Robust Cognitive Beamforming With Bounded Channel Uncertainties

This paper studies the robust beamforming design for a multi-antenna cognitive radio (CR) network, which transmits to multiple secondary users (SUs) and coexists with a primary network of multiple users. We aim to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINRs) of the SUs, subject to the constraints of the total SU transmit power and the received interference power at the primary users (PUs) by optimizing the beamforming vectors at the SU transmitter based on imperfect channel state information (CSI). To model the uncertainty in CSI, we consider a bounded region for both cases of channel matrices and channel covariance matrices. As such, the optimization is done while satisfying the interference constraints for all possible CSI error realizations. We shall first derive equivalent conditions for the interference constraints and then convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation, which leads to iterative algorithms for obtaining the robust optimal beamforming solution. Results demonstrate the achieved robustness and the performance gain over conventional approaches and that the proposed algorithms can obtain the exact robust optimal solution with high probability.      

Robust beamforming in cognitive radio

This letter considers the multi-antenna cognitive radio (CR) network, which has a single secondary user (SU) and coexists with a primary network of multiple users. Our objective is to maximize the service probability of the SU, subject to the interference constraints on the primary users (PUs) in the form of probability. Exploiting imperfect channel state information (CSI), with its error modeled by added Gaussian noise, we address the optimization for the beamforming weights at the secondary transmitter. In particular, this letter devises an iterative algorithm that can efficiently obtain the robust optimal beamforming solution. For the case with one PU, we show that a much simpler algorithm based on a closed-form solution for the antenna weights of a given power can be presented. Numerical results reveal that the optimal solution for the constructed problem provides an effective means to tradeoff the performance between the PUs and the SU, bridging the non-robust and worstcase based systems.     

非理想信道状态信息下RIS辅助的安全通信

利用可重构智能表面(Reconfigurable Intelligent Surface, RIS)辅助无线发射机,可提高多用户无线网络的安全传输能力。在非理想信道状态信息(Channel State Information, CSI)下提出了鲁棒波束形成优化方法来提高系统对抗干扰和窃听攻击的能力。具体地,使用RIS辅助发射机,对RIS的相位波束形成和基站的传输功率进行联合优化,在分别满足有界CSI的最坏情况速率约束和统计CSI的速率中断概率约束来最小化系统的总传输功率。由于存在CSI误差,针对有界CSI和统计CSI误差约束,分别利用S-procedure来松弛保密速率约束和大偏差不等式(Large Deviation Inequality, LDI)来松弛保密速率中断概率约束。仿真结果表明,相比于无源反射法和传统波束形成方案,该方法可分别降低约88%和93%总传输功率,同时提高约15 dBm和12 dBm的干扰容限。     

面向窃听用户的RIS-MISO系统鲁棒资源分配算法

针对信道不确定性影响、用户信息泄露和能效提升等问题,该文提出一种基于不完美信道状态信息的可重构智能反射面(RIS)多输入单输出系统鲁棒资源分配算法。首先,考虑能量收集最小接收功率约束、合法用户最小保密速率约束、基站最大发射功率约束及RIS相移约束,基于有界信道不确定性,建立一个联合优化基站主动波束、能量波束、RIS相移矩阵的多变量耦合非线性资源分配问题。然后,利用Dinkelbach,S-procedure和交替优化方法,将原非凸问题转换成确定性凸优化问题,并提出一种基于连续凸近似的交替优化算法。仿真结果表明,与传统非鲁棒算法对比,所提算法具有较低的中断概率。     

Joint beamforming and power control in downlink multiuser multiple‐input multiple‐output systems

In this paper, we study joint beamforming and power control for downlink multiple‐input multiple‐output systems with multiple users and target values for signal‐to‐interference plus noise ratios (SINRs). We formulate this as a constrained optimization problem of minimizing total interference subject to constraints on the beamforming vector norms, target SINRs, and total transmit power. Necessary and sufficient conditions satisfied by the optimal beamformer and power allocation are presented, and a new algorithm for joint beamforming and power control is proposed. This adapts the beamforming vectors and transmit powers incrementally, and it stops when the specified SINR targets are achieved with minimum powers. The proposed algorithm is illustrated with numerical results obtained from simulations, which study its convergence and compare it with other similar algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Low complexity margin adaptive resource allocation in downlink MIMO-OFDMA system

We study the downlink multiuser Multiple Input Multiple Output-Orthogonal Frequency Division Multiple Access (MIMO-OFDMA) system for margin adaptive resource allocation where the Base Station (BS) has to satisfy individual Quality of Service (QoS) constraints of the users subject to transmit power minimization. Low complexity solutions involve beamforming techniques for multiuser inter-stream interference cancellation. However, when beamforming is introduced in the margin adaptive objective, it becomes a joint beamforming and resource allocation problem. We propose a sub-optimal twostep solution which decouples beamforming from subcarrier and power allocation. First a reduced number of user groups are formed and then the problem is formulated as a convex optimization problem. Finally an efficient algorithm is developed which allocates the best user group to each subcarrier. Simulation results reveal comparable performance with the hugely complex optimal solution.     

