Direct blind MMSE channel equalization based on second-orderstatistics

A family of new MMSE blind channel equalization algorithms based on second-order statistics are proposed. Instead of estimating the channel impulse response, we directly estimate the cross-correlation function needed in Wiener-Hopf filters. We develop several different schemes to estimate the cross-correlation vector, with which different Wiener filters are derived according to minimum mean square error (MMSE). Unlike many known sub-space methods, these equalization algorithms do not rely on signal and noise subspace separation and are consequently more robust to channel order estimation errors. Their implementation requires no adjustment for either single- or multiple-user systems. They can effectively equalize single-input multiple-output (SIMO) systems and can reduce the multiple-input multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. The implementations of these algorithms on SIMO system are given, and simulation examples are provided to demonstrate their superior performance over some existing algorithms     

Second-order statistics-based blind equalization of 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 focus on direct design of finite-length minimum mean-square error (MMSE) blind equalizers. Unlike the past work on this problem, we allow infinite impulse response (IIR) channels. Our approaches also work when the “subchannel” transfer functions have common zeros as long as the common zeros are minimum-phase zeros. Illustrative simulation examples are provided     

Ranging in a Single-Input Multiple-Output (SIMO) System

In this letter, optimal ranging in a single-input multiple-output (SIMO) system is studied. The theoretical limits on the accuracy of time-of-arrival (TOA) (equivalently, range) estimation are calculated in terms of the Cramer-Rao lower bound (CRLB). Unlike the conventional phased array antenna structure, a more generic fading model is employed, which allows for the analysis of spatial diversity gains from the viewpoint of a ranging system. In addition to the optimal solution, a two-step suboptimal range estimator is proposed, and its performance is compared with the CRLBs.     

MMSE Equalization of Interference on Fading Diversity Channels

Adaptive equalization is used in digital transmission systems with parallel fading channels. The equalization combines the diversity channels and reduces intersymbol interference due to multipath returns. When interference is present and correlated from channel to channel, the equalizer can also reduce its effect on the quality of information transfer, important applications for interference cancellation occur in diversity troposcatter systems in the presence of jamming, diversity high frequency (HF) systems which must cope with interfering skywaves, and space diversity line-of-sight (LOS) radio systems where adjacent channel interference is a problem. In this paper we develop the general formulation for minimum mean square error (MMSE) equalization of interference in digital transmission diversity systems. The problem formulation includes the use of available receiver decisions to assist in MMSE processing. The effects of intersymhol interference are included in the analysis through a critical approximation which assumes sufficient processor capability to reduce ISI effects to levels small enough for satisfactory communication. The analysis also develops he concept of additional implicit or intrinsic diversity which results from channel multipath dispersion. It shows how the MMSE processor sacrifices diversity to suppress interference even when the interference arrives in the main beams of the receiver antenna patterns. The condition of near synchronous same-path interference is also addressed. Because the spatial angle of arrival of the interference may result in delay differences between interference signals in different antenna channels, interference delay compensation may be required. We show that this effect is compensated for with a small number of appropriately spaced equalizer taps.     

Asymptotic performance of successive interference cancellation in the context of linear precoded OFDM systems

Recent results on the asymptotic empirical eigenvalue distribution of random matrices have enabled the study of the asymptotic limits of linear precoded orthogonal frequency-division multiplexing systems with minimum mean-square error (MMSE) equalization. In this letter, we extend these results to the MMSE successive interference cancellation detector and quantify the nonlinearity gain for certain type of precoding matrices.     

Performance analysis of space shift keying for AF relaying with relay selection

In this paper, we propose an amplify-and-forward multiple-input multiple-output (MIMO) relaying scheme, which combines space shift keying (SSK) with the best and partial relay selection. In this scheme, SSK transmission is considered by using the source (S) transmit antennas. Besides the direct link transmission, a relay, which is selected according to the best or partial relay selection techniques, amplifies the data received from S and forwards it to the destination (D). Theoretical error probability expressions of the proposed cooperative SSK systems are derived and an asymptotic diversity analysis is also performed to demonstrate the achievable diversity orders of the systems. It is shown that the proposed SSK systems outperform the conventional cooperative single-input multiple-output (SIMO) systems. It is also revealed that there is an interesting trade-off between SSK with the best and the partial relay selection in terms of error performance and complexity as in conventional cooperative SIMO systems. However, it is shown that the partial relay selection provides an almost identical error performance compared to the best relay selection with a considerably lower complexity when the number of relays is less than or equal to the number of receive antennas at D in the cooperative SSK system.     

