Polyblock Outer Approximation Research Articles

Secure Computation Offloading for Marine IoT: An Energy-Efficient Design via Cooperative Jamming

In smart ocean, the Marine Internet of Things (M-IoT) is ubiquitously used for data acquisition, communication connections, task computation, and so on. However, high-efficient energy consumption and secure yet low-latency transmission are subject to IoT devices' computation capacity and transmit power limitation, as well as wireless communication's broadcast characteristics. In this paper, we investigate the secure computation offloading in M-IoT with the assistance of unmanned surface vehicles (USVs) subject to the eavesdropping attack. In particular, we consider a scenario in which USVs are firstly scheduled to set up a high-quality communication link to the high altitude platform (HAP) and then exploited to provide cooperative jamming for the communication security at the physical layer when the HAP is performing computation offloading. We jointly optimize the USVs' positions, the duration of data uploading, the workload offloaded by HAP, the HAP's transmission power, and each USV's jamming signal power to minimize the system-wise energy consumption for completing the total workloads under the latency constraint. Despite the non-convexity, we decompose the problem vertically into a top problem that optimizes the USVs' positions and a bottom problem that optimizes the other variables. The Polyblock outer Approximation and bisection Search based algorithm (PAS-Algorithm) is proposed to alternatively optimize the variables in the bottom problem. And the Code bAsed croSs Entropy algorithm (CASE-Algorithm) is proposed to obtain the suboptimal solution to the formulated joint optimization problem. Numerical results validate the accuracy and effectiveness of our algorithms as well as the performance of optimizing the total energy consumption compared with the benchmark algorithms

Performance Tradeoff of MVNOs in OFDMA-Based Virtualized Wireless Networks

In this paper, we analyze the tradeoff between the profits gained by mobile virtual network operators (MVNOs) in an orthogonal frequency division multiple access (OFDMA)-based virtualized wireless networks (VWNs). In this respect, MVNOs rent the network resources from a mobile network operator (MNO) to create virtual resources based on allocated rates and the cost due to allocated transmit powers in two different strategies: resource-based isolation strategy and rate-based isolation strategy. In resource-based isolation strategy, it is assumed that the whole bandwidth in each base station is divided equally between MVNOs whereas in rate-based isolation strategy, the whole bandwidth in each base station is allocated dynamically between MVNOs. We then formulate a multi-objective optimization problem (MOOP) to show the tradeoff between the maximum profit of each MVNO. To solve the formulated MOOP, we adopt the weighted Tchebycheff approach, which can provide the complete Pareto optimal region for nonconvex problems. Thus, by developing such formulation, we will be able to find the best profit gained by MVNOs. We also employ monotonic optimization to obtain the global optimal solutions of the non-convex problems by applying polyblock outer approximation algorithm. Our numerical results show the importance of the aforementioned tradeoffs and confirm that the proposed geometric programming (GP) based algorithm achieves excellent performance as compared to the monotonic method.

Association and Caching in Relay-Assisted mmWave Networks: A Stochastic Geometry Perspective

Limited backhaul bandwidth and blockage effects are two main factors limiting the practical deployment of millimeter wave (mmWave) networks. To tackle these issues, we study the feasibility of relaying as well as caching in mmWave networks. A user association and relaying (UAR) criterion dependent on both caching status and maximum biased received power is proposed by considering the spatial correlation caused by the coexistence of base stations (BSs) and relay nodes (RNs). Using stochastic geometry tools, we decouple the UAR and caching placement issues by analyzing the relationship between UAR probabilities and caching placement probabilities. We then optimize the formulated caching placement problem based on polyblock outer approximation by exploiting the monotonic property in the general case and utilizing convex optimization in the noise-limited case. Accordingly, we propose a BS and RN selection algorithm where caching status at BSs and maximum biased received power are jointly considered. Experimental results demonstrate a significant enhancement of backhaul offloading using the proposed algorithms, and show that deploying more RNs and increasing cache size in mmWave networks is a more cost-effective alternative than increasing BS density to achieve similar backhaul offloading performance.

