Differential detection with IIR filter for improving DPSK detectionperformance

This paper presents a method for improving the performance of differential detection of differentially encoded phase shift keying (DPSK). The structure of the proposed detection scheme consists of a conventional differential detection circuit equipped with an infinite impulse response (IIR) filter combined with decision feedback. The results of theoretical analysis and computer simulation show that performance of the proposed detection method can approach that of coherent detection of DPSK under additive white Gaussian noise (AWGN) conditions without any increase in architectural complexity. Furthermore, a parameter of the proposed detector can be varied to optimize performance for static or fading conditions. An adaptive scheme suitable for time varying Rician-fading channel conditions is presented, and performance results obtained by computer simulation are given     

Neural networks for signal detection in non-Gaussian noise

We employ neural networks to detect known signals in additive non-Gaussian noise. Training of the neural network for signal detection and its operation at some specified probability of false alarm are discussed. Performance of neural detectors are presented under several non-Gaussian noise environments and are compared with those of matched filter and locally optimum detectors     

Analytic behavior of the LMS adaptive line enhancer for sinusoidscorrupted by multiplicative and additive noise

The least mean squares adaptive line enhancer (LMS ALE) has been widely used for the enhancement of coherent sinusoids in additive wideband noise. This paper studies the behavior of the LMS ALE when applied to the enhancement of sinusoids that have been corrupted by both colored multiplicative and white additive noise. The multiplicative noise decorrelates the sinusoid, spreads its power spectrum, and acts as an additional corrupting noise. Closed-form expressions are derived for the optimum (Wiener filter) ALE output SNR as a function of the residual coherent sine wave power, the noncoherent sine wave power spectrum, and the background additive white noise. When the coherent to noncoherent sine wave power ratio is sufficiently small, it is shown that a nonlinear (e.g., square law) transformation of the ALE input results in a larger optimum ALE output SNR     

Generalized frequency division multiplexing–based acoustic communication for underwater systems

The underwater (UW) acoustic channel poses multiple challenges like coloured ambient noise, frequency‐dependent attenuation, and doubly selective fading. The availability of a robust underwater communication mechanism can largely enhance the success of human effort in a multitude of applications, ranging from pollution surveillance to defence and search/rescue operations. In this work, generalized frequency division multiplexing (GFDM), a non‐orthogonal multicarrier scheme, which has recently been studied for terrestrial wireless fading channels, is developed and tested for signalling in UW acoustic communication. UW noise, attenuation, and doubly selective fading channels are modelled with appropriate statistics. The BER performance of proposed system is systematically evaluated under different channel conditions, starting from simple additive white Gaussian noise (AWGN) and Rayleigh fading channels to a horizontally configured UW channel. The performance is also compared with contemporary orthogonal frequency‐division multiplexing (OFDM)– and filter bank multicarrier (FBMC)–based systems.     

An IIR median hybrid filter

A new class of nonlinear filters, the multidirectional infinite impulse response median hybrid (MIMH) filters, is presented and analyzed. The input signal is processed twice using a linear shift-invariant (LSI) infinite impulse response (IIR) filtering module: once with normal causality and a second time with inverted causality. The final output of the MIMH filter is the median of the two-directional outputs and the original input signal. Thus, the MIMH filter is a concatenation of linear filtering (a LSI IIR filtering module) and nonlinear filtering (a median filtering module). Because of this unique scheme, the MIMH filter possesses many desirable properties which are both proven and analyzed (including impulse removal, step preservation, and noise suppression). A comparison to other medium-type filters is also provided     

Nonlinear filtering methods for harmonic retrieval and model orderselection in Gaussian and non-Gaussian noise

This paper addresses the problem of high-resolution parameter estimation (harmonic retrieval) and model-order selection for superimposed sinusoids. The harmonic retrieval problem is analyzed using a nonlinear parameter estimation approach. Estimation is performed using several nonlinear estimators with signals embedded in white and colored Gaussian noise. Simulation results demonstrate that the nonlinear filters perform close to the Cramer-Rao bound. Model order selection is performed in Gaussian and non-Gaussian noise. The problem is formulated using a multiple hypothesis testing approach with assumed known a priori probabilities for each hypothesis. Parameter estimation is performed using the extended Kalman filter when the noise is Gaussian. The extended high-order filter (EHOF) is implemented in non-Gaussian noise. Simulation results demonstrate excellent performance in selecting the correct model order and estimating the signal parameters     

