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In practical Orthogonal Frequency Division Multiplexing (OFDM) systems, due to the presence of virtual subcarriers, the OFDM input–output relation is ill-conditioned in the Fourier basis. Therefore, an unbiased estimator does not exist and regularization methods, generally used to estimate the channel, provide biased time domain estimates. To estimate exact channel sparsity, we propose an unbiased estimator in discrete prolate spheroidal sequences (DPSS) basis. We theoretically show that our estimates recover exact sparsity information as the SNR increases. [ABSTRACT FROM PUBLISHER]

This paper addresses the development of analytical tools for the computation of the inverse moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics such as the average estimation error corresponding to the best linear unbiased estimator (BLUE) and the linear minimum mean square error (LMMSE) estimator or also other loss functions used to measure the accuracy of covariance matrix estimates. [ABSTRACT FROM AUTHOR]

In this paper, we propose a practical and scalable solution to mitigating interference on the uplink through static clustering and adaptive fractional frequency reuse (CFFR). The focus is on a three-cell clustered network due to its low complexity. Moreover, we have previously shown that a performance comparable to that of global coordination is achievable using a cluster size of three. In this paper, for a clustered planar Wyner network, we derive analytical capacity equations for zero forcing (ZF) and linear minimum mean squared error (LMMSE)-based receivers. The theoretical results show that inter-cluster interference is the major performance bottleneck and that the smallest interference from the neighbouring clusters is sufficient to significantly lower the system performance. We then switch our study to a more realistic network setting and augment our CFFR technique by adopting an entirely distributed architecture and by implementing a location classification algorithm based on logistic regression. We then show through simulations that CFFR performs significantly better than the widely studied dynamic clustering (DC) technique. Since the inter-cluster interference intensity of CFFR is much lower than DC, the per-cell sum rate performance is 1.5 × better, especially at high loads. We also show that the CFFR algorithm is a lot less complex than DC in terms of running time. [ABSTRACT FROM AUTHOR]

In this paper, we consider the resource-allocation problem for energy efficiency (EE)–spectral efficiency (SE) tradeoff. Unlike traditional research that uses the EE as an objective function and imposes constraints either on the SE or on the achievable rate, we propound a multiobjective optimization approach that can flexibly switch between the EE and SE functions or change the priority level of each function using a tradeoff parameter. Our dynamic approach is more tractable than the conventional approaches and more convenient to realistic communication applications and scenarios. We prove that the multiobjective optimization of the EE and SE is equivalent to a simple problem that maximizes the achievable rate/SE and minimizes the total power consumption. Then, we apply the generalized framework of the resource allocation for the EE–SE tradeoff to optimally allocate the subcarriers' power for orthogonal frequency-division multiplexing (OFDM) with imperfect channel estimation. Finally, we use numerical results to discuss the choice of the tradeoff parameter and study the effect of the estimation error, transmission power budget, and channel-to-noise ratio on the multiobjective optimization. [ABSTRACT FROM AUTHOR]

In an orthogonal frequency division multiplexing (OFDM) system, the linear-minimum-mean-square-error (LMMSE)-based channel estimator often requires a matrix inversion with cubic complexity. In this letter, by employing a K terms Neumann series expansion to approximate the matrix inversion, the computational complexity is reduced to \mathcal{O}(N \log L) per channel realization, where N$ is the number of subcarriers and $L$ is the number of non-zero time domain channel taps. Extensive simulation results show that even with small $K$ ($K \leq 2$), the performance loss caused by the proposed approximation is marginal. [ABSTRACT FROM PUBLISHER]

We consider cellular networks with co-operative clusters of neighboring base stations detecting multiple in-cluster users subject to interference from out-of-cluster users. We assume that the base stations, equipped with multiple antennas, are connected to a central processor in each cluster. For such a network, we first consider centralized processing where all the in-cluster user signals are sent to the central processor for linear minimum mean squared error (LMMSE) estimation. Next, we consider partially decentralized processing where the in-cluster user signals are locally estimated at each base station, and the local estimates are combined at the central processor. For both processing architectures, we derive new expressions for the achievable rate of an in-cluster user when the channels between the users and base stations are subject to independent Rayleigh fading and distance-dependent path loss. The solutions are based on accurate approximations we derive for the characteristic function (CF) and the probability density function (PDF) of each user’s signal-to-interference-plus-noise ratios (SINRs). Numerical examples highlight the accuracy of the analysis and compare the performance of centralized and partially decentralized processing under different cluster scenarios. [ABSTRACT FROM PUBLISHER]

