Exact BER for M-QAM with MRC and Imperfect Channel Estimation in Rician Fading Channels

In this paper, we study the effect of imperfect channel estimation (ICE) on the performance of M-level quadrature amplitude modulation (M-QAM) with maximum ratio combining (MRC) and pilot-symbol assisted modulation (PSAM) in generalized Rician fading channels. By expressing the bit error rate (BER) of MRC diversity M-QAM in terms of the distribution of new decision variables, we derive novel, exact, and easy-to-evaluate BER expressions for diversity M-QAM with channel estimation errors. Our results include versatile system and fading channel parameters (e.g., arbitrary spatial and temporal correlation patterns among the diversity branches), and are valid for arbitrary linear channel estimators and square and rectangular M -QAM with different constellation sizes. In addition, we evaluate the performance of minimum mean-squared error (MMSE)- and sinc-interpolator-based channel estimators with PSAM, and provide some new insights into the performance of M-QAM with PSAM in generalized fading channels     

Effect of Channel Estimation Errors on M -QAM With MRC and EGC in Nakagami Fading Channels

We study the effect of imperfect channel estimation (ICE) on the error probability performance of M-level quadrature amplitude modulation ( M-QAM) with maximal-ratio combining and equal-gain combining diversity formats in Nakagami fading channels. We provide a novel formulation of the bit-error rate (BER) of M-QAM with ICE in terms of the signal constellation-dependent effective signal-to-noise ratios (SNRs) or amplitudes, which allows us to derive the general, accurate, and easy-to-evaluate BER formulas for square and rectangular diversity M-QAM with channel estimation errors. Our result shows that the performance loss caused by ICE may be manifested by the signal decision space distortion and a scaling of the effective SNR. Using our analytical result, we evaluate the performance of M-QAM with pilot-symbol assisted modulation and present some insightful findings     

Effect of channel estimation error on M-QAM BER performance inRayleigh fading

We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider     

Exact error-rate analysis of diversity 16-QAM with channel estimation error

The bit-error rate (BER) performance of multilevel quadrature amplitude modulation with pilot-symbol-assisted modulation channel estimation in static and Rayleigh fading channels is derived, both for single branch reception and maximal ratio combining diversity receiver systems. The effects of noise and estimator decorrelation on the received BER are examined. The high sensitivity of diversity systems to channel estimation error is investigated and quantified. The influence of the pilot-symbol interpolation filter windowing is also considered.     

单载波频域均衡信道估计分析

针对高速率信息传输系统中多径衰落对单载波频域均衡(SC-FDE)信道估计造成的影响,在SC-FDE原理基础上,将无线通信中信噪比估计和SC-FDE中信道估计结合起来,对现有信噪比估计算法进行优化。分析和仿真结果表明,此方法能有效地改善多径衰落信道中信道估计的有效性,提高了频域均衡的效果,从而改善了SC-FDE系统的误码率(BER)性能。     

Quasi-synchronous code-division multiple access with high-ordermodulation

Code-division multiple access (CDMA) is a multiplexing technique where a number of users simultaneously access a transmission channel by modulating and spreading their signals with preassigned codewords. This paper studies the performance of CDMA signals with orthogonal (Walsh-Hadamard) codewords and synchronization errors smaller than the chip time. Two high-order modulation techniques, M-level quadrature amplitude modulation (M-QAM) and M-level phase-shift keying (M-PSK) are compared with respect to bit-error rate (BER). The results are especially important for the return channel of cable TV networks and summarized as follows: 1) Synchronization errors between transmitters lead to interference noise, whereas synchronization errors between the transmitter and the receiver lead to a decreased amplitude of the received user signal. Both effects have significant impact on the system performance. 2) Closed expressions are obtained for the BER of a CDMA signal with M-PSK and M-QAM with a given maximum synchronization error. 3) The higher the modulation order, the more sensitive the system gets for synchronization errors. 4) The BER is highly dependent on the assigned codewords out of the Walsh-Hadamard code set. 5) The BER performance of M-QAM outperforms that of M-PSK     

Hidden Pilot Based Precoder Design for MIMO-OFDM Systems

In order to improve bandwidth efficiency and bit error rate (BER) performance, a new hidden pilot scheme using a precoder is proposed for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We show that the inevitable data interference of the hidden pilot, which degrades the performance of channel estimation, can be reduced successfully by the precoder design for each antenna with the aid of an iterative scheme. We also show that frequency diversity gain can be achieved due to the spreading effect of the precoder. Computer simulations are presented in which the proposed scheme is compared with conventional methods with respect to channel estimation, BER and bandwidth efficiency.     

