Joint Data and Kalman Estimation for Rayleigh Fading Channels

Channel estimation is an essential part of many detection techniques proposed for data transmission over fading channels. For the frequency selective Rayleigh fading channel an autoregressive moving average representation is proposed based on the fading model parameters. The parameters of this representation are determined based on the fading channel characteristics, making it possible to employ the Kalman filter as the best estimator for the channel impulse response. For IS-136 formatted data transmission the Kalman filter is employed with the Viterbi algorithm in a Per-Survivor Processing (PSP) fashion and the ove rall bit error rate performance is shown to be superior to that of detection techniques using the RLS and LMS estimators. To allow more than one channel estimation per symbol interval, Per-Branch Processing (PBP) method is introduced as a general case of PSP and its effect on performance is evaluated. The sensitivity of performance to parameters such as fading model order and vehicle speed is also studied.     

Adaptive Equalization Techniques for HF Channels

Data transmission at rates of 1.2 kbits/s or higher through voiceband ionospheric channels is subject to impairment from severe linear distortion, fast channel time variations, and severe fading. In this paper, we have focused on the performance of DFE (decision feedback equalization) receivers for communication over 3 kHz bandwidth HF channels. We describe the results of simulations for a wide range of fading rates on simulated and real recorded HF channels, using fractionally spaced DFE receivers. Both LMS (least mean square) and FRLS (fast recursive least squares) adaptation algorithms with periodic restart were evaluated, and both ideal-reference and decision-directed operation was observed. The results indicate that FRLS adaptation yields superior performance to LMS in rapid fading conditions, but that this performance advantage diminishes at low signal-to-noise ratios. Also, fade rates greater than about 1 Hz produced relatively high error rates, irrespective of which adaptation method was employed. Finally, a novel modification of the simple LMS algorithm which improves its tracking ability was evaluated. This involved preceding the LMS DFE receiver with an adaptive lattice whitening filter.     

Analysis of stability and performance of adaptation algorithms with time-invariant gains

Adaptation laws that track parameters of linear regression models are investigated. The considered class of algorithms apply linear time-invariant filtering on the instantaneous gradient vector and includes least mean squares (LMS) as its simplest member. The asymptotic stability and steady-state tracking performance for prediction and smoothing estimators is analyzed for parameter variations described by stochastic processes with time-invariant statistics. The analysis is based on a novel technique that decomposes the inherent feedback of adaptation algorithms into one time-invariant loop and one time-varying loop. The impact of the time-varying feedback on the tracking error covariance can be neglected under certain conditions, and the performance analysis then becomes straightforward. Performance analysis in the presence of a non-negligible time-varying feedback is performed for algorithms that use scalar measurements. Convergence in mean square error (MSE) and the MSE tracking performance is investigated, assuming independent consecutive regression vectors. Closed-form expressions for the tracking MSE are thereafter derived without this independence assumption for a subclass of algorithms applied to finite impulse response (FIR) models with white inputs. This class includes Wiener LMS adaptation.     

A robust adaptive DFE receiver for DS-CDMA systems under multipathfading channels

This paper presents a novel receiver design from signal processing viewpoint for direct-sequence code-division multiple access (DS-CDMA) systems under multipath fading channels. A robust adaptive decision-feedback equalizer (DFE) is developed by using optimal filtering technique via minimizing the mean-square error (MSE). The multipath fading channels are modeled as tapped-delay-line filters, and the tap coefficients are described as Rayleigh distributions in order to imitate the frequency-selective fading channel. Then, a robust Kalman filtering algorithm is used to estimate the channel responses for the adaptation of the proposed DFE receiver under the situation of partially known channel statistics. The feedforward and feedback filters are designed by using not only the estimated channel responses but the uncertainties and error covariance of channel estimation as well. As shown in the computer simulations, the proposed adaptive DFE receiver is robust against the estimation errors and modeling dynamics of the channels. Hence, it is very suitable for receiver design in data transmissions through multipath fading channels encountered in most wireless communication systems     

Convolutional coding for BPSK system with orthogonal sounding tone on fast Rayleigh fading channel

For combating the fast Rayleigh fading usually encountered in mobile communication channels, convolutional coding and Viterbi decoding together with interleaving and the BPSK system using an orthogonal sounding tone are considered. The bit error probability performance of the system is analysed, and numerical results for the systems with rate-? optimum codes of constraint lengths K = 3 to 7 are also provided.     

