Is blind channel estimation feasible in mobile communicationsystems? A study based on GSM

We compare the effect of blind and nonblind channel estimates on the performance of Global System for Mobile communications (GSM) receivers. More precisely, we investigate whether two blind approaches, based on higher order statistics (HOS), can compete with two conventional methods, exploiting training sequences. For blind and nonblind estimates of six fast and slowly fading mobile radio channels, we give simulated bit error rates (BERs), after Viterbi detection, in terms of the signal-to-noise ratio (SNR). We also study the influence of cochannel interferers at different values of the signal-to-interference ratio (SIR). Averaged over the six channel examples, we demonstrate that the blind channel estimation algorithm eigenvector approach to blind identification (EVI) leads to an SNR loss of 1.2-1.3 dB only, while it saves the 22% overhead in GSM data rate caused by the transmission of training sequences. Since just 142 samples are used for blind channel estimation, we consider this performance outstanding for an approach based on HOS     

Prediction error method for second-order blind identification

Blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest. In this paper, we introduce a second-order blind identification technique based on a linear prediction approach. In contrast to eigenstructure-based methods, it will be shown that the linear prediction error method is “robust” to order overdetermination. An asymptotic performance analysis of the proposed estimation method is carried out, consistency and asymptotic normality of the estimates is established. A closed-form expression for the asymptotic covariance of the estimates is given. Numerical simulations and investigations are finally presented to demonstrate the potential and the “robustness” of the proposed method     

Robustness of least-squares and subspace methods for blind channelidentification/equalization with respect to effective channelundermodeling/overmodeling

The least-squares and the subspace methods are two well-known approaches for blind channel identification/equalization. When the order of the channel is known, the algorithms are able to identify the channel, under the so-called length and zero conditions. Furthermore, in the noiseless case, the channel can be perfectly equalized. Less is known about the performance of these algorithms in the practically inevitable cases in which the channel possesses long tails of “small” impulse response terms. We study the performance of the mth-order least-squares and subspace methods using a perturbation analysis approach. We partition the true impulse response into the mth-order significant part and the tails. We show that the mth-order least-squares or subspace methods estimate an impulse response that is “close” to the mth-order significant part. The closeness depends on the diversity of the mth-order significant part and the size of the tails. Furthermore, we show that if we try to model not only the “large” terms but also some “small” ones, then the quality of our estimate may degrade dramatically; thus, we should avoid modeling “small” terms. Finally, we present simulations using measured microwave radio channels, highlighting potential advantages and shortcomings of the least-squares and subspace methods     

Effective channel order estimation based on combined identification/equalization

Channel order estimation is a critical step in most blind single-input multiple-output (SIMO) channel identification/equalization algorithms. Several methods for estimating either the true channel order or its most significant part (the so-called effective channel order) have been recently proposed, but a solution able to work in practical scenarios (low or moderate signal-to-noise ratios (SNRs) and channels with small leading and/or trailing coefficients) has not been found yet. In this paper, a new criterion for effective channel order detection of SIMO channels is presented. The method is based on the fact that the cost function typically used in blind identification algorithms decreases monotonically with the estimated channel order, whereas for blind equalization algorithms, the cost function increases monotonically. In this paper, it is shown that a straightforward combination of both cost functions attains its minimum at the correct channel order even for moderate SNRs. The proposed method is able to work with small data sets, colored signals, and channels with small head and tail taps, which is a common problem in communication applications. The improvement of the proposed criterion over a number of existing algorithms is demonstrated through simulations.     

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.     

认知无线电中OFDM信号信噪比盲估计

针对认知正交频分复用(OFDM,orthogonal frequency division multiplexing)系统中低信噪比多径信道下传统的OFDM信号信噪比盲估计算法的估计性能差,计算复杂度高的问题,提出一种新的OFDM信号信噪比盲估计方法,该方法首先利用自相关函数的特性粗略估计出信道阶数,确定循环前缀部分中不受符号间干扰的数据区间,然后根据选定区间的数据的自相关函数值估计接收信号的信号功率,最后利用循环前缀数据为部分有用数据的复制这一特性估计出噪声功率,从而估计出接收信号的信噪比。仿真实验结果表明,提出的方法无需任何先验信息,在低信噪比多径信道下具有良好的估计性能,且计算复杂度低,更适合于认知OFDM系统。     

利用盖尔圆定理的SIMO系统信道阶数盲估计

目前盲信道估计大多采用基于二阶统计量的估计方法,然而这一类方法的性能受到信道阶数估计准确度的严重影响。在低信噪比、存在明显首尾系数的信道条件下,大多数信道阶数估计方法的性能并不理想。本文针对这种情况,分析了接收信号自协方差矩阵的秩与信道阶数的关系。由于盖尔圆理论能够有效实现矩阵秩的估计,因此我们提出一种基于盖尔圆理论的信道阶数估计方法。该方法构造了一种改进的自适应判决门限,能够在不同的信道条件下具有更强的鲁棒性。通过仿真验证,本文所提方法在低信噪比和存在首尾系数的信道条件下,能获得较高的信道阶数估计准确率。      

