Minimum Mean Square Error Sense Research Articles

MMSE Interference Suppression in MIMO Frequency Selective and Time-Varying Fading Channels

Multiple-input/multiple-output (MIMO) frequency selective fading channels introduce both the intersymbol interference (ISI) and the inter-(sub)channel interference (ICI) that are the major performance limiting factors for MIMO wireless data communications. This paper focuses on joint suppression of such two interferences in receiver design under the criterion of the minimum mean-squared error (MMSE). The well-known Kalman filtering arises as a natural design tool to achieve the optimum joint suppression of the ISI and ICI in the sense of MMSE that results in a two-stage design method that suppresses the ISI and ICI in series. Specifically, a state-space solution is derived for the optimum decision-feedback equalizer (DFE) based on temporal Kalman filtering, and is shown to be equivalent to a conventional finite length DFE for ISI suppression. A novel spatial Kalman filtering scheme is proposed as the second stage to successively cancel the ICI. It is shown that the proposed two-stage method yields the realizable and optimum joint ISI and ICI suppression, while it admits lower computational complexity than the conventional finite length DFE for ISI suppression and the MMSE V-BLAST receiver for ICI suppression. The results are applicable to any linear channels that admit state-space realizations, including MIMO frequency selective time-varying channels, and are thus the most general. Simulation results show the effectiveness of the proposed two-stage method and its robustness to channel estimation uncertainties that may arise in practical systems.

Iterative soft-minimum mean-square error equalization for digital nonlinear page-oriented memories

Digital page-oriented volume holographic memory (POVHM) is a promising candidate for next-generation ultrahigh capacity optical data storage technology. As the capacity of the POVHMs increases, the bit error rate performance of the system is degraded due to increased interpixel interference (IPI) and noise. To improve the system performance under these adverse effects and to increase the capacity, joint iterative soft equalization-detection and error correction decoding might be attractive. To address that, by considering the nonlinearity inherent in the channel, an iterative soft equalization method that is optimized in the minimum mean-square error (MMSE) sense, called the iterative soft-MMSE (ISMMSE) equalization, is devised. The performance of the ISMMSE is evaluated by use of numerical experiments under different amounts of IPI and optical noise. Simulation results suggest that the ISMMSE is a good candidate for an ultrahigh capacity POVHM, which employs joint iterative equalization-detection and decoding.

Speech enhancement based on minimum mean-square error estimation and supergaussian priors

This paper presents a class of minimum mean-square error (MMSE) estimators for enhancing short-time spectral coefficients of a noisy speech signal. In contrast to most of the presently used methods, we do not assume that the spectral coefficients of the noise or of the clean speech signal obey a (complex) Gaussian probability density. We derive analytical solutions to the problem of estimating discrete Fourier transform (DFT) coefficients in the MMSE sense when the prior probability density function of the clean speech DFT coefficients can be modeled by a complex Laplace or by a complex bilateral Gamma density. The probability density function of the noise DFT coefficients may be modeled either by a complex Gaussian or by a complex Laplacian density. Compared to algorithms based on the Gaussian assumption, such as the Wiener filter or the Ephraim and Malah (1984) MMSE short-time spectral amplitude estimator, the estimators based on these supergaussian densities deliver an improved signal-to-noise ratio.

MMSE-Optimal Approximation of Continuous-Phase Modulated Signal as Superposition of Linearly Modulated Pulses

The optimal linear modulation approximation of any M-ary continuous-phase modulated (CPM) signal under the minimum mean-square error (MMSE) criterion is presented in this paper. With the introduction of the MMSE signal component, an M-ary CPM signal is exactly represented as the superposition of a finite number of MMSE incremental pulses, resulting in the novel switched linear modulation CPM signal models. Then, the MMSE incremental pulse is further decomposed into a finite number of MMSE pulse-amplitude modulated (PAM) pulses, so that an M-ary CPM signal is alternatively expressed as the superposition of a finite number of MMSE PAM components, similar to the Laurent representation. Advantageously, these MMSE PAM components are mutually independent for any modulation index. The optimal CPM signal approximation using lower order MMSE incremental pulses, or alternatively, using a small number of MMSE PAM pulses, is also made possible, since the approximation error is minimized in the MMSE sense. Finally, examples of the MMSE-optimal CPM signal approximation and its comparison with the Laurent approximation approach are given using raised-cosine frequency-pulse CPM schemes.

Differentially coherent parallel interference cancellation for DS-CDMA

In this paper, we propose a novel differentially coherent (DC) parallel interference cancellation (PIC) scheme for direct-sequence code-division multiple access (DS-CDMA) employing differential phase-shift keying (DPSK). The proposed scheme combines decision-feedback differential detection (DF-DD) and PIC. For optimization of the DF-DD and interference cancellation (IC) filters three different criteria are adopted. The first (DC-PIC I) and the second (DC-PIC II) criteria assume a constant channel and a channel with a small constant frequency offset, respectively, whereas the third criterion (DC-PIC III) optimizes the filters in the minimum mean-squared error (MMSE) sense taking into account the statistical properties of the underlying channel. Simulations show the high achievable performance and the robustness of the novel DC-PIC receiver. A comparison with linear DC receivers and a previously proposed DC-PIC scheme show the superiority of the proposed approach.

