Semidefinite Relaxation Approach Research Articles

Joint Beamforming Design in Reconfigurable Intelligent Surface-Assisted Rate Splitting Networks

Reconfigurable Intelligent Surface (RIS) is an emerging technology that can improve the spectrum and energy efficiency of next-generation wireless networks. However, attaining accurate channel state information (CSI) for the cascaded RIS channel is particularly challenging. Imperfect CSI is a major bottleneck to achieving the spectral efficiency benefit of RIS-assisted networks. Rate splitting (RS), a promising multiple access technology, has been shown to be able to achieve an improved spectrum efficiency and be robust to channel uncertainties. This paper investigates the interplay between RIS and RS by considering a RIS-assisted RS beamforming problem. Active beamforming at the base station (BS) and passive beamforming at the RIS are jointly considered to maximize the minimum user rate under both the perfect CSI case and the imperfect CSI case. A block coordinate descent (BCD) algorithm is developed to solve this non-convex problem. Compared with the conventional semi-definite relaxation (SDR) approach, the proposed method does not require that the covariance matrix of the common beamforming vector be rank-one. Moreover, we present theoretical results to help reveal the impact of the system parameters and explain the performance gain resulting from the integration of RIS and RS. Extensive simulation results are also provided to show that RIS-assisted RS can improve the max-min rate performance significantly compared with conventional multiple access technologies, such as non-orthogonal multiple access (NOMA) and space division multiple access (SDMA) with/without RIS, especially in overloaded systems. With the proposed method, RS shows great potential in combating realistic CSI errors in RIS-assisted networks.

New convex approaches to general MVDR robust adaptive beamforming problems

AbstractConsider general minimum variance distortionless response (MVDR) robust adaptive beamforming problems based on the optimal estimation for both the desired signal steering vector and the interference‐plus‐noise covariance (INC) matrix. The optimal robust adaptive beamformer design problem is an array output power maximization problem, subject to three constraints on the steering vector, namely, a (convex or nonconvex) quadratic constraint ensuring that the direction‐of‐arrival (DOA) of the desired signal is separated from the DOA region of all linear combinations of the interference steering vectors, a double‐sided norm constraint, and a similarity constraint; as well as a ball constraint on the INC matrix, which is centered at a given data sample covariance matrix. To tackle the nonconvex problem, a new tightened semidefinite relaxation (SDR) approach is proposed to output a globally optimal solution; otherwise, a sequential convex approximation (SCA) method is established to return a locally optimal solution. The simulation results show that the MVDR robust adaptive beamformers based on the optimal estimation for the steering vector and the INC matrix have better performance (in terms of, e.g., the array output signal‐to‐interference‐plus‐noise ratio) than the existing MVDR robust adaptive beamformers by the steering vector estimation only.

Computation bits enhancement for IRS-assisted multi-UAV wireless powered mobile edge computing systems

Mobile edge computing (MEC) and wireless energy transfer are two important paradigms to improve the computation bits and provide more cost-effective energy for low-power internet of things (IoT) devices. However, the performance of energy transfer and task offloading is significantly affected by propagation loss, and hence the links between IoT devices and transmitters are frequently blocked. To address this issue, in this paper, an intelligent reflecting surfaces (IRS) system is utilized to enhance the energy harvesting and task offloading performances in a multi-unmanned aerial vehicle (UAV)-assisted MEC system. Also, a power beacon (PB) is deployed in the coverage area to provide suitable and stable energy for UAVs via a laser charging system. The sum computation bits of all IoT devices are maximized by jointly optimizing transmit power, time allocation, the phase shift in the energy transfer stage, the phase shift in the task offloading stage, CPU frequency of IoT devices, and UAVs' trajectory. An alternate search method (ASM) is proposed to tackle the non-convexity of the formulated problem in which the closed-form expressions of transmit power, time allocation, the phase shift in the task offloading stage, and CPU frequency are derived. Also, the semidefinite relaxation (SDR) approach and successive convex approximation (SCA) methods are exploited to obtain the phase shifts in the energy transfer stage and UAVs' trajectory via CVX optimizer, respectively. The numerical evaluations confirm the performance gain of the proposed IRS-assisted multi-UAV MEC system compared to existing benchmark designs.

