Linear Minimum Mean Square Error Estimator Research Articles

BLUE-Based Channel Estimation Technique for Amplify and Forward Wireless Relay Networks

The best linear unbiased estimator (BLUE) is most suitable for practical application and can be determined with knowledge of only the first and second moments of the probability density function. Although the BLUE is an existing algorithm, it is still largely unexplored and has not yet been applied to channel estimation in amplify and forward (AF)-based wireless relay networks (WRNs). In this paper, a BLUE-based algorithm is proposed to estimate the overall channel impulse response between the source and destination of AF strategy-based WRNs. Theoretical mean square error (MSE) performance for the BLUE is derived to show the accuracy of the proposed channel estimation algorithm. In addition, the Cramér-Rao lower bound (CRLB) is derived to validate the MSE performance. The proposed BLUE channel estimation algorithm approaches the CRLB as the length of the training sequence and number of relays increases. Further, the BLUE performs better than the linear minimum MSE estimator due to the minimum variance characteristic exhibited by the BLUE, which happens to be a function of signal-to-noise ratio.

Towards the Performance of ML and the Complexity of MMSE: A Hybrid Approach for Multiuser Detection

In this paper, we consider a low-complexity multiuser detection for downlink of high speed packet access (HSPA) of universal mobile telecommunications system (UMTS). Instead of attempting to perform maximum likelihood (ML) detection of all users in multiple cells, which is impractical for battery powered mobile receiver, we utilize interference cancelled chips obtained from iterative linear minimum mean square error (LMMSE) estimation to perform a near ML detection in a reduced dimensional system. As a result, the worst case complexity of the detection process, achieved by the closest lattice point search (CLPS), is bounded to a controllable level irrespective of multipath spans. Furthermore, by exploiting the LMMSE estimate in tightening the hypersphere condition of the CLPS algorithm so called sphere decoding, we achieve significant improvement in search complexity. From simulations on realistic downlink communication scenario in HSPA systems, we show that the proposed method offers substantial performance gain over conventional receiver algorithms with reasonable complexity.

On the Exploitation of the Redundant Energy in UW-OFDM: LMMSE Versus Sphere Detection

Unique word orthogonal frequency division multiplexing (UW-OFDM) inherently introduces a complex number Reed Solomon (RS) code. Originally, the code generator matrix of systematic coded UW-OFDM had been designed rather intuitively by minimizing the mean redundant energy. In this work we justify this approach by applying a cost function that incorporates the overall transceiver chain including a linear minimum mean square error (LMMSE) data estimator. In addition to the LMMSE estimator we investigate a nonlinear sphere detection (SD) receiver for both systematic and nonsystematic coded UW-OFDM. We study and interpret the estimators' performance and their diverse ability to exploit the redundant energy.

Image denoising and zooming under the linear minimum mean square-error estimation framework

Most of the existing image interpolation schemes assume that the image to be interpolated is noise free. This assumption is invalid in practice because noise will be inevitably introduced in the image acquisition process. Usually, the image is denoised first and is then interpolated. The denoising process, however, may destroy the image edge structures and introduce artefacts. Meanwhile, edge preservation is a critical issue in both image denoising and interpolation. To address these problems, in this study the authors propose a directional denoising scheme, which naturally endows a subsequent directional interpolator. The problems of denoising and interpolation are modelled as to estimate the noiseless and missing samples under the same framework of optimal estimation. The local statistics is adaptively calculated to guide the estimation process. For each noisy sample, the authors compute multiple estimates of it along different directions and then fuse those directional estimates for a more accurate output. The estimation parameters calculated in the denoising processing can be readily used to interpolate the missing samples. Compared with the conventional schemes that perform denoising and interpolation in tandem, the proposed noisy image interpolation method can reduce many noise-caused interpolation artefacts and preserve well the image edge structures.

Partially Linear Estimation With Application to Sparse Signal Recovery From Measurement Pairs

We address the problem of estimating a random vector from two sets of measurements and , such that the estimator is linear in . We show that the partially linear minimum mean-square error (PLMMSE) estimator does not require knowing the joint distribution of and in full, but rather only its second-order moments. This renders it of potential interest in various applications. We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of and . We demonstrate our approach in the context of recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version. We show that in this setting PLMMSE estimation has a clear computational advantage, while its performance is comparable to state-of-the-art algorithms. We apply our approach both in static and in dynamic estimation applications. In the former category, we treat the problem of image enhancement from blurred/noisy image pairs. We show that PLMMSE estimation performs only slightly worse than state-of-the art algorithms, while running an order of magnitude faster. In the dynamic setting, we provide a recursive implementation of the estimator and demonstrate its utility in tracking maneuvering targets from position and acceleration measurements.

