On channel estimation using optimal training sequences in Cyclic-Prefix-based Single-Carrier systems with Space-Time Block-Coding

In this paper, a new scheme that combines Space-Time Block-Coding （STBC） based on an Alamouti-like scheme and the Least Squares （LS） channel estimation using optimal training sequences in Cyclic-Prefix-based （CP）／Single-Carrier （SC） systems is proposed. With two transmit antennas, based on Cramer-Rao lower bound for channel estimation, it is shown that the Periodic Complementary Set （PCS） is optimal over frequency-selective fading channels. Compared with the normal scheme without STBC, 3dB Mean Square Error （MSE） performance gains and fewer restrictions on the length of channel impulse response are demonstrated.     

宽带MIMO-OFDM系统信道估计算法研究

本文提出了MIMO-OFDM系统中基于LS准则的参数化信道估计方法(LSPCE),推导出其MSE性能的下界并给出一种最优导频序列.为了降低复杂度,本文还提出了一种迭代的算法,它利用有限冲击响应信道的抽头之间的相关性从噪声中提取出信道信息并同时估计出多径时延.仿真和分析表明,相比传统的LS信道估计算法,这种基于参数化的信道估计算法可以大大提高信道估计的精度,接收端的检测性能接近理想信道估计的性能.     

Least Square Channel Estimation for Two‐Way Relay MIMO OFDM Systems

This letter considers the channel estimation for two‐way relay MIMO OFDM systems. A least square (LS) channel estimation algorithm under block‐based training is proposed. The mean square error (MSE) of the LS channel estimate is computed, and the optimal training sequences with respect to this MSE are derived. Some numerical examples are presented to evaluate the performance of the proposed channel estimation method.     

Time‐varying channel estimation for MIMO/OFDM systems using superimposed training and basis expansion models

An approach of superimposed training (ST)‐aided time‐varying (TV) channel estimation for multiple‐input multiple‐output orthogonal frequency division multiplexing systems is presented. By modeling the TV channel with the truncated discrete basis expansion model, a two‐step approach is adopted to estimate the TV channel. In addition, the mean square error (MSE) of the proposed channel estimation is analyzed, and its closed‐form expression is derived, which is a function of the data‐to‐ST power ratio. Using the developed channel MSE, we case the problem of ST power‐allocation by minimizing the lower bound on the average channel capacity. To enhance the performance of channel estimation, a low‐complexity decision feedback mechanism is introduced to iteratively mitigate the unknown data interference. Numerical results verify the performances of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

适用于LPTV系统的周期自适应滤波器的研究

该文讨论了平稳(或周期平稳)随机信号通过线性时不变(或周期时变)系统后,输出信号的周期平稳性质,给出了两种可用于线性周期时变(LPTV)系统的周期自适应滤波器算法和一种系统周期的自适应估计算法;仿真结果表明了上述算法的有效性。     

基于Kronecker积的无线通信系统参量分离方法

针对无线通信系统中发射机非线性与多径衰落信道问题,提出了一种根据接收无线信号联合估计无线设备功率放大器(PA)非线性与无线信道单位脉冲响应的方法.首先,根据通信帧训练符号及发射机非线性模型构造卷积矩阵;接着,采用一次最小二乘(LS),根据接收信号估计PA的非线性模型系数与实际发送符号;然后,再采用一次LS,得到无线信道的单位脉冲响应估计;两估计可迭代或直接加取平均进行积累.理论推导与实验结果显示,采用过采样技术,所提方法可应用于单载波或多载波通信,实现PA非线性与无线信道单位脉冲响应的有效分离.新方法在无线通信的物理层射频指纹认证与信号可靠传输中具有应用价值.     

Alias-Component Matrices of Multirate Systems

We consider a multirate system, which is a generalization of linear time-invariant systems. Such a system is invariant to a certain shift in the input sequence. In particular, assume that p and q are coprime. A multirate system with the property that a delay of mq samples in its input sequence results in a delay of mp samples in its output sequence is called an (mp, mq)-periodic system. This multirate system can be obtained by cascading an upsampler, followed by a linear periodically time-varying (LPTV) kernel system, then followed by a downsampler. Here, we study the alias-component matrices of multirate systems. We show that they can be obtained from the alias-component matrices of their LPTV kernels by some row and column additions. An example shows the use of the method to design rate changers for a specified frequency band swap.     

Performance Analysis of Tikhonov Regularized LS Channel Estimation for MIMO OFDM Systems with Virtual Carriers

In this paper the effect of virtual carriers (VCs) on channel estimation performance is considered for multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The link between the number of VCs and the inverse problem in a conventional LS channel estimation is identified. It is observed that a linear increase in VCs contributes to an exponential increase of the system inverse problem as the condition number of the inverse matrix is exponentially increased. A solution is proposed using a low complexity modified LS channel estimation. The performance analysis of the modified LS channel estimation, regarding the effect of VCs, show gains in both the mean square error (MSE) performance of channel estimation as well as bit error rate (BER) system performance compared to conventional LS. The performance is improved irrespective of the increasing number of VCs as the estimator is shown to be insensitive to the increase of VCs in the OFDM system. The complexity reduction is also considered and an approach is proposed showing a similar complexity as LS.     

