A Toeplitz displacement method for blind multipath estimation forlong code DS/CDMA signals

The problem of blind channel identification for direct-sequence/code-division multiple-access (DS/CDMA) multiuser systems is explored. For wideband DS/CDMA signals, multipath distortion is well modeled by a finite-impulse response filter. In this work, a blind channel identification technique based on second-order statistics is investigated. The method exploits knowledge of the spreading code of the user of interest via matched filtering, as well as properties of spreading codes. The current scheme focuses on a method appropriate for randomized long sequence DS/CDMA. This access scheme poses special challenges as the spreading codes are time varying. An analytical approximation of the mean-squared error is derived using perturbation techniques. The performance of the algorithm is studied via simulation and through the mean-squared error approximation, which is observed to be tight     

长码MIMO CDMA信道的一阶聚类盲估计

该文提出了一种长码多输入多输出CDMA系统的信道盲估计方法。使用解相关匹配滤波器作为接收机前端,其输出信号可以剖分为信道矢量张成的线性空间。使用聚类算法提取集合的中心,从而仅利用解相关器输出的一阶统计量便可很好地估计出信道参数。同时对K-均值聚类算法的初始值设定进行了改进以提高收敛速度。所提出的算法有较低的计算复杂度。仿真结果表明该算法的有效性以及对信道阶数过估计有很好的鲁棒性。     

Decision feedback sequence estimation for unwhitened ISI channelswith applications to multiuser detection

Decision feedback sequence estimation (DFSE), which is a reduced-complexity alternative to maximum likelihood sequence estimation (MLSE), can be used effectively for equalization of intersymbol interference (ISI) as well as for multiuser detection. The algorithm performs very well for whitened (minimum-phase) channels. For nonminimum-phase channels, however, the algorithm is not very effective. Moreover, DFSE requires a noise-whitening filter, which may not be feasible to compute for time-varying channels such as a multiuser direct-sequence code division multiple access (DS-CDMA) channel. Noise-whitening is also cumbersome for applications that involve bidirectional equalization such as the global system for mobile communication (GSM) system. In such conditions, it is desirable to use the Ungerboeck (1974) formulation for sequence estimation, which operates directly on the discrete-time unwhitened statistic obtained from conventional matched filtering. Unfortunately, DFSE based on matched filter statistics is severely limited by untreated interference components. We identify the anticausal interference components, using an error probability analysis. This leads us to a modified unwhitened decision feedback sequence estimator (MUDFSE) in which the components are canceled, using tentative decisions. We obtain approximate error probability bounds for the proposed algorithm. Performance results indicate that the modified algorithm, used on unwhitened channels with relatively small channel correlations, provides similar performance/complexity tradeoffs as the DFSE used on the corresponding whitened minimum-phase channels. The algorithm is especially attractive for multiuser detection for asynchronous DS-CDMA channels with long spreading codes, where it can achieve near-MLSE performance with exponentially lower complexity     

Performance analysis of LMMSE receivers for M-ary QAM in Rayleigh faded CDMA channels

We develop approximations for the symbol error rate in a wireless code-division multiple-access channel. We assume that each user employs spectrally efficient M-ary quadrature amplitude modulation and undergoes independent Rayleigh fading. We study the performance of linear minimum mean-squared error receivers in situations where: i) the channels of all users are known perfectly; ii) the receiver knows only the average powers of the interferers but the channel of the user of interest is still assumed to be perfectly known; iii) the channels of the interferers are unknown and there is an error in the channel estimation of the user of interest. In the last of these cases, the symbol error rate is a function of the variance of the channel estimation error. We also determine an expression for this error variance when the channel estimate is obtained from optimal linear smoothing of a sequence of pilot symbols. Recent results on the performance of linear receivers in large systems with random spreading play an important role in our developments.     

Analysis and Performance Evaluation of Linear Multiuser Detectors in the Downlink of DS-CDMA Systems Applying Spectral Decomposition

This paper studies the performance of linear multiuser detectors for direct-sequence code division multiple access systems at different loading levels and users' powers, using singular value decomposition (SVD) techniques in the downlink of Rayleigh flat-fading and additive white Gaussian channels. The performance of the matched filter (MF), decorrelator (zero-forcing), and minimum mean-squared error (MMSE) detectors are studied and compared. Analytical and simulation results are also presented in terms of the bit error rate. From this analysis, a simple linear multiuser detector is developed that exploits the structure of the system's spreading codes matrix from the SVD viewpoint. Also, the numerical performance of this proposed detector is compared to that of the conventional detector (MF) as a function of the signal-to-noise ratio. Finally, the performance limits are established in terms of the singular values of the spreading codes matrix. Extensive simulation results validate the analysis presented in the paper for equal or unequal users' powers.     

