Training Signal Design for Estimation of Correlated MIMO Channels With Colored Interference

In this paper, we study the problem of estimating correlated multiple-input multiple-output (MIMO) channels in the presence of colored interference. The linear minimum mean square error (MMSE) channel estimator is derived and the optimal training sequences are designed based on the MSE of channel estimation. We propose an algorithm to estimate the long-term channel statistics needed for the construction of the optimal training sequences. We also design an efficient scheme to feed back the required information to the transmitter where we can approximately construct the optimal sequences. Numerical results show that the optimal training sequences provide substantial performance gain for channel estimation when compared with other training sequences     

一种新的基于参数信道模型的MIMO信道估计算法

针对频率选择性块衰落MIMO信道,该文提出一种改进的基于参数信道模型的信道估计方法。该方法首先通过修正后的TST-MUSIC算法估计多径的传播时延和角度。由时延和角度信息,得到一种基于参数信道模型的信道估计方法。仿真结果表明此种方法可以有效地减少参数估计的维数,其性能要远远优于非参数的最小二乘估计器。     

Parameter Estimation for Correlated MIMO Channels with Frequency-Selective Fading

In this paper, we address the problem of frequency offset and channel gain estimation for frequency-selective multi-input multi-output (MIMO) correlated fading channels. A maximum-likelihood (ML) frequency offset (FO) estimator is proposed by using the Bayesian approach. We show that the proposed FO estimator is efficient and asymptotically optimal. Based on the FO estimate, we derive the linear minimum mean square error (LMMSE) channel estimator and analytically investigate the effect of frequency offset estimation error on the mean square error (MSE) performance of the channel estimator. Finally, the performances of the FO and channel estimation are evaluated by simulation results.     

Capacity and performance of lattice reduction aided linear processing with lattice encoding and decoding in limited feedback systems

Linear processing for multi-input multi-output (MIMO) antenna systems is preferred to non-linear ones for computational efficiency. Using channel state information (CSI) at the receiver, channel matrix can be decomposed via singular value decomposition (SVD), and if the transmitter can be fed back with the right-unitary-matrix of the SVD from the receiver, the maximum channel-capacity can be achieved with linear processing in point-to-point wireless MIMO communications. However, if the transmitter receives no-feedback, the optimal linear detector at the receiver is the minimum-mean-squareerror- estimator, of which capacity is far below the channelcapacity. In practice, reducing the amount of feedback information to achieve a "reasonably close channel-capacity" is an important issue in point-to-point wireless communications. In this paper, we propose a limited feedback system employing linear processing, which achieves near-channel-capacity. The feedback information is only an integer matrix, which is much less than that of the right-unitary-matrix of the SVD. Key ideas of the proposed scheme are the lattice reduction and modulo operation. Moreover, the amount of feedback information can be further reduced to a binary matrix using multi-level/multi-stage encode and decode. Under the turbo channel code the proposed scheme shows excellent performance at high data rates. We compare our simulation results with Shannon capacity limits for ergodic MIMO channels.     

基于MUSIC和ML方法的MIMO系统参数估计

该文提出了一种基于MUSIC和ML方法联合估计MIMO系统频偏和信道增益的算法,该算法首先使用MUSIC方法估计出多个发射天线到某一接收天线的频偏子集,然后利用最大似然方法在这个有限子集中分离出不同天线对之间的频偏,最后在频率同步的基础上利用最大似然估计器对信道增益进行估计。该算法解决了在估计多个频偏时直接使用最大似然估计进行多维搜索的问题,将多维搜索转化为一维搜索,降低了算法的复杂度。     

SPECTRAL EFFICIENCY ANALYSIS OF NEW QUADRATURE OVERLAPPED MODULATIONS OVER BAND-LIMITED NON-LINEAR CHANNELS

In this paper, two new quadrature overlapped modulations, the overlapped minimum shift keying (OMSK) and minimum shift keying triangular cosine (MSKTC), are introduced for their promising spectral efficiency over band-limited non-linear channels. They possess fast power spectral density (PSD) side lobe reduction rates over either a linear or a (band-limited) non-linear channel and their PSD side lobe regeneration caused by channel non-linearity is under much better control than that of the offset QPSK, minimum shift keying (MSK) and staggered quadrature overlapped raised cosine (QORC) modulations (a reported quadrature overlapped modulation). An effective algorithm is introduced to study spectral efficiency for various (both overlapped or non-overlapped) modulations over band-limited non-linear channels. Third-order Butterworth and Chebyshev filters with various cut-off frequencies are considered as band-limiting transmitter filters. It is concluded that the impairment (to signal spectral efficiency) caused by channel non-linearity can be minimized by using the proposed modulations. © 1997 by John Wiley & Sons, Ltd.     