Representations of linear periodically time-varying and multirate systems

The linear switched time-varying (LSTV), polyphase (blocked), and alias-component representations of linear periodically time-varying (LPTV) systems are studied. In particular, alias-components are related to the time-shifted versions of the system. It is shown that in general, a filterbank is equivalent to the cascade connection of two LPTV systems. By generalizing some of the results of the LSTV representation of LPTV systems, it is shown that for relatively coprime integers p and m, a p-channel filterbank that has LPTV filters with period m is equivalent to an mp-channel filterbank with LTI filters. The representation of multirate systems that have LPTV kernels is discussed next. Due to the presence of the upsampler and downsampler, there are some degrees of freedom in the choice of the kernel. This redundancy is dealt with by choosing from various subclasses so that there is a one-to-one relationship between a multirate system and its kernel. Then, we find the LPTV kernel that has the least period.     

Adaptive recovery of a chirped sinusoid in noise. II. Performanceof the LMS algorithm

For pt.I see ibid., vol.39, no. 3, p.583-94 (1991). The authors present a methodology for evaluating the tracking behavior of the least-mean square (LMS) algorithm for the nontrivial case of recovering a chirped sinusoid in additive noise. A complete closed-form analysis of the LMS tracking properties for a nonstationary inverse system modeling problem is also presented. The mean-square error (MSE) performance of the LMS algorithm is calculated as a function of the various system parameters. The misadjustment or residual of the adaptive filter output is the excess MSE as compared to the optimal filter for the problem. It is caused by three errors in the adaptive weight vector: the mean lag error between the (time-varying mean) weight and the time-varying optimal weight; the fluctuations of the lag error; and the noise misadjustment which is due to the output noise. These results are important because they represent a precise analysis of a nonstationary deterministic inverse modeling system problem with the input being a colored signal. The results are in agreement with the form of the upper bounds for the misadjustment provided by E. Eweda and O. Macchi (1985) for the deterministic nonstationarity     

Optimal training design for MIMO OFDM systems in mobile wireless channels

This paper describes a least squares (LS) channel estimation scheme for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems based on pilot tones. We first compute the mean square error (MSE) of the LS channel estimate. We then derive optimal pilot sequences and optimal placement of the pilot tones with respect to this MSE. It is shown that the optimal pilot sequences are equipowered, equispaced, and phase shift orthogonal. To reduce the training overhead, an LS channel estimation scheme over multiple OFDM symbols is also discussed. Moreover, to enhance channel estimation, a recursive LS (RLS) algorithm is proposed, for which we derive the optimal forgetting or tracking factor. This factor is found to be a function of both the noise variance and the channel Doppler spread. Through simulations, it is shown that the optimal pilot sequences derived in this paper outperform both the orthogonal and random pilot sequences. It is also shown that a considerable gain in signal-to-noise ratio (SNR) can be obtained by using the RLS algorithm, especially in slowly time-varying channels.     

Cramer–Rao bound based mean‐squared error and throughput analysis of superimposed pilots for semi‐blind multiple‐input multiple‐output wireless channel estimation

This work presents a study of the mean‐squared error (MSE) and throughput performance of superimposed pilots (SP) for the estimation of a multiple‐input multiple‐output (MIMO) wireless channel. The Cramer–Rao bound (CRB) is derived for SP based estimation of the MIMO channel matrix. Employing the CRB analysis, it is proved that the asymptotic MSE bound is potentially 3 dB lower than the MSE performance of the existing SP mean based estimation (SPME) schemes. Motivated by this observation, a novel SP semi‐blind scheme is presented for MIMO channel estimation. This scheme asymptotically achieves the CRB and hence has a lower MSE of estimation when compared with SPME schemes. We also derive closed form expressions for the optimal source‐pilot power allocation in SP by maximizing the post‐processing signal‐to‐noise power ratio at the receiver. In the final part, a new result is presented for the worst‐case capacity of a communication channel with correlated information symbols and noise. This framework is employed to quantify the throughput performance of SP and also to demonstrate the bandwidth efficiency of SP compared with that of a conventional pilot based system. Copyright © 2012 John Wiley & Sons, Ltd.     

Cumulants: A powerful tool in signal processing

The impulse response of a linear, time-invariant system is related in a simple closed-form solution to the output cumulants, when the input is assumed to be non-Gaussian and independent. This expression permits the use of one-dimensional processing of the output cumulants for identification of non-minimum-phase systems, and opens new directions in other signal processing applications.     

一种降低OFDM移动通信系统中LS信道估计均方误差的算法

在基于OFDM的移动通信系统中,针对LS信道估计时域结果的构成特点,同时结合无线信道冲激响应在时域为有限持续长度的特性,提出一种新的算法估计信道有效阶数,然后利用该估计值对LS信道估计时域结果进行加窗处理以减小LS算法中由噪声和子信道间干扰引起的均方误差:LS算法性能的提高及其对系统误符号性能的改善通过计算机仿真得以验证.     

