基于输出过采样的IIR信道迫零盲均衡

本文提出一种新的针对单输入单输出IIR信道的盲均衡算法.首先通过对信道输出的过采样建立特殊的多信道模型.对多信道模型的输出应用线性预测,证明了预测误差只包含多信道模型冲激响应在第一个时隙的参数,并给出最佳线性预测器的长度.通过预测误差的协方差矩阵可以求解该冲激响应参数.基于该参数可构造出不同时延的迫零均衡器.仿真结果显示了本文算法的有效性.     

A blind multichannel identification algorithm robust to orderoverestimation

Active research in blind single input multiple output (SIMO) channel identification has led to a variety of second-order statistics-based algorithms, particularly the subspace (SS) and the linear prediction (LP) approaches. The SS algorithm shows good performance when the channel output is corrupted by noise and available for a finite time duration. However, its performance is subject to exact knowledge of the channel order, which is not guaranteed by current order detection techniques. On the other hand, the linear prediction algorithm is sensitive to observation noise, whereas its robustness to channel order overestimation is not always verified when the channel statistics are estimated. We propose a new second-order statistics-based blind channel identification algorithm that is truly robust to channel order overestimation, i.e., it is able to accurately estimate the channel impulse response from a finite number of noisy channel measurements when the assumed order is arbitrarily greater than the exact channel order. Another interesting feature is that the identification performance can be enhanced by increasing a certain smoothing factor. Moreover, the proposed algorithm proves to clearly outperform the LP algorithm. These facts are justified theoretically and verified through simulations     

Blind channel estimation for single‐input multiple‐output OFDM systems: zero padding based or cyclic prefix based?

Orthogonal frequency division multiplexing (OFDM) transmission equipped with multiple receive antennas constitutes a single‐input multiple‐output (SIMO) OFDM system. SIMO‐OFDM systems have been widely used in wireless communications. Compared to those approaches using training sequences, blind channel estimation methods for SIMO‐OFDM systems have the advantage of saving bandwidth and improving energy efficiency and system throughput. As far as blind channel identification is concerned, it is known that zero padding (ZP)‐based single‐input single‐output (SISO)‐OFDM systems have desirable features compared to conventional cyclic prefix (CP)‐based SISO‐OFDM systems. However, it is yet unknown whether ZP‐ or CP‐based SIMO‐OFDM systems are favourable for blind channel estimation. To investigate this problem, we first propose a short‐data effective method for blind channel estimation for ZP‐based SIMO‐OFDM systems. Then we analyse a number of issues surrounding blind channel estimation for ZP‐ and CP‐based SIMO‐OFDM systems. The issues brought up in the paper have not been discussed in the existing research. The significance of our investigation is that it provides a deep insight into blind channel estimation for ZP‐ and CP‐based SIMO‐OFDM systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Deterministic linear prediction methods for blind channel estimation based on dual concept of zero-forcing equalization

This paper investigates a class of second-order blind channel estimation algorithms based on deterministic linear prediction, which includes double-sided as well as forward and backward single-sided, for single input multiple output (SIMO) finite impulse response (FIR) channels. By introducing the dual problem of well-known zero-forcing equalization concept, we first derive a double-sided deterministic linear prediction (D-DLP) algorithm that has, good channel estimation performance with the knowledge of exact channel order. By further exploiting the interference subspace cancellation technique and the triangular block-Toeplitz structure of a portion of the channel filtering matrix (upper-left or lower-right part), we obtain the forward and backward single-sided deterministic linear prediction (FS-DLP and BS-DLP) algorithms that can work in the absence of knowledge of channel order with a cost of relatively poor channel estimate. Moreover, a channel order estimation method is also studied based on results from both FS-DLP and BS-DLP. Simulation examples are finally presented to demonstrate the potential of the proposed methods.     

Performance of Reduced-Rank Equalization

We evaluate the performance of reduced-rank equalizers for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) frequency-selective channels. Each equalizer filter is constrained to lie in a Krylov subspace, and can be implemented as a reduced-rank multistage Wiener filter (MSWF). Both reduced-rank linear and decision-feedback equalizers (DFEs) are considered. Our results are asymptotic as the filter length goes to infinity. For SISO channels, the output mean-squared error (MSE) is expressed in terms of the moments of the channel spectrum. For MIMO channels, both successive and parallel interference cancellation are considered. The asymptotic performance in that case requires the computation of moments, which depend on shifted versions of the channel impulse response for different users. Those are also expressed in terms of the MIMO channel frequency response. Numerical results are presented, which show that near full-rank performance can be achieved with relatively low-rank equalizers     

