Range Estimation in a Time Varying Multipath Channel

In this paper, range estimation in a time varying multipath channel is investigated, on the basis of which a multicarrier (MC) signal is compared with its pseudo-random (PN) counterpart in terms of the Cramer-Rao lower bound (CRLB) and the maximum likelihood estimator (MLE). The CRLB for range estimation in a time varying multipath channel is derived for three cases: (1) known channel state information (CSI); (2) unknown CSI; and (3) a special case of unknown CSI where the channel is modeled via Doppler shift. Furthermore, the MLE is developed for range estimation for each one of the above three cases and is investigated for a multipath Doppler channel with respect to the separability of its multipath components. Besides, the condition for a multipath Doppler channel to be separable is explored for a PN signal as well as for a MC signal. Simulation results show that range estimation with a MC signal outperforms its PN counterpart in a time varying channel, similar as that in a time invariant channel.     

Over-sampling basis expansion model aided channel estimation for OFDM systems with ICI

The rapid variation of channel can induce the intercarrier interference in orthogonal frequency-division multiplexing （OFDM） systems. Intercarrier interference will significantly increase the difficulty of OFDM channel estimation because too many channel coefficients need be estimated. In this article, a novel channel estimator is proposed to resolve the above problem. This estimator consists of two parts： the channel parameter estimation unit （CPEU）, which is used to estimate the number of channel taps and the multipath time delays, and the channel coefficient estimation unit （CCEU）, which is used to estimate the channel coefficients by using the estimated channel parameters provided by CPEU. In CCEU, the over-sampling basis expansion model is resorted to solve the problem that a large number of channel coefficients need to be estimated. Finally, simulation results are given to scale the performance of the proposed scheme.     

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     

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     

Frequency-offset estimation for HIPERLAN

Frequency-offset correction is considered for a HIPERLAN (HIgh-PErformance Radio LAN) system over the indoor radio channel. Since the multipath channel response is not known a priori, a viable frequency-offset estimator should not depend on such knowledge. Such an estimator, using a single sample per symbol, is derived for HIPERLAN. The estimator is shown to approach the Cramer-Rao bound for frequency-offset estimation over a multipath channel. A HIPERLAN system simulation example shows that the performance with an offset of 150 kHz is within 0.5 dB of that of a system with zero frequency offset     

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     

A robust channel estimator for DS-CDMA systems under multipath fading channels

This paper addresses the problem of channel estimation for direct-sequence code-division multiple-access (DS-CDMA) systems with time-varying multipath fading channels. The multipath fading channels are modeled as autoregressive (AR) models. A method is first proposed to convert the time-varying regression model due to the time-varying nature of users' information symbols into a time-invariant one. Then, a polynomial approach is proposed to obtain the minimum mean square error (MMSE) estimator. The uncertainty of the channel model and decision errors of the DS-CDMA detector are taken into consideration in the design of the MMSE estimator. Compared with the Kalman estimator, the computational complexity of the proposed algorithm is much lower. The simulation results show that the proposed estimator provides a comparable estimation performance with the Kalman estimator and is robust for fast-fading channels.     

On pilot-based multipath channel estimation for uplink CDMA systems: an overloaded case

The paper considers a coding scheme for multipath channel estimation in uplink code-division multiple-access systems where each user transmits an individual pilot signal (sequence) to estimate its multipath channel coefficients. Assuming a common radio channel model with a uniform power delay profile, we derive lower bounds on the maximum mean square error for two types of linear channel estimators: an inverse filter and a linear minimum mean square error (MMSE) estimator. In contrast to previous work, the main focus here is on overloaded systems where the total number of multipath channel coefficients of all users is greater than processing gain. We show that the inverse filter bound is attained if and only if each pilot sequence is a perfect root-of-unity sequence. Interestingly, the conventional matched filter achieves the same lower bound if pilot sequences form a complementary periodic sequence set. In case of the MMSE estimator, the lower bound is either met or not depending on some system parameters. We provide a necessary and sufficient condition for achieving the bound when pilot sequences are arbitrary vectors on the unit sphere. This paper gives insight into the performance limits of practical systems.     

A digital DS spread-spectrum receiver with joint channel andDoppler shift estimation

A digital spread-spectrum receiver design is presented for communication over multipath channels with severe Doppler shifts. The characteristics of the underwater channel relevant to spread-spectrum system design are discussed, and a channel model for short-range communications (less than 10 km) is defined. The receiver considered uses a digital coherent RAKE combiner, coupled with an extended Kalman filter (EKF)-based estimator for channel parameters and pseudonoise code delay. Receiver performance is evaluated by computing average bit-error rate (BER) versus iterations of the EKF joint estimator, using both fixed and time-varying channels. It is shown that the BER obtained using the EKF joint estimator closely tracks the optimum BER obtained when the channel, delay, and Doppler parameters are known exactly. Finally, the Cramer-Rao lower bound for time-invariant joint channel, delay, and Doppler estimation is derived, and compared with the ensemble averaged mean-squared error of the EKF estimator     

Filtered decision feedback channel estimation for OFDM-based DTVterrestrial broadcasting system