Vector orthogonal frequency-division multiplexing (V-OFDM) for single-transmit-antenna systems is a generalization of OFDM where single-carrier frequency-domain equalization and OFDM are just two special cases. Phase noise in a V-OFDM system leads to a common vector block phase error (CVBPE) and an intervector block carrier interference effect. Severe performance degradation may occur if these two effects are not estimated and compensated well. In this paper, blind and semiblind phase noise estimation and compensation in a V-OFDM system is investigated by using the expectation-maximization (EM) algorithm. This is motivated by the fact that the conventional frequency-domain phase noise suppression schemes based on pilot-aided common phase error (CPE) or CVBPE estimation and compensation are not spectrally efficient as the vector block size is increased. Two novel schemes are proposed: One estimates the CVBPE only, and the other estimates the entire phase noise sequence in the time domain. General closed-form formulas for the maximization step of the EM algorithm for the two schemes are derived, and their computational complexity values are analyzed. The performances of the two schemes are investigated by using linear-minimum-mean-square-error (LMMSE) receivers. Simulations show that the two proposed schemes are very effective in estimating and compensating for phase noise in V-OFDM systems. It turns out that the second proposed scheme not only outperforms the traditional CPE or CVBPE schemes but is computationally efficient as well when applied to V-OFDM systems. [ABSTRACT FROM PUBLISHER]

In order to reduce the equalization delay induced by iteration, two parallel methods were proposed respectively based on maximum a-posteriori probability （MAP） and linear minimum mean-squared error （LMMSE） equalization algo-rithm in Turbo equalization. Through theoretical analysis, simulation and hardware complexity discussion, it is concluded that the proposed two parallel equalization schemes can fully reduced the equalization delay with small hardware com-plexity and excellent performance.

This paper deals with the minimum mean square error (MMSE)-based multipath channel and noise variance estimation in the case of a pilot-aided orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) system. The theoretical expression of the LMMSE channel estimation is formulated and a simpler closed-form is derived. The MSE analysis shows that LMMSE inevitably reaches an error floor due to the interference inherent to OFDM/OQAM modulation. Furthermore, an algorithm for the joint MMSE estimation of both the channel and the noise variance (J-MCNE) is proposed and features a reduced complexity thanks to the low-rank approximation method. The noise level estimation represents a challenge as it is concealed in the intrinsic interferences generated by the OFDM/OQAM. Simulations reveal the capability of the proposed J-MCNE method to estimate the noise variance and show that the achieved bit error rate (BER) is close to that of the perfect estimation. [ABSTRACT FROM PUBLISHER]

Vector orthogonal frequency division multiplexing (V-OFDM) for single transmit antenna systems is a generalization of OFDM where single-carrier frequency domain equalization (SC-FDE) and OFDM are just two special cases. It has been shown to be able to collect multipath diversity and thus generally outperforms OFDM. The performance of OFDM under phase noise has been extensively studied in the literature. These effects can be summarized as introducing a common phase error (CPE) and inter carrier interference (ICI) resulting in poor performance. The performance of V-OFDM under phase noise still remains uninvestigated and in this paper it is shown that phase noise in V-OFDM systems leads to a common vector block phase error (CVBPE) as well as an inter vector block carrier interference (IVBCI) effect. An expression for the signal plus interference noise ratio (SINR) for a V-OFDM system is derived and found to agree closely with simulation results. A pilot vector CVBPE based phase noise estimation technique is derived, and then combined with the maximum likelihood (ML) and the linear minimum mean square error (LMMSE) estimators to estimate the phase noise. It turns out that compared with OFDM, V-OFDM systems can perform phase noise estimation with lower complexity. The decorrelation and cancellation techniques are then used to compensate for the phase noise impairment. Numerical results for both coded and uncoded systems with perfect and practical channel estimation are provided to validate the analysis and effectiveness of the proposed phase noise estimation and compensation methods. [ABSTRACT FROM AUTHOR]