Performance analysis of hybrid transmit antenna selection/maximal‐ratio transmission in Nakagami‐m fading channels

Hybrid diversity systems have been of great importance because they provide better diversity orders and robustness to the fading effects of wireless communication systems. This paper focuses on the performance analysis of multiple‐input gle‐output systems that employ combined transmit antenna selection (TAS)/maximal‐ratio transmission (MRT) techniques (i.e., hybrid TAS/MRT). The probability density function, the moment generating function and the n ^th order moments of the output signal‐to‐noise ratio of the investigated diversity scheme are derived for independent identically distributed flat Nakagami‐m fading channels. The system capacity of the hybrid TAS/MRT scheme is examined from the outage probability perspective. Exact bit/symbol error rate (BER/SER) expressions for binary frequency shift keying, M‐ary phase shift keying and square M‐ary quadrature amplitude modulation signals are derived by using the moment generating function‐based analysis method. By deriving the upper bounds for BER/SER expressions, it is also shown that the investigated systems achieve full diversity orders at high signal‐to‐noise ratios. Also, by Monte Carlo simulations, analytical performance results are validated and the effect of feedback delay, channel estimation error and feedback quantization error on BER/SER performances are examined. Copyright © 2011 John Wiley & Sons, Ltd.     

On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel Estimation Error

By employing spatial multiplexing, multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. Zero-forcing (ZF) detection is a simple and effective technique for retrieving multiple transmitted data streams at the receiver. However the detection requires knowledge of the channel state information (CSI) and in practice accurate CSI may not be available. In this letter, we investigate the effect of channel estimation error on the performance of MIMO ZF receivers in uncorrelated Rayleigh flat fading channels. By modeling the estimation error as independent complex Gaussian random variables, tight approximations for both the post-processing SNR distribution and bit error rate (BER) for MIMO ZF receivers with M-QAM and M-PSK modulated signals are derived in closed-form. Numerical results demonstrate the tightness of our analysis     

Practical Multiuser Diversity With Outdated Channel Feedback

Inspired by the information theoretic results concerning multiuser diversity, we address practical issues in implementing multiuser diversity in a multiple access wireless setting. Considering a channel-assigning strategy that assigns the channel only to the user with the best instantaneous SNR [3], our emphasis is on the effects of channel feedback delay in downlink transmissions. A finite set of M-ary quadrature amplitude modulation (M-QAM) constellations is adopted and a constant transmit power is assumed in this practical multiuser adaptive modulation scheme. Based on the closed-form expressions for average bit error rate (BER) and average data rate, we illustrate the impact of channel feedback delay on the achievable multiuser diversity gain with the number of users. Simple and accurate asymptotic approximations are also provided in the limit of large numbers of users. Focusing on different applications, we propose two optimization criteria for the switching thresholds, based on either an average BER, or an outage probability constraint. Two novel constant power, variable rate M-QAM schemes that are less sensitive to feedback delay are proposed using the optimal switching thresholds, which are derived to maximize the average data rate subject to these two constraints, respectively. To obtain a certain degree of fairness among the users, we also consider a fair channel-assigning strategy that assigns the channel to only the user with the greatest normalized SNR.     

