SUs) and the general scenario, we exploit the optimal time allocation between PUs and SUs, and balance the tradeoff between energy harvesting and packet transmission to obtain the maximum total achievable throughput. To be specific, we first formulate the throughput maximization problems as non-linear optimization problems, and then prove them as convex problems by monotonicity analysis. Moreover, we obtain the closed-form optimal solution in the energy cooperation mode. We prove the existence of the optimal solution in the joint cooperation mode, obtain the upper and lower bounds, and provide numerical analysis for the optimal solution. Finally, we highlight the benefits of information cooperation and the impact of multi-user gain on the maximum of the total achievable throughput.

Economic production quantity model with backorders and items with imperfect/perfect quality options

In this paper, an economic production quantity (EPQ) model with backorders considering two options for replenishing of items is proposed; with partially imperfect and perfect quality items. First option assumes a produced shipment contains a fraction of imperfect quality items and supplier does not conduct a full inspection. Therefore, these items are detected by a fully perfect screening process by buyer and are sold as a single batch at a discounted price. While the second one assumes that all items that are produced are fully inspected by supplier and all delivered items are perfect; of course with higher unit production price. Ordering size and backordering level are used as decision variables to derive the closed-form optimal solution. The proposed model is ilustrated and discussed by a numerical example. Finally, a sensitivity analysis is done for identifying the impact of crucial parameters on the optimal solution.

Uplink resource allocation for multiple access computational offloading

The mobile edge computing framework offers the opportunity to reduce the energy that devices must expend to complete computational tasks. The extent of that energy reduction depends on the nature of the tasks, and on the choice of the multiple access scheme. In this paper, we first address the uplink communication resource allocation for offloading systems that exploit the full capabilities of the multiple access channel (FullMA). For indivisible tasks we provide a closed-form optimal solution of the energy minimization problem when a given set of users with different latency constraints are offloading, and a tailored greedy search algorithm for finding a good set of offloading users. For divisible tasks we develop a low-complexity algorithm to find a stationary solution. To highlight the impact of the choice of multiple access scheme, we also consider the TDMA scheme, which, in general, cannot exploit the full capabilities of the channel, and we develop low-complexity optimal resource allocation algorithms for indivisible and divisible tasks under that scheme. The energy reduction facilitated by FullMA is illustrated in our numerical experiments. Further, those results show that the proposed algorithms outperform existing algorithms in terms of energy consumption and computational cost.

Joint Transmitter-Receiver Spatial Modulation Design via Minimum Euclidean Distance Maximization

Joint transmitter-receiver spatial modulation (JSM) is an appealing transmission scheme in the spatial modulation family, where transmit diversity, receive diversity, and multiplexing gain are achieved simultaneously. However, the conventional JSM technique is neither spectrum efficient nor antenna efficient due to its limited candidates of bit-to-antenna mapping. In this paper, we propose a novel JSM approach that involves more mapping candidates to relax the implementation constraint and achieve better reliability. The proposed JSM scheme maximizes the minimum Euclidean distance (MED) between the received signals of different antenna mappings by optimizing the antenna selection and the power allocation over the transmit antennas, named MED-JSM. In particular, an optimal closed-form power allocation solution is derived when there are two receive antennas. For more receive antennas, a lower bound of the minimum Euclidean distance is derived, and a corresponding lower bound-approaching power allocation algorithm is proposed accordingly. Then, the proposed power allocation algorithm and antenna selection are used in a hybrid manner to further enhance the system reliability. Since the optimal MED-JSM requires an exhaustive search over all the received signals, we propose a suboptimal scheme with reduced computational complexity, which shrinks the search space via the Rayleigh-Ritz theorem. Numerical results show that the proposed MED-JSM outperforms the conventional JSM schemes in system's reliability.

Hand-Eye Calibration: 4-D Procrustes Analysis Approach

We give a universal analytical solution to the hand-eye calibration problem ${AX} = {XB}$ with known matrices ${A}$ and ${B}$ and unknown variable ${X}$ , all in the set of special Euclidean group SE(3). The developed method relies on the 4-D Procrustes analysis. A unit-octonion representation is proposed for the first time to solve such a Procrustes problem through which an optimal closed-form eigendecomposition solution is derived. By virtue of such a solution, the uncertainty description of ${X}$ , being a sophisticated problem previously, can be solved in a simpler manner. The proposed approach is then verified using simulations and real-world experimentations on an industrial robotic arm. The results indicate that it owns better accuracy and better description of uncertainty and consumes much less computation time.