Performance of adaptive MC-CDMA detectors in rapidly fading Rayleigh channels

Multicarrier code-division multiple access (MC-CDMA) combines multicarrier transmission with direct sequence spread spectrum. Different approaches have been adopted which do not assume a perfectly known channel. We examine the forward-link performance of decision-directed adaptive detection schemes, with and without explicit channel estimation, for MC-CDMA systems operating in fast fading channels. We analyze theoretically the impact of channel estimation errors by first considering a simpler system employing a threshold orthogonality restoring combining (TORC) detector with a Kalman channel estimator. We show that the performance deteriorates significantly as the channel fading rate increases and that the fading rate affects the selection of system parameters. We examine the performance of more realistic schemes based on the minimum mean square error (MMSE) criterion using least mean square (LMS) and recursive least square (RLS) adaptation. We present a discussion which compares the decision-directed and pilot-aided approaches and explores the tradeoffs between channel estimation overhead and performance. We find that there is a fading rate range where each method provides a good tradeoff between performance and overhead. We conclude that the MMSE per carrier decision-directed detector with RLS estimation combines good performance in low to moderate fading rates, robustness in parameter variations, and relatively low complexity and overhead. For higher fading rates, however, only pilot-symbol-aided detectors are appropriate.     

Turbo编码OFDM系统中一种判决反馈的WLMS信道跟踪算法

在Turbo译码时对信息位和校验位都进行MAP译码,避免了传统基于译码再编码判决反馈信道估计和跟踪算法中反馈信号重构时的错误传播问题,降低了反馈信号的错误概率,提高了信道估计和跟踪的性能,解决了在信道变化较快条件下文献[8]提出的维纳LMS(WLMS)算法信噪比门限过高的问题。仿真结果表明,算法性能接近理想判决反馈时的性能限,与直接判决反馈的维纳LMS算法相比,在系统误比特率为10~(-4)条件下系统性能约提高2dB。     

Noncoherent adaptive channel identification algorithms fornoncoherent sequence estimation

In this letter, two novel noncoherent adaptive algorithms for channel identification are introduced. The proposed noncoherent least-mean-square (LMS) and noncoherent recursive least squares (RLS) algorithms can be combined easily with noncoherent sequence estimation (NSE) for M-ary differential phase-shift keying signals transmitted over intersymbol interference (ISI) channels. It is shown that the resulting adaptive noncoherent receivers are very robust against carrier phase variations. For zero frequency offset, the convergence speed and the steady-state error of the noncoherent adaptive algorithms are similar to those of conventional LMS and RLS algorithms. However, the conventional algorithms diverge even for relatively small frequency offsets, whereas the proposed noncoherent algorithms converge for relatively large frequency offsets. Simulations confirm the good performance of NSE combined with noncoherent adaptive channel estimation in time-variant (fading) ISI channels     

一种基于LMS滤波的OFDM系统信道估计方法

提出了一种适用于OFDM系统的最小均方(LMS)滤波的信道估计算法,对发送序列中导频位置的信道响应进行LMS滤波,进一步得出所有子载波上的信道响应。仿真结果表明,该方法同基于离散傅里叶变换(DFT)的信道估计算法相比,改善了估计的均方误差(MSE)和误码率(BER)性能。     

Sequential sequence estimation for trellis-coded modulation onmultipath fading ISI channels

A new receiver structure is proposed for trellis-coded modulation on multipath fading intersymbol interference (ISI) channels that permits the use of large-state trellis codes. The receiver uses a sequential sequence estimator with the Fano algorithm, and a channel estimator consisting of a fast nonrecursive start-up algorithm for training and the LMS algorithm for tracking. During the tracking mode, the channel estimates are updated dynamically by using recent tentative decisions produced by the sequential sequence estimator. This approach results in good tracking even on rapidly varying channels, and reduces the degradation in performance of the sequential sequence estimator due to channel estimation error. The effect of fading is mitigated using both implicit time diversity in the form of interleaved trellis-coded modulation and explicit antenna diversity     

Adaptive reception of MPSK signals in fast fading and AWGN channels

The author describes the adaptive Viterbi coherent detection (AVCD) of MPSK signals. The adaptive LMS channel estimation used requires no knowledge of channel statistical properties. The simulated BER performances in fast Rayleigh fading and AWGN channels are reported     

Tracking of fast-fading channels in long-code CDMA

A new technique for blind tracking of fast-fading channels in long-code code division multiple access (CDMA) is proposed by exploiting multipath diversity. Based on a linear interpolation channel model, the proposed method blindly identifies a time-varying channel at arbitrary estimating points within a block up to a scale factor and increases bandwidth efficiency allowing only one pilot symbol within a block, which is much larger than channel coherence time. The proposed method can be implemented using an efficient state-space inversion technique for multiuser cases. The mean square error (MSE) performance of the proposed estimator is compared with the Cramer-Rao bound (CRB) for interpolated channel. Modeling error and bit error rate (BER) are also evaluated using Monte-Carlo simulations and compared with the block fading model and a decision-directed tracking technique.     

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.     

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.     

Performance of DPSK with Convolutional Encoding on Time-Varying Fading Channels

The bit error probability performance of a differentiallycoherent phase-shift keyed (DPSK) modem with convolutional encoding and Viterbi decoding on time-varying fading channels is examined. We consider both the Rician and the lognormal channels. Bit error probability upper bounds on fully-interleaved (zero-memory) fading channels are derived and substantiated by computer simulation. It is shown that the resulting coded system performance is a relatively insensitive function of the choice of channel model provided that the channel parameters are related according to the correspondence developed as part of this paper. Finally, a comparison of DPSK with a number of other modulation strategies is provided.     