A Semidefinite Relaxation Approach for Mobile Target Localization Based on TOA and Doppler Frequency Shift Measurements

In this paper, we discuss mobile source localization using both time of arrival and Doppler frequency shift (TOA-DFS) measurements, where the source moves at a nonuniform velocity. To obtain the position of a mobile source, we first formulate the weighted least squares (WLS) problem by ignoring the second-order noise terms. Due to the non-convexity, we apply the convex relaxation technique to transform the problem into a semi-definite programming problem. However, ignoring the second-order noise terms is only reasonable in the case of small noise levels. In view of this, we then directly establish the maximum likelihood (ML) estimator based on the measurements model without ignoring the second-order noise terms. Since the ML estimator is a non-convex problem, we also propose implementable semidefinite relaxation (SDR) technique to tackle it. Finally, the Cramér-Rao lower bound (CRLB) analysis and results verify that the proposed methods based on the TOA-DFS measurements can significantly enhance localization accuracy.

Relative Entropy-Based Waveform Optimization for Rician Target Detection With Dual-Function Radar Communication Systems

In this paper, we consider waveform design for dual-function radar-communication systems based on multiple-input-multiple-out arrays. To achieve better Rician target detection performance, we use the relative entropy associated with the formulated detection problem as the design metric. We also impose a multi-user interference energy constraint on the waveforms to ensure the achievable sum-rate of the communications. Two algorithms are presented to tackle the nonlinear non-convex waveform design problem. In the first algorithm, we derive a quadratic function to minorize the objective function. To tackle the quadratically constrained quadratic programming problem at each iteration, a semidefinite relaxation approach followed by a rank-one decomposition procedure and an efficient alternating direction method of multipliers (ADMM) are proposed, respectively. In the second algorithm, we present a novel ADMM algorithm to tackle the optimization problem and employ an efficient minorization-maximization approach in the inner loop of the ADMM algorithm. Numerical results demonstrate the superiority of both algorithms. Moreover, the presented algorithms can be extended to synthesize peak-to-average-power ratio constrained waveforms, which allows the radio frequency amplifier to operate at an increased efficiency.

Elliptic Localization of a Moving Object by Transmitter at Unknown Position and Velocity: A Semidefinite Relaxation Approach

This paper investigates the elliptic localization for moving object problem from time delay (TD) and Doppler frequency shift (DFS) measurements, where the transmitter position and velocity are unknown. The transmitter is not perfectly time syncronized such that unknown offsets exist in the TD and DFS measurements. We propose to jointly estimate the object and transmitter positions and velocities and the offsets. Using the TD and DFS measurements from both the indirect and direct paths between the transmitter and the receivers, we formulate a non-convex weighted least squares (WLS) problem. Local convergence may occur when solving the non-convex WLS problem, implying that good estimate is not guaranteed. Thus, we relax the non-convex WLS problem into a convex semidefinite program by applying semidefinite relaxation (SDR). Moreover, we theoretically show that the performance can be improved by using multiple transmitters as compared to that using single transmitter, although more unknown parameters are introduced. We then extend the proposed SDR method to handle the multiple transmitters case. Finally, the mean square error analysis is provided to show that the proposed WLS method reaches the Cramer-Rao lower bound accuracy under small Gaussian noise condition. Simulation results validate the theoretical analysis and show the superior performance over the existing methods.

MIMO radar design with joint constant-modulus and any p-norm similarity constraints

MIMO radar plays a key role in many applications, e.g., autonomous driving, smart parking, and gesture recognition. The similarity waveform constraint is an important constraint for radar waveform design. However, the joint constant-modulus and similarity constraints pose a big challenge in MIMO radar design. Only the special case with ∞-norm similarity and constant-modulus constraints is tackled by the semidefinite relaxation (SDR) and the successive quadratic refinement (SQR) methods. In this paper, the joint constant-modulus and any p-norm (1≤p≤∞) similarity constraints are tackled by the proposed relax-and-retract algorithm. In particular, the nonconvex constant-modulus constraint is first relaxed to a convex constraint, and then the retract operation is guaranteed to recover a constant-modulus solution within a fixed iteration number. Extensive simulation results show that full range similarity control and constant-modulus constraints are satisfied under different p-norms. For the special case with 1-norm, it is firstly found to be a constant-modulus-inducing norm. For the special case with ∞-norm, the proposed relax-and-retract method has less computational complexity than the SDR and SQR approaches.