Mathematical model of the 5-DOF sled dynamics of an electrodynamic maglev system with a passive sled

A model that describes the five-degrees-of-freedom (5-DOF) dynamics of a passively levitated electrodynamic maglev system is presented. The model is based on the flux-current-force interactions and the geometric relationships between the levitation coils and the permanent magnets on the sled. The model is presented in a parametric state-space formulation, suitable to extract model parameters from input-output measurements in a minimum mean-square error sense. The proposed structure is very well suited for parameter estimation and to later develop robust feedback control of the sled dynamics.

Design of Multiple MMSE Subequalizers for Faster-Than-Nyquist-Rate Transmission

We consider an equalization problem when the transmitted symbol rate is higher than the available channel bandwidth. This situation can happen in the uplink of the voiceband pulse-code modulation (PCM) modems whose transmit signal bandwidth is larger than the available channel bandwidth. Although the use of a minimum mean-squared error (MMSE) pre-equalizer is considered in the International Telecommunications Union (ITU)-T V.92 Recommendation, it may not provide an acceptable performance unless the channel condition is mild. As another approach to this problem, we consider the use of a bank of subequalizers, each of which compensates the part of the channel distortion, enabling the PCM-mode transmission over the channel where the V.92 scheme may fail. In this paper, a multiple subequalizer scheme is optimally designed in the MMSE sense, and its performance is compared with the MMSE pre-equalizer of V.92 in terms of the bit-rate-normalized signal-to-noise ratio.

Aggregation of linear dynamic models: an application to life-cycle consumption models under habit formation

This paper provides a general framework for aggregating linear dynamic models by deriving the aggregate model as the optimal prediction (in the minimum mean-squared error sense) of the aggregate variable of interest with respect to an aggregate information set generated by current and past values of available aggregate observations. The approach is applied to a number of aggregation problems that have been considered in the literature. It is shown how the results in much of the literature can be readily obtained using the proposed forecasting approach, and a number of important extensions and generalizations are provided. Our approach does not require the assumption of independence of the microdistributed lag coefficients from the other microcoefficients, and establishes that in general the long-run coefficients obtained from the optimal aggregate relation are equal to the averages of the long-run coefficients from the microrelations. The approach is then applied to life-cycle consumption decision rules under habit formation and the implications of the heterogeneity in habit formation coefficients across individuals for the analysis of aggregate consumption is investigated. Using stochastic simulations it is shown that the estimates of the habit persistence coefficient are likely to be biased downward if they are based on analogue aggregate consumption functions, which could partly explain the excess smoothness and excess sensitivity puzzles in terms of neglected heterogeneity.

Finite-memory denoising in impulsive noise using Gaussian mixture models

We propose an efficiently structured nonlinear finite-memory filter for denoising (filtering) a Gaussian signal contaminated by additive impulsive colored noise. The noise is modeled as a zero-mean Gaussian mixture (ZMGM) process. We first derive the optimal estimator for the static case, in which a Gaussian random variable (RV) is contaminated by an impulsive ZMGM RV. We provide an analytical derivation of the resulting mean-squared error (MSE), and compare the performance to that of the optimal linear estimator, identifying cases of significant improvement. Building upon these results, we develop a suboptimal finite-memory filter for the dynamic case, which is nearly optimal in the minimum MSE sense. The resulting filter is a nonlinearly weighted combination of a fixed number of linear filters, for which a computationally efficient architecture is proposed. Substantial improvement in performance over the optimal linear filter is demonstrated using simulation results.

Blind multiuser MMSE detector for CDMA signals in ISI channels

A technique is introduced that allows the blind and direct estimation of an optimal, in the minimum mean-squared error sense, linear multiuser receiver for direct-sequence code-division multiple-access signals. We consider the case of an asynchronous multiple access channel in the presence of possibly large intersymbol-interference. Our approach does not require channel estimation and uses the knowledge of the code for the user of interest only, Unlike other comparable techniques, this method converges to the true optimum receiver as the sample size increases, regardless of signal-to-noise ratio.

On fractionally spaced blind adaptive equalization under symbol timing offsets using Godard and related equalizers

The problem of fractionally spaced (FS) blind adaptive equalization under symbol-timing-phase offsets is considered. In the case of trained (nonblind) equalizers, the performance of FS equalizers is known to be independent of the timing-phase unlike that of baud-rate equalizers. Moreover, trained FS equalizers synthesize optimal filters in the minimum mean-square error sense, and hence are superior to baud-rate trained equalizers. It is an open question whether such properties hold true for FS Godard blind equalizers. We present a simulation example where such advantages do not materialize. We also present a solution based upon a parallel multimodel Godard baud-rate filter bank approach which yields a performance almost invariant w.r.t. symbol-timing-phase and superior to that of baud-rate equalizers.

