Performance of cross-layer design for orthogonal space-time block coded MIMO systems with imperfect CSI in Ricean fading channels

A cross-layer design (CLD) scheme for orthogonal space-time block coded MIMO systems with imperfect channel state information is presented by combining adaptive modulation and automatic repeat request, and the corresponding system performance is investigated over Ricean fading channel. The fading gain value is partitioned into a number of regions by which the modulation is adapted in terms of the region the fading gain falls in. The fading gain switching thresholds subject to a target packet error rate (PER) constraint are derived. According to these results, and using the generalized Marcum Q-function, we derive the theoretical formulae of average PER and spectrum efficiency (SE) of the system with CLD for both perfect and imperfect estimation in detail. As a result, closed-form expressions for average PER and SE are obtained. These expressions include some existing expressions in Rayleigh channel as special cases. With these expressions, the system performance in Ricean channel with perfect and imperfect estimation information can be evaluated effectively. Computer simulation for average PER and SE show that the theoretical analysis and simulation are consistent. The results show that the system performance will be effectively improved as Ricean factor increases, but it will be degraded as estimation errors increases.     

Performance of heterogeneous multiuser MIMO system with cross-layer design and multiple outdated estimations in Rayleigh fading channel

By combining adaptive modulation and automatic repeat request protocol as well as user scheduling, a cross-layer design (CLD) scheme for multiuser MIMO system with the normalized signal-to-noise ratio (SNR)-based scheduling under heterogeneous case is developed, where perfect and imperfect channel state information (CSI) are both considered. Based on this, by exploiting previous channel estimation information, the multiple outdated estimates method is presented to improve the system performance under imperfect CSI. According to the performance analysis and the normalized-SNR based scheduling scheme, the average spectral efficiency (SE) and packet error rate (PER) of the system are derived, respectively. As a result, closed-form SE and PER expressions are attained. These expressions include the ones with conventional single outdated estimate as special cases, and can provide good performance evaluation for the multiuser CLD system under heterogeneous case. Simulation results show that the derived theoretical SE and PER are in consistent with the corresponding simulations. Moreover, the presented CLD scheme with multiple estimates can provide higher SE and lower PER than that with conventional single estimate in the presence of imperfect CSI. Besides, multiuser MIMO-CLD has superior performance over the conventional single user counterpart due to the multiuser diversity.     

Performance analysis of cross-layer design with average PER constraint over MIMO fading channels

In this article, a cross-layer design (CLD) scheme for multiple-input and multiple-output system with the dual constraints of imperfect feedback and average packet error rate (PER) is presented, which is based on the combination of the adaptive modulation and the automatic repeat request protocols. The design performance is also evaluated over wireless Rayleigh fading channel. With the constraint of target PER and average PER, the optimum switching thresholds (STs) for attaining maximum spectral efficiency (SE) are developed. An effective iterative algorithm for finding the optimal STs is proposed via Lagrange multiplier optimisation. With different thresholds available, the analytical expressions of the average SE and PER are provided for the performance evaluation. To avoid the performance loss caused by the conventional single estimate, multiple outdated estimates (MOE) method, which utilises multiple previous channel estimation information, is presented for CLD to improve the system performance. It is shown that numerical simulations for average PER and SE are in consistent with the theoretical analysis and that the developed CLD with average PER constraint can meet the target PER requirement and show better performance in comparison with the conventional CLD with instantaneous PER constraint. Especially, the CLD based on the MOE method can obviously increase the system SE and reduce the impact of feedback delay greatly.     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

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.     

Space-time trellis codes over rapid rayleigh fading channels with channel estimation?part ii: performance analysis and code design for non-identical channels

We consider the maximum likelihood (ML) receiver design, performance analysis and code design for space-time trellis codes (STTC) over non-identical, rapid fading channels with imperfect channel state information (CSI). The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. A new code design criterion exploiting the statistical information of the channel estimates is proposed, which can minimize the performance loss caused by channel estimation error. New codes are obtained via an iterative search algorithm with reduced complexity. Under actual channel estimation conditions, our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels, and perfect CSI at the receiver. More performance gain can be achieved by our codes when the degree of imbalance among the links is higher.     