Over-the-air beamforming with reconfigurable intelligent surfaces

Reconfigurable intelligent surface (RIS)-empowered communication is a revolutionary technology that enables to manipulate wireless propagation environment via smartly controllable low-cost reflecting surfaces. However, in order to outperform conventional communication systems, an RIS-aided system with solely passive reflection requires an extremely large surface. To meet this challenge, the concept of active RIS, which performs simultaneous amplification and reflection on the incident signal at the expense of additional power consumption, has been recently introduced. In this paper, deploying an active RIS, we propose a novel beamforming concept, over-the-air beamforming, for RIS-aided multi-user multiple-input single-output (MISO) transmission schemes without requiring any pre/post signal processing hardware designs at the transmitter and receiver sides. In the proposed over-the-air beamforming-based transmission scheme, the reflection coefficients of the active RIS elements are customized to maximize the sum-rate gain. To tackle this issue, first, a non-convex quadratically constrained quadratic programming (QCQP) problem is formulated. Then, using semidefinite relaxation (SDR) approach, this optimization problem is converted to a convex feasibility problem, which is efficiently solved using the CVX optimization toolbox. Moreover, taking inspiration from this beamforming technique, a novel high-rate receive index modulation (IM) scheme with a low-complexity sub-optimal detector is developed. Through comprehensive simulation results, the sum-rate and bit error rate (BER) performance of the proposed designs are investigated.

Optimal transmit beamforming for near-field integrated sensing and wireless power transfer systems

The integrated sensing and wireless power transfer (ISWPT) technology, in which the radar sensing and wireless power transfer functionalities are implemented using the same hardware platform, has been recently proposed. In this paper, we consider a near-field ISWPT system where one hybrid transmitter deploys extremely large-scale antenna arrays, and multiple energy receivers are located in the near-field region of the transmitter. Under such a new scenario, we study radar sensing and wireless power transfer performance trade-offs by optimizing the transmit beamforming vectors. In particular, we consider the transmit beampattern matching and max-min beampattern gain design metrics. For each radar performance metric, we aim to achieve the best performance of radar sensing, while guaranteeing the requirement of wireless power transfer. The corresponding beamforming design problems are non-convex, and the semi-definite relaxation (SDR) approach is applied to solve them globally optimally. Finally, numerical results verify the effectiveness of our proposed solutions.

STAR-RIS Integrated Nonorthogonal Multiple Access and Over-the-Air Federated Learning: Framework, Analysis, and Optimization

This paper integrates non-orthogonal multiple access (NOMA) and over-the-air federated learning (AirFL) into a unified framework using one simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). The STAR-RIS plays an important role in adjusting the decoding order of hybrid users for efficient interference mitigation and omni-directional coverage extension. To capture the impact of non-ideal wireless channels on AirFL, a closed-form expression for the optimality gap (a.k.a. convergence upper bound) between the actual loss and the optimal loss is derived. This analysis reveals that the learning performance is significantly affected by the active and passive beamforming schemes as well as wireless noise. Furthermore, when the learning rate diminishes as the training proceeds, the optimality gap is explicitly shown to converge with linear rate. To accelerate convergence while satisfying quality-of-service requirements, a mixed-integer non-linear programming (MINLP) problem is formulated by jointly designing the transmit power at users and the configuration mode of STAR-RIS. Next, a trust region-based successive convex approximation method and a penalty-based semidefinite relaxation approach are proposed to handle the decoupled non-convex subproblems iteratively. An alternating optimization algorithm is then developed to find a suboptimal solution for the original MINLP problem. Extensive simulation results show that i) the proposed framework can efficiently support NOMA and AirFL users via concurrent uplink communications, ii) our algorithms achieve faster convergence rate on IID and non-IID settings compared to existing baselines, and iii) both the spectrum efficiency and learning performance is significantly improved with the aid of the well-tuned STAR-RIS.

A Stackelberg Game Approach for IRS-Aided WPCN Multicast Systems

This paper investigates an intelligent reflecting surface (IRS) aided wireless powered communication network (WPCN) with a focus on multicast transmissions in a game-theoretic way, where a transmitter first harvests energy from a power station (PS) and then transmits the information to multiple Internet of Things (IoT) devices in a multicast form. An IRS is deployed to assist the wireless energy transfer (WET) and wireless information transfer (WIT) processes. Considering that the PS and the transmitter belong to different service providers, we propose two schemes based on Stackelberg game, namely IRS-aided transmitter dominant energy trading (IRS-TDET) with the transmitter as the leader and IRS-aided PS dominant energy trading (IRS-PDET) with the PS as the leader. To solve the non-convex optimization problem of the leader-level game in the IRS-TDET scheme, we first derive the closed-form optimal phase shifts in the WET stage, and then use the semidefinite relaxation approach to solve the max-min problem about the phase shifts of the WIT stage. Finally, a low-complexity alternating optimization algorithm is developed to solve the simplified non-convex optimization problem with regard to the energy price and WET time. Numerical results show that the performance of proposed IRS-TDET and IRS-PDET is superior to that of the corresponding non-IRS aided schemes, and the deployment of IRS can effectively improve the utilities of both the PS and the transmitter. In addition, it is preferred to deploy the IRS near the transmitter in WPCN, and the transmitter can be deployed near the PS or the IoT devices to obtain higher utility.