Robust beamforming in the MISO downlink with quadratic channel estimation and optimal training

Estimation of the channel state information (CSI) in quadratic form (i.e., quadratic channel estimation) in the downlink can be performed at the base station by using the relayed signals from the mobile users, which facilitates optimization with transmitter CSI. In this letter, the condition for the optimal training sequence for quadratic channel estimation in a multiuser multiple-input single-output (MISO) antenna system in the downlink is first obtained. The mean-square-error (MSE) in the CSI estimate is then analyzed. Based on the quadratic CSI estimates, a robust beamforming optimization algorithm to minimize the base station power while achieving individual users' quality-of-service (QoS) constraints, measured by the MSE in data reception, is proposed.     

多用户MISO干扰信道中的安全协同波束成形

针对多用户多输入单输出(MISO, multiple-input single-output)干扰信道中保密信息泄露问题,提出了理想信道状态信息(CSI, channel state information)下的安全协同波束成形(SCB, secure coordinated beamforming)方案和非理想CSI下的顽健安全协同波束成形(RSCB, robust secure coordinated beamforming)方案。对于理想CSI情况,联合设计最优的协同波束成形向量,最大化最小安全速率。采用半定松弛(SDR, semidefinite relaxation)技术和连续的凸估计(SCA, successive convex approximation)算法得到原始非凸问题的局部最优解。进一步,将该框架扩展到信道向量和信道协方差矩阵存在确定误差的情况,提出的RSCB方案能够最大化最差情况的安全速率。仿真结果验证了所提方案的有效性和顽健性。     

Worst-case performance optimization for robust power control in downlink beamforming

In this paper,¹ we examine the problem of robust power control in a downlink beamforming environment under uncertain channel state information (CSI). We suggest that the method of power control using the lower bounds of signal-to-interference-and-noise ratio (SINR) is too pessimistic and will require significantly higher power in transmission than is necessary in practice. Here, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach employs the explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices and optimizes the amount of transmission power while guaranteeing the worst-case performance to satisfy the quality of service (QoS) constraints for all users. This optimization problem is non-convex and intractable. In order to arrive at an optimal solution to the problem, we propose an iterative algorithm to find the optimum power allocation and worst-case uncertainty matrices. The iterative algorithm is based on the efficient solving of the worst-case uncertainty matrices once the transmission power is given. This can be done by finding the solutions for two cases: (a) when the uncertainty on the DCC matrices is small, for which a closed-form optimum solution can be obtained and (b) when the uncertainty is substantial, for which the intractable problem is transformed into a convex optimization problem readily solvable by an interior point method. Simulation results show that the proposed robust downlink power control using the approach of worst-case performance optimization converges in a few iterations and reduces the transmission power effectively under imperfect knowledge of the channel condition.     

Optimal precoder design for non‐regenerative multiple‐input multiple‐output cognitive relay systems with perfect and imperfect channel state information

This paper studies optimal precoder design for non‐regenerative multiple‐input multiple‐output (MIMO) cognitive relay systems, where the secondary user (SU) and relay station (RS) share the same spectrum with the primary user (PU). We aim to maximize the system capacity subject to the transmit power constraints at the SU transmitter (SU‐Tx) and RS, and the interference power constraint at the PU. We jointly optimize precoders for the SU‐Tx and RS with perfect and imperfect channel state information (CSI) between the SU‐Tx/RS and PU, where our design approach is based on the alternate optimization method. With perfect CSI, we derive the optimal structures of the RS and SU‐Tx precoding matrices and develop the gradient projection algorithm to find numerical solution of the RS precoder. Under imperfect CSI, we derive equivalent conditions for the interference power constraints and convert the robust SU‐Tx precoder optimization into the form of semi‐definite programming. For the robust RS precoder optimization, we relax the interference power constraint related with the RS precoder to be convex by using an upper bound and apply the gradient projection algorithm to deal with it. Simulation results demonstrate the effectiveness of the proposed schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

