Communicating over nonstationary nonflat wireless channels

We develop the concept of joint time-frequency estimation of wireless channels. The motivation is to optimize channel usage by increasing the signal-to-noise ratio (SNR) after demodulation while keeping training overhead at a moderate level. This issue is important for single-input single-output (SISO) and multiple-input multiple-output (MIMO) systems but particularly so for the latter. Linear operators offer a general mathematical framework for symbol modulation in channels that vary both temporally and spectrally within the duration and bandwidth of one symbol. In particular, we present a channel model that assumes first-order temporal and spectral fluctuations within one symbol or symbol block. Discrete prolate spheroidal sequences (Slepian sequences) are used as pulse-shaping functions. The channel operator in the Slepian basis is almost tridiagonal, and the simple intersymbol interference pattern can be exploited for efficient and fast decoding using Viterbi's algorithm. To prove the concept, we use the acoustic channel as a meaningful physical analogy to the radio channel. In acoustic 2 /spl times/ 2 MIMO experiments, our method produced estimation results that are superior to first-order time-only, frequency-only, and zeroth-order models by 7.0, 9.4, and 11.6 db. In computer simulations of cellular wireless channels with realistic temporal and spectral fluctuations, time-frequency estimation gains us 12 to 18 db over constant-only estimation in terms of received SNR when signal-to-receiver-noise is 10 to 20 db. The bit error rate (BER) decreases by a factor of two for a binary constellation.     

Robust and Improved Channel Estimation Algorithm for MIMO-OFDM Systems

Multiple-input multiple-output (MIMO) system using orthogonal frequency division multiplexing (OFDM) technique has become a promising method for reliable high data-rate wireless transmission system in which the channel is dispersive in both time and frequency domains. Due to multiple cochannel interferences in a MIMO system, the accuracy of channel estimation is a vital factor for proper receiver design in order to realize the full potential performance of the MIMO-OFDM system. A robust and improved channel estimation algorithm is proposed in this paper for MIMO-OFDM systems based on the least squares (LS) algorithm. The proposed algorithm, called improved LS (ILS), employs the noise correlation in order to reduce the variance of the LS estimation error by estimating and suppressing the noise in signal subspace. The performance of the ILS channel estimation algorithm is robust to the number of antennas in transmit and receive sides. The new algorithm attains a significant improvement in performance in comparison with that of the regular LS estimator. Also, with respect to mean square error criterion and without using channel statistics, the ILS algorithm achieves a performance very close to that of the minimum mean square error (MMSE) estimator in terms of the parameters used in practical MIMO-OFDM systems. A modification of the ILS algorithm, called modified ILS (MILS), is proposed based on using the second order statistical parameters of channel. Analytically, it is shown that the MILS estimator achieves the exact performance of the MMSE estimator. Due to no specific data sequences being required to perform the estimation, in addition to the training mode, the proposed channel estimation algorithms can also be extended and used in the tracking mode with decision-aided method.     

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     

Construction of block orthogonal golay sequences and application to channel estimation of mimo-ofdm systems

In this paper, we construct a family of block orthogonal Golay sequences that have low peak-to-mean envelope power ratio (PMEPR) as well as block wise orthogonal properties. We then present an application of the sequences to channel estimation of multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We compare the performance of the proposed algorithm with that of a frequency division multiplexing (FDM) piloting algorithm, and investigate the effect of co-channel interference (CCI) on the channel estimation performance.     

NGB-W广播信道估计实现算法设计

针对下一代广播电视网无线系统(NGB-W)广播接收信道估计,提出了一种基于二次一维维纳滤波的信道估计实用算法.该算法实时估计信道多普勒频偏、时延扩展和噪声方差等参数,并根据参数估计值分别从离线获得的预选集中选择时域和频域的一维维纳滤波系数.通过Cocentric System Studio(CCSS)平台仿真,给出了参数估计对算法性能的影响,以及所提信道估计算法的均方误差和误块率性能.仿真结果表明该算法在不同移动速度下,与采用理想插值系数信道估计相比性能损失不超过0.4 dB,与理想信道估计相比性能损失在1 dB以内.     

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.     

