Power allocation schemes for wireless powered NOMA systems with imperfect CSI: An application in multiple antenna–based relay

The simultaneous wireless information and power transfer or energy harvesting (EH) can be combined in nonorthogonal multiple access (NOMA) as green applications towards 5G. This paper investigates a new cooperative EH‐NOMA protocol, where the intermediate relay has not equipped the fixed power source and acts as a wireless powered relay to help signal transmission to representative weak user and strong user in NOMA. However, impacts of imperfect channel estimation contribute to outage system performance evaluations. We formulate the power resource assignment paradigms as two schemes, namely, fixed power allocation and dynamic power allocation, by considering imperfect channel state information (CSI). To solve this problem, we derive the closed‐form expressions of outage probability under imperfect CSI and the power allocation constraints. The expected numerical results related to the derived expressions for the outage probability are examined that numerical and the Monte Carlo simulations are strictly matching lines.     

Three-phase two-way relaying with imperfect channel estimation and asymmetric traffic requirements: performance analysis and optimization

We study the effect of imperfect channel estimation (ICE) and asymmetric traffic requirements (ATRs) on the performance of bidirectional relaying with a direct link by employing three-phase analog network coding under Nakagami-m fading. Under such a realistic scenario, a tight lower bound on the overall outage probability is derived in closed-form, while a useful expression is presented for the asymptotically low outage regime. We also deduce the tight closed-form expression for the ergodic sum-rate. Furthermore, we formulate and solve analytically three optimization problems viz., relay power allocation under fixed location of the relay, relay position with fixed relay power allocation, and joint optimization of relay power allocation and location. Our results reveal that for given ICE, the optimal relay location offers significant system performance enhancement under ATRs, whilst the optimal relay power allocation has a more noticeable impact under symmetric traffic. It is also shown that the joint optimization of relay power allocation and location can further enhance the system performance, regardless of ATRs and ICE. Above all, based on the direct link quality, we show that the considered scheme outperforms its two-phase counterpart, even in the low signal-to-noise ratio regime.

     

Performance Analysis of Dual-Hop AF Relay Networks in the Presence of Channel Estimation Errors and Feedback Delay

In this letter, we investigate the performance of multiple-input multiple-output two hop beamforming amplify-and-forward (AF) relay networks under imperfect channel state information (CSI) including channel estimation errors (CEE) and feedback delay (FD). To quantify the effect of imperfect CSI on our considered network, we derive the closed-form expression for the outage probability. To gain more insight, we also present an asymptotic analysis which provides the details of the diversity order and array gain. Through our works, one can see the effect of CEE and FD on the system as well as the benefits of deploying multiple antennas at the terminals. Numerical and simulation results are provided to verify the analysis and compare the performance of the considered network for two different models for channel estimation error.     

Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

In this paper, we presents an analytical link capacity and outage performance analysis of downlink multiuser diversity (MUD) in multiple-input multiple-output (MIMO) system employing maximal-ratio combining (MRC) with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The unified achievable analysis is appropriate for MUD–MIMO with TAS/MRC systems in which effective output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form channel capacity and outage probability expressions are examined for the MUD–MIMO exploiting TAS/MRC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate upper bound capacity as well as capacity at high SNR and low SNR region under delayed feedback CSI. The upper and lower bound of outage probability under delayed feedback CSI is also evaluated. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.     

Outage Performance of Cognitive AF Relay Networks with Imperfect CSI Based on Geometrical Analysis

This paper studies the outage performance of a cognitive Amplify-and-forward (AF) relay network subject to Rayleigh fading.Under the condition of imperfect Channel state information (CSI) estimations of the links from the secondary system to the Primary user (PU),the closed-form upper and lower bounds of the outage probability are derived through a geometrical analysis method.An asymptotic analysis of the outage probability is also derived in the high Signal-to-noise ratio (SNR) regime to gain additional insights on the system.The simulation results corroborate our theoretical analysis,and the effectiveness of the geometrical analysis method is verified with the conventional approach as a benchmark.The asymptotic results are very tight with the analytical lower bound in the high SNR regime.It also can be observed from the simulation results that the impact of the number of relays as well as the imperfect CSI on the outage probability and the diversity order.     