A new modified Min Sum decoding algorithm based on parameter estimation theory for Low Density Parity Check (LDPC) codes is presented in this paper. First, Linear Minimum Mean Square Error (LMMSE) estimate criterion is used to model the magnitude of check-to-variable message and calculate estimated parameters, furthermore the golden section search algorithm is used to speed up getting the boundary, with which the parameters can be determined. Then, the parameters are modified further on the basis of the relationship between the iteration number and the estimated parameters. Finally, the same estimated parameters are used for different signal to noise ratio (SNR) to ensure the decoding performance and reduce the hardware complexity. The simulation results show that a gain of 0.3-0.5dB can be achieved in comparison with other kinds of modified Min Sum algorithms, which is very close to that of BP algorithm. What's more, the algorithm has the following characteristics: low computation complexity, small decoding delay, easiness of calculation for estimated parameters, and simplicity in hardware implementation. [ABSTRACT FROM AUTHOR]

Unique word-orthogonal frequency division multiplexing (UW-OFDM) is a novel signaling concept where the guard interval is implemented as a deterministic sequence, the so-called unique word. The UW is generated by introducing a certain level of redundancy in the frequency domain. Different data estimation strategies and the favourable bit error ratio (BER) performance of UW-OFDM, as well as comparisons to competing concepts have already extensively been discussed in previous papers. This work focuses on the different possibilities on how to generate UW-OFDM signals. The optimality of the two-step over the direct approach in systematic UW-OFDM is proved analytically, we present a heuristic algorithm that allows a fast numerical optimization of the redundant subcarrier positions, and we show that our original intuitive approach of spreading the redundant subcarriers in systematically encoded UW-OFDM by minimizing the mean redundant energy is practically also optimum w.r.t. transceiver based cost functions. Finally, we derive closed form approximations of the statistical symbol distributions on individual subcarriers as well as the redundant energy distribution and compare them with numerically found results. [ABSTRACT FROM AUTHOR]

In this paper, a low-sampling-rate scheme for ultra-wideband channel estimation is proposed. The scheme exploits multiple observations generated by transmitting multiple pulses. In the proposed scheme, P pulses are transmitted to produce channel impulse response estimates at a desired sampling rate, while the ADC samples at a rate that is P times slower. To avoid loss of fidelity, the number of sampling periods (based on the desired rate) in the inter-pulse interval is restricted to be co-prime with P. This condition is affected when clock drift is present and the transmitted pulse locations change. To handle this case, and to achieve an overall good channel estimation performance, without using prior information, we derive an improved estimator based on the bounded data uncertainty (BDU) model. It is shown that this estimator is related to the Bayesian linear minimum mean squared error (LMMSE) estimator. Channel estimation performance of the proposed sub-sampling scheme combined with the new estimator is assessed in simulation. The results show that high reduction in sampling rate can be achieved. The proposed estimator outperforms the least squares estimator in almost all cases, while in the high SNR regime it also outperforms the LMMSE estimator. In addition to channel estimation, a synchronization method is also proposed that utilizes the same pulse sequence used for channel estimation. [ABSTRACT FROM PUBLISHER]

Conventional implementations of the linear minimum mean-square (LMMSE) and minimum variance distortionless response (MVDR) estimators rely on the sample matrix inversion (SMI) technique, i.e., on the sample covariance matrix (SCM). This approach is optimal in the large sample size regime. Nonetheless, in small sample size situations, those sample estimators suffer a large performance degradation. Thus, the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations. To this aim, a twofold approach is proposed. First, shrinkage estimators are considered, as they are known to be robust to the small sample size regime. Namely, the proposed methods are based on shrinking the sample LMMSE or sample MVDR filters towards a variously called matched filter or conventional (Bartlett) beamformer in array processing. Second, random matrix theory is used to obtain the optimal shrinkage factors for large filters. The simulation results highlight that the proposed methods outperform the sample LMMSE and MVDR. Also, provided that the sample size is higher than the observation dimension, they improve classical diagonal loading (DL) and Ledoit–Wolf (LW) techniques, which counteract the small sample size degradation by regularizing the SCM. Finally, compared to state-of-the-art DL, the proposed methods reduce the computational cost and the proposed shrinkage of the LMMSE obtains performance gains. [ABSTRACT FROM AUTHOR]