Optimal Design of Source and Relay Pilots for MIMO Relay Channel Estimation

In this paper, we consider a channel estimation scheme for a two-hop nonregenerative MIMO relay system without the direct link between source and destination. This scheme has two phases. In the first phase, the source does not transmit while the relay transmits and the destination receives. In the second phase, the source transmits, the relay amplifies and forwards, and the destination receives. At the destination, the data received in the first phase are used to estimate the relay-to-destination channel, and the data received in the second phase are used to estimate the source-to-relay channel. The linear minimum mean-square error estimation (LMMSE) is used for channel estimation, which allows the use of prior knowledge of channel correlations. For phase 1, an algorithm is developed to compute the optimal source pilot matrix for use at the relay. For phase 2, an algorithm is developed to compute the optimal source pilot matrix for use at the source and the optimal relay pilot matrix for use at the relay.

Superimposed Training Based Channel Estimation for OFDM Modulated Amplify-and-Forward Relay Networks

In this paper, we consider the channel estimation for the classical three-node relay networks that employ the amplify-and-forward (AF) transmission scheme and the orthogonal frequency division multiplexing (OFDM) modulation. We propose a superimposed training strategy that allows the destination node to separately obtain the channel information of the source→relay link and the relay→destination link. Specifically, the relay superimposes its own training signal over the received one before forwarding it to the destination. The proposed training strategy can be implemented within two transmission phases and is thus compatible with the two-phase data transmission scheme, i.e., the training can be embedded into data transmission. We also derive the Cramér-Rao bound for the random channel parameters, from which we compute the optimal training sequence as well as the optimal power allocation. Since the optimal minimum mean square error (MMSE) estimator and the maximum a posteriori (MAP) estimator cannot be expressed in closed-form, we propose to first obtain the initial channel estimates from the low complexity linear estimators, e.g., linear minimum mean-square error (LMMSE) and least square (LS) estimators, and then resort to the iterative method to improve the estimation accuracy. Simulation results are provided to corroborate the proposed studies.

An Autocorrelation-Based Interference Rejection Signal Detection Scheme

This presentation proposed an autocorrelation-based signal detection scheme to get a better resulting. The signal detection scheme is combined by Autocorrelation Filter and an improved linear Minimum Mean Square Error (MMSE) estimator. The Autocorrelation Filter is used to reject the interference, and the improved linear MMSE estimator is used to get the least error. Both two methods are based on the non-overlapping property of the signals in autocorrelation domain. The theory consequence and Simulation results indicate that this signal detection scheme can achieve a high detection quality.

Decentralised Solutions to the Cooperative Multi-Platform Navigation Problem

The problem of cooperative navigation for a team of platforms employing inter-platform observations is investigated. A decentralised solution in the framework of an information filter with delayed states is presented. In this structure, each platform first estimates its motion using only local sensor data, then shares its information across the network using an algorithm that employs a distributed Cholesky modification. The decentralised solution permits each platform to act in the same modular manner, providing robustness to individual platform failure. The solution yields linear minimum mean-square error estimation performance. As such the estimates generated are optimal; it generates exactly the same estimates as would a conventional extended Kalman filter (EKF), if given the same data. Efficient sparse implementation is accomplished without resorting to approximate methods. Simulation experiments employing a team of ten mobile platforms are described and used to evaluate the decentralised estimation performance. The robustness, flexibility, and cost of the decentralised approach are analyzed and compared with an existing distributed solution.

Channel estimation technique in multi-antenna AF relay communication systems

The channel estimation technique is investigated in OFDM communication systems with multi-antenna Amplify-and-Forward (AF) relay. The Space-Time Block Code (STBC) is applied at the transmitter of the relay to obtain diversity gain. According to the transmission characteristics of OFDM symbols on multiple antennas, a pilot-aided Linear Minimum Mean-Square-Error (LMMSE) channel estimation algorithm with low complexity is designed. Simulation results show that, the proposed LMMSE estimator outperforms least-square estimator and approaches the optimal estimator without error in the performance of Symbol Error Ratio (SER) under several modulation modes, and has a good estimation effect in the realistic relay communication scenario.