Orthogonal frequency division multiplexing (OFDM) is one of the transmission techniques used for digital television (DTV) terrestrial broadcasting. A high quality channel estimator with a low training overhead is the key to the successful delivery of DTV services which require high spectrum efficiency and robustness to strong and dynamic ghosts. Robustness to multipath distortion is especially important in a single frequency emission environment. This paper presents an application of a filtered decision feedback channel estimator for OFDM-based DTV systems using high order QAM modulations. The implementation and the performance of the channel estimator are discussed. Computer simulations were conducted to evaluate the performance of the channel estimator. The channel estimation loss is about 1.2 dB from the ideal case where the channel is assumed to be known by the receiver. For a given multipath spread, the loss can be further reduced by increasing the FFT size. The FFT size is however subject to an upper limit imposed by the Doppler spread     

A new time-delay estimation in multipath

This paper addresses a new approach to time-delay estimation based upon the autocorrelation estimator (AE). The primary aim of this paper is to estimate time-delays in a multipath environment in absence of prior knowledge of the channel. The maximum likelihood estimator (MLE) and AE are two computational tools that are used to determine the parameters of a multipath channel. MLE requires some priori knowledge of the source signal and the channel; AE can be a blind estimator but it is more suitable for a simple propagation model (one extra path). Under the multipath assumption we prove that if the observation sequence is zero padded the performance of MLE exceeds that of AE, however, at the price of higher computational efforts. The general autocorrelator estimator (GAE), based on autocorrelation of the received signal, is introduced. The GAE is formulated as a blind estimator, and the pertinent Cramer-Rao lower bounds (CRLB) are derived. We also develop an algorithm to estimate the parameters of a multipath environment based on the new generalization. The performance of this algorithm is examined for different signal-noise scenarios. Our results show that the time-delays are estimated accurately based on the proposed algorithm.     

Pilot-based estimation of time-varying multipath channels forcoherent CDMA receivers

Reliable coherent wireless communication requires accurate estimation of the time-varying multipath channel. This paper addresses two issues in the context of direct-sequence code-division multiple access (CDMA) systems: (i) linear minimum-mean-squared-error (MMSE) channel estimation based on a pilot transmission and (ii) impact of channel estimation errors on coherent receiver performance. A simple characterization of the MMSE estimator in terms of a bank of filters is derived. A key channel characteristic controlling system performance is the normalized coherence time, which is approximately the number of symbols over which the channel remains strongly correlated. It is shown that the estimator performance is characterized by an effective signal-to-noise ratio (SNR)-the product of the pilot SNR and the normalized coherence time. A simple uniform averaging estimator is also proposed that is easy to implement and delivers near-optimal performance if properly designed. The receivers analyzed in this paper are based on a time-frequency RAKE structure that exploits joint multipath-Doppler diversity. It is shown that the overall receiver performance is controlled by two competing effects: shorter coherence times lead to degraded channel estimation but improved inherent receiver performance due to Doppler diversity, with opposite effects for longer coherence times. Our results demonstrate that exploiting Doppler diversity can significantly mitigate the error probability floors that plague conventional CDMA receivers under fast fading due to errors in channel estimation     

Joint estimation of carrier frequency offset and statistical parameters of the multipath fading channel

In this paper, we focus on the joint estimation of the carrier frequency offset and statistical parameters of the multipath mobile channel. By modeling the multipath fading channel with a complex bandpass autoregressive (AR) model, we show how the estimates for the frequency offset, Doppler spread, and power profile of the multipath channel can be extracted from the estimated complex AR coefficients obtained via the expectation-maximization algorithm. A main advantage of the proposed joint estimator is that while it has a capability of performing equally well in all scattering environments, it can provide accurate estimates even in high-mobility channel conditions. We also demonstrate how the complexity of the estimator can be significantly reduced, while only slightly trading off performance, by applying the mean field approximation technique. Moreover, we derive a fully adaptive joint synchronization and channel-estimation scheme, as well as a novel Kalman-smoother-based frequency-error detector that can be used in feedback frequency-recovery schemes and is particularly well suited for fast-fading channel conditions. Finally, we revisit the Cramer-Rao lower bound analysis, and show how the Fisher information matrix can be conveniently computed in the presence of a frequency-selective Rayleigh fading channel.     

A new adaptive equalizer with channel estimator for mobile radiocommunication

For unknown mobile radio channels with severe intersymbol interference (ISI), a maximum likelihood sequence estimator, such as a decision feedback equalizer (DFE) having both feedforward and feedback filters, needs to handle both precursors and postcursors. Consequently, such an equalizer is too complex to be practical. This paper presents a new reduced-state, soft decision feedback Viterbi equalizer (RSSDFVE) with a channel estimator and predictor. The RSSDFVE uses maximum likelihood sequence estimation (MLSE) to handle the precursors and truncates the overall postcursors with the soft decision of the MLSE to reduce the implementation complexity. A multiray fading channel model with a Doppler frequency shift is used in the simulation. For fast convergence, a channel estimator with fast start-up is proposed. The channel estimator obtains the sampled channel impulse response (CIR) from the training sequence and updates the RSSDFVE during the bursts in order to track changes of the fading channel. Simulation results show the RSSDFVE has nearly the same performance as the MLSE for time-invariant multipath fading channels and better performance than the DFE for time-variant multipath fading channels with less implementation complexity than the MLSE. The fast start-up (FS) channel estimator gives faster convergence than a Kalman channel estimator. The proposed RSSDFVE retains the MLSE structure to obtain good performance and only uses soft decisions to subtract the postcursor interference. It provides the best tradeoff between complexity and performance of any Viterbi equalizers     