基于不完美CSI的D2D通信网络鲁棒能效资源分配算法

针对设备到设备(D2D)直连通信网络传统最优资源分配算法在随机信道时延、信道估计误差影响下鲁棒性弱的问题,该文在考虑参数不确定性影响的条件下,提出D2D用户总能效最大的鲁棒资源分配算法。考虑干扰功率门限、用户最小速率需求、最大传输功率和子信道分配约束,建立了下垫式频谱共享模式下多用户D2D网络资源分配模型。基于有界信道不确定性模型,利用最坏准则方法将原非凸鲁棒资源分配问题转换为确定性的凸优化问题。然后利用拉格朗日对偶理论求得资源分配的解析解。仿真结果表明所提出的算法具有很好的鲁棒性。     

Outage Probability Based Robust Distributed Beam-Forming in Multi-User Cooperative Networks with Imperfect CSI

In this paper, a new robust problem is proposed for relay beamforming in relay system with stochastic perturbation on channels of multi user and relay network. The robust problem aims to minimize the transmission power of relay nodes while the imperfect channel information (CSI) injects stochastic channel uncertainties to the parameters of optimization problem. In the power minimization framework, the relays amplification weights and phases are optimized assuming the availability of Gaussian channel distribution. The power sum of all relays is minimized while the outage probability of the instantaneous capacity (or SINR) at each link is above the outage capacity (or SINR) for each user. The robust problem is a nonconvex SDP problem with Rank constraint. Due to the nonconvexity of the original problem, three suboptimal problems are proposed. Simulation and numerical results are presented to compare the performance of the three proposed solutions with the existing worst case robust method.     

KKT-based iterative algorithm for beamforming in cognitive radio system

In this paper,we consider the downlink channel of multi-user multi-input single-output(MU-MISO)system in cognitive radio network,where the cognitive base station(CBS)resort to beamforming scheme to relief co-channel interference.The design criterion is to minimize the transmit power at CBS,subject to the signal-to-interference-plus-noise-ratio(SINR)constraints of cognitive users(CUs)and the interference constraints at primary users(PUs).Standard conic optimization packages can handle the problem,however,the...     

Optimal Relaying Beamforming in Multiple Access Broadcast Channel (MABC) Bidirectional Cognitive Radio Networks in Presence of Interferers

In this paper, a general cognitive radio system consisting of a set of users with different level of spectrum access including two primary transceivers and several types of secondary users is considered. It is assumed that two secondary users operate based on an underlay model at the same frequency bandwidth and at the same time as the primary users based on a multiple access broadcast channel bidirectional beamforming scheme. Other secondary users provide a relaying service to the primary users in exchange for the opportunity to send their messages towards their own destinations for a fixed portion of the communication cycle. In addition, it is assumed that some interferers are active during the communication cycle and cause interference for the network. Furthermore, it is assumed that only partial channel state information (CSI) between interferers and other nodes in the network is available. We provide a robust optimization method against imperfection on the interferers’ CSI to maximize the joint primary and secondary signal-to-interference-plus-noise-ratio with the assumption of limited available power at the secondary relays. An amplify-and-forward relaying scheme is deployed at the secondary relays and the optimal beamforming is obtained using second order convex programming method. The simulation results show the performance of the proposed beamforming method against the existence of interferers, and demonstrate the effectiveness of our robust method against uncertainty in knowledge of interferers’ CSIs.     

Multi-cell uplink-downlink beamforming throughput duality based on Lagrangian duality with per-base station power constraints

Despite significant research efforts in beamforming, the maximum achievable downlink throughput with beamforming in a multi-cell environment is not available due to difficulty in finding optimal downlink beamforming. Thus, to reformulate the problem into a more solvable form, we derive dual uplink throughput optimization problem to multi-cell downlink beam- forming throughput maximization with per-base station (BS) power constraints based on Lagrangian duality. The optimal downlink beamforming is shown to be a minimum mean squared error (MMSE) beamforming in the dual uplink. It is also shown that the dual uplink problem achieves the same optimal throughput as the primal downlink problem.     

User clustering and robust beamforming design in multicell MIMO-NOMA system for 5G communications

In this paper, we present a robust beamforming design to tackle the weighted sum-rate maximization (WSRM) problem in a multicell multiple-input multiple-output (MIMO) – non-orthogonal multiple access (NOMA) downlink system for 5G wireless communications. This work consider the imperfect channel state information (CSI) at the base station (BS) by adding uncertainties to channel estimation matrices as the worst-case model i.e., singular value uncertainty model (SVUM). With this observation, the WSRM problem is formulated subject to the transmit power constraints at the BS. The objective problem is known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an robust beamforming design which establishes on majorization minimization (MM) technique to find the optimal transmit beamforming matrix, as well as efficiently solve the objective problem. In addition, we also propose a joint user clustering and power allocation (JUCPA) algorithm in which the best user pair is selected as a cluster to attain a higher sum-rate. Extensive numerical results are provided to show that the proposed robust beamforming design together with the proposed JUCPA algorithm significantly increases the performance in term of sum-rate as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.     

Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

The problem of joint beamforming and power allocation for cognitive multi-input multi-output systems is studied via game theory. The objective is to maximize the sum utility of secondary users (SUs) subject to the primary user (PU) interference constraint, the transmission power constraint of SUs, and the signal-to-interference-plus-noise ratio (SINR) constraint of each SU. In our earlier work, the problem was formulated as a non-cooperative game under the assumption of perfect channel state information (CSI). Nash equilibrium (NE) is considered as the solution of this game. A distributed algorithm is proposed which can converge to the NE. Due to the limited cooperation between the secondary base station (SBS) and the PU, imperfect CSI between the SBS and the PU is further considered in this work. The problem is formulated as a robust game. As it is difficult to solve the optimization problem in this case, existence of the NE cannot be analyzed. Therefore, convergence property of the sum utility of SUs will be illustrated numerically. Simulation results show that under perfect CSI the proposed algorithm can converge to a locally optimal pair of transmission power vector and beamforming vector, while under imperfect CSI the sum utility of SUs converges with the increase of the transmission power constraint of SUs.     

非理想信道状态信息的认知无线网络下行功率分配和波束赋形方法

针对非理想信道状态信息(CSI)条件下工作于underlay模式的认知无线网络(CRN)多用户下行功率分配和波束赋形研究中普遍存在的问题,包括忽略主网络(PN)对认知用户(SU)的干扰、传统的凸优化SDR方法对约束条件的近似要求以及实现算法复杂、实用性受限等,首先建立CRN模型,增添PN对SU的干扰项,而后在非理想CSI的最差条件下形成优化问题。再通过Lagrange对偶对问题的约束条件进行变换,并基于变换后的问题形式,利用上行和下行的对偶特性,引入虚拟功率,将优化问题转换为上行功率分配和波束赋形问题,进一步得到简便、快速和实用的迭代算法。数值仿真显示,算法收敛很快。并且发现非理想CSI引起的误差不仅对下行功率影响明显而且还改变优化问题的可行解区域;PN基站(PBS)的发送功率的变化对可行解区域有显著的影响。     

Robust Tomlinson-Harashima Precoders for Multiuser MISO Downlink with Imperfect CSI

In this paper, we consider robust non-linear precoding for the downlink of a multiuser multiple-input single-output (MISO) communication system in the presence of imperfect channel state information (CSI). The base station (BS) is equipped with multiple transmit antennas and each user terminal is equipped with a single receive antenna. We propose two robust Tomlinson-Harashima precoder (THP) designs. The first design is based on the minimization of the total BS transmit power under constraints on the mean square error (MSE) at the individual user receivers. We show that this problem can be solved by an iterative procedure, where each iteration involves the solution of a pair of convex optimization problems that can be solved efficiently. A robust linear precoder with MSE constraints can be obtained as a special case of this robust THP. The second design is based on the minimization of a stochastic function of the sum MSE under a constraint on the total BS transmit power. We formulate this design problem as an optimization problem that can be solved by the method of alternating optimization, the application of which results in a second-order cone program that can be numerically solved efficiently. Simulation results illustrate the improvement in performance of the proposed precoders compared to other robust linear and non-linear precoders in the literature.     

Optimal Precoder Design for Non-Regenerative MIMO Cognitive Two-Way Relay Systems with Underlay Spectrum Sharing

We study the optimal precoder design for a MIMO cognitive two-way relay system with underlay spectrum sharing. The system consists of two secondary users (SUs) and one relay station (RS). We jointly optimize the precoders for SUs and RS with perfect and imperfect channel state information (CSI) between SUs/RS and the primary user, where our design approach is based on the alternate optimization method. For the perfect CSI case, we derive the optimal structure of the RS precoding matrix, which generalizes the result for single-antenna SUs and helps to reduce the search complexity. We develop gradient projection (GP) algorithm to calculate the optimal RS precoder numerically. When the RS precoder is given, we propose a fast algorithm based on generalized water-filling theorem to compute the optimal SU precoders. For the imperfect CSI case, we derive equivalent conditions for the interference power constraints and convert the robust SU precoder optimization into the form of semi-definite programming. As for the robust RS precoder optimization, we relax the interference power constraint related with the RS precoder to be convex and then the GP algorithm can be applied. Finally, simulation results demonstrate the effectiveness of the proposed schemes.