Bayesian Post-Processing Methods for Jitter Mitigation in Sampling

Minimum mean squared error (MMSE) estimators of signals from samples corrupted by jitter (timing noise) and additive noise are nonlinear, even when the signal prior and additive noise have normal distributions. This paper develops a stochastic algorithm based on Gibbs sampling and slice sampling to approximate the optimal MMSE estimator in this Bayesian formulation. Simulations demonstrate that this nonlinear algorithm can improve significantly upon the linear MMSE estimator, as well as the EM algorithm approximation to the maximum likelihood (ML) estimator used in classical estimation. Effective off-chip post-processing to mitigate jitter enables greater jitter to be tolerated, potentially reducing on-chip ADC power consumption.

Distributed Adaptive Node-Specific Signal Estimation in Fully Connected Sensor Networks—Part I: Sequential Node Updating

We introduce a distributed adaptive algorithm for linear minimum mean squared error (MMSE) estimation of node-specific signals in a fully connected broadcasting sensor network where the nodes collect multichannel sensor signal observations. We assume that the node-specific signals to be estimated share a common latent signal subspace with a dimension that is small compared to the number of available sensor channels at each node. In this case, the algorithm can significantly reduce the required communication bandwidth and still provide the same optimal linear MMSE estimators as the centralized case. Furthermore, the computational load at each node is smaller than in a centralized architecture in which all computations are performed in a single fusion center. We consider the case where nodes update their parameters in a sequential round robin fashion. Numerical simulations support the theoretical results. Because of its adaptive nature, the algorithm is suited for real-time signal estimation in dynamic environments, such as speech enhancement with acoustic sensor networks.

Adaptive Power Allocation in Wireless Sensor Networks with Spatially Correlated Data and Analog Modulation: Perfect and Imperfect CSI

We address the problem of power allocation in a wireless sensor network where distributed sensors amplify and forward their partial and noisy observations of a Gaussian random source to a remote fusion center (FC). The FC reconstructs the source based on linear minimum mean-squared error (LMMSE) estimation rule. Motivated by the availability of limited energy in the sensor networks, we undertake the design of power allocation based on minimization of the reconstruction distortion subject to a constraint on the network transmit power. The design is based on the following two cases: (i) exact knowledge of the channel gains and (ii) the estimates of the channel gains. We show that the distortion can be represented as a convex function of the transmit powers of the sensors. Moreover, we show that the power allocation based on this distortion function does not bear any closed form solution. To this end, we propose a novel design based on the successive approximation of the LMMSE distortion, which turns out to be simple, computationally efficient, and exhibits excellent convergence properties. The simulation examples illustrate that the proposed design holds considerable performance gain compared to a uniform power allocation scheme.

이중 선택적 채널 OFDM 시스템에서 시간 영역 윈도우와 검출 순서가 순차적 간섭 제거에 미치는 영향

이중 선택적 채널 OFDM(Orthogonal Frequency Division Multiplexing) 시스템에서 시변 채널 특성은 주파수 영역에서 부반송파 사이의 간섭 현상으로 나타난다. 시간 영역 윈도우의 사용은 주파수 영역 채널 행렬의 대역폭을 한정시키는 효과가 있으며, OFDM 시스템을 간략화된 선형 입출력 모델로 근사화시킬 수 있다. OFDM 시스템의 채널 등화에 선형 MMSE(Minimum Mean Square Error) 예측에 기반한 순차적인 간섭 제거 기법을 사용하는 경우, 심볼의 검출 순서가 전체적인 시스템 성능에 큰 영향을 미친다. 본 논문에서는 시간 영역 윈도우의 사용으로 인한 잔류 ICI의 감소와 이에 따른 성능 개선 효과를 확인하고, SINR(Signal to Interference and Noise Ratio)과 CSEP(Conditional Symbol Error Probability) 값을 기준으로 하는 심볼 검출 순서가 순차적 간섭 제거 방식의 성능에 미치는 영향을 조사한다. Time-varying channel characteristics in OFDM systems over doubly selective channels cause inter-carrier interferences(ICI) in the frequency domain. Time domain windowing gives rise to restriction on the bandwidth of the frequency domain channel matrix and makes it possible to approximate the OFDM system as a simplified linear input-output model. When successive interference cancellation based on linear MMSE estimation is employed for channel equalization in OFDM systems, symbol detection ordering produces considerable effects on overall system performances. In this paper, we show the reduction of the residual ICI by time domain windowing and the resultant performance improvements, and investigate the effects of SINR- and CSEP-based symbol detection ordering on the performance of successive interference cancellation.