System state estimation relies heavily on the measurements. With the advance of sensing technology, the ability to measure is no longer a bottleneck in many systems, and more and more researchers now focus on the rich-information setting, i.e., big data. However, although information never hurts, it does not help unconditionally. How to make the most of it depends on whether we can process the data efficiently. In some systems, the inherent constraint such as the bandwidth and cost makes it necessary to reduce the dimension of the measurement before further processing. The problem that the raw measurements are first preprocessed to reduce size and then used for estimation is addressed in this paper. It is shown that there is a lower bound on the size of the preprocessed data such that if the size is beyond the bound, there exists a closed-form estimator design that the linear minimum mean-square estimation can be obtained. Moreover, we propose an algorithm that is guaranteed to converge to a stationary point to design an estimator in the conditions that the lower bound cannot be reached. Besides convergence, the proposed algorithm guarantees bounded performance loss compared with the global optimal solution under some additional conditions. Finally, simulation results in three different applications are shown to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

High speed multimedia services with flexible data rate are main cause of popularity of 3 G WCDMA. WCDMA air interface of UMTS has the bandwidth of 5 MHz and chip rate of 3.84 Mcps. The flexibility in data rate is achieved by varying the length of its spreading code. WCDMA supports seamless connections of dynamic data rate ranging from 15 Kbps to 1 Mbps and respective spreading factors are 256 and 4 respectively for indoor and outdoor applications. The conventional RAKE receiver is near far and interference limited. Its performance at high data is limited due to short spreading factor of a code. A simple MIMO receiver structure of LMMSE in downlink asynchronous direct-sequence code division multiple access is proposed in this paper. This paper investigates RAKE receiver characteristics and does the analysis of zero forcing and LMMSE equalizer for MIMO channels. [ABSTRACT FROM AUTHOR]

Highlights: [•] A low computational complexity weighted linear SIC detector is proposed. [•] It can converge to either the decorrelator or the LMMSE detector for two distinct values. [•] A reduced complexity version of the weighted linear SIC detector is also proposed. [•] The proposed scheme is convergent if the weighting factor is between 0 and 1. [ABSTRACT FROM AUTHOR]

The conventional linear minimum mean square error (LMMSE) estimator is commonly implemented through the sample covariance matrix. This estimator can only be implemented if the sample size N is higher than the observation dimension M. Moreover, this estimator performs poorly when the sample size is not sufficiently large. To address this problem, we propose a new shrinkage LMMSE estimator. The proposed estimator performs efficiently over a wide range of observation dimensions and sample sizes. In contrast to existing methods, the proposed estimator can be applied if M\geq N. Even if M

Abstract: Parallel magnetic resonance imaging (MRI) yields noisy magnitude data, described in most cases as following a noncentral χ distribution when the signals received by the coils are combined as the sum of their squares. One well-known case of this noncentral χ noise model is the Rician model, but it is only valid in the case of single-channel acquisition. Although the use of parallel MRI is increasingly common, most of the correction methods still perform Rician noise removal, yielding an erroneous result due to an incorrect noise model. Moreover, the existence of noise correlations in phased array systems renders noise nonstationary and further modifies the noise description in parallel MRI. However, the noncentral χ model has been demonstrated to work as a good approximation as long as effective voxelwise parameters are used. A good correction step, adapted to the right noise model, is of paramount importance, especially when working with diffusion-weighted MR data, whose signal-to-noise ratio is low. In this paper, we present a noise removal technique designed to be fast enough for integration into a real-time reconstruction system, thus offering the convenience of obtaining corrected data almost instantaneously during the MRI scan. Our method employs the noncentral χ noise model and uses a simplified method to account for noise correlations; this leads to an efficient and rapid correction. The method consists of an anisotropic extension of the Linear Minimum Mean Square Error estimator (LMMSE) that is a far better edge-preserving method than the traditional LMMSE and addresses noncentral χ distributions along with empirically computed global effective parameters. The results on simulated and real data demonstrate that this anisotropic extended LMMSE outperforms the original LMMSE on images corrupted by noncentral χ noise. Moreover, in comparison with the existing LMMSE technique incorporating the estimation of voxelwise effective parameters, our method yields improved results. [Copyright &y& Elsevier]

In this work, we consider the front-end receivers for flat fading MIMO transmission, whose essential feature is the calculation of the log-likelihood ratios (LLRs) for the transmitted bits. When the number of transmit antennas and the modulation size grow, the exact calculation of the LLRs becomes unfeasible due to the necessity to enumerate the symbols affecting the output. In this work, to avoid the burden of explicit enumeration, instead of calculating the likelihoods exactly, we explore the possibilities offered by the saddlepoint approximation of the likelihood functions. The resulting fixed-complexity approach significantly outperforms the well known linear-filter based minimum mean square error detection. A complexity analysis identifies the main computational bottleneck of the proposed detection algorithm. [ABSTRACT FROM PUBLISHER]