Blind Channel Equalization Using Second-Order Statistics: A Necessary and Sufficient Condition

In this work the blind equalization of a single-input, multiple-output channel has been carried out using second-order statistics. A sufficient and necessary condition for blind equalization based on second order statistics has been given. It has been proved that a single autocorrelation matrix of the source symbols is sufficient for blind equalization. The proposed scheme is generalized; that is, it is valid for white as well as colored source symbols. A linear artificial neural network is developed with a learning algorithm based on the new condition. The results of the new algorithm verify its validity and superior performance.     

Linear MMSE Space–Time Equalizer for MIMO Multicode CDMA Systems

We propose an enhanced chip-level linear space–time (ST) equalizer for multiple-input multiple-output (MIMO) multicode code-division multiple-access (CDMA) systems. In the MIMO multicode CDMA systems, the reuse of the same spreading codes in different transmit antennas significantly degrades the equalization performance if the ST equalizer uses a minimum mean-squared error (MMSE) weighting vector that minimizes the mean-squared error of the equalizer output chip sequence. As the CDMA despreader concatenated to an ST equalizer distorts interstream interference components differently from multipath interference and background noise components, the chip-level MMSE weighting vector usually steers in suboptimal directions in the signal space. Therefore, we propose a new MMSE weighting vector that takes the despreading effect into account in this paper. Simulation results show a substantial performance improvement through the new weighting vector.     

Linear and nonlinear preequalization/equalization for MIMO systems with long-term channel state information at the transmitter

A transceiver structure for frequency-flat multiple-input multiple-output (MIMO) systems that comprises linear/nonlinear preequalization/equalization is optimized according to the minimum mean square error (MMSE) criterion under the assumption that only long-term channel state information (i.e., correlation matrices of fading channel and noise) is available at the transmitter. The structure generalizes different techniques known from the literature, such as BLAST, linear preequalization and equalization, and Tomlinson-Harashima precoding (THP). Simulations show that relevant benefits can be obtained by exploiting the long term channel state information at the transmitter in both dense multipath channels with relatively large correlation at the transmitter side and in sparse multipath channels.     

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     

基于EM-SBL迭代的稀疏SIMO信道频域盲均衡算法

针对单输入多输出系统下稀疏信道均衡问题,提出了一种新的基于最大似然准则的频域迭代均衡算法.首先将多天线联合均衡问题建模为非完整观测数据集下频域信号序列的最大似然估计问题,利用期望最大化算法进行近似迭代求解,最终得到各个单频信号加权求和形式的均衡输出表达式.在每次迭代过程中,算法依次完成均衡输出的更新和信道参数联合条件后验分布的更新.考虑到信道固有的稀疏特性,在求解信道参数联合条件后验时,引入具有稀疏促进作用的先验分布对信道系数加以约束,使用稀疏贝叶斯学习迭代求解信道参数联合条件后验.仿真结果表明,本文算法具有较好的收敛特性和稳态性能,在中高信噪比条件下可以获得接近信道已知条件下的稳态系统误符号率性能.     

Equalization and semi-blind channel estimation for space-time block coded signals over a frequency-selective fading channel

In this paper, we investigate the equalization and channel identification for space-time block coded signals over a frequency-selective multiple-input multiple-output (MIMO) channel. The equalization has been considered by taking into account the cyclostationarity of space-time block coded signals. The minimum mean square error (MMSE) solutions have been derived for the linear and decision feedback (DF) equalizers. The channel estimation is required for the equalization. With known symbols (as pilot symbols), MIMO channels can be estimated. In addition, due to the redundancy induced by space-time block code, it is possible to identify MIMO channels blindly using the subspace method. We consider both blind and semi-blind channel estimation for MIMO channels. It is shown that the semi-blind channel estimate has fewer estimation errors, and it results in less (bit error rate) performance degradation of the MMSE linear and DF equalizers.     

Delay-limited capacity: multiple antennas, moment constraints, and fading statistics

Different performance measures are an important mean in order to analyze and design wireless communications systems. Examples of common performance measures are the ergodic capacity, the outage capacity, and the average mean-square error (MSE). In this work, we study the delay-limited capacity (DLC). The DLC depends on the properties of the fading channel, e.g. on the spatial correlation and on the line-of-sight (LOS) component. In this letter, we derive the DLC for the general class of parallel fading channels, including the multiple antenna channels under moment and long-term power constraint. We prove that the DLC is Schur-concave with respect to the spatial correlation in single-input multiple-output (SIMO), and multiple-input single-output (MISO). Bounds for the DLC of multiple-input multiple-output (MIMO) and parallel fading channels are derived and the impact of the the mean component and spatial correlation on these bounds is characterized.     