Sequence estimation over the slow nonselective Rayleigh fadingchannel with diversity reception and its application to Viterbi decoding

The authors consider minimum error probability detection of a data sequence transmitted using linear-suppressed carrier modulations, specifically phase-shift keying (PSK), over the Gaussian channel with slow nonselective Rayleigh fading. Complete channel interleaving/deinterleaving and diversity reception are assumed. The problem is considered with application to Viterbi decoding in particular. It is first shown that the two presently available receivers, namely, the conventional maximum likelihood (ML) receiver and the simultaneous estimation receiver, do not perform adequately for this problem. A two-stage receiver is proposed in which the unknown channel fading gains are estimated in the first stage prior to data sequence estimation in the second stage. This receiver is shown to perform adequately, and leads to an efficient receiver/decoder for Viterbi decoding of convolutionally trellis-coded sequences. The issue of optimum estimation of channel fading gains is clarified. The bit error probability of the receiver/decoder is analyzed, and numerical performance results are presented     

OFDM系统中基于Turbo迭代的WLMS联合信道估计和检测算法

利用Turbo迭代原理,该文提出了一种迭代的维纳LMS联合信道估计和检测算法,该算法利用软映射和软解映射算法提供的软值信息,实现检测译码模块和信道估计模块之间的信息交换,通过WLMS信道估计和跟踪算法实现信道响应的逐符号更新。仿真结果表明,通过2次迭代,系统误码率性能已经基本收敛,而且在系统误码率低于10-3 时,与理想信道估计性能相比,联合估计和检测算法性能信噪比损失仅为0.5-0.8dB。     

Multiuser channel estimation and tracking for long-code CDMA systems

Channel estimation techniques for code-division multiple access (CDMA) systems need to combat multiple access interference (MAI) effectively. Most existing estimation techniques are designed for CDMA systems with short repetitive spreading codes. However, current and next-generation wireless systems use long spreading codes whose periods are much larger than the symbol duration. We derive the maximum-likelihood channel estimate for long-code CDMA systems over multipath channels using training sequences and approximate it using an iterative algorithm to reduce the computational complexity in each symbol duration. The iterative channel estimate is also shown to be asymptotically unbiased. The effectiveness of the iterative channel estimator is demonstrated in terms of squared error in estimation as well as the bit error rate performance of a multistage detector based on the channel estimates. The effect of error in decision feedback from the multistage detector (used in the absence of training sequences) is also shown to be negligible for reasonable feedback error rates using simulations. The proposed iterative channel estimation technique is also extended to track slowly varying multipath fading channels using decision feedback. Thus, an MAI-resistant multiuser channel estimation and tracking scheme with reasonable computational complexity is derived for long-code CDMA systems over multipath fading channels.     

Channel estimation and long-range prediction of fast fading channels for adaptive OFDM system

This correspondence presents the channel estimation and long-range prediction technique for adaptive-orthogonal-frequency-division-multiplexing (AOFDM) system. The efficient channel loading is accomplished by feeding the accurately predicted channel-state-information (CSI) back to transmitter. The frequency-selective wireless fading channel is modelled as a tapped-delay-line-filter governed by a first-order autoregressive (AR1) process; and an adaptive channel estimator based on the generalised-variable-step-size least-mean-square (GVSS-LMS) algorithm tracks AR1 correlation coefficient. To compensate for the signal fading due to channel state variations, a modified-Kalman-filter (MKF)-based channel estimator is utilised. In addition, channel tracking is also performed for predicting future CSI at receiver, based on the numeric-variable-forgetting-factor recursive-least-squares (NVFF-RLS) algorithm. Subsequently, adaptive bit allocation for AOFDM system is employed by using predicted CSI at transmitter. Here, the proposed combination of GVSS-LMS and MKF algorithms for robust channel estimation and the NVFF-RLS algorithm for efficient channel prediction is incorporated. The performance validation of presented method is carried out by using different channel realisations through simulation, and also by comparing it with fixed step-size LMS, MKF and fixed forgetting-factor RLS algorithm based conventional techniques. Eventually, the reliable performance of underlying AOFDM system can be achieved in terms of the lower mean squared estimation/prediction errors and alleviated symbol error rate.     

Analysis of LMS-adaptive MLSE equalization on multipath fadingchannels

We consider a practical maximum-likelihood sequence estimation (MLSE) equalizer on multipath fading channels in conjunction with an adaptive channel estimator consisting of a least mean square (LMS) estimator and a linear channel predictor, instead of assuming perfect channel estimates. A new LMS estimator model is proposed which can accurately characterize the statistical behavior of the LMS estimator over multipath fading channels. Based on this model, a new upper-bound on block error rate is derived under the consideration of imperfect channel estimates. Computer simulations verify that our analytical results can correctly predict the real system performance and are applicable over a wide range of the step size parameter of the LMS estimator