PN sequence blind estimation in multiuser DS‐CDMA systems with multipath channels based on successive subspace scheme

In this paper, we proposed a new method based on expanding subspace algorithm and finite alphabet characteristics, for blind estimation of the users' spreading sequences in the multiuser direct sequence code division multiple access system in the presence of the multipath channels. In the proposed scheme, we show that the estimation of the users' overall channels in the direct sequence code division multiple access system is equivalent to the impulse response estimation of the multi‐input multi‐output finite impulse response channels. Our proposed approach is based on the successive estimation of the columns of the equivalent multi‐input multi‐output finite impulse response channels from the lowest degree columns to the highest degree ones. Accordingly, each user's overall channel that is the convolution of the original multipath channel and the spreading sequence is estimated. Then we extract PN sequences from the overall channel using finite alphabet characteristics of the spreading sequence chips for each user. According to simulation results, our proposed scheme outperforms the conventional methods in that it does not require symbol synchronization and does not have channel constraints (for example, AWGN and single user system) in the multipath channels.     

Adaptive blind channel estimation by least squares smoothing

A least squares smoothing (LSS) approach is presented for the blind estimation of single-input multiple-output (SIMO) finite impulse response systems. By exploiting the isomorphic relation between the input and output subspaces, this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output. LSS has the finite sample convergence property, i.e., in the absence of noise, the channel is estimated perfectly with only a finite number of data samples. Referred to as the adaptive least squares smoothing (A-LSS) algorithm, the adaptive implementation has a high convergence rate and low computation cost with no matrix operations. A-LSS is order recursive and is implemented in part using a lattice filter. It has the advantage that when the channel order varies, channel estimates can be obtained without structural change of the implementation. For uncorrelated input sequence, the proposed algorithm performs direct deconvolution as a by-product     

基于均衡代价函数的信道阶数盲估计算法

针对信道阶数估计问题,利用单输入多输出(Single-Input Multiple-Output,SIMO)有限冲激响应(Finite Impulse Response,FIR)信道的结构特点和输入/输出信号的统计特征,提出了一种基于均衡代价函数的信道阶数盲估计算法.首先计算了归一化最小二乘均衡(Normalized Least Squares Equalization,NLSE)代价函数在理想条件下的理论渐近值,并指出其拐点与信道阶数之间的对应关系.然后分析了NLSE代价函数在实际条件下的近似值.最后引入了拐点优化因子,提出了一种基于NLSE代价函数拐点检测的信道阶数估计算法.理论分析和仿真结果表明,在信噪比(Signal-to-Noise Ratio,SNR)较低和信道首尾系数较小的情况下,该算法比现有其它方法具有更强的鲁棒性,可以获得更小的接收信号均衡误差.     

Multistep linear predictors-based blind identification andequalization of 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 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 the estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. We extend the multistep linear prediction approach to MIMO channels where the multichannel transfer function need not be column reduced. Moreover, we allow infinite impulse response (IIR) channels as well as the case where the “subchannel” transfer functions have common zeros. In the past, this approach has been confined to SIMO finite impulse response (FIR) channels with no common subchannel zeros. A related existing approach applicable to MIMO channels is restricted to FIR column-reduced systems with equal length subchannels. In our approach, the knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the “subchannel” transfer functions have common zeros, as long as the common zeros are minimum-phase zeros. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. Illustrative computer simulation examples are provided     

Multistep linear predictors-based blind equalization of FIR/IIRsingle-input multiple-output channels with common zeros

The problem of blind equalization of single-input multiple-output (SIMO) communications channels is considered using only the second order statistics of the data. Such models arise when a single receiver data is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We extend the multistep linear prediction approach to infinite impulse response (IIR) channels as well as to the case where the “subchannel” transfer functions have common zeros. In the past, this approach has been confined to finite impulse response (FIR) channels with no common subchannel zeros. We focus on the design of finite-length minimum mean-square error (MMSE) blind equalizers. Knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the “subchannel” transfer functions have common zeros as long as the common zeros are minimum-phase zeros. Illustrative simulation examples are provided     

Column-anchored zeroforcing blind equalization for multiuserwireless FIR channels