Energy Efficiency Maximization in the Uplink Delta-OMA Networks

Delta-orthogonal multiple access (D-OMA) has been recently investigated as a potential technique to enhance the spectral efficiency in the sixth-generation (6G) networks. D-OMA enables partial overlapping of the adjacent sub-channels that are assigned to different clusters of users served by non-orthogonal multiple access (NOMA), at the expense of additional interference. In this paper, we analyze the performance of D-OMA in the uplink and develop a multi-objective optimization framework to maximize the uplink energy efficiency (EE) in a multi-access point (AP) network enabled by D-OMA. Specifically, we optimize the sub-channel and transmit power allocations of the users as well as the overlapping percentage of the spectrum between the adjacent sub-channels. The formulated problem is a mixed binary non-linear programming problem. Therefore, to address the challenge we first transform the problem into a single-objective problem using Tchebycheff method. Then, we apply the monotonic optimization (MO) to explore the hidden monotonicity of the objective function and constraints, and reformulate the problem into a standard MO in canonical form. The reformulated problem is then solved by applying the outer polyblock approximation method. Our numerical results show that D-OMA outperforms the conventional non-orthogonal multiple access (NOMA) and orthogonal frequency division multiple access (OFDMA) when the adjacent sub-channel overlap and scheduling are optimized jointly.

Latency Minimization for Wireless Powered Mobile Edge Computing Networks With Nonlinear Rectifiers

This paper investigates a wireless powered mobile edge computing (MEC) network where a hybrid access point (H-AP) serves energy-constrained devices. For such a wireless powered MEC network, the H-AP first transmits wireless information and energy simultaneously in the downlink. Then, by utilizing the harvested energy, the device processes both its local data and the received data from the H-AP. In this system, we minimize the latency by jointly optimizing the power splitting ratio of rectifiers, the data offloading power, the local computing frequency, and the data offloading ratio at the device. By applying a polyblock outer approximation procedure, we propose an algorithm which guarantees the optimal solution. Simulation results verify the efficiency of the proposed algorithm compared to conventional schemes.

Resource Allocation for Non-Orthogonal Multiple Access-Enabled Fog Radio Access Networks

Non-orthogonal multiple access (NOMA) has been considered as a promising communication technology to enhance the spectral efficiency and support massive connections in fog radio access networks (F-RANs). In this paper, with the aim of maximizing the weighted sum rate while taking co-channel interference into consideration, a joint resource block (RB) and power allocation problem is formulated. To solve this problem, we first propose the optimal resource allocation scheme. Specifically, the monotonic optimization is applied and an outer polyblock approximation algorithm is proposed to get the global optimal solution. In order to reduce the computational complexity, we then propose the suboptimal resource allocation scheme. In particular, the original problem is decomposed into separated RB and power allocation problems. The RB allocation problem is modeled as a many-to-one matching game and a modified swap-enabled matching algorithm is proposed. The power allocation problem is converted into a convex form through some approximations and solved by a successive convex approximation algorithm. Simulation results demonstrate that the suboptimal scheme can achieve almost the same performance as the optimal scheme, while requiring much less computational complexity. In addition, the superiority of NOMA-enabled F-RANs over the conventional OMA-enabled F-RANs is verified.

3D UAV Trajectory and Communication Design for Simultaneous Uplink and Downlink Transmission

In this paper, we investigate the unmanned aerial vehicle (UAV)-aided simultaneous uplink and downlink transmission networks, where one UAV acting as a disseminator is connected to multiple access points (AP), and the other UAV acting as a base station (BS) collects data from numerous sensor nodes (SNs). The goal of this paper is to maximize the system throughput by jointly optimizing the 3D UAV trajectory, communication scheduling, and UAV-AP/SN transmit power. We first consider a special case where the UAV-BS and UAV-AP trajectories are pre-determined. Although the resulting problem is an integer and non-convex optimization problem, a globally optimal solution is obtained by applying the polyblock outer approximation (POA) method based on the problem's hidden monotonic structure. Subsequently, for the general case considering the 3D UAV trajectory optimization, an efficient iterative algorithm is proposed to alternately optimize the divided sub-problems based on the successive convex approximation (SCA) technique. Numerical results demonstrate that the proposed design is able to achieve significant system throughput gain over the benchmarks. In addition, the SCA-based method can achieve nearly the same performance as the POA-based method with much lower computational complexity.

Multiobjective Optimization Based Sensor Selection for TDOA Tracking in Wireless Sensor Network

This paper investigates the sensor selection problem in time difference of arrival (TDOA) tracking scenario to find the optimal sensor activation strategy for the upcoming time step. We propose a multiobjective optimization framework to minimize two conflicting objectives, i.e., tracking accuracy and quantity budget, which are represented by the trace of the conditional posterior Cramér Rao lower bound (CPCRLB) and the number of selected sensors, respectively. Due to the reduced measurement dimension and correlated noise caused by the common reference sensor (CRS), sensor selection algorithms for the general nonlinear model in existing literature cannot be applied to the TDOA tracking directly as they mostly assume that each sensor produces an independent measurement. Therefore, we introduce two Boolean vectors to indicate the CRS and ordinary sensors respectively. The sensor selection problem is then formulated as a multiobjective optimization problem (MOP), which can be further transformed as a single objective optimization problem (SOOP) using the linear weighted-sum method. We prove that the SOOP satisfies the rules of discrete monotonic optimization (DMO), and propose the polyblock outer approximation (POA)-based algorithms to seek for a globally optimal solution. For comparison, we introduce the conventional semidefinite program (SDP)-based algorithm to solve the SOOP with multi-step relaxation. Simulation results demonstrate that the proposed POA-based algorithms can considerably outperform the SDP-based ones in solving the optimization problem.