Kalman filter is a powerful tool in target tracking and self-localization across wireless sensor networks with many constraints. This paper considers the filters design for networked systems with combined constraints of bandwidth and random delay, and proposes a kind of universal networked Kalman estimator for given linear time invariant (LTI) or determinate parameters (DP) systems, which are also called linear and determinate parameters (LDP) systems jointly. Firstly, two modeling ways to treat bit quantization error vector are given and the corresponding LDP systems taken after bit quantization are established. Secondly, we introduce an equivalent weighted summation form of the conventional linear Kalman filter, which fully uses two essential characteristics, namely offline computation property from the LDP systems and linear weighted summation property from the linear minimum mean square error estimate. Finally, by adopting the replacement and innovation compensation operations, a kind of integrated networked estimator, involving two estimation algorithms with different modeling ways to bit quantization error actually, is presented based on the weighted summation filter for random delay systems. The proposed universal networked estimation algorithms have some outstanding advantages such as extensive application, concise algorithm structure, high estimate accuracy, and good running performance. Several examples are demonstrated to validate the proposed networked estimation algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the problem of speech deconvolution is solved. This problem is encountered in limited-bandwidth speech communication systems such as telephone systems. Three solutions are presented for this problem. In the first solution, a Linear Minimum Mean Square Error (LMMSE) approach is used. The necessary assumptions required to reduce the computational complexity of the LMMSE solution are presented. In the second solution, an inverse filter deconvolution approach is presented. Finally, the regularization theory is used to solve this problem. The common thread between all these solutions is that they treat the speech deconvolution problem as an inverse problem considering the speech degradation model. Simulation results reveal the superiority of these solutions for solving the speech deconvolution problem. [ABSTRACT FROM AUTHOR]

The coefficients of a Linear Minimum Mean Square Error (LMMSE) equalizer for a stationary random signal are defined by a Toeplitz system. The Toeplitz structure can be exploited to reduce computational complexity. In this paper we investigate the Levinson and Schur algorithm, as well as circulant embedding and circulant approximation methods applied to the Preconditioned Conjugate Gradient (PCG) method and Frequency Domain Equalization (FDE). We develop a novel circulant approximation method which improves the performance/complexity tradeoff. We show that the optimal choice of algorithms largely depends on the antenna configuration. Investigated configurations are Single Input Single Output (SISO), Single Input Multiple Output (SIMO) and Multiple Input Multiple Output (MIMO). All considered algorithms are benchmarked in terms of implementation complexity and capacity achieved by a High Speed Downlink Packet Access (HSDPA) receiver in a multipath fading scenario. [ABSTRACT FROM AUTHOR]

In distributed estimation fusion, processed data from each sensor is sent to the fusion center. By taking linear transformation of the raw measurements of each sensor, two optimal distributed fusion algorithms are proposed in this paper. Compared with existing fusion algorithms, they have three nice properties. First, they are optimal in the sense that they are equivalent to the optimal centralized fusion. Second, their communication requirements from each sensor to the fusion center are equal to or less than those of the centralized and most existing distributed fusion algorithms. Third, they do not need the inverses of estimation error covariance matrices, which are assumed to exist in most existing algorithms but can not be guaranteed to exist. So the proposed algorithms can be applied in more cases. Pros and cons of these two new algorithms are analyzed. A possible way to reduce the computational complexity of the new algorithms, an extension to the case of a singular covariance matrix of measurement noise, and an extension to the reduced-rate communication case for some simple systems are also discussed. [ABSTRACT FROM PUBLISHER]

In this paper, we analyze the frequency domain linear equalization (FDLE) of single carrier block transmission (SCBT) systems under fast fading channel. First, we propose a new approximating model in which the channel is assumed to be static in sub-blocks vary each other. Based on this model, we derive a new 2-orthogonal-sub-blocked frequency domain equalization method. Then, we derive the conditions of the channel under which the equalization method can be applied to the 2-orthogonal-sub-blocked systems. Simulation demonstrates that the proposed method can improve the anti-Doppler ability of SC-FDLE and at the same time keep its high efficiency and low complexity. [ABSTRACT FROM AUTHOR]