A semidefinite relaxation approach for the offloading problem in edge computing

In traditional cloud computing, tasks will be offloaded to the could, which often leads to high latency and low quality of service. To avoid this disadvantage, edge computing was introduced. The fundamental issue in edge computing is selecting some tasks to be computed in the edge, which is called the offloading problem. In most previous studies, the communication cost between any two tasks is often assumed to be symmetric in different sides and is often ignored within the same side. In this paper, we consider a heterogeneous offloading model, where the communication cost exists everywhere and is asymmetric. With the help of semidefinite relaxation, we give an algorithm for the offloading problem. If the Laplacian matrix with respect to the offloading problem is positive semidefinite, the theoretical guarantee can be proved to be 2π. The performance of the proposed algorithm is also evaluated via numerical analysis. The experimental results show that the algorithm is very effective.

Mobility-Aware Multi-Hop Task Offloading for Autonomous Driving in Vehicular Edge Computing and Networks

Vehicular Edge Computing (VEC) has gained increasing interest due to its potential to provide low latency and reduce the load in backhaul networks. In order to meet drastically increasing computation demands from emerging ever-growing vehicular applications, e.g., autonomous driving, abundant computation resources of individual vehicles can play a crucial role in task execution in a VEC scenario, that can further contribute in considerably improving user experience. This is however an extremely challenging task due to high mobility of vehicles that can easily lead to intermittent connectivity, thereby disrupting on-going task processing. In this paper, we propose a task offloading scheme by exploiting multi-hop vehicle computation resources in VEC based on mobility analysis of vehicles. In addition to the vehicles within one hop from the task vehicle that generates computation tasks, certain multi-hop vehicles that meet the given requirements in terms of link connectivity and computation capacity, are also leveraged to carry out the tasks offloaded by the task vehicle. An optimization problem is formulated for the task vehicle to minimize the weighted sum of execution time and computation cost of all tasks. A semidefinite relaxation approach with an adaptive adjustment procedure is proposed to solve the formulated optimization problem for obtaining the corresponding offloading decisions. The simulation results show that our proposed offloading scheme can achieve significant improvement in terms of response delay by at least 34% compared with the other algorithms (e.g., local processing and random offloading).

Cramér-Rao Bound Optimization for Joint Radar-Communication Beamforming

In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cram\'er-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can always be obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks.

Adaptive channel estimation for cognitive fully adaptive radar

The paper addresses channel state information estimation for a cognitive radar system. The underlying radar signal model considered in this paper is based on a stochastic Green's function approach. In the radar model, the clutter returns can be expressed as a convolution of the stochastic Green's function impulse response with the transmit radar waveform. The paper proposes and solves constrained channel estimation algorithms that exploit the cosine similarity constraint and the inner product constraint to improve conventional least squares solutions. Using the fact that adjacent channel transfer functions have a close relationship in terms of a cosine similarity metric, the cosine similarity constraint can be exploited in the least squares problem. It turns out that the derived optimisation problem under the cosine similarity constraint is non-convex. However, since strong duality holds for the non-convex optimisation problem, it can be solved using the semi-definite relaxation (SDR) approach. The paper also proposes a new optimisation problem with an additional inner product constraint, which results in a convex second-order cone programming (SOCP) and is robust to the signal-to-noise ratio (SNR) in terms of the cosine similarity measurement. Numerical simulations are provided to verify the performance of the proposed methods on a challenge dataset generated using the high-fidelity modelling and simulation tool, RFView®.

Joint optimization scheme for intelligent reflecting surface aided multi‐relay networks

The latest research on hybrid networks of decode-and-forward (DF) relay and intelligent reflecting surface (IRS) is limited to just a single relay. To harvest multiple relay gains, this paper proposes a hybrid communication networks that combines multiple DF relays with an IRS. The authors formulate and address the joint optimization problem to maximize the end-to-end transmission rate by jointly optimizing the reflect beam forming, the best relay selection and the power allocation, subject to total transmit power constraint. Moreover, to better exploit the degrees of freedom, it is proposed that the source also transmits signals in the second time slot. While the optimization problem is difficult to solve, the authors propose some efficient approaches to make the problem tractable. First, power allocation problem is simplified by applying Cauchy-Schwarz inequality and introducing equivalent channel gain, second, non-convex rank-one constraint is overcome by utilizing semidefinite relaxation (SDR) approach, then the slacked non-convex constraint is overcome by applying first-order Taylor expansion approximation. The simulation results demonstrate that our proposed joint optimization scheme for hybrid networks of multiple DF relays with an IRS has significant performance improvement over the other optimization schemes, such as the optimization scheme for hybrid networks of single DF relay and an IRS.