Secure Users Oriented Downlink MISO NOMA

This paper proposes a secure users oriented multiple-input and single-output (MISO) non-orthogonal multiple access (NOMA) downlink transmission scheme, where multiple legitimate users are categorized as quality of service (QoS)-required users (QU) and the security-required users (SU) overheard by a passive eavesdropper. The basic idea is to exploit zero-forcing beamforming (ZFBF) to cancel interference among SUs, and then several QUs are efficiently scheduled based on the obtained beamforming vectors to divide the legitimate users into several user clusters, in such a way that the QUs could share the concurrent transmissions and help to interfere with the eavesdropper to enhance SU secrecy. The goal is to maximize the achievable minimum secrecy rate (MSR) and sum secrecy rate (SSR) of all SUs, respectively, subject to the secrecy outage probability (SOP) constraint of each SU and the QoS constraint of each QU. To provide a comprehensive investigation we consider two extreme cases that the eavesdropper has perfect multiuser detection ability (lower bound of secrecy) or does not have multiuser detection ability (upper bound of secrecy). In the lower bound case, the Dinkelbach algorithm and the monotonic optimization (MO)-based outer polyblock approximation algorithm are proposed to solve the max-min secrecy rate (MMSR) and max-sum secrecy rate (MSSR) problems, respectively. As for the upper bound case, an alternative optimization (AO)-based algorithm is proposed to solve the two non-convex problems. Finally, the superiority of the proposed cases to the conventional orthogonal multiple access (OMA) one is verified by numerical results.

Weighted Sum-Rate Maximization for the Ultra-Dense User-Centric TDD C-RAN Downlink Relying on Imperfect CSI

The weighted sum-rate maximization problem of ultra-dense cloud radio access networks is considered. The user-centric clustering is adopted for reducing the complexity. To reduce the training overhead, one only needs to estimate the intra-cluster channel-state information (CSI), while only the large-scale channel gains are available outside the cluster. We first derive the rate lower bound (LB) relying on Jensen’s inequality. For the special case of non-overlapping clusters, the accurate data rate expression is derived in the closed form. The simulation results show the tightness of the LB for both the overlapped and non-overlapped cases. Then, we consider an alternative problem where the actual data rate is replaced by its LB, which constitutes a non-convex optimization problem. First, the globally optimal solution is obtained by applying the high-complexity outer polyblock approximation (OPA) algorithm. Then, we invoke the reduced-complexity modified weighted minimum mean square error (WMMSE) algorithm for mitigating the deleterious effects of the realistic imperfect CSI. For the subproblem solved by each WMMSE iteration, the beamforming vectors are derived in the closed form relying on the Lagrangian dual decomposition method. Finally, our simulation results show that the modified WMMSE algorithm’s performance is comparable to that of the high-complexity OPA algorithm, which outperforms other benchmark algorithms.

Joint Spectrum Sensing and Resource Allocation in Multi-Band-Multi-User Cognitive Radio Networks

In this paper, the joint spectrum sensing and resource allocation problem is investigated in a multi-band-multi-user cognitive radio (CR) network. Assuming imperfect spectrum sensing information, our goal is to jointly optimize the sensing threshold and power allocation strategy such that the average total throughput of secondary users (SUs) is maximized. In Addition, the power of SUs is constrained to keep the interference introduced to primary users under certain limit, which gives rise to a nonconvex mixed integer non-linear programming (MINLP) optimization problem. Our contribution in this paper is threefold. First, it is illustrated that the dimension of the nonconvex MINLP problem can be significantly reduced, which helps to re-formulate the optimization problem without resorting to integer variables. Second, it is demonstrated that the simplified formulation admits the canonical form of a monotonic optimization, and an $\epsilon $ -optimal solution can be achieved using the polyblock outer approximation algorithm. Third, a practical low-complexity spectrum sensing and resource allocation algorithm is developed to reduce the computational cost. Finally, the effectiveness of proposed algorithms is verified by simulations.