Blind equalization of IIR channels using hidden Markov models andextended least squares

In this paper, we present a blind equalization algorithm for noisy IIR channels when the channel input is a finite state Markov chain. The algorithm yields estimates of the IIR channel coefficients, channel noise variance, transition probabilities, and state of the Markov chain. Unlike the optimal maximum likelihood estimator which is computationally infeasible since the computing cost increases exponentially with data length, our algorithm is computationally inexpensive. Our algorithm is based on combining a recursive hidden Markov model (HMM) estimator with a relaxed SPR (strictly positive real) extended least squares (ELS) scheme. In simulation studies we show that the algorithm yields satisfactory estimates even in low SNR. We also compare the performance of our scheme with a truncated FIR scheme and the constant modulus algorithm (CMA) which is currently a popular algorithm in blind equalization     

Estimation of continuous flat fading MIMO channels

Multiple-input-multiple-output (MIMO) systems can provide high data rate wireless services in a rich scattering environment. We study one of the proposals for MIMO systems, the Bell Labs Layered Space-Time (BLAST) architecture. Channel estimation using training sequences is required for coherent detection in BLAST. We apply the maximum-likelihood channel estimator and the optimal training sequences for block flat fading channels to continuous flat fading channels and analyze the estimation error. The optimal training length and training interval that maximize the throughput for a given target bit error-rate are found by computer simulations as functions of the Doppler frequency and the number of antennas.     

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。      

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     

基于深度学习的单载波频域均衡算法研究

单载波频域均衡(Single-Carrier Frequency-Domain Equalization,SC-FDE)是一种有效的抗码间干扰的算法,在无线通信系统中得到了广泛的应用。传统线性SC-FDE算法主要包括信道估计、噪声功率估计和信道均衡三个模块,其中每个模块都是单独优化的。为了联合优化这三个模块,本文提出了一种基于深度学习的SC-FDE算法。为了减少网络收敛所需的训练数据量,本文为SC-FDE中的三个模块分别设计了一个子网络。此外,本文还提出了一种训练机制,通过平等地对待每条无线路径,提高了所提算法的信道泛化能力。仿真结果表明,所提算法可以在较小的训练数据集下收敛,且具有鲁棒的信道泛化能力,与基于最小二乘信道估计和最小均方误差信道均衡的SC-FDE算法相比,所提算法具有更优的误码率性能。      

A channel estimation algorithm for MIMO-SCFDE

This letter proposes a novel method for channel estimation in a single-carrier multiple input-multiple output (MIMO) system with frequency-domain equalization/detection. To this end, we construct novel short MIMO training sequences that have constant envelope in the time domain to preclude the peak-to-average power ratio problem encountered in many systems that utilize the frequency domain for data recovery. Simultaneously, the spectrum in the frequency domain is flat except for a grid of s for predefined frequency tones. Armed with these sequences, we provide an algorithm that is optimal in the least squares (LS) sense at a potentially low computational cost. Results show that the algorithm performs identically to other proposed LS techniques. Furthermore, the algorithm is extremely bandwidth efficient in that the total training overhead required to obtain full CSI is just one block.     

Noise-constrained least mean squares algorithm

We consider the design of an adaptive algorithm for finite impulse response channel estimation, which incorporates partial knowledge of the channel, specifically, the additive noise variance. Although the noise variance is not required for the offline Wiener solution, there are potential benefits (and limitations) for the learning behavior of an adaptive solution. In our approach, a Robbins-Monro algorithm is used to minimize the conventional mean square error criterion subject to a noise variance constraint and a penalty term necessary to guarantee uniqueness of the combined weight/multiplier solution. The resulting noise-constrained LMS (NCLMS) algorithm is a type of variable step-size LMS algorithm where the step-size rule arises naturally from the constraints. A convergence and performance analysis is carried out, and extensive simulations are conducted that compare NCLMS with several adaptive algorithms. This work also provides an appropriate framework for the derivation and analysis of other adaptive algorithms that incorporate partial knowledge of the channel     

MUI-free receiver for a synchronous DS-CDMA system based on blockspreading in the presence of frequency-selective fading

We discuss a synchronous direct-sequence code division multiple-access (DS-CDMA) system based on block spreading in the presence of frequency-selective fading. Note that block spreading, which is also known as chip interleaving, refers to a spreading of a data block sequence, which is obtained by dividing a data symbol sequence into consecutive blocks. For such a system, we develop a simple new receiver that completely removes the multiuser interference (MUI) without using any channel information. The MUI-free operation is obtained by the use of a shift-orthogonal set of code sequences on which this receiver is based. Within the framework of the MUI-free receiver, we further present a subspace deterministic blind single-user channel estimation algorithm. As a benchmark for the MUI-free receiver and the corresponding subspace deterministic blind single-user channel estimation algorithm, we consider the linear multiuser equalizer and the corresponding subspace deterministic blind multiuser channel estimation algorithm developed by Liu and Xu (1996) for a standard synchronous DS-CDMA system in the presence of frequency-selective fading. We show that the complexity of the MUI-free receiver using the corresponding subspace deterministic blind single-user channel estimation algorithm is much smaller than the complexity of the linear multiuser equalizer using the corresponding subspace deterministic blind multiuser channel estimation algorithm. We further show that the performance of the MUI-free receiver is comparable with the performance of the linear multiuser equalizer. This is for the case in which the channels are known as well as for the case in which the channels are estimated with the corresponding subspace deterministic blind channel estimation algorithm     

