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.     

Channel capacity of adaptive transmission with maximal ratio combining in correlated Rayleigh fading

We derive closed-form expressions for the single-user capacity of maximal ratio combining diversity systems taking into account the effect of correlation between the different branches. We consider a Rayleigh fading channel with two kinds of correlation: 1) equal branch signal-to-noise ratios (SNRs) and the same correlation between any pair of branches and 2) unequal branch SNRs and arbitrary correlation between branches such that the eigenvalues of the branch covariance matrix are all distinct. Three adaptive transmission schemes are analyzed: 1) optimal simultaneous power and rate adaptation; 2) optimal rate adaptation with constant transmit power; and 3) channel inversion with fixed rate.     

Selection-and-stay combining on correlated Nakagami fading channels

Selection-and-stay combining (SSTC) is addressed and its outage probability is derived for dual-branch diversity on correlated Nakagami fading channels. In the SSTC scheme, the receiver uses the branch with a larger signal-to-noise ratio (SNR) until its SNR is lower than a preset threshold, and selection combining (SC) is used only at the switching instance. Numerical results from analyses and simulations are also presented.     

Robust space-time codes for correlated Rayleigh fading channels

Space-time (ST) coding has emerged as an effective strategy to enhance performance of wireless communications in fading environments. Many different ST coding schemes have been proposed to achieve reliable communications in independent fading channels. However, a design of robust ST codes for correlated fading channels has not been addressed. We propose a simple robust ST coding scheme that achieves robust performance over a wide range of fading conditions. The key to achieve robust performance is to formulate code design criteria that are not dependent on the channel correlation statistics. A provably robust scheme can be formulated by concatenating a full-rank ST block code with an outer encoder. We derive several robust code examples via the concatenated orthogonal ST block code and TCM construction. The simulation results show that some traditional ST codes perform poorly, whereas the proposed codes achieve robust performance over a broad range of fading conditions.     

Effective capacity of a correlated Rayleigh fading channel

The next generation wireless networks call for quality of service (QoS) support. The effective capacity (EC) proposed by Wu and Negi provides a powerful tool for the design of QoS provisioning mechanisms. In their previous work, Wu and Negi derived a formula for effective capacity of a Rayleigh fading channel with arbitrary Doppler spectrum. However, their paper did not provide simulation results to verify the accuracy of the EC formula derived in their paper. This is due to difficulty in simulating a Rayleigh fading channel with a Doppler spectrum of continuous frequency, required by the EC formula. To address this difficulty, we develop a verification methodology based on a new discrete‐frequency EC formula; different from the EC formula developed by Wu and Negi, our new discrete‐frequency EC formula can be used in practice. Through simulation, we verify that the EC formula developed by Wu and Negi is accurate. Furthermore, to facilitate the application of the EC theory to the design of practical QoS provisioning mechanisms in wireless networks, we propose a spectral‐estimation‐based algorithm to estimate the EC function, given channel measurements; we also analyze the effect of spectral estimation error on the accuracy of EC estimation. Simulation results show that our proposed spectral‐estimation‐based EC estimation algorithm is accurate, indicating the excellent practicality of our algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information

We analyze a mobile multiple input multiple output wireless link with M transmit and N receive antennas operating in a spatially correlated Rayleigh flat fading environment. Only the correlations between the channel coefficients are assumed to be known at the transmitter and the receiver. The channel coefficients are correlated in space and uncorrelated in time from one coherence interval to another. These coefficients remain constant for a coherence interval of T symbol periods after which they change to another independent realization according to the spatial correlation model. For this system we characterize the structure of the input signal that achieves capacity. The capacity achieving transmit signal is expressed as the product of an isotropically distributed unitary matrix, an independent nonnegative diagonal matrix and a unitary matrix whose columns are the eigenvectors of the transmit fade covariance matrix. For the case where the number of transmit antennas M is larger than the channel coherence interval T, we show that the channel capacity is independent of the smallest M-T eigenvalues of the transmit fade covariance matrix. In contrast to the previously reported results for the spatially white fading model where adding more transmit antennas beyond the coherence interval length (M>T) does not increase capacity, we find that additional transmit antennas always increase capacity as long as their channel fading coefficients are spatially correlated with the other antennas. We show that for fast hopping or fast fading systems (T=1) with only channel covariance information available to the transmitter and receiver, transmit fade correlations are beneficial. Mathematically, we prove this by showing that capacity is a Schur-convex function of the vector of eigenvalues of the transmit fade correlation matrix. We also show that the maximum possible capacity gain due to transmitter fade correlations is 10logM dB.     