On a whitening approach to partial channel estimation and blindequalization of FIR/IIR multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when a single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. The basis of the approach is the design of a zero-forcing equalizer that whitens the noise-free data. We allow infinite impulse response (IIR) channels. Moreover, the multichannel transfer function need not be column reduced. Our approaches also work when the “subchannel” transfer functions have common zeros as long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. A linear prediction approach is also considered under the above conditions of possibly IIR channels, common subchannel zeros/factors, and not-necessarily column reduced channels. Four illustrative simulation examples are provided     

Blind channel estimation using fractional sampling

We consider the problem of blind estimation of a communication channel based on the oversampled channel output. We propose a nonparametric approach that, based on the cyclic spectrum of the output, finds the channel phase response without neither the need of phase unwrapping nor channel length information. For band-limited channels, the cyclic spectrum has limited support. For this case, we propose an approximation for the discretized phase of the cyclic spectrum that, under certain conditions, results in a simpler channel estimation method. The proposed approach is applied to simulated data and real recordings and is compared to existing methods.     

空时编码多载波码分多址MIMO系统下行频率选择性信道盲估计

基于子空间方法的无线信道盲估计由于其算法的固有特性,使得估计结果与实际信道之间存在一个不确定复系数,无法得到无线信道的精确估计。在利用子空间分解方法对空时编码多输入多输出MC-CDMA系统下行频率选择性信道盲估计的基础上,利用发射符号的有限码集特性,将单载波系统下的模糊复系数盲辨识方法推广到多载波多输入多输出系统,从而得到信道的精确估计。Monte-Carlo仿真表明,在信噪比较低的情况下,本方法的信道估计误差仍然较小。     

基于子空间投影的信道阶数盲估计算法

根据联合阶数估计最小二乘平滑算法(J-LSS)中投影误差矩阵的特点,利用其零空间向量形成的特殊矩阵的秩与信道阶数的关系,分别构造2个阶数估计代价函数。将2个代价函数归一化后联合构建成新的代价函数,新的代价函数较使用单一代价函数提升了在低信噪比下的辨识率。仿真结果表明,与传统算法相比,该算法在较低的信噪比和小样本观测数据条件下,有很好的估计性能。     

利用特征极值比的盲信道阶数估计方法

确定性辨识方法是盲信道辨识的主流方法,然而确定性方法性能受信道阶数估计的严重影响。本文针对大多数信道阶数估计算法在坏信道条件下失效问题,分析子空间方法中噪声子空间矢量构成特殊矩阵的奇异性与信道阶数之间的关系,对该特殊矩阵最大特征值最小特征值的变化情况进行对比分析,利用特征极值的比值来反映信号子空间到噪声子空间的变化情况,从而提出特征极值比定理。针对观测数据有限且含噪声的实际应用条件,提出一种盲信道阶数估计算法,该算法以不同信道阶数的特征极值比作为参数构造目标函数,得到在真实信道阶数处目标函数取全局最大值,同时对该算法进行了复杂度分析。最后针对两种常用仿真信道参数对算法进行了验证,结果表明,在短数据和低信噪比条件下,本文算法能以较高的估计概率得到好信道和坏信道的有效阶数。      

地空衰落信道下JTIDS信号信噪比盲估计

针对地空衰落信道下联合战术信息分发系统（JTIDS）信号信噪比的估计问题,提出了一种适用于单脉冲和双脉冲时隙结构JTIDS信号的接收信噪比盲估计方法。首先,利用信道实时最大时延粗估计值确定无符号间干扰的数据区间;其次,基于JTIDS信号脉冲时隙结构中静默时间的保护间隔特性估计噪声功率;最后,根据选定区间数据的自相关函数估计接收信号的信号功率,从而估计出接收链路的信噪比。仿真实验结果表明,取单时隙样本长度时,在巡航、起降两种空中平台状态下,提出估计方法在较宽信噪比范围内具有良好的均方误差估计性能,可满足JTIDS系统的信噪比估计需求。     

A Linear Prediction Based Estimation of Signal‐to‐Noise Ratio in AWGN Channel

Most signal‐to‐noise ratio (SNR) estimation techniques in digital communication channels derive the SNR estimates solely from samples of the received signal after the matched filter. They are based on symbol SNR and assume perfect synchronization and intersymbol interference (ISI)‐free symbols. In severe channel distortion where ISI is significant, the performance of these estimators badly deteriorates. We propose an SNR estimator which can operate on data samples collected at the front‐end of a receiver or at the input to the decision device. This will relax the restrictions over channel distortions and help extend the application of SNR estimators beyond system monitoring. The proposed estimator uses the characteristics of the second order moments of the additive white Gaussian noise digital communication channel and a linear predictor based on the modified‐covariance algorithm in estimating the SNR value. The performance of the proposed technique is investigated and compared with other in‐service SNR estimators in digital communication channels. The simulated performance is also compared to the Cramér‐Rao bound as derived at the input of the decision circuit.     