Low-complexity multipath diversity through fractional sampling in OFDM

Orthogonal frequency division multiplexing (OFDM) enables low-complexity equalization and has been adopted in several wireless standards. However, OFDM cannot exploit multipath diversity without computationally complex coding and decoding. We show here that by sampling at a rate higher than the symbol rate, which is also known as fractional sampling (FS), one can improve the diversity that the wireless channel can provide in an OFDM system. We propose maximal ratio combining at each subcarrier for the FS-OFDM system, argue that the diversity gains acquired through this approach are related to the spectral shape of the pulse and its excess bandwidth, and derive analytical bit error and symbol error rate expressions for our scheme. We also explore extensions to differentially encoded systems that do not require channel status information at the receiver, multiple-input multiple-output (MIMO) systems that exploit space diversity, and low peak-to-average (PAR) options such as zero-padded (ZP) and cyclic-prefix only (CP-only) transmissions. We corroborate our approach with simulations.     

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.     

Soft-Output MMSE V-BLAST Detector under ML Channel Estimation and Channel Correlation

Channel estimation errors have not been taken into account by existing soft-output minimum mean square error (MMSE) vertical Bell Lab Space Time (V-BLAST) detectors. As a result, the system performance will be degraded under practical channel estimation. In this letter, we propose a novel soft-output MMSE V-BLAST detector, which takes the estimation error of maximum likelihood (ML) multiple-input multiple-output (MIMO) channel estimation and receiver spatially correlation into account in the computation of the MMSE filter and loglikelihood ratio (LLR) of each coded bit. When compared with existing MMSE V-BLAST detectors, simulation results show that the proposed novel detector can obtain sizable performance gain.     

CMA盲均衡在MIMO MC DS-CDMA系统中的应用研究

本文首先建立了采用TR-STBC发送分集的MIMO MC DS-CDMA系统模型,然后在此基础上,研究了SDCMA盲均衡在该系统中的应用,最后进行了仿真和分析.结论是对采用TR-STBC方案的MIMO MC DS-CDMA系统进行常模盲均衡,算法简单,较易实现,但当多址干扰较大时,仅采用此均衡方法不能较好地改善系统性能,还需要进一步采用其他方法来减小或消除多址干扰.     

A New Blind-Equalization Algorithm for an FIR SIMO System Driven by MPSK Signal

We consider the problem of blind equalization of a finite impulse response and single-input multiple-output system driven by an M-ary phase-shift-keying signal. The existing single-mode algorithms for this problem include the constant modulus algorithm (CMA) and the multimodulus algorithm (MMA). It has been shown that the MMA outperforms the CMA when the input signal has no more than four constellation points, i.e., Mles4. In this brief, we present a new adaptive equalization algorithm that jointly exploits the amplitude and phase information of the input signal. Theoretical analysis shows that the proposed algorithm has less mean square error, i.e., better equalization performance, at steady state than the CMA regardless of the value of M. The superior performance of our algorithm to the CMA and the MMA is validated by simulation examples     

A transmit MIMO scheme with frequency domain pre-equalization for wireless frequency selective channels

In this paper, we introduce a transmit multiple-input multiple-output (MIMO) scheme with frequency domain pre-equalization for a multipath or frequency selective channel. In this scheme, MIMO processing in the frequency domain is performed at the transmitter or base station so that the receiver or mobile station only requires limited processing. This scheme provides high data rates and also inherits from the frequency domain equalization the property of relatively low complexity in severe multipath environments. The MIMO transmit processing is derived by minimizing the minimum mean square errors (MMSE), and expressions for the signal-to-interference-plus-noise ratio and error probability based on the Gaussian approximation of the interference term are provided. Some important associated issues, such as channel errors and computational complexity, are also investigated. Numerical simulations are also provided and these demonstrate the improved performance of our proposed scheme compared to other transmit MIMO schemes. In particular, they show that the proposed system can attain multipath or frequency diversity of the channel.     

Layered space-frequency equalization in a single-carrier MIMO system for frequency-selective channels

Frequency-domain equalization (FDE) has been shown to be an effective approach to combat frequency-selective wireless channels. In this letter, we propose a layered space-frequency equalization (LSFE) architecture for a single-carrier (SC) multiple-input multiple-output (MIMO) system, where MIMO FDE is employed at each stage or (layer) of detection. At a particular stage, a group of the best data streams in the minimum mean square error sense are detected and are canceled from the received signals. Simulation results show that our proposed LSFE structures can outperform layered space-time equalization (LSTE) structures and uncoded orthogonal frequency division multiplex (OFDM), especially at a higher delay spread. Performance is enhanced further, by incorporating the FDE with time-domain decision feedback at each stage of LSFE. We also provide performance analysis for LSFE, in comparison with OFDM.