Capacity of correlated nakagami-m fading channels with diversity combining techniques

We derive closed-form expressions for the capacity of dual-branch maximal ratio combining, equal gain combining, selection combining, and switch and stay combining (SSC) diversity systems over correlated Nakagami-m fading channels. Because the final capacity expressions contain infinite series, we truncate the series and present upper bounds on the truncation errors. We also derive an expression that can be used to numerically determine the optimum adaptive switching threshold for the capacity of a dual-branch SSC system over correlated Nakagami-m fading channels. However, a closed-form expression for the optimum adaptive switching threshold is derived for the case of independent branches. The corresponding expressions for Rayleigh fading are obtained as a special case of Nakagami-m fading. Finally, numerical examples are presented for illustration.     

Performance of the combining received differential encoding transmit diversity with imperfect carrier recovery over correlated Nakagami fading channels

A differential detection scheme for transmit diversity was proposed by Tarokh, which can achieve full diversity order without the requirement to estimate the channel state at the receiver. This paper investigates the potential of using multiple receive antennas for differential space time coded MPSK signals over correlated Nakagami fading channels. We also investigate the effect of the carrier frequency offset (CFO) and channel correlation on its performance and present some results on its maximal tolerable frequency offsets for different MPSK signals. The results have shown that the differential encoding transmit diversity is very robust to the CFO and channel correlation. Copyright © 2004 John Wiley & Sons, Ltd.     

Iterative diversity detection for correlated continuous-time Rayleigh fading channels

An antenna array is proposed as a means of achieving a space-diversity effect that partly overcomes the severity of continuous-time Rayleigh fading channels. The investigated channel is assumed to be frequency-nonselective with correlated diversity links, where the correlation is related to the array geometry and the spatial and Doppler dispersions. Further, the error performance is improved by bit interleaving and channel coding, where the encoders/channel is viewed as a serially concatenated system: a convolutional code constitutes the outer code, whereas a differential encoder and the fading channel (having truncated memory) form a joint inner code. In order to obtain a practical detector structure it is desirable to perform iterative decoding by applying some a posteriori probability (APP) algorithms. For this purpose, we propose a novel generalization of the well-known Bahl-Cocke-Jelinek-Raviv (1974) algorithm that calculates the APPs over channels having memory. Numerical results indicate that iterative decoding becomes more powerful when the exploited channel memory depth is extended. Also, the error performance is significantly improved by introducing multiple antennas. The interleaver gain is, however, seen to be quite moderate, in contrast to additive white Gaussian noise channels.     

A trellis-coded DS-CDMA system in correlated Rayleigh fading channels

We present the trellis-coded code-division multiple-access (TC-CDMA) system based on a multisequence signaling, called orthogonal plane sequence modulation (OPSM), in correlated Rayleigh fading channels and derive its pairwise error probability with different degrees of channel state information. Numerical results show that the OPSM-based TC-CDMA system outperforms conventional convolutionally coded CDMA or TC-CDMA systems.     

Pilot-symbol-assisted LDPC coded BICM over correlated Rayleigh fading channels

Pilot-symbol-assisted low-density parity-check (LDPC)-coded bit-interleaved coded modulation (BICM) is analyzed using the density evolution (DE) and the extrinsic information-transfer (EXIT) chart for correlated Rayleigh fading channels. The key parameter (the power correlation coefficient) is identified, and the threshold degradation is quantified. The optimal tradeoff of energy allocation between pilots and coded symbols is found to be sensitive to the normalized Doppler spread of the channel, the interpolation filter, the modulation scheme, and the pilot selection. In addition, a simple upper bound on the performance of any receiver that performs joint iterative decoding and channel estimation is derived. Extension to irregular code design is also discussed.     