Opportunistic Relay Selection with Outdated CSI: Outage Probability and Diversity Analysis

In this paper, we analyze the outage probability and diversity order of opportunistic relay selection in a scenario based on decode and forward and where the available channel state information (CSI) is outdated. The study is conducted analytically by obtaining a closed-form expression for the outage probability, which is defined as the probability that the instantaneous capacity is below a target value. We derive high-SNR approximations for the outage probability. By doing so, we demonstrate that the diversity order of the system is reduced to 1 when CSI is outdated, being this behavior independent of the level of CSI accuracy. A physical explanation for this extreme loss of diversity is provided along with numerical results to support the analytical study.     

On the information throughput and optimized power allocation for MIMO wireless systems with imperfect channel estimation

In this paper, we focus on the throughput analysis, outage evaluation and optimized power allocation for Multiple-Input Multiple-Output (MIMO) pilot-based wireless systems subject to short-term constraints on the radiated power and equipped with a feedback-path for communicating back to the transmitter the imperfect MIMO channel estimates available at the receiver. The case of the ergodic throughput for Gaussian distributed input signals is analyzed, and the conditions for the (asymptotical) achievement of the Shannon capacity are pointed out. The main contributions of this work may be so summarized. First, we develop closed-form analytical expressions for the computation of the ergodic information throughput conveyed by the considered MIMO system for the case of ideal feedback link. Second, we present an iterative algorithm for the optimized power allocation over the transmit antennas that explicitly accounts for the imperfect MIMO channel estimates available at the receiver. Third, after relaxing the assumption of ideal feedback link, we test the sensitivity of the proposed power allocation algorithm on errors possibly introduced by the feedback channel, and then, we numerically evaluate the resulting throughput loss. Finally, we develop closed-form upper and lower bounds on the outage probability that are asymptotically tight.     

Outage probability of multiple-input single-output (MISO) systems with delayed feedback

We investigate the effect of feedback delay on the outage probability of multiple-input single-output (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect CSIR and (b) CSI estimated at the receiver using training symbols. With perfect CSIR, under a short-term power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BF-IC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BF-IC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a longterm power constraint, we show that BF-IC is better for low SNR and USPA is better at high SNR. With imperfect CSIR, we obtain an upper bound on the outage probability with USPA and BF-IC. Results show that the loss in performance due to imperfection in CSIR is not significant, if the training power is chosen appropriately.     

基于双向中继和网络编码的NOMA网络性能分析

针对实际场景中存在的具有上下行双向传输任务的通信系统,本文提出了一种双向中继协作非正交多址接入(NOMA, non-orthogonal multiple access)传输方案,基于解码转发(DF, Decode and Forward)协议研究信号的上行和下行双向传输技术,与现有NOMA方案不同,本方案为近端用户分配较大的功率,利用网络编码(NC, network coding)原理在两个时隙内实现基站和用户之间的双向信息交换。进一步考虑不完美信道状态信息(CSI, Channel State Information)条件,分析系统的传输性能并推导了系统中断概率以及遍历和速率闭合表达式。仿真结果表明,在完美CSI和不完美CSI条件下,相比于现有文献所提方案、单向中继(OWR,One-Way Relay)和正交多址(OMA, Orthogonal Multiple Access)网络,本文所提方案有效降低了系统的传输中断概率,提高了系统的遍历和速率以及系统吞吐量。      

Joint user pairing and power allocation in uplink virtual MIMO with imperfect CSI

User pairing strategy for virtual multi-input multi-output （VMIMO） has been widely studied to improve system throughput, but most studies are based on perfect channel state information （CSI） and uniform power allocation. However, perfect CSI is very difficult or even impossible to obtain in practical system. Moreover power allocation has significant impact on algorithm performance. Therefore, in this paper, a low-complex joint user pairing and power allocation algorithm based on aggressive discrete stochastic optimization and Lagrangian dual solution is proposed for uplink VMIMO with imperfect CSI. Simulation results show that the proposed algorithm can achieve desirable throughput performance, and restrict inter-user interference （IUI） efficiently.     

