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Due to the addition of new underwater vessels and other natural noise contributors, the underwater environment is becoming congested and noisy. Undersea monitoring sonobuoys receive multiple mixed acoustic signals from different vessels that need to be separated and identified in the presence of underwater noise (UWN). It is extremely challenging to separate highly correlated acoustic signals from a noisy mixture without prior knowledge of mixing process and propagation channel. Also, in many cases, the separated signals from the noisy mixture doesn’t accurately describe the correct signal. This study proposes a novel multi-stage method to separate underwater acoustic source signals from noisy mixture with suppression in noise. The first stage applies multivariate blind source separation (BSS) technique known as non-negative matrix factorization (NMF) that extracts the source signals from the noisy signal mixture. In the second stage, Minimum mean square error (MMSE) estimator is used to reduce noise in separated/reconstructed source signals by minimizing the mean square error (MSE) between reconstructed acoustic signal and original clean signal, enhancing signal reconstruction quality. The results of this study indicate the effectiveness of the proposed method in terms of MSE, signal-to-distortion ratio (SDR) and cepstral distance (CD) and compare it with existing techniques. Based on both simulation outcomes our proposed method demonstrates superior separation performance by reducing MSE upto 47% and improving SDR of reconstructed acoustic signals upto 28% compared to existing solutions.

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors (FMSE) and the true mean square errors (TMSE) become inconsistent, while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters. Obviously, it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models. Aiming at this, the concept of credibility is adopted to discuss the inconsistency problem in this paper. In order to formulate the degree of the credibility, a trust factor is constructed based on the FMSE and the TMSE. However, the trust factor can not be directly computed since the TMSE cannot be found for practical applications. Based on the definition of trust factor, the estimation of the trust factor is successfully modifled to online estimation of the TMSE. More importantly, a necessary and sufficient condition is found, which turns out to be the basis for better design of Kalman filters with high performance. Accordingly, beyond trust factor estimation with Sage-Husa technique (TFE-SHT), three novel trust factor estimation methods, which are directly numerical solving method (TFE-DNS), the particle swarm optimization method (PSO) and expectation max-imization-particle swarm optimization method (EM-PSO) are proposed. The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance. Meanwhile, the proposed EM-PSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online., QC 20230508

The performance of the uplink of multiuser multiple input multiple output systems depends critically on the receiver architecture and on the quality of the acquired channel state information. A popular approach is to design linear receivers that minimize the mean squared error (MSE) of the received data symbols. Unfortunately, most of the literature does not take into account the presence of channel state information errors in the MSE minimization. In this letter we develop a linear minimum MSE (MMSE) receiver that employs the noisy instantaneous channel estimates to minimize the MSE, and highlight the dependence of the receiver performance on the pilot-to-data power ratio. By invoking the theory of random matrices, we calculate the users' signal-to-interference-plus-noise ratio as a function of the number of antennas and the pilot-to-data power ratio of all users. Numerical results indicate that this new linear receiver outperforms the classical mismatched MMSE receiver., QC 20190312

[Abstract]: The design of zero-delay Joint Source-Channel Coding (JSCC) schemes for the transmission of correlated information over fading Multiple Access Channels (MACs) is an interesting problem for many communication scenarios like Wireless Sensor Networks (WSNs). Among the different JSCC schemes so far proposed for this scenario, Distributed Quantizer Linear Coding (DQLC) represents an appealing solution since it is able to outperform uncoded transmissions for any correlation level at high Signal-to-Noise Ratios (SNRs) with a low computational cost. In this paper, we extend the design of DQLC-based schemes for fading MACs considering sphere decoding to make the optimal Minimum Mean Squared Error (MMSE) estimation computationally affordable for an arbitrary number of transmit users. The use of sphere decoding also allows to formulate a practical algorithm for the optimization of DQLC-based systems. Finally, non-linear Kalman Filtering for the DQLC is considered to jointly exploit the temporal and spatial correlation of the source symbols. The results of computer experiments show that the proposed DQLC scheme with the Kalman Filter decoding approach clearly outperforms uncoded transmissions for medium and high SNRs.

We consider the uplink of a single cell multi-user multiple input multiple output (MU-MIMO) system, in which the base station acquires channel state information at the receiver by means of uplink pilot signals. Since each mobile station has a sum power budget that is used to transmit pilot and data symbols, the pilot power ratio (PPR) has a large impact on the system performance in terms of spectral and energy efficiency. We formulate the problem of PPR setting as a non-cooperative game, in which each mobile station aims at minimizing the mean squared error of the uplink received data symbols at the base station. We show that in this game a unique Nash equilibrium exists, and propose an iterative decentralized algorithm-termed best PPR algorithm (BPA)-that is guaranteed to converge to that Nash equilibrium. Since BPA dynamically responds to the measured interference, it outperforms widely used schemes that use a predetermined PPR. BPA also performs close to the global optimum, especially when mobile stations with similar path loss values are co-scheduled in the MU-MIMO system. Based on these insights, we propose a practical signaling mechanism for implementing BPA in MU-MIMO systems., QC 20180514