Maximum achievable diversity order for cascaded Rayleigh fading channels

In this Letter, we investigate the error rate performance of coherent M-ary phase shift keying (M-PSK) modulation over cascaded Rayleigh fading with receive antenna diversity. Through the derived symbol error rate (SER) expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels.     

16-QAM BICM-ID in fading channels with imperfect channel state information

We analyze the impact of imperfect channel state information (CSI) on the performance of bit-interleaved coded modulation with iterative decoding (BICM-ID) over fading channels. We develop a general, accurate and efficient theoretical error-free feedback bound (EF bound) to analyze the asymptotic bit-error rate (BER) of BICM-ID with imperfect CSI, and predict the BER floor due to channel estimation error. The convergence to the EF bound and the accuracy of the BER floor prediction are verified by simulation with various sets of code and channel parameters. These results are canonical, in that they apply to a variety of system configurations. Pilot symbol assisted modulation is used as a particular example for Rayleigh-fading channels.     

Ergodic capacity of switch-and-examine combining under flat Rayleigh fading channels

Switch-and-examine combining (SEC) is an interesting diversity technique that is simpler than selection combining (SC), whereas its performances is similar in terms of bit error rate (BER) and diversity order. As ergodic capacity is also a key performance index in modern wireless systems, this article analyzes the ergodic capacity of the SEC system. The numerical results show that the ergodic capacity of SEC with optimal threshold is similar to that of SC for arbitrary number of diversity branches.     

Closed-form analysis of dual-diversity equal-gain combining over Rayleigh fading channels

Starting with a new expression for the probability density function of the signal-to-noise ratio at the output of dual-diversity equal-gain combining (EGC) over Rayleigh channels, we provide closed-form expressions for the average bit and symbol error rate of M-ary phase-shift keying signals. Numerical examples indicate that EGC maintains a good diversity gain as long as the degree of unbalance is not very low but suffers a sharp and significant degradation when the degree of unbalance approaches zero.     

Performance analysis of TCM with generalized selection combining on Rayleigh fading channels

We derive the computational cutoff rate, R/sub 0/, for coherent trellis-coded modulation (TCM) schemes on independent identically distributed (i.i.d.) Rayleigh fading channels with (K, L) generalized selection combining (GSC) diversity, which combines the K paths with the largest instantaneous signal-to-noise ratios (SNR) among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. We also derive the union bound on the bit error probability of TCM schemes with (K, L) GSC in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.     

Analysis of equal gain diversity receivers in correlated Rayleigh fading channels

Utilizing a desirable exponential integral representation of Gaussian probability integral, this letter derives the average bit error rate (ABER) expressions for coherent binary signals that employ a dual branch equal gain combining receiver. Our numerical results reveal that the branch correlations do not affect the ABER significantly provided power correlation coefficient is less than 0.3 in Rayleigh fading.     

室内环境下指数分布非对称几何统计信道模型

为了对无线信道中的多径分量进行合理分簇,提出了一种毫米波信道二分K均值聚类多径分簇方法,解决了传统的K均值聚类分簇方法只能实现局部最优分簇的问题. 采用马氏距离（Mahalanobis distance, MD）衡量多径分量距离（multi-path component distance, MCD）,以簇分裂和迭代计算的方式对多径进行分簇. 采用毫米波室内信道实验测试数据,验证了所提算法的有效性和可行性. 结果表明,所提算法比传统K均值聚类分簇方法获得的分簇结果更合理,能将信道中多径参数相似度较高的多径有效且唯一地分配到同一簇.     

Cooperative decode-and-forward quadrature spatial modulation over correlated and imperfect η–μ fading channels

Wireless Networks - This paper analyzes the performance of quadrature spatial modulation (QSM) multiple-input multiple-output (MIMO) system in cooperative decode and forward (DF) networks over...