Multiuser channel estimation and tracking for long-code CDMA systems

Channel estimation techniques for code-division multiple access (CDMA) systems need to combat multiple access interference (MAI) effectively. Most existing estimation techniques are designed for CDMA systems with short repetitive spreading codes. However, current and next-generation wireless systems use long spreading codes whose periods are much larger than the symbol duration. We derive the maximum-likelihood channel estimate for long-code CDMA systems over multipath channels using training sequences and approximate it using an iterative algorithm to reduce the computational complexity in each symbol duration. The iterative channel estimate is also shown to be asymptotically unbiased. The effectiveness of the iterative channel estimator is demonstrated in terms of squared error in estimation as well as the bit error rate performance of a multistage detector based on the channel estimates. The effect of error in decision feedback from the multistage detector (used in the absence of training sequences) is also shown to be negligible for reasonable feedback error rates using simulations. The proposed iterative channel estimation technique is also extended to track slowly varying multipath fading channels using decision feedback. Thus, an MAI-resistant multiuser channel estimation and tracking scheme with reasonable computational complexity is derived for long-code CDMA systems over multipath fading channels.     

OFDM系统中时变信道下信道估计方法的研究

为减少OFDM系统中子信道间干扰(ICI)的影响,分析了分段频域均衡方法、近似分段线性的相邻符号ICI消除方法和卡尔曼滤波方法等几种快衰落环境下的信道估计方法的优劣,在此基础上提出了一种基于梳状导频的卡尔曼滤波信道估计方法.对滤波的结果,利用信道的频域相关函数和估计误差的协方差矩阵,在频域进行最小均方误差意义上的优化.仿真结果表明,该方法具有良好的估计性能.     

Capacity regions and optimal power allocation for groupwise multiuser detection

In this letter, optimal power allocation and capacity regions are derived for groupwise successive interference cancellation (GSIC) systems operating in multipath fading channels, under imperfect channel estimation conditions. It is shown that the impact of channel estimation errors on the system capacity is two-fold: It affects the receiver performance within a group of users, as well as the cancellation performance (through cancellation errors). An iterative power allocation algorithm is derived, based on which it can be shown that that the total required received power is minimized when the groups are ordered according to their cancellation errors, and the first detected group has the smallest cancellation error. Performance/complexity tradeoff issues are also discussed by directly comparing the system capacity for different implementations: GSIC with linear minimum-mean-square error (LMMSE) receivers within the detection groups; GSIC with matched filter (MF) receivers; multicode LMMSE systems; and simple all MF receivers systems.     

无线OFDM系统传输信道模型化参数检测

利用导频子载波时频相位相关性统计检测与QAM信号解映射判决误差统计，提出了一种适用于频域导频无线OFDM系统的传输信道模型化参数检测方案，包括信道最大多径时延、最大多普勒频率和信噪比检测；能够有效解决传统的OFDM信道估计算法通常按照最恶劣信道情况上限进行设计，以及基于MMSE准则最优信道估计器中信道先验信息统计运算复杂度高的缺陷；仿真结果表明，在低复杂度条件下可以有效获知当前传输信道模型参数的近似统计信息。     

Blind decorrelating RAKE receivers for long-code WCDMA

The problem of blind and semiblind channel estimation and symbol detection is considered for long-code wideband code division multiple access (CDMA) systems, including systems with multirate and multicode transmissions. A decorrelating matched filter, implemented efficiently in state-space, eliminates multiaccess interference and produces a bank of vector processes. Each vector process spans a one-dimensional (1-D) subspace from which channel parameters and data symbols of one user are estimated jointly by least squares. A new identifiability condition is established, which suggests that channels unidentifiable, in short-code CDMA systems are almost surely identifiable when aperiodic spreading codes are used. The decorrelating matched filter is implemented efficiently based on time-varying state-space realizations that exploit the structure of sparsity of the code matrix. The mean square error of the estimated channel is compared to the Cramer-Rao bound, and a bit error rate (BER) expression for the proposed algorithm is presented.     