Performance Analysis of Rate-Adaptive Modulation with Imperfect Estimation in Space?CTime Coded MIMO System

Based on the imperfect estimation information, the performance analysis of multi-input multi-out (MIMO) systems with rate-adaptive modulation and space?Ctime coding over flat Rayleigh fading channels is presented in this paper. The fading gain value is partitioned into a number of regions by which the modulation is adapted according to the region the fading gain falls in. Under a target bit error rate (BER) and constant power constraint, the fading gain region boundaries are given. By utilizing the minimum mean squared error estimation, the correlation between the channel gains and their estimates, which contributes to imperfect channel information, is evaluated. With this correlation, the probability density function of fading gain is obtained. Based on these results, the closed-form expressions for the SE and average BER are derived in detail, respectively. The theoretical expressions will be more accurate than the existing schemes, and they include perfect estimation as a special case. Numerical results show that the SE and BER of the system with imperfect estimation are worse than those with perfect estimation due to the estimation error. Moreover, the simulation results for SE and BER are in good agreement with the theoretical analysis.     

Performance of STTC-MC-CDMA Systems with Imperfect Channel Estimation

Since, in a practical system perfect channel state information (CSI) is not possible due to presence of noise. This paper deals with the performance of space-time trellis code (STTC) in multi-carrier code-division multiple-access systems in presence of channel estimation (CE) error and results are compared with perfect CSI at the receiver. The pilot symbol assisted (PSA) technique is used for CE employing minimum mean-square error method. The symbol error rate (SER) performance is observed by employing Viterbi decoding algorithm to decode STTC code at the receiver in multi-path fading channel. The simulated SER performances in presence of CE error and with perfect CSI are compared with the theoretical performances to validate the theoretical analysis.     

Performance of M-PSK with GSC and EGC with Gaussian weighting errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.     

Performance Analysis of Space-Time Coded CDMA System Over Nakagami Fading Channels with Perfect and Imperfect CSI

In this paper, the performance of multiuser CDMA systems with different space time code schemes is investigated over Nakagami fading channel. Low-complexity multiuser receiver schemes are developed for space-time coded CDMA systems with perfect and imperfect channel state information (CSI). The schemes can make full use of the complex orthogonality of space-time coding to obtain the linear decoding complexity, and thus simplify the exponential decoding complexity of the existing scheme greatly. Moreover, it can achieve almost the same performance as the existing scheme. Based on the bit error rate (BER) analysis of the systems, the theoretical calculation expressions of average BER are derived in detail for both perfect CSI and imperfect CSI, respectively. As a result, tight closed-form BER expressions are obtained for space-time coded CDMA with orthogonal spreading code, and approximate closed-form BER expressions are attained for space-time coded CDMA with quasi-orthogonal spreading code. Computer simulation for BER shows that the theoretical analysis and simulation are in good agreement. The results show that the space-time coded CDMA systems have BER performance degradation for imperfect CSI.     

Practical robust uniform channel decomposition scheme for CSI mismatch in limited feedback MIMO systems

Uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) is assumed to be available at both the transmitter and receiver side. In practice, CSI can be obtained by channel estimation at receiver and conveyed to transmitter via a limited-rate feedback channel. In such case, the implementation of traditional UCD by treating the imperfect CSI as perfect CSI cause significant performance degradation due to inevitable channel estimation error and vector quantization error. To overcome this problem, a practical robust UCD scheme was proposed in this paper, which includes two steps, firstly, a matching architecture was proposed to eliminate the mismatch between CSI at receiver (CSIR) and CSI at transmitter (CSIT), secondly, an MMSE based robust UCD scheme considering channel estimation error and vector quantization error as an integral part of the design was derived. Simulation results show that the proposed practical robust UCD scheme is capable of improving the BER performance greatly in the context of channel estimation error and vector quantization error compared with the traditional UCD scheme.     

非精确信道信息下的自适应MIMO-OFDM系统性能分析

由于自适应多入多出正交频分复用系统(MIMO-OFDM)可以大大提高系统的频谱效率,已经成为人们研究的热点,该文分析并讨论了自适应MIMO-OFDM系统中导致非精确信道信息的两个主要因素信道估计误差和信道信息时延对系统的频谱效率和误码率性能的影响。仿真结果表明,在22 MIMO-OFDM系统中,当信道估计误差小于-12dB时,系统频谱效率损失很小。此外信道预测可以大大降低系统对信道信息时延的敏感程度。     

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.     