The incorporation of Gallium Nitride (GaN) Power Amplifiers (PAs) into future high power aperture radar systems is certain; however, the introduction of this technology into multifunction radar systems will present new challenges to radar engineers. This dissertation describes a broad investigation into amplitude and phase transients produced by GaN PAs when they are excited with multifunction radar waveforms. These transients are the result of self-heating electrothermal memory effects and are manifested as interpulse instabilities that can negatively impact the coherent processing of multiple pulses. A behavioral model based on a Foster network topology has been developed to replicate the measured amplitude and phase transients accurately. This model has been used to develop a digital predistortion technique that successfully mitigates the impact of the transients. The Moving Target Indicator (MTI) Improvement Factor and the Root Mean Square (RMS) Pulse-to-Pulse Stability are used as metrics to assess the impact of the transients on radar system performance and to test the effectiveness of a novel digital predistortion concept.

The incorporation of Gallium Nitride (GaN) Power Amplifiers (PAs) into future high power aperture radar systems is certain; however, the introduction of this technology into multifunction radar systems will present new challenges to radar engineers. This dissertation describes a broad investigation into amplitude and phase transients produced by GaN PAs when they are excited with multifunction radar waveforms. These transients are the result of self-heating electrothermal memory effects and are manifested as interpulse instabilities that can negatively impact the coherent processing of multiple pulses. A behavioral model based on a Foster network topology has been developed to replicate the measured amplitude and phase transients accurately. This model has been used to develop a digital predistortion technique that successfully mitigates the impact of the transients. The Moving Target Indicator (MTI) Improvement Factor and the Root Mean Square (RMS) Pulse-to-Pulse Stability are used as metrics to assess the impact of the transients on radar system performance and to test the effectiveness of a novel digital predistortion concept.

[Abstract]: Analog transmission of correlated information over Gaussian broadcast channels (BCs) using analog joint source- channel coding (JSCC) is addressed. This communication strategy has attractive advantages, such as low complexity, minimal delay, graceful degradation, and adaptation to time-varying environments. In this paper, we focus on the optimization of parametric continuous mappings that satisfy individual quality of service requirements over Gaussian BCs. This optimization is based on the balancing of the user distortions to ensure the feasibility of the resulting optimization problems. An analysis of the overall distortion corresponding to the considered mappings is carried out to design algorithms that determine the optimal values for the mappings parameters. Results show that the proposed analog JSCC scheme provides near optimal performance and an adequate balancing of the individual distortions.

[Abstract]: Joint source-channel coding for discrete-time analog sources is an appealing transmission approach because of its extremely low delay and complexity. When the users access the channel orthogonally, analog transmission of correlated information over fading multiple access channels (MACs) using modulo-like mappings provides better performance than uncoded transmission. In this paper, we propose a simplified decoder for modulo mappings in possibly non-orthogonal MAC scenarios with a single-antenna users and a multiple-antenna receiver. Sphere decoding is investigated to reduce the computational complexity when the number of users is large. In addition, affordable strategies are proposed to optimize the mapping parameters according to the channel conditions and the source correlation. The obtained results show that the use of modulo mappings is suitable when the number of antennas at the receiver is larger than the number of users and for high correlation between user data.

Aggressive frequency reuse in the return link (RL) of multibeam satellite communications (SatComs) is crucial towards the implementation of next generation, interactive satellite services. In this direction, multiuser detection has shown great potential in mitigating the increased intrasystem interferences, induced by a tight spectrum reuse. Herein we present an analytic framework to describe the linear Minimum Mean Square Error (MMSE) performance of multiuser channels that exhibit full receive correlation: an inherent attribute of the RL of multibeam SatComs. Analytic, tight approximations on the MMSE performance are proposed for cases where closed form solutions are not available in the existing literature. The proposed framework is generic, thus providing a generalized solution straightforwardly extendable to various fading models over channels that exhibit full receive correlation. Simulation results are provided to show the tightness of the proposed approximation with respect to the available transmit power., QC 20140306

This paper considers the joint precoder design problem for multiple-input single-output (MISO) systems with coordinated base stations (BSs). We consider maximization of the total sum rate with per BS antenna power constraint problem. For this problem, we propose a novel linear iterative algorithm. The problem is solved as follows. First, by introducing additional optimization variables and applying matrix fractional minimization, we reformulate the original problem as a new problem. Second, for the given precoder vectors of all users, we optimize the introduced variables of the latter problem using Geometric Programming (GP) method. Third, keeping the introduced variables constant, the precoder vectors of all users are optimized by using phase rotation technique. The second and third steps are repeated until convergence. We have shown that the proposed algorithm is guaranteed to converge. Moreover, for the total sum power constraint case, simulation results show that the proposed iterative algorithm achieves almost the same average performance as that of the algorithm which utilizes mean-square-error (MSE) uplink-downlink duality approach. We also show that our iterative algorithm can be used to solve sum rate maximization and weighted sum MSE minimization problems for an arbitrary power constraint.