Optimal Beamforming for IRS-Assisted SWIPT System with an Energy-Harvesting Eavesdropper

In this paper, we study a simultaneous wireless information and power transfer (SWIPT) system aided by the intelligent reflecting surface (IRS) technology, where an AP transmits confidential information to the legitimate information receiver (IR) in the presence of an energy harvesting (EH) receiver that could be a potential eavesdropper. We aim to maximize the secrecy rate at the legitimate IR by jointly optimizing the information beamforming vector and the energy transfer beamforming vector at the access point (AP), and the phase shift matrix at the IRS, subject to the minimum harvested power required by the EH receiver. The semi-definite relaxation (SDR) approach and the alternating optimization (AO) method are proposed to convert the original non-convex optimization problem to a series of semi-definite programs (SDPs), which are solved iteratively. Numerical results show that the achievable secrecy rate of the proposed IRS-assisted SWIPT system is higher than that of the SWIPT system without the assistance of the IRS.

Joint Service Caching, Computation Offloading and Resource Allocation in Mobile Edge Computing Systems

Mobile Edge Computing (MEC) brings abundant cloud resources to the edge of the network and provides great opportunities to improve user's quality of experience. While many recent studies have investigated the problem of computation offloading, service caching is also an important design topic of MEC. Service caching stores application-related databases or libraries in advance and enables corresponding user tasks to be offloaded. Due to the limited resources in the edge server, service caching decisions have to be made judiciously to maximize the system performance. In this paper, we study the problem of joint service caching, computation offloading, transmission and computing resource allocation in a general scenario of multiple users with multiple tasks. We aim to minimize the overall computation and delay costs for all users and formulate the optimization problem as a quadratically constrained quadratic program (QCQP) which is non-convex and NP-hard. To solve this challenging problem, we propose an efficiently approximate algorithm based on semidefinite relaxation (SDR) approach and alternating optimization which always computes a locally optimal solution. Moreover, we extend the study to the scenario where each user has a computation cost constraint. Simulation results show that our algorithm can minimize the system cost effectively by utilizing the available system resources.

RIS Optimization on the Complex Circle Manifold for Interference Mitigation in Interference Channels

In this paper, we investigate the use of reconfigurable intelligent surfaces (RIS) to allow multiple user pairs to communicate simultaneously over the same channel. We propose a Riemannian manifold optimization approach to solve the problem of configuring the RIS passive reflection coefficients to minimize the total interference under constant modulus constraints. We compare the proposed approach to the widely-used semidefinite relaxation approach (SDR) for dealing with the constant modulus constraints. We investigate, using extensive numerical simulations, the effects of various system parameters, such as the number of users, the number of RIS elements, and the fraction of power received through the RIS. Our results demonstrate that RISs can substantially minimize interference allowing multiple user pairs to simultaneously communicate over the same channel and that the proposed approach vastly outperforms the semidefinite relaxation-based approach, which fails to find satisfactory solutions.

Max–min fair robust beamforming design for underlay device‐to‐device communications in cellular networks

SummaryThis paper investigates the robust downlink beamforming designs based on max–min fairness and base station (BS) power consumption constraint for device‐to‐device (D2D) communications underlaying cellular network, under the assumption of imperfect channel state information (CSI) at the BS. Our objective is to maximize the minimum signal‐to‐interference‐plus‐noise ratio (SINR) or non‐outage probability of users while guaranteeing that the consumed power at the BS is less than a threshold. In particular, three max–min fairness scenarios are considered. In the first scenario, the worst‐case SINR of cellular users (CUs) is maximized where the D2D SINR is guaranteed to be above a specified predetermined threshold. In the second scenario, we extend the first scenario and maximized D2D SINR while maximizing CUs' SINR. In these two scenarios, it is assumed that the errors are upper bounded in their Frobenius norms. In the third scenario, the minimum non‐outage probability of users is maximized, while a probabilistic model is considered for the uncertainty of channel covariance matrices. Although such optimization problems are not convex, the semidefinite relaxation (SDR) approach is used to obtain the optimal beamforming matrix, which always complies the rank‐one constraint. Simulation results show that significant improvement in terms of minimum SINR of CUs, the minimum non‐outage probability of CUs, and the probability of feasibility and the fairness index can be achieved with our proposed algorithms in comparison with other beamforming schemes.