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.     

非理想信道估计下最大比合并的实现

在信道估计理想和各分支具有相等噪声功率的分集系统中,利用信道估计的共轭作为合并系数的传统最大比合并是最优的合并方法.然而在实际的宽带码分多址系统中,由于Rake接收机每个指峰上的噪声功率是不等的,且信道估计也是非理想的,所以传统的最大比合并实现方法并不是最优的.针对这种情况,本文研究了一种改进最大比合并实现方法在宽带码分多址系统中的应用.仿真表明它比传统的最大比合并实现方法更适合实际的宽带码分多址系统.     

Performance analysis of maximum ratio combining with imperfect channel estimation in the presence of cochannel interferences

In this paper, we analyze the performance of maximum ratio combining (MRC) systems with imperfect channel estimation in the presence of cochannel interference (CCI) with an arbitrary power interference-to-noise ratio (INR). The maximum combining weights are the imperfect estimates of the desired user's fading channel coefficients and are assumed to be complex Gaussian distributed. The quantified measure for estimation error is the correlation coefficient between the true fading channel coefficients and their estimates. Exact closedform expressions are derived for the probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR), as well as performance metrics including outage probability and the average symbol error probability (ASEP) for some modulation formats. Simulation results demonstrate the accuracy of our theoretic analysis.     

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。     

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.     

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.     

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.     

Maximum ratio combining of correlated Rayleigh fading channels with imperfect channel knowledge

The bit error probability for binary modulation and multiple correlated Rayleigh fading diversity branches is derived. The receiver performs maximum ratio combining of the diversity branches based on noisy channel estimates. Our results provide new analytical insights into performance, design, and optimization of some known communication receivers.     

Diversity and channel estimation errors

We study the relation between a training-based detector and a coherent maximum-likelihood detector. We prove that under quite general conditions, the diversity gains associated with these two receivers are equal. Finally, we discuss the relation between our analysis and a related result in the literature.     

Optimum power control for successive interference cancellation with imperfect channel estimation

Successive interference cancellation, in conjunction with orthogonal convolutional codes, has been shown to approach the Shannon capacity for an additive white Gaussian noise channel. However, this requires highly accurate estimates for the amplitude and phase of each user's signal. We derive an optimal power control strategy specifically designed to maximize the overall capacity under the constraint of a high degree of estimation error. This power control strategy presents a general formula of which other power control algorithms are special cases. Even with estimation error as high as 50%, capacity can be approximately doubled relative to not using interference cancellation. In addition, when properly applied to multicell mobile networks, this power control scheme can reduce the handset transmit power, and therefore other-cell interference, by more than an order of magnitude.     

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。     

Robust channel estimation for the OFDM-based WLAN systems with imperfect synchronization

As an effective technique for combating multipath fading and for high data rate transmission over wireless channels, orthogonal frequ- ency division multiplexing (OFDM) is extensively used in wireless local area network (WLAN) systems to support high-performance bandwidth- efficient multimedia services. In this paper, a robust channel estimation scheme is proposed for the OFDM-based WLAN systems with imperfect synchronization. The frame structure information, the preamble information, the pilot information are efficiently utilized in the proposed channel estimation scheme. Simulation results are used to illustrate the performance of the proposed scheme.     

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.     

Blind channel estimation via combining autocorrelation and blind phase estimation

Symbol spaced blind channel estimation methods are presented which can essentially use the results of any existing blind equalization method to provide a blind channel estimate of the channel. Blind equalizer's task is reduced to only phase equalization (or identification) as the channel autocorrelation is used to obtain the amplitude response of the channel. Hence, when coupled with simple algorithms such as the constant modulus algorithm (CMA) these methods at baud rate processing provide alternatives to blind channel estimation algorithms that use explicit higher order statistics (HOS) or second-order statistics (subspace) based fractionally-spaced/multichannel algorithms. The proposed methods use finite impulse response (FIR) filter linear receiver equalizer or matched filter receiver based infinite impulse response+FIR linear cascade equalizer configurations to obtain blind channel estimates. It is shown that the utilization of channel autocorrelation information together with blind phase identification of the CMA is very effective to obtain blind channel estimation. The idea of combining estimated channel autocorrelation with blind phase estimation can further be extended to improve the HOS based blind channel estimators in a way that the quality of estimates are improved.     

Improving power allocation to MIMO eigenbeams under imperfect channel estimation

Eigenbeamforming exploits the spatial diversity of the MIMO channel by multiplexing data substreams along orthogonal modes. Estimation errors result in self-interference, which must be taken into account in the selection of modes for transmission and the allocation of transmitter power. Using perturbation analysis to evaluate the self-interference, a technique is proposed for determining the power allocation which achieves a specified performance, based only on the information available at the receiver.     

Symbol error probability of two-dimensional signaling in Ricean fading with imperfect channel estimation

In this paper, a general analytical framework is developed for calculating the symbol error rate of two-dimensional (2-D) signaling in Ricean fading with imperfect channel estimation. We show that in the presence of channel estimation errors, the symbol error rate of arbitrary 2-D signaling in Ricean fading can be expressed as a two-fold proper integral with finite integration limits, which is suitable for numerical evaluation. This new analysis is applicable to any channel estimation scheme where the estimated and the actual channel gains are jointly complex-Gaussian. System parameters related to specific channel estimation schemes are optimized and the effect of Doppler frequency shift in the channel line-of-sight component on the error performance is investigated using our analysis.     

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.     

基于不完美信道估计的闭环MIMO-MRC跨层设计

为提高无线通信的频谱效率,提出一种MIMO-MRC(multiple-input multiple-output-maximal ratio combining)跨层方案。是物理层的自适应调制(adaptive modulation,AM)和数据链路层的自动重传(automatic repeat request,ARQ)协作,发射端利用估计信道信息反馈,自适应调节调制模式,选择最优发射权矢量和自动重传发射数据。分析了估计误差对MIMO-MRC跨层系统的影响,给出了MIMO-MRC系统在信道估计存在误差时的频谱效率和中断概率的闭合表达式。通过仿真实验证明,对比SISO(single-input single-output)跨层系统和A lamouti's跨层系统,MIMO-MRC跨层系统的性能有明显提高,可获得约3 d B的分集增益。     

Effect of imperfect channel estimation on transmit diversity in CDMA systems

In this paper, the effect of imperfect channel estimation on the transmit diversity based on space-time block coding for the downlink of a direct-sequence code-division multiple-access system is studied. Two transmit antenna and one receiving antennas are employed. However, the results of this paper can be extended to the system with more receiving antennas. Each channel is modeled as frequency-selective Rayleigh fading and the pair of channels corresponding to two transmit antennas are mutually independent. Both spatial diversity gain and multipath diversity gain are obtained in the system. The system performance is evaluated in terms of bit-error rate under the perfect and imperfect channel estimation. A pilot-assisted channel-estimation scheme with one common spreading code sequence is exploited. It is shown that the inaccurate channel estimates suffering from multiple access and multipath interference significantly degrade the system performance and can be effectively improved by use of a simple low-pass filter. The investigation of the power ratio of pilot to data channels illustrates that the base station should dynamically adjust the transmit power of the pilot channel according to the varying system configurations in order to achieve the best performance.