A comparison of long versus short spreading sequences in codedasynchronous DS-CDMA systems

The performance of turbo-coded asynchronous direct sequence code division multiple access (DS-CDMA) using long and short spreading sequences is compared by both analysis and simulation. For coded systems with a conventional matched filter (MF) receiver, three analytical methods with different complexity are compared: the standard Gaussian approximation, the improved Gaussian approximation (IGA), and the density function approach. It is shown that while the standard Gaussian approximation is fairly accurate for the long sequences, it is too optimistic for the short sequences. For the short-sequence systems, the IGA gives an accurate estimate for the performance with much less complexity than the density function approach. The analysis shows that for either the additive white Gaussian noise (AWGN) channel or the flat Rayleigh fading channel and a MF receiver, there is a degradation in the average performance of the turbo-coded short-sequence systems compared to the long-sequence systems due to the fact that the cross-correlations are not time-varying. However, the short-sequence systems are amenable to the use of an interference suppression technique designed to minimize the mean square error. Such a minimum mean square error (MMSE) receiver in the turbo-coded system is shown to outperform the long-sequence system with the MF receiver, especially when there is a near-far problem, as previously observed in a convolutionally-coded system. Finally, similar results are obtained by computer simulations for the turbo-coded CDMA systems on a frequency-selective Rayleigh fading channel     

The Kalman filter as the optimal linear minimum mean-squared errormultiuser CDMA detector

It is shown that a first-order linear state-space model applies to the asynchronous code-division multiple-access (CDMA) channel, and thus the Kalman filter produces symbol estimates with the minimum mean-squared error (MMSE) among all linear filters, in long- or short-code systems for a given detection delay. This result may be used as a benchmark against which to compare the performance of other linear detectors in asynchronous channels. It also reveals that a time-varying recursive filter with a fixed and finite complexity implements the fixed-lag linear MMSE (LMMSE) detector, which hitherto has been assumed to require a processing window (and hence complexity) that grows with time     

Average bit-error-rate performance of band-limited DS/SSMA communications

Direct-sequence spread-spectrum multiple-access (DS/SSMA) communications, strictly band-limited transmitter chip waveforms with excess bandwidth in the interval between zero and one, pseudo-random spreading sequences, an additive white Gaussian noise channel, and matched filter receivers are considered. First, a new expression for the average bit error rate (BER) is derived for systems with quaternary phase-shift keying (QPSK) spreading, the conventional matched filter receiver, a coherent detector for binary phase-shift keying (BPSK) data symbols, and chip waveforms that result in no interchip interference. The expression consists of a well known BER expression based on the standard Gaussian approximation to multiple-access interference and a few correction terms. It enables accurate BER evaluations without any numerical integration for various choices of system parameters of interest. The accuracy of the expression is guaranteed as long as the conditional Gaussian approximation to the cross-correlation coefficients between the desired user's spreading sequence and the interfering users' spreading sequences is valid. The expression well reflects the effect of filtering on the system performance. Extensions of the expression are discussed for systems with QPSK spreading and different detection schemes, systems with BPSK spreading, and systems with different transmit and receive filters. Monte Carlo simulation results are also provided to verify the accuracy.     

Blind multiuser detection in uplink CDMA with multipath fading: a sequential EM approach

We consider joint channel estimation and data detection in uplink asynchronous code-division multiple-access systems employing aperiodic (long) spreading sequences in the presence of unknown multipath fading. Since maximum-likelihood (ML) sequence estimation is too complex to perform, multiuser receivers are proposed based on the sequential expectation-maximization (EM) algorithm. With the prior knowledge of only the signature waveforms, the delays and the second-order statistics of the fading channel, the receivers sequentially estimate the channel using the sequential EM algorithm. Moreover, the snapshot estimates of each path are tracked by linear minimum mean-squared error filters. The user data are detected by a ML sequence detector, given the channel estimates. The proposed receivers that use the exact expressions have a computational complexity O(2/sup K/) per bit, where K is the number of users. Using the EM algorithm, we derive low-complexity approximations which have a computational complexity of O(K/sup 2/) per bit. Simulation results demonstrate that the proposed receivers offer substantial performance gains over conventional pilot-symbol-assisted techniques and achieve a performance close to the known channel bounds. Furthermore, the proposed receivers even outperform the single-user RAKE receiver with Nyquist pilot-insertion rate in a single-user environment.     