In this article, the training-based channel estimation (TBCE) and semi-blind channel estimation (SBCE) schemes in Rayleigh flat fading multiple-input multiple-output (MIMO) channels are investigated. First, least squares (LS), linear minimum mean square error (LMMSE), maximum likelihood (ML), and maximum a posteriori (MAP) channel estimators are presented and simulated. Owing to faster processing and lower bit error rate (BER), the LS estimator is the proper choice for both TBCE and SBCE-ML. It is illustrated that when the number of transmitter and/or receiver antennas increases, the performance of both TBCE and SBCE-ML schemes significantly improves. In addition, Alamouti coding has more effect on the performance of SBCE-ML rather than TBCE. Comparing LS-based TBCE and LS-based SBCE-ML, the simulation results introduce the most appropriate channel estimation method that uses an iterative algorithm. This new proposed method is based on LS estimator and ML detector. Simulation results of this investigation show that LS-based SBCE-ML method compared with LS-based TBCE method in different signal-to-noise ratios (SNRs) offers lower BER, 25% higher processing time, and 100 times lower training bits. [ABSTRACT FROM AUTHOR]

Few works have addressed the effect of CFO (carrier frequency offset) on channel estimation performance. In this paper, compact analytical expressions on the mean square error of channel estimation in the presence of CFO are derived for OFDM (orthogonal frequency division multiplexing) systems employing single and multiple antennas. Concise upper bounds are also derived for SISO-OFDM systems. It is revealed that channel estimation MSE (mean square error) increases at the rate of approximately the square of the CFO and increasing the number of pilots does not contribute to better suppression of the MSE caused by CFO. In addition, it is observed that LMMSE (linear minimum mean square error) channel estimation is more resistant to CFO compared to LS (least square) in terms of channel estimation MSE. Furthermore, from the results derived herein, a clue for the pilot design of OFDM systems with CFO can be obtained [ABSTRACT FROM PUBLISHER]

Multi-carrier code-division-multiple-access (MC-CDMA) is a promising transmission technique for high-speed wireless multimedia communication in frequency-selective fading channels. In this letter, allocations of physical transmission rate, sub-carrier, and power are proposed for a MC-CDMA system that applies multi-code (MC)/variable-spreading-length (VSL) multi-rate access to minimize total transmitted power, where we consider users have different data rate and BER.requirements and LMMSE multiuser detection is used in the receivers. We derive transmission rate capacity and propose a simple admission control criterion that linearly relates the code length, data rate and BER requests of all users. The proposed iterative allocation algorithm jointly allocates the sub-carrier power of each user and solves the sub-carrier allocation problem [ABSTRACT FROM PUBLISHER]

In this paper, a joint symbol timing and frequency-offset estimator based on the maximum likelihood (ML) criterion, is derived for OFDM systems over frequency selective fading channels. .We use the linear minimum mean square estimation technique (LMMSE) to estimate the nuisance parameters such as transmitted signals and fading gains, and arrive at an algorithm to jointly estimate symbol timing and frequency offset. Simulation results show that our proposed symbol timing estimator performs better than the estimator reported by van de Beek et al (1997), while our proposed frequency offset estimator achieves a lower MSE at higher SNR (ges 15 dB). Simulation results also show that our proposed symbol timing and frequency offset estimator has better MSE performance than the cyclostationarity-based estimator studied in T. Pollet and M. Moeneclaey (1995) at higher SNR (for example 15 dB). However, in terms of probability of correct timing synchronization and MSE, our symbol timing estimator achieves roughly the same performance as the estimator by Lee et al (2002), although a different approach is used in our estimator. Our proposed estimator is next modified to two practical ones independent of SNR, furthermore, one of which needs only the knowledge of the maximum delay spread to perform estimation. We also extend our proposed estimator to applications where multiple OFDM symbols can be observed to perform synchronization [ABSTRACT FROM PUBLISHER]

This paper exploits both the inter- and intra-scale interdependencies that exist in wavelet coefficients to improve image restoration from noise-corrupted data. Using an over-complete wavelet expansion, we group the wavelet coefficients with the same spatial orientation at several scales. We then apply the linear minimum mean squared-error estimation to smooth noise. This scheme exploits the inter-scale correlation information of wavelet coefficients. To exploit the intra-scale dependencies, we calculate the co-variance matrix of each vector locally using a centered square-shaped window. Experiments show that the proposed hybrid scheme significantly outperforms methods exploiting only the intra- or inter-scale dependencies. The performance of noise removal also depends on wavelet filters. In our experiments a biorthogonal wavelet, which best characterizes the image inter-scale dependencies, achieves the best results. [Copyright &y& Elsevier]