Adaptive modulation in ad hoc DS/CDMA packet radio networks

This paper investigates the benefit of adaptive modulation based on channel state information (CSI) in direct-sequence/ code-division multiple-access (DS/CDMA) multihop packet radio networks. By exploiting varying channel conditions, adaptive modulation can be used in ad hoc networks to provide upper layers with higher capacity links over which to relay traffic. Using the /spl alpha/-stable interference model, the distribution of the signal-to-interference ratio (SIR) is obtained for a slotted system of randomly, uniformly distributed nodes using multilevel coherent modulation schemes. Performance is evaluated in terms of the information efficiency, which is a new progress-related measure for multihop networks. Three types of adaptivity are analyzed, differing in the level of CSI available: 1) full knowledge of the SIR at the receiver; 2) knowledge of only the signal attenuation due to fading; and 3) knowledge of only the slow fading component of the signal attenuation. The effect of imperfect channel information is also investigated. Sample results are given for interference-limited networks experiencing fourth-power path loss with distance, Ricean fading, and lognormal shadowing.     

Performance of Transmit and Receive Antenna Selection in the Presence of Channel Estimation Errors

This letter considers the effect of channel estimation errors on the performance of space-time coded (STC) systems with transmit and receive antenna selection over quasi-static flat fading channels. By performing pairwise error probability analysis and presenting numerical examples, we show that the diversity order achieved with perfect channel state information (CSI) is still achievable with imperfect CSI used both at the antenna selection and the space-time decoding processes. We note that our results apply to general STC systems with both transmit and/or receive antenna selection based on largest received powers which can be estimated by any channel estimator.     

相干DS-SS/MPSK系统中频差影响的简化评估

该文针对单径慢衰落信道模型下的相干DS-SS/MPSK系统,分析了频差对系统性能的影响,得到了误比特率的封闭表达式。首先推导了匹配滤波解扩符号的信噪比特性和相干相位估计误差的分布;然后给出了衰落信道中误比特率的精确积分式,并利用MPSK条件误符号率的麦克劳林级数形式,推导了AWGN,Nakagami-m衰落和瑞利衰落信道中BPSK,QPSK误比特率的简化逼近式。最后的数值结果表明:逼近式的精度非常高,基本没有损失,可应用于实际系统设计和性能评估。     

Iterative decision‐directed estimation and compensation of nonlinear distortion effects for OFDM systems

Orthogonal frequency division multiplexing (OFDM) has been adopted for several wireless network standards due to its robustness against multipath fading. Main drawback of OFDM is its high peak‐to‐average power ratio (PAPR) that causes a signal degradation in a peak‐limiting (e.g., clipping) channel leading to a higher bit error rate (BER). At the receiver end, the effect of peak limitation can be removed to some extent to improve the system performance. In this paper, a joint iterative channel estimation/equalization and clipping noise reduction technique based on minimum mean square error (MMSE) criterion is presented. The equalization weight that minimizes the mean square error (MSE) between the signal after channel equalization and feedback signal after clipping noise reduction is derived assuming imperfect channel state information (CSI). The MSE performance of the proposed technique is theoretically evaluated. It is shown that the BER performance of OFDM with proposed technique can be significantly improved in a peak‐limited and doubly‐selective (i.e., time‐ and frequency‐selective) fading channel. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Performance Analysis and Enhancement for Opportunistic Analog Network Coding with Imperfect CSI

Imperfect channel state information (CSI) is among the main factors that affect system performance in wireless networks. In this paper, we investigate the impact of imperfect CSI on the performance of analog network coding (ANC) for a two-way relaying system based on opportunistic relay selection (ORS). An exact and generalized closed-form expression for system outage probability is presented in a Rayleigh flat-fading environment. To provide more insights, the closed-form asymptotic expression is then obtained. It is shown that the presence of channel estimation error causes outage probability maintain a fixed level even when a noiseless channel is adopted. Therefore, to mitigate the negative impact of imperfect CSI, we deduce the power allocation to minimize the system outage probability based on the knowledge of instantaneous channel information. Numerical results validate the accuracy of the derived expressions and highlight the effect of proposed power allocation algorithm compared with conventional uniform power allocation.     

Exact BER analysis for M-QAM modulation with transmit beamforming under channel prediction errors

Significant throughput improvements can be obtained in multiple-inputmultiple-output (MIMO) fading channels by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. In general, accurate channel state information (CSI) is required to achieve these performance gains. In this paper, we analyze the impact of channel prediction error on the bit error rate (BER) of combined beamforming and MRC in slow Rayleigh fading channels. Exact closed-form BER expressions are obtained in terms of elementary functions. Numerical results show that imperfect CSI causes little BER degradation using channel prediction of moderate complexity.