We propose a direct blind zeroforcing approach to cancel intersymbol interference (ISI) in multiple user finite impulse response (FIR) channels. By selectively anchoring columns of the channel convolution matrix, we present two column-anchored zeroforcing equalizers (CAZE), one without output delay and one with a chosen delay. Unlike many known blind identification algorithms, these equalizers do not need an accurate estimate of the channel orders. Exploiting second-order statistics (SOS) of the received signals, they can retain preselected d columns in the channel convolution matrix (d is the number of users) and force the remaining columns to zero. CAZE can effectively equalize single-input-multiple-output (SIMO) systems and can reduce dynamic multiple-input-multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. Simulation results show that the CAZE is not only effective for blind equalization of linear quadrature amplitude modulation (QAM) systems, but it is also applicable to the nonlinear GMSK modulation in the popular wireless GSM systems when computational cost severely limits the use of nonlinear methods such as the Viterbi algorithm     

Minimal Euclidean distance‐inspired optimal and suboptimal modulation schemes for vector OFDM system

In single‐input and single‐output (SISO) systems, the vector orthogonal frequency division multiplexing (VOFDM) has been proposed to reduce the cyclic prefix length, whereas the precoded OFDM has been proposed to overcome spectral‐null channels. However, VOFDM does not show robustness to spectral‐null channels, and the precoded OFDM system has expanded data rate. This work proposes the optimal and suboptimal modulation schemes in vector OFDM systems with knowledge of the channel impulse response (CIR) in order to reduce the bit error rate (BER). As the BER performance is determined by the diversity of the received vector symbols, the proposed modulation scheme mainly concerns the minimal Euclidean distance of all the possible received vector symbols. Through the analysis of the vector input and output equations, we derive the Euclidean distance of the received vector symbols. Then, we propose optimal and suboptimal modulation schemes in VOFDM system to overcome spectral‐null channels by improving the minimal Euclidean distance. Both theoretical performance analysis and simulation results are presented to show the robustness of our system. Finally, we conduct a compared performance analysis of the proposed VOFDM system, the conventional precoded OFDM system, and the conventional VOFDM system. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive equalization for frequency-selective channels of unknown length

This paper studies adaptive equalization for time-dispersive communication channels whose impulse responses have unknown lengths. This problem is important, because an adaptive equalizer designed for an incorrect channel length is suboptimal; it often estimates an unnecessarily large number of parameters. Some solutions to this problem exist (e.g., attempting to estimate the "channel length" and then switching between different equalizers); however, these are suboptimal owing to the difficulty of correctly identifying the channel length and the risk associated with an incorrect estimation of this length. Indeed, to determine the channel length is effectively a model order selection problem, for which no optimal solution is known. We propose a novel systematic approach to the problem under study, which circumvents the estimation of the channel length. The key idea is to model the channel impulse response via a mixture Gaussian model, which has one component for each possible channel length. The parameters of the mixture model are estimated from a received pilot sequence. We derive the optimal receiver associated with this mixture model, along with some computationally efficient approximations of it. We also devise a receiver, consisting of a bank of soft-output Viterbi algorithms, which can deliver soft decisions. Via numerical simulations, we show that our new method can outperform conventional adaptive Viterbi equalizers that use a fixed or an estimated channel length.     

Joint order detection and blind channel estimation by least squaressmoothing

A joint order detection and blind estimation algorithm for single input multiple output channels is proposed. By exploiting the isomorphic relation between the channel input and output subspaces, it is shown that the channel order and channel impulse response are uniquely determined by finite least squares smoothing error sequences in the absence of noise. The proposed subspace algorithm is shown to have marked improvement over existing algorithms in performance and robustness in simulations     

基于遗传算法的盲信道估计新算法

基于单输入多输出的信道模型,该文提出一种基于遗传算法的信道盲估计算法,该算法的特点是基于低阶统计量,计算速度快;并且把信道阶数作为染色体的一部分参与估计,从而能在信道阶数未知的条件下同时对信道阶数和参数进行估计。仿真结果表明该算法的性能优于现有的非迭代算法。     

Soft-Input Soft-Output Equalizers for Turbo Receivers: A Statistical Physics Perspective

Many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations, i.e., the inference problem, as well as with the problem of estimating the model parameters. Such an inference and estimation problem is encountered, for e.g., in adaptive turbo equalization/demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty, given the received signal samples and a priori information provided by the decoder. An exact inference algorithm computes the a posteriori probability (APP) values for all transmitted symbols, but the computation of APPs is known to be an NP-hard problem, thus, rendering this approach computationally prohibitive in most cases. In this paper, we show how many of the well-known low-complexity soft-input soft-output (SISO) equalizers, including the channel-matched filter-based linear SISO equalizers and minimum mean square error (MMSE) SISO equalizers, as well as the expectation-maximization (EM) algorithm-based SISO demodulators in the presence of the Rayleigh fading channel, can be formulated as solutions to a variational optimization problem. The variational optimization is a well-established methodology for low-complexity inference and estimation, originating from statistical physics. Importantly, the imposed variational optimization framework provides an interesting link between the APP demodulators and the linear SISO equalizers. Moreover, it provides a new set of insights into the structure and performance of these widely celebrated linear SISO equalizers while suggesting their fine tuning as well.     