Optimal and mismatched detection of QAM signals in fast fading channels with imperfect channel estimation

In this paper, we derive an optimal detector for pilot-assisted transmission in Rayleigh fading channels with imperfect channel estimation. The classical approach is based on obtaining channel estimates and treating them as perfect in a minimum distance detector (this is called mismatched detector). The optimal detector jointly processes the received pilot and data symbols to recover the data. The optimal detector is specified for fast frequency-flat fading channels.We consider spline approximation of the channel gain time variations and compare the detection performance of different mismatched detectors with the optimal one. Further, we investigate the detection performance of an iterative receiver in a system transmitting turbo-encoded data, where a channel estimator provides either maximum likelihood estimates, minimum mean square error (MMSE) estimates or statistics for the optimal detector. Simulation results show that the optimal detector outperforms the mismatched detectors. However, the improvement in the detection performance compared to the mismatched detector with the MMSE channel estimates is modest.     

空时分组码系统的盲信道估计

空时编码是实现宽带无线数据通信的一种极有潜力的技术,随着发射天线个数的增加,对空时编码进行信道估计时,所需训练符号的个数也将增加,减少了传输数据的有效时间.本文将子空间方法同空时分组码的特性有机地结合,提出了无需训练序列,直接进行信道估计的方法.它充分利用空时分组码的特性,使得接收信号中,表示信道衰落影响的矩阵各向量间存在一定联系,利用这些联系,结合子空间方法,从接收信号中解得信道信息.Monte-Carlo仿真表明,在信噪比较低时,本文算法带来的信道估计误差对于解码性能影响较小.     

Bilinear approach to multiuser second-order statistics-based blindchannel estimation

We present a bilinear approach to multiple-input multiple-output (MIMO) blind channel estimation where products of the channel parameters are first estimated from the covariance of the received data. The channel parameters are then obtained as the dominant eigenvectors of the outer-product estimate. Necessary and sufficient identifiability conditions are presented for a single channel and extended to the multichannel case. It is found that this technique can identify the channel to within a subspace ambiguity, as long as the basis functions for the channel satisfy certain constraints, regardless of the left invertability of the channel matrix. One important requirement for identifiability is that the number of channel parameters is small compared with the channel length; advantageously, this is exactly the situation in which this algorithm has significantly lower complexity than competing (parametric, multiuser) blind algorithms. Simulations show that the technique is applicable in situations where typical identifiability conditions fail: common nulls, a single symbol-spaced channel, and more users than channels. These simulations are for the “almost flat” faded situation when the propagation delay spread is a fraction of the transmission pulse duration (as might be found in current TDMA systems). Comparisons are made, when possible, to a subspace method incorporating knowledge of the basis functions. The bilinear approach requires significantly less computation but performs better than the subspace method at low SNR, especially for multiple users     

Performance analysis of semiblind channel estimation in long-code DS-CDMA systems

The performance of second-order statistics (SOS)-based semiblind channel estimation in long-code direct-sequence code-division multiple-access systems is analyzed. The covariance matrix of second-order statistics estimates is obtained in the large system limit and is used to analyze the large-sample performance of two SOS-based semiblind channel estimation algorithms. A notion of blind estimation efficiency is also defined and is examined via simulation results.     

一种基于矩阵外积分解的信道盲辨识与盲均衡算法

本文提出了一种鲁棒性较好的信道盲辨识和盲均衡算法.在仅需知道信道阶数上界的条件下,首先采用改进的信道阶数估计算法对信道阶数进行精确估计,与现有算法相比,所需信噪比降低、对信道的适应性提高;然后,在矩阵外积分解算法的基础上,加入特征值扰动分析,提高了信道盲辨识和盲均衡性能.仿真结果证明了算法的有效性.     

Performance analysis of a deterministic channel estimator for blocktransmission systems with null guard intervals

A deterministic algorithm was proposed for channel identification in block communication systems. The method assumed that the channel has a finite impulse response (FIR) and that null guard intervals of length greater than the channel order are inserted between successive blocks to prevent interblock interference and allow block synchronization. In the absence of noise, the algorithm provides error-free channel estimates, using a finite number of received data, without requiring training sequences and without imposing a restriction neither on the channel, except for finite order and time invariance, nor on the symbol constellation. Using small perturbation analysis, we derive approximate expressions of the estimated channel covariance matrix, which are used to quantify the resilience of the estimation algorithm to additive noise and channel fluctuations. Specifically, we consider channel fluctuations induced by transmitter/receiver relative motion, asynchronism, and oscillators' phase noise. We also compare the channel estimation accuracy with the Cramer-Rao bound (CRB) and prove that our estimation method is statistically efficient at practical SNR values for any data block length. Finally, we validate our theoretical analysis with simulations and compare our transmission scheme with an alternative system using training sequences for channel estimation