In this companion paper, the choice of kernels for estimating the impulse response of linear stable systems is considered from a classical, “frequentist”, point of view. The kernel determines the regularization matrix in a regularized least squares estimate of an FIR model. The quality is assessed from a mean square error (MSE) perspective, and measures and algorithms for optimizing the MSE are discussed. The ideas are tested on the same data bank as used in Part I of the companion papers. The resulting findings and conclusions in the two papers are very similar despite the different perspectives.

Distributed consensus algorithms for estimation of parameters or detection of events in wireless sensor networks have attracted considerable attention in recent years. A necessary condition to achieve a consensus on the average of the initial values is that the topology of the underlying graph is balanced or symmetric at every time instant. However, communication impairments can make the topology vary randomly in time, and instantaneous link symmetry between pairs of nodes is not guaranteed unless an acknowledgment protocol or an equivalent approach is implemented. In this paper, we evaluate the convergence of the consensus algorithm in the mean square sense in wireless sensor networks with random asymmetric topologies. For the case of links with equal probability of connection, a closed form expression for the mean square error of the state along with the dynamical range and the optimum value of the link weights that guarantee convergence are derived. For the case of links with different probabilities of connection, an upper bound for the mean square error of the state is derived. This upper bound can be computed for any time instant and can be employed to compute a link weight that reduces the convergence time of the algorithm., Peer Reviewed, Postprint (published version)

[Abstract] We consider the robust precoder design for multiuser multiple-input single-output (MU-MISO) systems where the channel state information (CSI) is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas. We propose to compress the feedback data by projecting the channel estimates onto a vector basis, known at the receivers and the transmitter, and quantizing the resulting coefficients. The channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean-square error (MSE) between the true and the rank-reduced CSI. Expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design. These expressions take into account the following sources of error: channel estimation, truncation for rank reduction, quantization, and feedback channel delay. As an example for the robust problem formulation, vector precoding (VP) is designed based on the expectation of the MSE conditioned on the fed-back CSI. Our results show that robust precoding based on fed-back CSI clearly outperforms conventional precoding designs which do not take into account the errors in the CSI.

This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented., © 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20110411

This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented., © 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20110411

This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented., © 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20110411

This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented., © 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20110411

This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented., © 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20110411

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. © 2007 IEEE.

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. © 2007 IEEE.

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. © 2007 IEEE.

This paper studies the problem of non-binary index assignment for scalar quantizer with M-ary Phase Shift Keying (M-PSK). An interesting observation enables us to well approximate this problem to the well-known Traveling Salesman Problem (TSP). A unique optimum solution to the approximation is resulted. Optimality of the solution is agreed by simulation results.

This paper presents a Bayesian approach to the design of transmit prefiltering matrices in closed-loop schemes robust to channel estimation errors. The algorithms are derived for a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. Two different optimization criteria are analyzed: the minimization of the mean square error and the minimization of the bit error rate. In both cases, the transmitter design is based on the singular value decomposition (SVD) of the conditional mean of the channel response, given the channel estimate. The performance of the proposed algorithms is analyzed, and their relationship with existing algorithms is indicated. As with other previously proposed solutions, the minimum bit error rate algorithm converges to the open-loop transmission scheme for very poor CSI estimates., Peer Reviewed

This paper studies the problem of non-binary index assignment for scalar quantizer with M-ary Phase Shift Keying (M-PSK). An interesting observation enables us to well approximate this problem to the well-known Traveling Salesman Problem (TSP). A unique optimum solution to the approximation is resulted. Optimality of the solution is agreed by simulation results.

This paper studies the problem of non-binary index assignment for scalar quantizer with M-ary Phase Shift Keying (M-PSK). An interesting observation enables us to well approximate this problem to the well-known Traveling Salesman Problem (TSP). A unique optimum solution to the approximation is resulted. Optimality of the solution is agreed by simulation results.

This paper presents a Bayesian approach to the design of transmit prefiltering matrices in closed-loop schemes robust to channel estimation errors. The algorithms are derived for a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. Two different optimization criteria are analyzed: the minimization of the mean square error and the minimization of the bit error rate. In both cases, the transmitter design is based on the singular value decomposition (SVD) of the conditional mean of the channel response, given the channel estimate. The performance of the proposed algorithms is analyzed, and their relationship with existing algorithms is indicated. As with other previously proposed solutions, the minimum bit error rate algorithm converges to the open-loop transmission scheme for very poor CSI estimates., Peer Reviewed

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

Local models and methods construct function estimates or predictions from observations in a local neighborhood of the point of interest. The bandwidth, i.e., how large the local neighborhood should be, is often determined based on asymptotic analysis. In this paper, an alternative, non-asymptotic approach that minimizes a uniform upper bound on the mean square error for a linear estimate is proposed. It is shown, for the scalar case, that the solution is obtained from a quadratic program, and that it maintains many of the key features of the asymptotic approaches. Moreover, examples show that the proposed approach in some cases is superior to an asymptotically based local linear estimator.

QC 20100525. QC 20111108. QC 20111215.