Single-machine lot scheduling problem for deteriorating items with negative exponential deterioration rate

Determining production-inventory level is one of the most important and challenging problems in a manufacturing system.Economic Batch Quantity(EBQ) is the simplest and the most employed inventory model in this field. Here, a single-source production lot-sizing model for deteriorating products with negative exponential deterioration rate is developed. In this manufacturing system, we assume that all items are manufactured using a single source. In this paper the optimal values for cycle length and lot size are derived in a way that the total cost (consists of machine setup cost, manufacturing cost, carrying and disposal costs of the deteriorating items) is minimized. Consequently, the developed model for the proposed problem is formulated. According to the derived mathematical model, we could not provide a closed form optimal solution, but we show that there is a unique optimal solution for the cycle length. At first, the upper and lower bounds of the optimal solution are determined, then using a Bi-section method (root-finding method) the problem is solved. To demonstrate the applicability of this method, we solve a simple example for a manufacturing system with three products. Finally, results of ten experiment that obtain from this method compare to answers from Newton-Raphson method, then it has been shown that this method has great effectiveness and less calculation efforts for the single-machine problem with deteriorating items.

Robust Design of AC Computing-Enabled Receiver Architecture for SWIPT Networks

Inspired by the direct use of alternating current (AC) for computation, we propose a novel integrated information and energy receiver architecture for simultaneous wireless information and power transfer networks. In this context, the AC computing method, in which wirelessly harvested AC energy is directly used to supply the computing block of receivers, enhances not only computational ability but also energy efficiency over the conventional direct current one. Further, we aim to manage the tradeoff between the information decoding and energy harvesting (EH) optimally while taking imperfect channel estimation into account. It results in a worst-case optimization problem of maximizing the data rate under the constraints of an EH requirement, the energy needed for supplying the AC computational logic, and a transmit power budget. Then, we propose a method to derive closed-form optimal solutions. The numerical results demonstrate that the proposed architecture with AC computing significantly improves the rate-energy region.

Cooperative Downlink Interference Transmission and Cancellation for Cellular-Connected UAV: A Divide-and-Conquer Approach

The line-of-sight dominant air-ground channels have posed critical interference issues in cellular-connected unmanned aerial vehicle (UAV) communications. In this paper, we propose a new base station (BS) cooperative beamforming (CB) technique for the cellular downlink to mitigate the strong interference caused by the co-channel terrestrial transmissions to the UAV. Besides the conventional CB by cooperatively transmitting the UAV's message, the serving BSs of the UAVs exploit a novel interference transmission scheme to effectively suppress the terrestrial interference to the UAV. Specifically, the co-channel terrestrial users' messages are shared with the UAV's serving BSs and transmitted via CB to cancel their resultant interference at the UAV. To balance between the CB gains for UAV signal enhancement and interference cancellation, we aim to maximize the UAV's receive signal-to-interference-plus-noise ratio by jointly optimizing the power allocations at all of its serving BSs for transmitting the UAV's and co-channel terrestrial users' messages. First, we derive the closed-form optimal solution to this problem in a special case and draw useful insights. Then, we propose an algorithm to solve the problem optimally in the general case. As the optimal solution requires centralized implementation with exorbitant message/channel information exchanges among the BSs, we further propose a distributed algorithm that is amenable to practical implementation, based on a new divide-and-conquer approach, whereby each co-channel BS divides its perceived interference to the UAV into multiple portions, each to be canceled by a different serving BS of the UAV with its best effort. Numerical results show that the proposed centralized and distributed CB schemes with interference transmission and cancellation (ITC) can both significantly outperform the conventional CB without applying ITC.

Double Full Diversity Massive Unitary Space–Time Codes for MIMO Channels

In this paper, we consider a flat fading noncoherent wireless communication system with double transmitter antennas and massive multiple receiver antennas, in which the channel coherence time is divided into four orthogonal time slots, and these are used within a complete transmission cycle. For such a system, we systematically design a family of noncoherent unitary space–time codes. Then, within this family and with the noncoherent maximum likelihood (ML) detector, we propose the design of an optimal unitary space-time code that minimizes the worst-case pairwise error probability (PEP) subject to a constraint on total transmission bits. A closed-form optimal solution is attained by first characterizing the optimal structure for any fixed bits on each parameter space and then finding an optimal bit assignment that further minimizes the worst-case PEP. Also, asymptotic PEP performance analysis on such an optimal code further shows that it enables full receiver-diversity gain when the number of the receiver antennas goes to infinity, with the increasing rate of the coding gain in terms of signal-to-noise ratio (SNR) being the number of the transmitter antennas. In other words, it also provides full diversity gain, i.e., the product of the number of the receiver antennas and the number of the transmitter antennas, when SNR goes to infinity. Therefore, we call such a code double full diversity code. One of the significant advantages of the proposed optimal design for our considered massive multiple-input multiple-output system is that it has no error floor with SNR increasing. Another significant advantage is that it enables a fast ML detector.