BER Analysis of M-QAM with Packet Combining Over Space-Time Block Coded MIMO Fading Channels

We analyze the bit error rate (BER) performance of M-ary quadrature amplitude modulation (M-QAM) when using space-time block coding (STBC) along with packet combining triggered by automatic repeat request (ARQ) retransmission over multiple-input multiple-output (MIMO) fading channels. Specifically, adopting a log-likelihood ratio (LLR) based approach and considering the 16-QAM case of study, we provide an exact formulation for the aggregate LLR distribution in the case the STBC codeword can be transmitted twice, and derive the resulting BER. For higher number of retransmissions, an approximation of the error function is used to derive the LLR distributions and the system's ensuing BER. Considering different values of combined transmissions and M-QAM with possible constellation rearrangement (CoRe), validation of the proposed BER analytical model through simulations and assessment of the advantages of packet combining are provided for transmissions over additive white Gaussian noise (AWGN) channel and orthogonalized MIMO Rayleigh fading channels with different STBC mappings.     

Antenna Selection for MIMO-OFDM Systems With Channel Estimation Error

We study space–time–frequency coded multiple-input–multiple-output (MIMO) orthogonal frequency-division multiplexed (OFDM) systems employing receiver antenna selection (AS), where training has been utilized to perform linear minimum mean square error (LMMSE)-based channel estimation. To minimize the mean square error (MSE) of this estimator, equispaced and equipowered training symbols are used, with the number of training symbols per OFDM symbol equal to the channel length. The maximum received signal power AS rule is proposed, which decouples the AS process from the channel estimation process. By upper bounding the pairwise error probability (PEP) expression, we show that the system with a channel-estimation error (CEE) still achieves maximum spatial and multipath diversity. The performance of the system for the special case of square unitary and orthogonal codes has been analyzed. For the case of orthogonal codes using constant modulus symbols, we also derive the exact bit-error-rate (BER) expression. The degradation in performance, due to the presence of the CEE, is captured by the loss-in-coding-gain (LCG) and loss-in-performance (LP) expressions. To minimize the loss due to the CEE, an optimal power-allocation scheme that distributes the total available power between training symbols and data symbols is defined. Compared with the perfect channel knowledge case, equal power training for the CEE case performs at least 3 dB worse, whereas optimal power training for the CEE case suffers a loss less than 3 dB always. Analytical and simulation results are presented to validate our analysis and results.      

Study of BER of 64-QAM signal and OMI-window of feasible operationin analog/digital hybrid SCM transmission systems

In an analog/digital hybrid subcarrier multiplexed (SCM) transmission, carriers have generally been substituted for transmission signals such as AM vestigal sideband (AM-VSB) AM signals and M-QAM signals to evaluate transmission quality. In practical hybrid SCM, however, carriers are modulated by video signals or digital data, and the amplitude of a multiplexed signal composed of these modulation signals is more compressed than that of the carriers. This causes a decrease in the frequency of clipping of the multiplexed signal at the laser threshold. Consequently, the BER of the M-QAM signal in a practical hybrid SCM is lower than that of the experimental results for the same optical modulation index (OMI). However, it is difficult to prepare many practical modulation signals for experiments in a laboratory. Therefore, there is demand for a bit error rate (BER) analysis method for a multiplexed signal that includes the modulation signals needed to sufficiently evaluate the BER and determine the optimum OMI in a practical hybrid SCM. In this paper, we describe such a BER analysis method that can effectively estimate the BER in a practical hybrid SCM. In practical systems, the BER was greatly improved over the BER of a multiplexed signal of carriers. Furthermore, BER degradations due to clipping can be neglected for the AM signals in setting a practical OMI range. We used this analysis method to study the effective OMI range of AM and M-QAM signals. By assuming modulation signals, the OMI range is enlarged and, significantly, the OMI of an AM signal becomes suitable for setting practical values in AM-SCM transmission. This OMI range is more practical than those of former studies     

Modeling fading channel-estimation errors in pilot-symbol-assisted systems, with application to turbo codes

In this paper, we address the issue of imperfect channel estimation in coded systems on fading channels. Since performance of channel codes is influenced in different ways by different components of channel-estimation errors, we develop a simplified model which separates the estimation errors of a Wiener-filtered received signal into the amplitude error and the phase error. Based on the model, we derive tight bounds on component error variances. Moreover, we prove that the classical Wiener filter results in a biased estimate of the channel amplitude. We also show that the probability of having a phase-estimation error large enough to cause decision errors in the receiver is significant. Using our model, we derive an approximate upper limit on the optimum pilot-symbol spacing and approximate lower limit on bit-error rate performance of coded systems with a given pilot-symbol separation. The proposed model and derivations are confirmed by extensive simulations.     