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.     

Space-time channel estimation and performance analysis for wireless MIMO-OFDM systems with spatial correlation

This paper treats channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with correlation at the receive antenna array. A two-step channel estimation algorithm is proposed. Firstly, the iterative quadrature maximum likelihood based time delay and spatial signature estimation is presented by utilizing special training signals with a cyclic structure. The receive spatial correlation matrix of the vector valued channel impulse response is formulated as a function of the spatial signature, the time delay, and the pulse shaping filter. The joint spatio-temporal (JST) filtering based minimum mean squared error channel estimator is derived by virtue of the spatial correlation. In addition, the effect of channel estimation errors on the bit error probability performance of the space-time block coded OFDM system over correlated MIMO channels is derived. The Cramer-Rao lower bound on the time delay estimate is provided for a benchmark of the performance comparison. The performance of proposed algorithms is illustrated based on analysis and computer simulations. The JST channel estimator achieves significant gains in the mean squared error compared to the temporal filtering. It also enables remarkable savings in the pilot symbol power level.     

Channel estimation for OFDM transmission in multipath fadingchannels based on parametric channel modeling

We present an improved channel estimation algorithm for orthogonal frequency-division multiplexing mobile communication systems using pilot subcarriers. This algorithm is based on a parametric channel model where the channel frequency response is estimated using an L-path channel model. In the algorithm, we employ the ESPRIT (estimation of signal parameters by rotational invariance techniques) method to do the initial multipath time delays acquisition and propose an interpath interference cancellation delay locked loop to track the channel multipath time delays. With the multipath time delays information, a minimum mean square error estimator is derived to estimate the channel frequency response. It is demonstrated that the use of the parametric channel model can effectively reduce the signal subspace dimension of the channel correlation matrix for the sparse multipath fading channels and, consequently, improve the channel estimation performance     

A Novel Environment Characterization Metric for Clustered MIMO Channels

In this work we introduce a novel metric for characterizing the double-directional propagation environment and use this metric to assess the performance of a SAGE parameter estimator for MIMO channels. Using the IlmProp, a geometry-based MIMO channel modeling tool, we construct synthetic channels for three different scenarios showing: (i) well separated clusters containing dense propagation paths, and single-bounce scattering; (ii) partly overlapping clusters containing widely spread propagation paths, and single-bounce scattering; (iii) unclustered multipath components (“rich scattering”), and double-bounce-only scattering. We model the scatterers and the receiver in the environment as fixed, but the transmitter as moving. The Initialization and Search-Improved SAGE (ISIS) estimation tool is used to extract the propagation paths from the constructed channels. Both true and estimated paths are fed to the new system-independent metric which genuinely reflects the structure of the channel and the compactness of the propagation paths. We use this metric to decide on the accuracy of the channel estimator. The results show a convincing agreement between true and estimated paths.     

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO–OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO–OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator.     

大规模MIMO系统上行链路时间-空间结构信道估计算法

针对大规模多入多出(MIMO)系统上行链路非平稳空间相关信道的估计问题,该文利用信道的时间-空间2维稀疏结构信息,应用狄利克雷过程(DP)和变分贝叶斯推理(VBI),设计了一种低导频开销和计算复杂度的信道估计迭代算法,提高了信道估计精度。由于平稳空间相关信道难以适用于大规模MIMO系统,该文借助于狄利克雷过程构建了非平稳空间相关信道先验模型,可将具有空间关联的多个物理信道映射为具有相同时延结构的概率信道,并应用变分贝叶斯推理设计了低导频开销和计算复杂度的信道估计迭代算法。实验结果验证了所提算法的有效性,且具有对系统关键参数鲁棒性的优点。     

Aperiodic complementary sets of sequences-based MIMO frequency selective channel estimation

Accurate estimation of MIMO frequency selective fading channels is important for reliable communication. In this letter, a new channel estimator which relies on aperiodic complementary sets of sequences is proposed. Theoretical analysis and Monte-Carlo simulation have shown that it achieves the minimum possible Cramer-Rao lower bound. A low-complexity hardware implementation of the estimator is also provided.     