Frequency-Domain Channel Estimation for SC-FDE in UWB Communications

Recently, single-carrier block transmission with frequency-domain equalization (SC-FDE) has been shown to be a promising candidate for ultra-wideband (UWB) communications. In this paper, we address the channel estimation problem for SC-FDE transmission over UWB channels. A mean-square error (MSE) lower bound for the frequency-domain linear minimum mean-squared error (LMMSE) channel estimator is derived, and the optimal pilot sequence that achieves this lower bound is obtained. Further simplification leads to a frequency-domain channel estimator with reduced computational complexity. The performance of the simplified estimator for SC-FDE over UWB channels is evaluated and compared with that with perfect channel state information. The effects of nonoptimal and optimal pilot symbols are also investigated. Our results show that the proposed frequency-domain channel estimator performs well over UWB channels with only small performance degradation, compared with that with perfect channel estimation     

A multistep linear prediction approach to blind asynchronous CDMAchannel estimation and equalization

A multistep linear prediction approach is presented for blind channel estimation, multiuser interference (MUI) suppression, and detection of asynchronous short-code direct sequence code division multiple access signals in multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. We exploit the previously proposed multistep linear prediction approach for blind multiple-input multiple-output channel estimation in conjunction with the structure imposed by the desired user's spreading code sequence. With the knowledge of the desired user's code sequence, only the second-order statistics of the data are needed under certain sufficient conditions on the underlying multiuser MIMO transfer function. Based on the desired user's channel estimate, a linear minimum mean square error filter is designed for simultaneous equalization and MUI suppression. Three illustrative simulation examples are presented     

Iterative interference cancellation for DS-CDMA systems with highsystem loads using reliability-dependent feedback

In this paper, coded transmission over time-variant multipath Rayleigh-fading channels employing direct-sequence code division multiple access (DS-CDMA) is considered. Assuming ideal knowledge of the actual channel state and randomly chosen spreading sequences, we show that iterative multi-user interference suppression based on adapted minimum mean-squared error (MMSE) filters combined with serial successive cancellation and single user decoding can reach near optimum performance within a few iteration cycles. This holds even for doubly loaded systems, i.e., when the number of users K in the system is two times as large as the spreading factor N. Further, we evidence that for sufficiently reliable symbol estimates soft decision feedback can be replaced by hard decision feedback without any performance degradation but with significant savings in complexity     

Noncoherent MMSE multiuser receivers and their blind adaptiveimplementations

Three noncoherent minimum mean-squared error (NMSE)-based multiuser receivers are proposed for multipulse modulation. These receivers have a common MMSE prefilter and are followed by one of three phase-independent decision rules. The simplest decision rule selects the maximum magnitude of the MMSE filter outputs, and the other two account for the second-order statistics of the residual multiple-access interference that remains after MMSE filtering. Blind adaptive algorithms are then proposed for the three noncoherent MMSE receivers. The common adaptive algorithm for the MMSE prefilter, which is based on the stochastic approximation method, is shown to converge in the mean-squared error sense to the nonblind NMSE prefilter. Our convergence analysis yields new insight into the tradeoff between the rate of convergence and the residual mean-squared error. The noncoherent blind receivers obtained here do not require the knowledge of the received signals of any of the interfering users, and are hence well-suited for distributed implementation in cellular wireless networks or in communication systems that must operate in noncooperative environments     

Approximate ML Decision-Feedback Block Equalizer for Doubly Selective Fading Channels

To effectively suppress intersymbol interference (ISI) at low complexity, in this paper, we propose an approximate maximum-likelihood decision-feedback block equalizer (A-ML-DFBE) for doubly selective (frequency- and time-selective) fading channels. The proposed equalizer design makes efficient use of the special time-domain representation of multipath channels through a matched filter, a sliding window, a Gaussian approximation, and a decision feedback. The A-ML-DFBE has the following features: 1) It achieves a performance that is close that to that of maximum-likelihood sequence estimation (MLSE) and significantly outperforms minimum mean square error (MMSE)-based detectors. 2) It has substantially lower complexity than conventional equalizers. 3) It easily realizes complexity and performance tradeoff by adjusting the length of the sliding window. 4) It has a simple and fixed-length feedback filter. The symbol error rate (SER) is derived to characterize the behavior of the A-ML-DFBE and can also be used to find the key parameters of the proposed equalizer. In addition, we further prove that the A-ML-DFBE obtains full multipath diversity.      

Maximum Likelihood Receiver for Multiple Channel Transmission Systems

A maximum likelihood (ML) estimator for digital sequences disturbed by Gaussian noise, intersymbol interference (ISI) and interchannel interference (ICI) is derived. It is shown that the sampled outputs of the multiple matched filter (MMF) form a set of sufficient statistics for estimating the input vector sequence. Two ML vector sequence estimation algorithms are presented. One makes use of the sampled output data of the multiple whitened matched filter and is called the vector Viterbi algorithm. The other one is a modification of the vector Viterbi algorithm and uses directly the sampled output of the MMF. It appears that, under a certain condition, the error performance is asymptotically as good as if both ISI and ICI were absent.