Error Rate Analysis for Coded Multicarrier Systems Over Quasi-Static Fading Channels

Several standards such as IEEE 802.11a/g, IEEE 802.16, and the European Computer Manufacturers Association (ECMA) multiband orthogonal frequency division multiplexing (MB-OFDM) for high data-rate ultra-wideband employ bit-interleaved convolutionally coded multicarrier modulation over quasi-static fading channels. Motivated by the lack of appropriate error rate analysis techniques for this popular type of system and channel model, we present two novel analytical methods for bit error rate (BER) estimation of coded multicarrier systems operating over frequency-selective quasi-static channels with nonideal interleaving. In the first method, the approximate performance of the system is calculated for each realization of the channel, which is suitable for obtaining the outage BER performance (a common performance measure for, e.g., MB-OFDM systems). The second method assumes Rayleigh distributed frequency-domain subcarrier channel gains and knowledge of their correlation matrix, and can be used to directly obtain the average BER performance. Both methods are applicable to convolutionally coded interleaved multicarrier systems employing quadrature amplitude modulation, and are also able to account for narrowband interference (modeled as a sum of tone interferers). To illustrate the application of the proposed analysis, both methods are used to study the performance of a tone-interference-impaired MB-OFDM system.     

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.     

Effects of channel-estimation errors on receiver selection-combining schemes for Alamouti MIMO systems with BPSK

The bit-error rate (BER) of binary phase-shift keying in Rayleigh fading, using the Alamouti transmission scheme and receiver selection diversity in the presence of channel-estimation error, is studied. Closed-form expressions for the BER of log-likelihood ratio selection, signal-to-noise ratio (SNR) selection, switch-and-stay combining selection, and maximum ratio combining are derived in terms of the SNR and the cross-correlation coefficient of the channel gain and its corrupted estimate. Two new selection schemes, space-time sum-of-squares combining selection diversity and space-time sum-of-magnitudes selection diversity, are proposed and proven to provide almost the same performance as SNR selection, but with much simpler implementations. The effects of channel-estimation errors on each selection scheme are examined.     

Combined turbo coding and unitary space-time modulation

Space-time coding is well understood for high data rate communications over wireless channels with perfect channel state information. On the other hand, channel coding for multiple transmit antennas when channel state information is unknown has only received limited attention. A new signaling scheme, named unitary space-time modulation, has been proposed for the latter case. In this paper, we consider the use of turbo coding together with unitary space-time modulation. We demonstrate that turbo coded space-time modulation systems are well suited to wireless communication systems when there is no channel state information, in the sense that the turbo coding improves the bit error rate (BER) performance of the system considerably. In particular, we observe that the turbo-coded system provides 10-15 dB coding gain at a BER of 10/sup -5/ compared to the unitary space-time modulation for various transmit and receive antenna diversity cases.     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

时变信道下ADF协作车载通信误码率分析

智能车载协作系统中车辆快速移动使得无线通信信道具有时变特性,为有效评估系统的误码性能,给出了符合车载时变信道的一阶自回归(AR1)模型,提出了一种基于AR1模型的自适应解码转发(ADF)协作误码率分析方法.该方法通过AR1模型的多普勒频偏相关系数来刻画时变信道特性,根据中继译码结果自适应选择是否协作转发,提升了智能交通系统的可靠性.此外,利用矩生成函数(MGF)推导出ADF协作下多进制正交幅度调制(M-QAM)信号误码率封闭表达式,并分析了车载移动速度和信道状态信息(CSI)估计精度对误码性能的影响.数值仿真结果表明,车载系统能通过增加CSI估计精度,有效地减少车载快速移动引起的误码平顶值.该方法相对于放大转发(AF)协作通信方式,平均误码性能提高约8.7 dB.