OFDM/OQAM系统中联合迭代信道估计和信号检测

与基于复数域空间正交条件的传统正交频分复用系统(OFDM with Cyclic Prefix, CP-OFDM)有所不同,基于交错正交调制的正交频分复用系统(OFDM/Offset QAM, OFDM/OQAM)满足实数域空间严格正交条件。因此在多径衰落信道条件下,CP-OFDM系统中的信道估计方法会导致OFDM/OQAM系统严重的字符间干扰和载波间干扰。该文结合OFDM/OQAM系统结构特点,提出了一种基于迭代信道估计和信号检测算法。该算法通过信道估计器和接收到的信号互相交换信息,消除导频序列中的字符间干扰和载波间干扰,提高信道估计和信号检测的准确度。仿真分析结果表明,经过一定次数迭代处理后,OFDM/OQAM迭代信道估计性能趋近于理想信道估计性能。     

Tracking Performance of an Adaptive MIMO-OFDM LS Estimator via MSE Criterion Over a Wireless Time Correlated Fading Channel

In this contribution, the performance of an adaptive least squares channel estimator for a time correlated MIMO-OFDM channel is presented in a closed form relation. As a criterion for performance evaluation, the well-known mean square error (MSE) is employed. The pilot aided channel estimation is used to extract the channel coefficients. To minimize the MSE and arrange phase shift orthogonally, the pilots are constructed with equal power and space. The model of the channel is developed by implementing a first order Markov model, and it is proved that the performance of the system is dependent upon the defined forgetting factor, the number of transmit antennas, the number of multipath channel taps, transmitted power, and Doppler shift. The effect of each parameter on the performance of the system is discussed separately. The computer simulation results follow with the analytical results comprehensively.     

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。     

$H_{infty}$ Channel Estimator Design for DS-CDMA Systems: A Polynomial Approach in Krein Space

This paper considers the problem of robust channel estimation for direct-sequence code-division multiple-access (DS-CDMA) systems with time-varying multipath fading channels. Due to the lack of accurate knowledge of model dynamics and statistics of system noises, a polynomial channel estimator is developed by virtue of the Krein space theory. The estimator is calculated by performing a J-spectral factorization. In this paper, under some conditions, we obtain a closed-form solution to this J-spectral factorization, which greatly reduces the computational load of the estimator design. The simulation results show that the proposed estimator provides a robust estimation performance against various types of noises and modeling errors.     

Fundamental Limit of OFDM Range Estimation in a Separable Multipath Environment

In this paper, orthogonal frequency division multiplexing (OFDM) for time-based range estimation (TBRE) in a separable multipath channel is investigated and analyzed with respect to its accuracy. First, the Cramer–Rao lower bound (CRLB) in a separable multipath channel is theoretically derived, and indicates a similar expression to that for a single path channel. The CRLB for non-data-bearing (NDB) OFDM transmission is compared to that for pseudo-noise (PN) transmission, demonstrating a large performance gap in favor of the NDB OFDM. Furthermore, the maximum likelihood estimator (MLE) for TBRE in a separable multipath channel is theoretically derived, also demonstrating a similar expression to that in a single path channel, except that several peaks instead of one peak are expected in a separable multipath channel corresponding to all arrival paths. The MLE for TBRE is then compared to the commonly used MLE for channel estimation, showing an equal performance in terms of mean square error when using an NDB OFDM transmission. Simulation results demonstrate a good agreement with our proposed theory.     

Parallel structures for joint channel estimation and data detectionover fading channels

Joint data and channel estimation for mobile communication receivers can be realized by employing a Viterbi detector along with channel estimators which estimate the channel impulse response. The behavior of the channel estimator has a strong impact on the overall error rate performance of the receiver. Kalman filtering is an optimum channel estimation technique which can lead to significant improvement in the receiver bit error rate (BER) performance. However, a Kalman filter is a complex algorithm and is sensitive to roundoff errors. Square-root implementation methods are required for robustness against numerical errors. Real-time computation of the Kalman estimator in a mobile communication receiver calls for parallel and pipelined structures to take advantage of the inherent parallelism in the algorithm. In this paper different implementation methods are considered for measurement update and time update equations of the Kalman filter. The unit-lower-triangular-diagonal (LD) correction algorithm is used for the time update equations, and systolic array structures are proposed for its implementation. For the overall implementation of joint data and channel estimation, parallel structures are proposed to perform both the Viterbi algorithm and channel estimation. Simulation results show the numerical stability of different implementation techniques and the number of bits required in the digital computations with different estimators