Outage performance of amplify-and-forward two-way relaying with asymmetric traffics

This letter conducts the outage analysis for an amplify-and-forward (AF) based two-way relaying by jointly considering outage events at the two senders with asymmetric traffics. Unlike the current research activities, our goal is to explore the impact of traffic asymmetry on the system outage probability. We first derive the exact expressions of outage probability for the AF scenario over Rayleigh fading channels. To gain more insight, approximated expressions are developed at high signal-to-noise ratio (SNR) region. After that we interestingly find that the asymmetry of system traffics has significant impact on the system outage probability and the outage probability in the system is determined only by the one-way channel or related simultaneously to the two-way links, depending on the level of asymmetry between the two senders’ information rates. Simulation experiments are done. The simulation results verify our propositions and validate the accuracy of our derived expressions.     

Diversity combining with imperfect channel estimation

The optimal diversity-combining technique is investigated for a multipath Rayleigh fading channel with imperfect channel state information at the receiver. Applying minimum mean-square error channel estimation, the channel state can be decomposed into the channel estimator spanned by channel observation, and the estimation error orthogonal to channel observation. The optimal combining weight is obtained from the first principle of maximum a posteriori detection, taking into consideration the imperfect channel estimation. The bit-error performance using the optimal diversity combining is derived and compared with that of the suboptimal application of maximal ratio combining. Numerical results are presented for specific channel models and estimation methods to illustrate the combined effect of channel estimation and detection on bit-error rate performance.     

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.     

Performance analysis of multi-antenna relay networks with imperfect channel estimation

In this paper, we present the performance of multi-antenna selective combining decode-and-forward (SC-DF) relay networks over independent but non-identical Nakagami-m fading channels with imperfect channel estimation. The outage probability, moment generating function (MGF) and symbol error probability (SEP) will be derived in closed-form using the SNR statistical characteristics. To make the analysis trackable, we have derived the MGF and SEP for integer values of fading severity, m. Also, to make the relations more simple, we develop high signal to noise ratio (SNR) analysis for the performance metrics of our system. Subsequently, we propose optimal and adaptive power allocation algorithms along with the equal power allocation method. Finally, for comparison with analytical formulas, we perform some Monte-Carlo simulations.     

非理想信道估计下的放大转发协同通信系统性能分析

针对两跳多中继放大转发协同通信系统,分析了信道估计误差对系统性能的影响。考虑机会中继和全参与中继两种中继策略,分别推导了系统误码率的闭式表达式,并分析了不同信道估计质量阶数下的系统分集增益。平均信噪比损失率分析表明机会中继较全参与中继对信道估计误差更为敏感。仿真结果验证了理论分析。     

Outage analysis of ANC in the FDD two-way fading channel with channel estimation error

This paper considers a frequency-division duplex (FDD) two-way channel with channel estimation error, where channel gains are independent of each other. It derives the exact closed-form outage probability expressions in the FDD system with analog network coding (ANC) by use of probability theory. To provide more insights, an approximated version for the exact outage probability is also developed in the medium-to-high signal-to-noise ratio (SNR) region. The simulation results show that the derived exact outage probabilities match the results of Monte Carlo simulations in all SNR regions, while the approximated outage probabilities also approach the simulation results when the channel condition is good. It is interesting that ANC in the FDD two-way channel is proved to outperform that of in the time-division duplex (TDD) channel by the computer simulation.     

多中继双向协作转发的分布式实现方案设计及其渐进最优性分析

研究了多个双向中继协作传输的分布式实现方案,并给出了其渐进最优性的理论分析.首先,通过高信噪比近似推导出系统均方误差函数的上界,并且利用该上界建立了相应的数学模型;其次,通过矩阵变换和公式推导得到该数学模型的最优解;最后得到相应的分布式实现方案.该方案避免了集中式处理方案中需要"每个中继必须获知整个系统的全部信道信息"这一苛刻条件,而只需要"每个中继获知各自的前后信道信息"就能达到多个双向中继协作转发的效果.所提方案不但避免了集中式处理所需要的中央控制器和很大的反馈开销,而且获得了明显的性能增益.理论分析表明该方案具有渐进最优性.     