Tracking Performance of Least Squares MIMO Channel Estimation Algorithm

In this paper, the tracking performance analysis of the least squares (LS) multiple-input multiple-output (MIMO) channel estimation and tracking algorithm is presented. MIMO channel estimation is a novel application of the LS algorithm that presents near-optimum performance by Karami and Shiva in 2003 and 2006. In this paper, the mean square error (MSE) of tracking of the LS MIMO channel estimator algorithm is derived as a closed-form function of the Doppler shift, forgetting factor, channel rank, and the length of training sequences. In the analysis, all training symbols are considered as randomly generated equal-power vectors on the unit circle, or in other words, phase-shift keying (PSK) signaling. By evaluating this function, some insights into the tracking behavior of the LS MIMO channel estimator are achieved. Then, the calculated tracking error is compared with the tracking error derived from Monte Carlo simulation for quaternary-PSK-based training signals to verify the validation of the presented analysis. Finally, the optimum forgetting factor is derived to minimize the error function, and it is shown that the optimum forgetting factor is highly dependent on the training length, Doppler shift, and E_b/N_o. Also, it is concluded that in low E_b/N_o values, the number of transmitter antennas has negligible effect on the optimal value of the forgetting factor.     

Adaptive Channel Estimation Using Pilot-Embedded Data-Bearing Approach for MIMO-OFDM Systems

Multiple-input multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) systems employing coherent receivers crucially require channel state information (CSI). Since the multipath delay profile of channels is arbitrary in the MIMO-OFDM systems, an effective channel estimator is needed. In this paper, we first develop a pilot-embedded data-bearing (PEDB) approach for joint channel estimation and data detection, in which PEDB least-square (LS) channel estimator and maximum-likelihood (ML) data detection are employed. Then, we propose an LS fast Fourier transform (FFT)-based channel estimator by employing the concept of FFT-based channel estimation to improve the PEDB-LS one via choosing a certain number of significant taps for constructing a channel frequency response. The effects of model mismatch error inherent in the proposed LS FFT-based estimator when considering noninteger multipath delay profiles and its performance analysis are investigated. The relationship between the mean-squared error (MSE) and the number of chosen significant taps is revealed, and hence, the optimal criterion for obtaining the optimum number of significant taps is explored. Under the framework of pilot embedding, we further propose an adaptive LS FFT-based channel estimator employing the optimum number of significant taps to compensate the model mismatch error as well as minimize the corresponding noise effect. Simulation results reveal that the adaptive LS FFT-based estimator is superior to the LS FFT-based and PEDB-LS estimators under quasi-static channels or low Doppler's shift regimes     

16-state nonlinear equalizer for IS-54 digital cellular channels

A performance evaluation for a number of equalizers for frequency selective fading channels has been carried out. Linear and decision feedback equalizers have been considered. IS-54 digital cellular channels based on TDM concepts have delay spreads that result in at most one data symbol of overlap. Using a standard fading model, we find that a 16-state sequence estimator, following a receive filter matched to the transmitter filter, provides excellent performance for delay spreads from zero to one symbol interval. It is a low-complexity detector, and for this situation it is superior to both linear and decision feedback equalizers in this application. We assume perfect channel state information to establish ultimate performance. In practical applications, at most three complex samples of the overall channel impulse that includes the receiver filter must be estimated. The frequency selective channel is a two-path model with time variation following standard Doppler variations for IS-54 channels and co-channel interference is included. We present results for both root-raised-cosine filtered π/4-DQPSK and QPSK modulation formats. In the appendix, we provide an analysis to support our best result. It is shown that if the interbeam delay is one symbol interval on a slowly varying, two-beam channel, and maximum likelihood sequence estimation has a performance that attains Mazo's (1991) matched filter lower bound, even when the root-Nyquist receiver filter is only matched to its transmitter filter counterpart and not to the complete channel response     

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.     

Linear expansions for frequency selective channels in OFDM

Modeling the frequency selective fading channels as random processes, we employ a linear expansion based on the Karhunen–Loeve (KL) series representation involving a complete set of orthogonal deterministic vectors with a corresponding uncorrelated random coefficients. Focusing on OFDM transmissions through frequency selective fading, this paper pursues a computationally efficient, pilot-aided linear minimum mean square error (MMSE) uncorrelated KL series expansion coefficients estimation algorithm. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Moreover, truncation in the linear expansion of channel is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the estimation algorithm. The performance of the proposed approach is studied through analytical and experimental results. We first exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also provide performance analysis results studying the influence of the effect of SNR and correlation mismatch on the estimator performance. Simulation results confirm our theoretical results and illustrate that the proposed algorithm is capable of tracking fast fading and improving performance.     

一种下行多用户MIMO系统中的鲁棒波束形成算法

提出了一种下行多用户MIMO系统中的鲁棒性线性处理算法.该算法利用了信道均值和天线相关矩阵等信道统计信息,在总发射功率不大于目标值的约束条件下,能够使所有用户的均方误差(total mean square error,TMSE)在随机信道上的平均值最小.该算法不明显依赖瞬时信道信息(channel state information,CSI),当信道估计得到的CSI不准确时,它能够有效降低由CSI偏差带来的性能损失.仿真结果表明提出的算法能够有效地降低由于不准确CSI带来的误码率和平均MSE的损失.     

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