Power allocation for AF relaying aided spatial modulation in the presence of imperfect channel state information

By combining Spatial modulation (SM) with cooperative communication, the diversity gain brought by cooperative relaying and high rate of SM can be obtained. In this paper, considering amplify-and-forward (AF) protocol, the performance of cooperative SM system with imperfect channel state information (CSI) over Rayleigh channel is analyzed. According to the performance analysis, the moment generating functions (MGFs) of effective signal-to-noise ratios (SNRs) are derived. With the MGFs, closed-form expressions of the error probability of antenna index detection and the error probability of symbol detection for imperfect CSI are achieved. Thereby, the approximate overall average bit error ratio (BER) is obtained, and these theoretical expressions include those under perfect CSI as special cases. Besides, the asymptotically approximate BER for large SNR is also derived. Based on this, a suboptimal power allocation (PA) scheme is developed, and the corresponding PA coefficients are attained by minimizing the asymptotical BER. As a result, closed-form PA can be attained for the system with multiple receive antennas. Computer simulations show that the theoretical BERs are close to the corresponding simulated results, which illustrates the effectiveness of the derived theoretical expressions. Compared with the conventional equal PA scheme, the proposed PA scheme enhances the BER performance efficiently.     

Ergodic capacity and outage probability optimization for secondary user in cognitive radio networks under interference outage constraint

This paper considers a cognitive radio network where a secondary user (SU) coexists with a primary user (PU). The interference outage constraint is applied to protect the primary transmission. The power allocation problem to jointly maximize the ergodic capacity and minimize the outage probability of the SU, subject to the average transmit power constraint and the interference outage constraint, is studied. Suppose that the perfect knowledge of the instantaneous channel state information (CSI) of the interference link between the SU transmitter and the PU receiver is available at the SU, the optimal power allocation strategy is then proposed. Additionally, to manage more practical situations, we further assume only the interference link channel distribution is known and derive the corresponding optimal power allocation strategy. Extensive simulation results are given to verify the effectiveness of the proposed strategies. It is shown that the proposed strategies achieve high ergodic capacity and low outage probability simultaneously, whereas optimizing the ergodic capacity (or outage probability) only leads to much higher outage probability (or lower ergodic capacity). It is also shown that the SU performance is not degraded due to partial knowledge of the interference link CSI if tight transmit power constraint is applied.     

具有不完全信道状态信息MIMO系统的优化设计

 本文研究了不完全信道状态信息(CSI)对多输入多输出(MIMO)系统容量的影响.基于平均功率和平均误码率的约束条件,我们提出了一种利用不完全CSI进行功率自适应调制的优化设计方案.根据Wishart矩阵的统计分布,我们导出了该系统容量的封闭表达式.研究结果表明:在具有不完全CSI的MIMO系统中,利用不完全CSI进行设计可以显著地提高系统的容量.     

Variable rate and variable power MQAM system based on bayesian bit error rate and channel estimation techniques

The impact of inaccurate channel state information at the transmitter for a variable rate variable power multilevel quadrature amplitude modulation (VRVP-MQAM) system over a Rayleigh flat-fading channel is investigated. A system model is proposed with rate and power adaptation based on the estimates of instantaneous signal-to-noise ratio (SNR) and bit error rate (BER). A pilot symbol assisted modulation scheme is used for SNR estimation. The BER estimator is derived using a maximum a posteriori approach and a simplified closed-form solution is obtained as a function of only the second order statistical characterization of the channel state imperfection. Based on the proposed system model, rate and power adaptation is derived for the optimization of spectral efficiency subject to an average power constraint and an instantaneous BER requirement. The performance of the VRVP-MQAM system under imperfect channel state information (CSI) is evaluated. We show that the proposed VRVP-MQAM system that employs optimal solutions based on the statistical characterization of CSI imperfection achieves a higher spectral efficiency as compared to an ideal CSI assumption based method.     

Performance of cognitive relay network with energy harvesting relay under imperfect CSI

This paper evaluates the performance of an underlay cognitive relay network under imperfect channel state information (CSI) where a secondary user (SU) transmits using a secondary relay (SR) based on decode and forward scheme. The outage probability (OP) of SU is investigated in a scenario where the decode and forward relay harvests energy from radio frequency signal of SU. The relay uses a fraction of time for harvesting in time switching–based relaying (TSR) while a fraction of received power is used for harvesting in power splitting–based relaying (PSR) scheme. The SU and relay control their transmit power using a scaling factor, based on CSI of the interfering links (ie, links from SU transmitter and SR to the primary user [PU] receiver) to protect the quality of service of PU. The available CSI at the SU and SR are imperfect due to practical limitation. Analytical expressions of the OP are derived for TSR‐ and PSR‐based schemes. The impact of harvesting time, power splitting ratio, imperfect CSI, PU outage constraint and interference threshold on the OP of the SU network, and average transmit power of SR is indicated. Further, the impact of multiple SRs is also shown.     