Secure Routing with Power Optimization for Ad-hoc Networks

In this paper, we consider the problem of joint secure routing and transmit power optimization for a multi-hop ad-hoc network under the existence of randomly distributed eavesdroppers following a Poisson point process (PPP). Secrecy messages are delivered from a source to a destination through a multi-hop route connected by multiple legitimate relays in the network. Our goal is to minimize the end-to-end connection outage probability (COP) under the constraint of a secrecy outage probability (SOP) threshold, by optimizing the routing path and the transmit power of each hop jointly. We show that the globally optimal solution could be obtained by a two-step procedure where the optimal transmit power has a closed-form and the optimal routing path can be found by Dijkstra's algorithm. Then a friendly jammer with multiple antennas is applied to enhance the secrecy performance further, and the optimal transmit power of the jammer and each hop of the selected route is investigated. This problem can be solved optimally via an iterative outer polyblock approximation with one-dimension search algorithm. Furthermore, suboptimal transmit powers can be derived using the successive convex approximation (SCA) method with a lower complexity. Simulation results show the performance improvement of the proposed algorithms for both non-jamming and jamming scenarios, and also reveal a non-trivial trade-off between the numbers of hops and the transmit power of each hop for secure routing.

Robust beamforming designs for multiuser MISO downlink with per-antenna power constraints

This paper studies the robust beamforming designs for a multiuser multiple-input single-output (MISO) downlink system. Different from the conventional sum-power constraint across all transmit antennas, we consider individual power constraints per antenna at the base station. Assuming that the channel uncertainty is bounded by a spherical region, we develop the optimal robust designs to maximize the minimum worst-case signal-to-interference-plus-noise ratio (SINR) among all users. Specifically, we show that the optimal max-min SINR beamformers can be obtained by solving a sequence of “dual” min-max power problems. Relying on the S-procedure and the linear matrix inequality representation for the cone of Lorentz-positive maps (LPMs), respectively, two designs, which are referred to as Robust-SP and Robust-LPM, are proposed to efficiently solve such min-max power problems. Building on either Robust-SP or Robust LPM, a bisection search algorithm is then developed to find the robust max-min SINR beamformers with guaranteed global optimality and geometrically fast convergence speed. Using the max-min SINR solutions as a cornerstone, we further put forth the optimal robust design for the worst-case weighted sum-rate (WSR) maximization. By formulating the worst-case WSR maximization problem into a monotonic program (MP), we develop a polyblock outer approximation algorithm to obtain the globally optimal solution. Numerical results are presented to demonstrate the merits of the proposed robust beamforming designs.

Joint admission control and beamforming design for the interference cognitive radio network with partial channel state information case

In order to effectively utilise the spectrum of wireless network, secondary users (SUs) are often authorised to share spectrum with primary users (PUs) in cognitive networks. To guarantee effective transmission of PUs and SUs, the interference from the SUs to the PUs is limited and only the SUs that have the information rates (rates) than the corresponding thresholds are allowed to transmit their data. In order to select proper SUs to transmit and to maximise their achievable weighted sum rate (WSR) under rate requirement and interference constraint, the authors propose a joint admission control and beamforming design algorithm for partial channel state information (CSI) case. The WSR maximisation problem is first constructed by using approximation and convex relaxation, according to the statistical property of the CSI. Then a penalty factor is introduced to check the feasibility of such problem and instruct the admission of the SUs. Beyond the feasible SUs set, the WSR is maximised by updating the achievable rate of each user with rate profile technique and polyblock outer approximation method. Simulation results show that the proposed beamforming can achieve higher WSR than the beamforming of the existing baseline method.

Multicell Coordinated Beamforming With Rate Outage Constraint—Part II: Efficient Approximation Algorithms

This paper studies the coordinated beamforming (CoBF) design for the multiple-input single-output interference channel, provided that only channel distribution information is known to the transmitters. The problem under consideration is a probabilistically constrained optimization problem which maximizes a predefined system utility subject to constraints on rate outage probability and power budget of each transmitter. Our recent analysis has shown that the outage-constrained CoBF problem is intricately difficult, e.g., NP-hard. Therefore, the focus of this paper is on suboptimal but computationally efficient algorithms. Specifically, by leveraging on the block successive upper bound minimization (BSUM) method in optimization, we propose a Gauss-Seidel type algorithm, called distributed BSUM algorithm, which can handle differentiable, monotone and concave system utilities. By exploiting a weighted minimum mean-square error (WMMSE) reformulation, we further propose a Jocobi-type algorithm, called distributed WMMSE algorithm, which can optimize the weighted sum rate utility in a fully parallel manner. Both algorithms are shown to converge to the stationary points of the original NP-hard problems. To further provide a performance benchmark, a relaxed approximation method based on polyblock outer approximation is also proposed. Simulation results show that the proposed algorithms are significantly superior to the existing successive convex approximation method in both performance and computational efficiency, and can yield promising approximation performance by comparing with the performance benchmark.