Joint channel estimation and resource allocation for MIMO systems-part I: single-user analysis

Multiple antenna systems are known to provide very large data rates, when the perfect channel state information (CSI) is available at the receiver. However, this requires the receiver to perform a noise-free, multi-dimensional channel estimation, without using communication resources. In practice, any channel estimation is noisy and uses system resources. We shall examine the trade-off between improving channel estimation and increasing the achievable data rate. We consider transmitside correlated multi-input multi-output (MIMO) channels with block fading, where each block is divided into training and data transmission phases. The receiver has a noisy CSI that it obtains through a channel estimation process, while the transmitter has partial CSI in the form of covariance feedback. In Part I of this two-part paper, we consider the single-user case, and optimize the achievable rate jointly over parameters associated with the training phase and data transmission phase. In particular, we first choose the training signal to minimize the channel estimation error, and then, develop an iterative algorithm to solve for the optimum system resources such as time, power and spatial dimensions. Specifically, the algorithm finds the optimum training duration, the optimum allocation of power between training and data transmission phases, the optimum allocation of power over the antennas during the data transmission phase.     

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.     

循环前缀块传输系统中的一种MIMO盲信道估计算法

信道估计一直是无线通信领域的研究热点之一,信道参数估计的好坏对系统的整体性能有着至关重要的影响。针对采用循环前缀的多输入多输出(MIMO-CP)系统,本文提出了一种基于子空间的盲信道估计方法,该算法利用了循环前缀所引起的冗余信息。基于子空间的盲信道估计算法都是通过对接收块的自相关矩阵进行奇异值分解(SVD)来实现信道估计的,因此需要利用尽可能多的接收块来得到准确的自相关矩阵的估计值,这就意味着会产生过久的判决延迟以及不能准确对快变信道进行跟踪。利用MIMO-CP系统中系统矩阵特有的块循环特性,对于连续的两个接收数据块以及对应的循环前缀部分组成的向量,可以重新构造一组新的向量而不改变系统的信道矩阵,因此可以通过较少的接收块来得到准确的自相关矩阵的估计值,该方法十分适用于对快变信道的盲估计。文章通过仿真分析了在不同的重复系数以及不同的接收块下该算法的性能并且比较了该算法与现有的“预编码”、“虚拟子载波”等盲信道估计算法的性能。仿真结果表明,提出的算法利用较少的数据块个数就得到了一个可靠的信道估计值和很好的误码率性能。      

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.     

Sample rejection for efficient simulation of binary coding schemes over quantized additive white Gaussian noise channels

We re-examine sample rejection (SR), introduced previously as an easy-to-implement efficient simulation technique. Since the decoding operation often represents a major part of the required simulation time, SR can be used to avoid decoding of the received sequences that are known beforehand to be decoded error-free. Previous work seems to indicate that SR may be effective only for simulations having small dimensionality, less than 10. We assume estimation of decoded bit-error probabilities for a general coding scheme of finite block length transmitted over an additive white Gaussian noise channel with quantized output using binary antipodal signaling and maximum-likelihood sequence decoding. We show that knowledge of the minimum Hamming distance of the code and conditioning on the transmitted sequence can be exploited to form the rejection regions. In particular, we investigate hypersphere, hypercube, and hyperquadrant rejection regions. Our analysis shows that SR can be effective for some systems with dimensionality on the order of hundreds with soft-decision decoding, and some systems with dimensionality more than a thousand with hard-decision decoding if the rejection regions are properly chosen.     

A new symbol timing and carrier frequency offset estimationalgorithm for noncoherent orthogonal M-CPFSK

We present a new joint symbol timing and carrier frequency offset estimation algorithm for noncoherent orthogonal continuous-phase M-ary frequency-shift keying (M-CPFSK). Our algorithm performs nondata-aided feedforward processing of finite-length observations, and it is suited for an all-digital modem implementation based on a DSP or an ASIC processor. The algorithm exploits phase continuity of M-CPFSK in order to generate both a spectral component at the carrier frequency offset and a timing error signal. This is obtained without nonlinear transformations of the received signal involving noise×noise products. Thus, our algorithm can operate at a very low input signal-to-noise ratio. We discuss the operating range of our algorithm, and we show that no additional overhead (training sequence) in excess of the standard overhead of FDMA/TDMA packet transmission is required to resolve timing and frequency ambiguities. Moreover, we show that by differentially preceding the transmitted symbols, it is possible to eliminate automatically frequency ambiguities, at the price of a slight increase in the bit-error rate. An approximate mean-square error analysis of the estimators and simulation results prove that our algorithm provides good performance, even with a relatively short observation block length and large carrier frequency offset. Computer simulations show also that our algorithm is extremely robust to phase noise. These features make our algorithm a good candidate for satellite FDMA/TDMA applications in the 20-30 GHz band, with a large number of users and bursty transmission