Communication with causal CSI and controlled information outage

In this letter, a Rayleigh block-fading (BF) channel, subject to an information outage probability constraint, is considered. The transmitter is assumed to have causal knowledge of the channel state information (CSI), which is exploited to intelligently allocate the power over the blocks (and hence vary the channel mutual information) to minimize the average transmitted power per block for satisfying the outage probability constraint for a given target code-rate. We first show that the optimal solution to this problem can be obtained by solving the reverse problem of minimizing the outage probability for a range of long-term power constraints through repeated uses of dynamic programming (DP), which is nevertheless prohibitively complex. Then, we develop a suboptimal allocation algorithm which still uses DP to exploit the CSI causality but at a much reduced complexity. A performance lower-bound is further derived, which permits us to see that the proposed algorithm is near-optimal, especially in the small outage probability regime. A scheme called equal-outage-probability per block (EOPPB) which compromises the performance further for reducing the complexity is also devised. To compare the methods, we evaluate both analytically and numerically their complexities and performance. The results are finally generalized to multipleinput multiple-output (MIMO) BF channels.     

MIMO解码转发双向中继系统中的传输策略与中断概率分析

在多输入多输出(MIMO)解码转发(DF)双向中继系统中,分别设计了两种信道状态信息(CSI)情况下的系统传输策略,并推导了系统中断概率的闭合表达式.当已知完全CSI时,采用(最大比发送-最大比接收)MRT-MRC技术设计波束形成和合并向量;当未知完全CSI时,设计了基于有限反馈的传输策略,并采用随机向量量化和Grassmann两种码本进行数值仿真验证.仿真结论显示,所设计的双向中继传输策略的中断概率性能明显优于其他策略,所推导的闭合表达式能准确地表征系统中断概率性能.     

Outage analysis of the hybrid free-space optical and radio-frequency channel

We study the hybrid free-space optical (FSO) and radio-frequency (RF) channel from an information theoretic perspective. Since both links operate at vastly different carrier frequencies, we model the hybrid channel as a pair of parallel channels. Moreover, since the FSO channel signals at a higher rate than the RF channel, we incorporate this key feature in the parallel channel model. Both channels experience fading due to scintillation, which is slow compared to typical signalling rates. Under this framework, we study the fundamental limits of the hybrid channel. In particular, we analyse the outage probability in the large signal-to-noise ratio (SNR) regime, and obtain the outage diversity or SNR exponent of the hybrid system. First we consider the case when only the receiver has perfect channel state information (CSIR case), and obtain the exponents for general scintillation distributions. These exponents relate key system design parameters to the asymptotic outage performance and illustrate the benefits of using hybrid systems with respect to independent FSO or RF links. We next consider the case when perfect CSI is known at both the receiver and transmitter, and derive the optimal power allocation strategy that minimises the outage probability subject to peak and average power constraints. The optimal solution involves non-convex optimisation, which is intractable in practical systems. We therefore propose a suboptimal algorithm that achieves significant power savings (on the order of tens of dBs) over uniform power allocation. We show that the suboptimal algorithm has the same diversity as the optimal power allocation strategy.     

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。     

Performance analysis of maximum ratio transmission with imperfect channel estimation

Maximal ratio transmission (MRT) is designed assuming the availability of perfect channel state information (CSI) at both the transmitter and the receiver. However, perfect CSI is not available in practice. This paper investigates the impact of Gaussian estimation errors on the MRT performance in independently and identically distributed (i.i.d.) Rayleigh fading channels. We derive the cumulative distribution function (cdf), the probability density function (pdf) and the moment generating function (mgf) of the MRT output signal-to-noise ratio (SNR) with imperfect CSI, enabling the evaluation of some useful performance metrics such as the average error rate and the outage performance. Numerical and simulation results are provided to show the impact of imperfect CSI on the MRT performance.