Synthesis of mutual intensity distributions using the fractional Fourier transform

Our aim in this paper is to obtain the best synthesis of a desired mutual intensity distribution, by filtering in fractional Fourier domains. More specifically, we find the optimal fractional-domain filter that transforms a given (source) mutual intensity distribution into the desired one as closely as possible (in the minimum mean-square error sense). It is observed that, in some cases, closer approximations to the desired profile can be obtained by filtering in fractional Fourier domains, in comparison to filtering in the ordinary space or frequency domains.

Performance evaluation of linear equalizers in the presence of adjacent channel interference

Abstract An analytical technique is developed to evaluate the error rate and the minimum mean-square-error (MMSE) performance of linearly equalized Atf-ary quadrature amplitude modulation and quadrature partial response signalling in the presence of adjacent channel interference. Both symbol- and fractionally-spaced linear equalizers (SSE and FSE) are considered. The tap gains of these equalizers are evaluated in the MMSE sense. The transfer function and MMSE of the infinite tap SSE are derived in the presence of interfering channels. The underlying structure of the infinite-tap SSE is used to develop an infinitely long FSE. Numerical results indicate that the proposed structure does not yield the same MMSE as obtained by a sufficiently long FSE. A frequency domain analysis in conjunction with singular value decomposition reveals that the case for the failure of the proposed structure is due to a built-in rank reduced property.

Filters involving derivatives with application to reconstruction from scanned halftone images

This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters.

Discrete Wigner synthesis

An important application of the Wigner distribution (WD) is the synthesis of a discrete-time signal whose WD approximates a specified time-frequency distribution in the minimum mean-square error sense. One approach previously proposed (Yu and Cheng, Proc. ICASSP, 1985, pp. 1037–1040) is based upon the notion of expressing the desired signal in terms of orthonormal functions and applying the resulting induced Wigner distributions for WD synthesis. In this paper, we prove that the induced WDs cannot be orthonormal for any choice of the original orthonormal functions. We also prove that the induced WDs can be orthogonal only for particular original basis functions. We utilize these results to introduce a rigorous approach for discrete WD synthesis. We then illustrate our approach through analytical and computational examples.

Optimal source localization and tracking from passive array measurements

If the signal of a moving source is observed at several spatially separated locations during a common time interval, the received signals exhibit differential delays and Doppler shifts which provide information about source location and velocity. This paper deals with the optimal (in the minimum mean-square error sense) source localization and tracking by utilizing differential delay and Doppler observations at a linear array of receivers. We shall be concerned with source ranges large compared with array baseline and with the distance traversed by the source during the observation interval. It is shown that the optimal estimation procedure can be carried out in two sequential steps without any loss in performance. In the first step source location is estimated from the differential delay group of measurements. In the second step source velocity is estimated from the differential Doppler group of measurements and the outcome of the first step. Furthermore, by employing an intermediate track-dependent parameter set, the two-step algorithm yields a closed form solution of the estimation problem.

Quasi-Optimal Demodulation of Pulse-Frequency Modulated Signals

Novel demodulator structures are derived for quasioptimal on-line demodulation of pulse-frequency modulated (PFM) signals in the presence of white Gaussian channel noise. The basic demodulator consists of a phase-locked loop with its integrators appropriately reset as each new pulse is received. This modulator may be augmented with additional integrators and gain elements to achieve quasi-optimal demodulation with delay. The quasi-optimal demodulation approaches optimal demodulation, in the minimum mean-square error sense, as the signal-to-noise ratio increases. The various quasi-optimal receivers are derived by application of the extended Kalman filter theory to a state-space signal model.

An extended criterion for statistical linearization

The random-input describing function is the best linear approximation to an instantaneous nonlinearity in the sense of minimum mean-squared error. It is shown here that the describing function also satisfies a more comprehensive criterion which is important to the accuracy of approximate analysis and synthesis techniques for systems with nonlinear elements.

Adaptive antenna systems

A system consisting of an antenna array and an adaptive processor can perform filtering in both the space and the frequency domains, thus reducing the sensitivity of the signal-receiving system to interfering directional noise sources. Variable weights of a signal processor can be automatically adjusted by a simple adaptive technique based on the least-mean-squares (LMS) algorithm. During the adaptive process an injected pilot signal simulates a received signal from a desired "look" direction. This allows the array to be "trained" so that its directivity pattern has a main lobe in the previously specified look direction. At the same time, the array processing system can reject any incident noises, whose directions of propagation are different from the desired look direction, by forming appropriate nulls in the antenna directivity pattern. The array adapts itself to form a main lobe, with its direction and bandwidth determined by the pilot signal, and to reject signals or noises occurring outside the main lobe as well as possible in the minimum mean-square error sense. Several examples illustrate the convergence of the LMS adaptation procedure toward the corresponding Wiener optimum solutions. Rates of adaptation and misadjustments of the solutions are predicted theoretically and checked experimentally. Substantial reductions in noise reception are demonstrated in computer-simulated experiments. The techniques described are applicable to signal-receiving arrays for use over a wide range of frequencies.