Performance analysis of cooperative diversity for two-way multi-relay system with channel estimation error

In this work, we consider an amplify-and-forward two-way multi-relay system for wireless communication and investigate the effect of channel estimation error on the error rate performance. With the derivation of effective signal-to-noise ratio at the transceiver and its probability density function, we can get approximate expression for average bit error rate. Simulation results are performed to verify the analytical results.     

非理想信道估计下迫零接收的空间相关多输入多输出空分复用系统的误码率分析

分析了非理想信道估计和发射空间相关信道下,采用迫零接收的多输入多输出空分复用无线通信系统的误码率性能.基于随机矩阵理论,导出了闭合形式的M-PSK和M-QAM误码率近似解析表达式,并通过仿真验证了表达式的有效性.所获得的表达式形式简单、便于数值计算,可以用于系统性能评估.     

Energy efficiency optimization of one-way and two-way DF relaying considering circuit power

In this paper, the energy efficiency (EE) of a decode and forward (DF) relay system is studied, where two sources communicate through a half-duplex relay node in one-way and two-way relaying strategies. Both the circuitry power and the transmission power of all nodes are taken into consideration. In addition, three different coding schemes for two-way DF relaying strategy with two phases and two-way DF relaying with three phases are considered. The aim is to maximize the EE of the system for a constant spectral efficiency (SE). For this purpose, the transmission time and the transmission power of each node are optimized. Simulations are used to compare the EE–SE curve of different DF strategies with one-way and two-way amplify and forward (AF) strategies and direct transmission (DT), to find the best energy efficient strategy in different SE conditions. Analytical and simulation results demonstrate that in low SE conditions, DF relaying strategies are more energy efficient compared to that of AF strategies and DT. However, in high SE conditions, the EE of two-way AF relaying and DT strategy outperform some of the DF relaying strategies. In simulations, the impact of different circuitry power and different channel conditions on the EE–SE curves are also investigated.     

Effects of imperfect channel sensing and estimation on the performance of cognitive radio systems

In realistic scenarios of cognitive radio (CR) systems, imperfect channel sensing may occur due to false alarms and miss detections. Channel estimation between the secondary user transmitter and another secondary user receiver is another challenge in CR systems, especially for frequency‐selective fading channels. In this context, this paper presents a study of the effects of imperfect channel sensing and channel estimation on the performance of CR systems. In particular, different methods of channel estimation are analyzed under channel sensing imperfections. Initially, a CR system model with channel sensing errors is described. Then, the expectation maximization (EM) algorithm is implemented in order to learn the channel fading coefficients. By exploiting the pilot symbols and the detected symbols at the secondary user receiver, we can estimate the channel coefficients. We further compare the proposed EM estimation algorithm with different estimation algorithms such as the least squares (LS) and linear minimum mean square error (LMMSE). The expressions of channel estimates and mean squared errors (MSE) are determined, and their dependencies on channel sensing uncertainty are investigated. Finally, to reduce the complexity of EM algorithm, a sub‐optimal algorithm is also proposed. The obtained results show that the proposed sub‐optimal algorithm provides a comparable bit error rate (BER) performance with that of the optimal one yet with less computational complexity.     

Error performance of selection combining and switched combining systems in Rayleigh fading channels with imperfect channel estimation

In this paper, we present a general analysis of the performance of selection combining (SC), switch-and-stay combining (SSC), and switch-and-examine combining (SEC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The complex channel estimate and the actual fading are modeled as jointly Gaussian random variables. For SC systems with channel estimation error, closed-form expressions are obtained for the error rates of M/sub s/-ary pulse amplitude modulation (PAM) and rectangular-quadrature amplitude modulation (QAM), and simple single integral formulas with finite integration limits are derived for the symbol error probability of arbitrary two-dimensional (2-D) modulation formats. These error probability expressions are then applied to three types of channel estimation errors potentially encountered in practical systems to study their impact on the performance of selection diversity. Moreover, single integral formulas with finite integration limits are derived for the performance of SSC and SEC systems with minimum mean square error (MMSE) channel estimation. Optimum switching thresholds for 2-D modulation formats with MMSE based switched combining are acquired through numerical computation.     