Meta Distribution of SIR in Large-Scale Uplink and Downlink NOMA Networks

We develop an analytical framework to derive the meta distribution and moments of the conditional success probability (CSP), which is defined as success probability for a given realization of the transmitters, in large-scale co-channel uplink and downlink non-orthogonal multiple access (NOMA) networks with one NOMA cluster per cell. The moments of CSP translate to various network performance metrics such as the standard success or signal-to-interference ratio (SIR) coverage probability (which is the 1-st moment), the mean local delay (which is the −1st moment in a static network setting), and the meta distribution (which is the complementary cumulative distribution function of the success or SIR coverage probability and can be approximated by using the 1st and 2nd moments). For the uplink NOMA network, to make the framework tractable, we propose two point process models for the spatial locations of the inter-cell interferers by utilizing the base station (BS)/user pair correlation function. We validate the proposed models by comparing the second moment measure of each model with that of the actual point process for the inter-cluster (or inter-cell) interferers obtained via simulations. For downlink NOMA, we derive closed-form solutions for the moments of the CSP, success (or coverage) probability, mean local delay, and meta distribution for the users. As an application of the developed analytical framework, we use the closed-form expressions to optimize the power allocations for downlink NOMA users in order to maximize the success probability of a given NOMA user with and without latency constraints. Closed-form optimal solutions for the transmit powers are obtained for two-user NOMA scenario. We note that maximizing the success probability with latency constraints can significantly impact the optimal power solutions for low SIR thresholds and favor orthogonal multiple access.

The Optimal Emission Decisions of Sustainable Production with Innovative Baseline Credit Regulations

In the era of the fourth industrial revolution, the international community is striving to establish a coordinated system to prevent fatal climate change in a global sense. As a result of such changes in business environments, a new issue, sustainability, has recently presented a paradigm shift and new research opportunity in which the theories and practices in traditional production and operations management are being reinterpreted and reapplied in relation to this emerging issue. Under this research background, we consider an optimal emission-trading problem under a cap-and-trade (CAT) emission regulation when the customers’ demand is given as an arbitrary probability distribution. Such a CAT approach to reduce the amount of emissions is a normative system for the sustainable production of manufacturing firms, which is also closely related to a well-known open innovation in literature of inventory management. Then, we formulate two stochastic inventory optimization models, which can be applied immediately for two famous CAT policies that exist in reality. In particular, our objective is to draw theoretical and practical implications for baseline credit emission regulations, which are innovative and government-led emission regulation policies, with a well-known newsvendor analysis. For our analytical results, we first show that our objective functions are piecewise linear and (quasi)-concave. Thus, it is found that there exists a unique optimal solution to the problem. Second, we successfully obtain the closed-form optimal solutions for the two models considered. Finally, we conduct a sensitivity analysis through a comparative static analysis to examine how the model parameters can affect the optimal solution in each model. All these analytical results and implications are consistent with previous studies in the literature, as well as with our insights for the models.

Optimal Transmission Using a Self-Sustained Relay in a Full-Duplex MIMO System

This paper investigates wireless information and power transfer in a full-duplex MIMO relay channel where the self-sustained relay harvests energy from both source transmit signal and self-interference signal to decode and forward source information to a destination. We formulate a new problem to jointly optimize power splitting at the relay and precoding design for both the source and relay transmissions. Using duality theory, we establish closed-form optimal primal solutions in terms of the dual variables, based on which we then design a customized and efficient primal-dual algorithm to maximize the achievable throughput. Numerical results demonstrate the rate gains from using multiple transmit and receive antennas in both information decoding and energy harvesting, and the significant benefit of harvesting energy from self-interference signals. We also extend our analysis to the case when channel state information is only available at receiving nodes and show how our algorithm can optimize the power splitting at the relay for it to remain self-sustained. Through analysis and simulation, we demonstrate that an optimal combination of non-uniform power splitting, variable power allocation, and self-interference power harvesting can effectively exploit a full-duplex MIMO system to achieve significant performance gains over existing uniform power splitting and half-duplex transmissions.

Optimal Multicast of Tiled 360 VR Video

In this letter, we study optimal multicast of tiled 360 virtual reality (VR) video from one server (base station or access point) to multiple users. We consider random viewing directions and random channel conditions, and adopt time division multiple access (TDMA). For given video quality, we optimize the transmission time and power allocation to minimize the average transmission energy. For given transmission energy budget, we optimize the transmission time and power allocation as well as the encoding rate of each tile to maximize the received video quality. These two optimization problems are challenging non-convex problems. We obtain globally optimal closed-form solutions of the two non-convex problems, which reveal important design insights for multicast of tiled 360 VR video. Finally, numerical results demonstrate the advantage of the proposed solutions.