Universal Weighted MSE Improvement of the Least-Squares Estimator

Since the seminal work of Stein in the 1950s, there has been continuing research devoted to improving the total mean-squared error (MSE) of the least-squares (LS) estimator in the linear regression model. However, a drawback of these methods is that although they improve the total MSE, they do so at the expense of increasing the MSE of some of the individual signal components. Here we consider a framework for developing linear estimators that outperform the LS strategy over bounded norm signals, under all weighted MSE measures. This guarantees, for example, that both the total MSE and the MSE of each of the elements will be smaller than that resulting from the LS approach. We begin by deriving an easily verifiable condition on a linear method that ensures LS domination for every weighted MSE. We then suggest a minimax estimator that minimizes the worst-case MSE over all weighting matrices and bounded norm signals subject to the universal weighted MSE domination constraint.     

Blind identification of autoregressive system using chaos

The problem of identifying an autoregressive (AR) model using chaos is investigated here. Based on the Cramer-Rao bound (CRB) analysis, it is proved here that when chaos is used to drive an AR system, identification using only the output signal can be as good as that based on using both input and output signals, that is, blind identification is equivalent to nonblind identification. A deterministic maximum likelihood (ML) is, therefore, developed to blindly identify an AR system driven by chaos. Combined with the global search technique genetic algorithm (GA), the proposed GA-ML method is found to achieve the optimal identification performance imposed by the CRB. The theoretical mean square error (MSE) performance of the proposed GA-ML method is derived, and the result is validated using computer simulations. Compared to conventional methods based on white Gaussian driving signal, the chaos approach is shown to have superior performance. The improvement is proved to be the result of the positive and finite Lyapunov exponent of the chaotic signal. The proposed chaos identification method is applied to blind equalization of a spread spectrum (SS) communication system where chaos is used to modulate the information signal. Computer simulations show that the proposed chaos approach has a satisfactory equalization performance even under strong channel effects.     

模拟电路故障诊断的小波神经网络方法

利用小波和改进型BP神经网络相结合的方法,进行模拟电路故障诊断;通过分析被测电路的冲激响应,来识别电路中的故障元件;用小波对冲激响应信号进行多尺度分解,进行归一化后,提取特征信息作为神经网络的输入而进行分类。该方法减少了神经网络的输入、简化了其结构、并缩短了训练和处理时间。实验仿真结果表明:该方法能准确实现故障定位且准确率高。     

Impulse response shortening for discrete multitone transceivers

In discrete multitone (DMT) transceivers an intelligent guard time sequence, called a cyclic prefix (CP), is inserted between symbols to ensure that samples from one symbol do not interfere with the samples of another symbol. The length of the CP is determined by the length of the impulse response of the effective physical channel. Using a long CP reduces the throughput of the transceiver, To avoid using a long CP, a short time-domain finite impulse response (FIR) filter is used to shorten the effective channels impulse response. This paper explores various methods of determining the coefficients for this time-domain filter. An optimal shortening and a least-squares (LS) approach are developed for shortening the channel's impulse response. To provide a computationally efficient algorithm a variation of the LS approach is explored. In full-duplex transceivers the length of the effective echo path impacts the computational requirements of the transceiver. A new paradigm of joint shortening is introduced and three methods are developed to jointly shorten the channel and the echo impulse responses in order to reduce the length of the CP and reduce computational requirements for the echo canceller     

Linear bispectrum of signals and identification of nonminimum phaseFIR systems driven by colored input

The identification of non-minimum-phase finite-impulse-response (FIR) systems driven by third-order stationary colored signals that are not linear processes is addressed. Modeling the linear part of the bispectrum of a signal is discussed. The bispectrum of a signal is decomposed into two multiplicative factors. The linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third-order white-noise-driven linear shift-invariant (LSI) system. The linear bispectrum of the output of the unknown LSI system is represented using an ARMA (autoregressive moving average) model, where the MA parameters correspond to the unknown FIR system impulse response coefficients, and the AR parameters model the linear bispectrum of the input signal. An algorithm for identifying the MA and AR parameters is given. How the proposed method is different from fitting an ARMA model directly to the bicumulants or the bispectrum of the system output is discussed. The method is applied to blur identification     

BLUE‐Based Channel Estimation Technique for Amplify and Forward Wireless Relay Networks

The best linear unbiased estimator (BLUE) is most suitable for practical application and can be determined with knowledge of only the first and second moments of the probability density function. Although the BLUE is an existing algorithm, it is still largely unexplored and has not yet been applied to channel estimation in amplify and forward (AF)‐based wireless relay networks (WRNs). In this paper, a BLUE‐based algorithm is proposed to estimate the overall channel impulse response between the source and destination of AF strategy‐based WRNs. Theoretical mean square error (MSE) performance for the BLUE is derived to show the accuracy of the proposed channel estimation algorithm. In addition, the Cramér‐Rao lower bound (CRLB) is derived to validate the MSE performance. The proposed BLUE channel estimation algorithm approaches the CRLB as the length of the training sequence and number of relays increases. Further, the BLUE performs better than the linear minimum MSE estimator due to the minimum variance characteristic exhibited by the BLUE, which happens to be a function of signal‐to‐noise ratio.