Achieving Global Optimality for Joint Source and Relay Beamforming Design in Two-Hop Relay Channels

This paper deals with joint source and relay beam- forming (BF) design for an amplify-and-forward (AF) multi- antenna multirelay network. Considering that the channel state information (CSI) from relays to a destination is imperfect, we aim to maximize the worst-case received signal-to-noise ratio (SNR). The associated optimization problem is then solved in two steps. In the first step, by fixing the source BF vector, a semi-closed-form solution of the relay BF matrices is obtained, up to a power- allocation factor. In the second step, the global optimal source BF vector is obtained based on the polyblock outer approximation (PA) algorithm. We also propose two low-complexity methods for obtaining the source BF vector, which differ in their complexity and performances. The optimal joint source and relay BF solution obtained by the proposed algorithms serves as the benchmark for evaluating the existing schemes and the proposed low-complexity methods. Simulation results show that the proposed robust design can significantly reduce the sensitivity of the channel uncertainty to the system performance. Index Terms—Amplify and forward (AF), beamforming (BF), global optimal, multiantenna multirelay system.

Achieving Maximum Weighted Sum-Rate in Multicell Downlink MISO Systems

This paper considers the maximization of the weighted sum-rate (WSR) in multicell downlink multiple-input single-output (MISO) systems. The problem is non-convex and thus cannot be solved directly via conventional convex optimization methods. To achieve global optimality, we propose a novel monotonic optimization approach where a sensible search scheme first checks the feasibility of a chosen point and then utilizes a sequential partition method at each iteration to reduce the total number of feasibility evaluations. Besides, another relocating procedure also accelerates the convergence. Simulation results verify the improved convergence performance of the proposed approach compared with the previously proposed outer polyblock approximation algorithm and the branch-reduce-and-bound algorithm.

Achieving Global Optimality for Weighted Sum-Rate Maximization in the K-User Gaussian Interference Channel with Multiple Antennas

Characterizing the global maximum of weighted sum-rate (WSR) for the K-user Gaussian interference channel (GIC), with the interference treated as Gaussian noise, is a key problem in wireless communication. However, due to the users' mutual interference, this problem is in general non-convex and thus cannot be solved directly by conventional convex optimization techniques. In this paper, by jointly utilizing the monotonic optimization and rate profile techniques, we develop a new framework to obtain the globally optimal power control and/or beamforming solutions to the WSR maximization problems for the GICs with single-antenna transmitters and single-antenna receivers (SISO), single-antenna transmitters and multi-antenna receivers (SIMO), or multi-antenna transmitters and single-antenna receivers (MISO). Different from prior work, this paper proposes to maximize the WSR in the achievable rate region of the GIC directly by exploiting the facts that the achievable rate region is a "normal" set and the users' WSR is a "strictly increasing" function over the rate region. Consequently, the WSR maximization is shown to be in the form of monotonic optimization over a normal set and thus can be solved globally optimally by the existing outer polyblock approximation algorithm. However, an essential step in the algorithm hinges on how to efficiently characterize the intersection point on the Pareto boundary of the achievable rate region with any prescribed "rate profile" vector. This paper shows that such a problem can be transformed into a sequence of signal-to-interference-plus-noise ratio (SINR) feasibility problems, which can be solved efficiently by existing techniques. Numerical results validate that the proposed algorithms can achieve the global WSR maximum for the SISO, SIMO or MISO GIC.

Robust Monotonic Optimization Framework for Multicell MISO Systems

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasi-convex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.

Monotonic Optimization Framework for the Two-User MISO Interference Channel

Resource allocation and transmit optimization for the multiple-antenna Gaussian interference channel are important but difficult problems. The spatial degrees of freedom can be exploited to avoid, align, or utilize the interference. In recent literature, the upper boundary of the achievable rate region has been characterized. However, the resulting programming problems for finding the sum-rate, proportional fair, and minimax (egalitarian) operating points are non-linear and non-convex. In this paper, we develop a non-convex optimization framework based on monotonic optimization by outer polyblock approximation. First, the objective functions are represented in terms of differences of monotonic increasing functions. Next, the problems are reformulated as maximization of increasing functions over normal constraint sets. Finally, the idea to approximate the constraint set by outer polyblocks is explained and the corresponding algorithm is derived. Numerical examples illustrate the advantages of the proposed framework compared to an exhaustive grid search approach.