Distributed Estimation of Gauss - Markov Random Fields With One-Bit Quantized Data

We consider the problem of distributed estimation of a Gauss-Markov random field using a wireless sensor network (WSN), where due to the stringent power and communication constraints, each sensor has to quantize its data before transmission. In this case, the convergence of conventional iterative matrix-splitting algorithms is hindered by the quantization errors. To address this issue, we propose a one-bit adaptive quantization approach which leads to decaying quantization errors. Numerical results show that even with one bit quantization, the proposed approach achieves a superior mean square deviation performance (with respect to the global linear minimum mean-square error estimate) within a moderate number of iterations.

Competitive Linear Estimation Under Model Uncertainties

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We investigate a linear estimation problem under model uncertainties using a competitive algorithm framework under mean square error (MSE) criteria. Here, the performance of a linear estimator is defined relative to the performance of the linear minimum MSE estimator tuned to the underlying unknown system model. We then find the linear estimator that minimizes this relative performance measure, i.e., the regret, for the worst possible system model. Two definitions of regret are given: first as a difference of MSEs and second as a ratio of MSEs. We demonstrate that finding the linear estimators that minimize these regret definitions can be cast as a Semidefinite Programming (SDP) problem and provide numerical examples. </para>

Performance Improvement in Estimation of Spatially Correlated Rician Fading MIMO Channels Using a New LMMSE Estimator

In most of the previous researches on the multiple-input multiple-output (MIMO) channel estimation, the fading model has been assumed to be Rayleigh distributed. However, the Rician fading model is suitable for microcellular mobile systems or line of sight mode of WiMAX. In this paper, the training based channel es-timation (TBCE) scheme in the spatially correlated Rician flat fading MIMO channels is investigated. First, the least squares (LS) channel estimator is probed. Simulation results show that the Rice factor has no effect on the performance of this estimator. Then, a new linear minimum mean square error (LMMSE) technique, appropriate for Rician fading channels, is proposed. The optimal choice of training sequences with mean square error (MSE) criteria is investigated for these estimators. Analytical and numerical results show that the performance of proposed estimator in the Rician channel model compared with Rayleigh one is much better. It is illustrated that when the channel Rice factor and/or the correlation coefficient increase, the per-formance of the proposed estimator significantly improves.

A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large-Dimensional Signals

This paper is devoted to the performance study of the linear minimum mean squared error (LMMSE) estimator for multidimensional signals in the large-dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the signal-to-interference-plus-noise ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiple-antenna as well as spread-spectrum transmission models. The expression of the deterministic approximation of the SINR in the large-dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large-dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.

OPTIMAL FILTERING IN DISCRETE-TIME SYSTEMS WITH TIME DELAYS AND MARKOVIAN JUMP PARAMETERS

AbstractThis paper investigates the linear minimum mean-square error estimation for discrete-time Markovian jump linear systems with delayed measurements. The key technique applied for treating the measurement delay is reorganization innovation analysis, by which the state estimation with delayed measurements is transformed into a standard linear mean-square filter of an associated delay-free system. The optimal filter is derived based on the innovation analysis method together with geometric arguments in an appropriate Hilbert space. The solution is given in terms of two Riccati difference equations. Finally, a simulation example is presented to illustrate the efficiency of the proposed method.

Multi-rate optimal state estimation

This article formulates a multi-rate linear minimum mean squared error (LMMSE) state estimation problem, which includes four rates as follows: the state updating rate in the model, the measurement sampling rate, the estimate updating rate and the estimate output rate. This formulation is unique in two ways. First, the rate ratio between state measurement and state estimate is more general (a rational number), instead of just an integer or its reciprocal as considered in the existing literature. Second, state estimates are produced in blocks, which have never been considered before in the multi-rate estimator design. The multi-rate LMMSE estimation problem is solved by examining several distinctive cases for single-rate state estimation, obtained through the lifting technique. Also, sufficient conditions are given for asymptotic stability of the proposed multi-rate LMMSE estimators. An example in tracking a manoeuvering target is given to illustrate the proposed multi-rate state estimators.