An efficient approach to ARMA modeling of biological systems withmultiple inputs and delays

Presents a new approach to AutoRegressive Moving Average (ARMA or ARX) modeling which automatically seeks the best model order to represent investigated linear, time invariant systems using their input/output data. The algorithm seeks the ARMA parameterization,which accounts for variability in the output of the system due to input activity and contains the fewest number of parameters required to do so. The unique characteristics of the proposed system identification algorithm are its simplicity and efficiency in handling systems with delays and multiple inputs. The authors present results of applying the algorithm to simulated data and experimental biological data. In addition, a technique for assessing the error associated with the impulse responses calculated from estimated ARMA parameterizations is presented. The mapping from ARMA coefficients to impulse response estimates is nonlinear, which complicates any effort to construct confidence bounds for the obtained impulse responses. Here a method for obtaining a linearization of this mapping is derived, which leads to a simple procedure to approximate the confidence bounds     

Blind input, initial state, and system identification of SIMO Laguerre systems

Laguerre filters have infinite impulse responses (IIRs) but with finite tapped delay-line parameterizations. This paper investigates subspace-based blind identification of Laguerre filter tap coefficients, the internal filter state, and the input, given only noisy observations of the output. This paper deals only with single-input, multiple-output (SIMO) Laguerre models. A state space model for the SIMO Laguerre system is derived from which blind estimation algorithms are developed. As in the finite impulse response (FIR) case, the Laguerre filter taps coefficients can be estimated from the column space of a certain Hankel matrix constructed from noisy output observations, whereas the internal state and input can be estimated from the row space by exploiting state space structure. While not exactly uniquely identifiable, conditions are given for which the tap coefficients, the internal state, and the input can be determined to within a multiplicative scalar factor.     

Performance bounds for multistep prediction-based blindequalization

Blind equalization attempts to remove the interference caused by a communication channel without using any known training sequences. Blind equalizers may be implemented with linear prediction-error filters (PEFs). For many practical channel types, a suitable delay at the output of the equalizer allows for achieving a small estimation error. The delay cannot be controlled with one-step predictors. Consequently, multistep PEF-based algorithms have been suggested as a solution to the problem. The derivation of the existing algorithms is based on the assumption of a noiseless channel, which results in zero-forcing equalization. We consider the effects of additive noise at the output of the multistep PEF. Analytical error bounds for two PEF-based blind equalizers in the presence of noise are derived. The obtained results are verified with simulations. The effect of energy concentration in the channel impulse response on the error bound is also addressed     

Spectral efficiency improvement with SISO and SIMO in M‐QAM over millimeter‐wave links

This paper proposes a spectral efficiency improvement technique for millimeter wave (mmWave) links. The proposed technique provides an efficient utilization of the mmWave link capacity. This technique is applied in three cases the single‐input single‐output (SISO), single‐input multiple‐output (SIMO) with the maximal ratio combining and with the equal gain combining. The M‐ary quadrature amplitude modulation scheme is used in our work. The power series expansion is used for deriving closed‐form expressions for bit error rate (BER) performances in all studied cases. The BER closed‐form expressions are confirmed by the numerical solution of the integral equations. The simulation results show that a high spectral efficiency can be accomplished by the proposed technique. As well as the derived expressions closely match with the numerical solution of integration expressions at different values of modulations order the Rician factor. For instance, the spectral efficiency gain achievement is 8 at signal‐to‐noise ratio (SNR) equals 34 dB in the case of SISO system whereas in the case of SIMO system, the same gain is achieved at SNR equals 24 dB. As well as the BER performance is enhanced from 1.188 × 10^?4, 7.112 × 10^?4, 4.164 × 10^?3, and 3.286 × 10^?2 to 8.717 × 10^?16, 1.119 × 10^?12, 1.308 × 10^?9, and 4.905 × 10^?6 for M = 4, 16, 64, and 256, respectively, at SNR equals 30 dB.