非完美信道估计下大规模天线系统设计和研究

为满足用户对无线网络容量和覆盖范围日益提升的需求,大规模天线技术得到了广泛的研究。然而,在非完美信道估计情况下,大规模天线系统的天线数应该如何配置仍是一个亟需解决的问题。现考虑了一个发射端配备大规模天线阵列,且上行信道估计存在误差的系统模型,并以能量效率为优化准则,使用两种算法推导出了最优天线配置策略的闭式解,并通过仿真验证了该策略的优异性能。     

Optimizing antenna configuration for MIMO systems with imperfect channel estimation

We study the optimal antenna configuration (i.e. number of transmit and receive antennas) for multiple-input multiple-output systems in pilot-symbol-assisted modulation schemes with imperfect channel estimation. We assume block flat-fading channels and focus on a practical range of high signal-to-noise ratio. An ergodic capacity lower bound is used as the objective function to be maximized. We analytically study the capacity gain from adding extra antennas to the transmitter or to the receiver in two different scenarios. Our numerical results show that the optimal antenna configuration under imperfect channel estimation can be significantly different from that under perfect channel estimation assumption. In addition, we investigate the capacity gain from optimizing antenna configuration and find that the gain can be larger than that achieved by optimizing transmit power over pilot and data symbols, particularly for large block lengths.     

放大转发协作分布式STBC-SC-FDE系统的频率域信道估计与均衡

针对单中继放大转发协作D-STBC-SC-FDE系统,研究了频率选择性衰落信道的频率域估计与均衡,给出了一种基于训练的最小二乘信道估计算法。该算法在Chu序列的辅助下,可在目的端同时估计直接信道S→D和级联信道S→R→D,算法可达最小均方误差。Monte Carlo仿真验证了算法的正确性,仿真结果也表明,信道的估计与均衡性能很大程度上受信道可用发送功率分配方案的影响。     

Performance analysis of two-way Amplify-and-Forward relaying system with multiple interferers at the relay

In this paper, we investigate the performance of the two-way Amplify-and-Forward (AF) relaying systems in an interference-limited Rayleigh fading environment. More specifically, assuming the presence of Rayleigh faded multiple interferers at the AF relay and noisy sources, an approximate closed-form expression for the Overall Outage Probability (OOP) and an integral expression for the average Symbol Error Probability (SEP) are derived. The analysis results are verified through comparison with the Monte Carlo simulation results.     

非对称双向中继系统中的协作多址广播传输方案设计与数据率性能分析

在双向中继系统中,2个节点通过一个半双工中继交换信息,2个方向的数据率都会受到较差链路的制约。当节点位置变化或信道衰落造成,中继两端的信道质量不对称时,这将导致系统的和数据率下降。为了弥补较差链路带来的数据率损失,提出了一种新的三时隙协作多址广播传输方案,使得信道质量较好的源节点与中继节点进行协作传输,并且各节点充分利用各链路所支持的最大数据率进行传输,从而有效提高系统容量及加权和数据率。推导出新方案的容量上界以及解码转发模式下的可达数据率域,并对时隙及功率等资源进行优化分配。仿真结果表明,在加性白高斯和瑞利衰落信道下,新方案在非对称信道下的性能都大大优于已有方案。     

Power-allocation policy and optimized design of multiple-antenna systems with imperfect channel estimation

We here focus on the optimized design and performance of Rayleigh-faded multiple-antenna multiple-input-multiple-output systems when both transmitter and receiver share imperfect (i.e., error impaired) channel estimates computed via training sequences. In particular, according to the emerging principle of the so-called synchronized detection, for this operating scenario we propose a simple water-filling (WF)-like strategy for allocating power over transmit antennas and test its actual performance. Afterward, we introduce and evaluate some related figures of merit summarizing the overall system's performance and use these last for noting effective system's design guidelines. In particular, some optimized solutions for power-versus-bandwidth efficiency tradeoff are presented and their validity limits are debated. All the developed results explicitly take into account the actual reliability of the achievable channel estimates.