Cumulant-based method for bearing estimation in the presence ofnonGaussian noise

Bearing estimation algorithms based on the cumulants of array data have been developed to suppress additive spatially correlated Gaussian noises. In practice, however, the noises encountered in signal processing environments are often non-Gaussian, and the applications of those cumulant-based algorithms designed for Gaussian noise to non-Gaussian environments may severely degrade the estimation performance. The authors propose a new cumulant-based method to solve this problem. This approach is based on the fourth-order cumulants of the array data transformed by DFT, and relies on the statistical central limit theorem to show that the fourth-order cumulants of the additive non-Gaussian noises approach zero in each DFT cell. Simulation results are presented to demonstrate that the proposed method can effectively estimate the bearings in both Gaussian and non-Gaussian noise environments     

Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature

In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression (SLR) through a set of Gauss-Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other nonlinear filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve nonlinear non- Gaussian filtering problems.     

A constrained notch Fourier transform

The paper presents a new sliding algorithm for estimating the amplitude and phase of the Fourier coefficients of noise corrupted harmonic signals given a priori knowledge of the signal frequencies. The proposed method is similar in principle to the notch Fourier transform (NFT) technique suggested by Tadokoro et al. [1987] except that it employs an infinite impulse response (IIR) rather than a finite impulse response (FIR) notch filter parameterization. This modification provides bandwidth controlled bandpass (BP) filters whose center frequencies are equally spaced in the frequency spectrum. In this sense, the proposed technique can be regarded as a constrained notch Fourier transform (CNFT). Sliding algorithms have been derived for both the NFT and CNFT for the purpose of estimating the Fourier coefficients of the sinusoidal components. The paper also proposes a similar algorithm to the CNFT for the signals containing sinusoids at arbitrary known frequencies. The main feature of the modified CNFT is that it uses second-order IIR BP filters whose bandwidth and center frequency can be adjusted independently. The bandwidth control aspect provides the user with an efficient means of achieving the required resolution as well as reducing spectral leakage. In general, the proposed approach leads to considerable reduction in terms of computational burden and memory storage     

A CMOS analog multi-sinusoidal phase-locked-loop

An analog CMOS IC is described that is capable of tracking and isolating the sinusoidal components of a two-sinusoidal input signal, though the algorithm can be easily generalized to deal with a larger number of input sinusoids. It is based on adapting the parameters of an IIR filter; the filter topology takes on the form of resonators in a feedback loop, and the adaptive algorithm moves these resonator frequencies until they are equal to the input frequencies, at which point, the isolated sinusoids are available at the resonator outputs. The adaptive filter features a minimal hardware complexity (to track l sinusoids, exactly l second order resonators are needed), and also gets around the convergence problems normally associated with IIR adaptive filters. This filter was implemented in the continuous-time domain using a G_m-C architecture, with the G_m being used to tune the resonator frequency. The chip was fabricated using a 2-μm digital CMOS process, with poly resistors, and metal1-metal2 capacitors. It was tested and shown to be fully functional, with a useful tracking range of ≈500-800 kHz around the initial frequency of each resonator     

Wiener infinite impulse response filter design

The standard design approach for the Wiener IIR filter has been examined for the first- and second-order signal processes in the presence of additive white noise. Positions of the optimum filter poles have been derived as a function of the signal-to-noise ratio. Problems encountered in the design are interesting features of the resulting filter and are also discussed.     

A Model of HF Impulsive Atmospheric Noise

Determination of optimal receiver or detector and suboptimal estimator in the presence of additive atmospheric noise depends on the application of a mathematically tractable model of noise. In the tropics the atmospheric radio noise occurring mostly in the burst form above a relatively small continuous background does not deliver energy at a constant rate. This type of noise is non-Gaussian and has a very large dynamic range. The noise bursts consist of a number of short impulses. They are modelled here as the product of a narrow-band Gaussian noise and the reciprocal of a non-Gaussian random process. This paper includes the derivation of statistical information for the above noise viz, the probability distribution of amplitudes, and of separation between pulses, required for determining the error probabilities using various digital methods. This information can be used in filter optimization in digital systems, where the error probability is to be minimized.     

Nearest neighbor decoding for additive non-Gaussian noise channels

We study the performance of a transmission scheme employing random Gaussian codebooks and nearest neighbor decoding over a power limited additive non-Gaussian noise channel. We show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white Gaussian noise channel with signal and noise power equal to those of the original channel. The results are presented for single-user channels as well as multiple-access channels, and are extended to fading channels with side information at the receiver     

Efficient bit-level systolic array implementation of FIR and IIRdigital filters

Bit-level systolic architectures based on an inner-product computation scheme for finite-impulse response (FIR) and infinite-impulse-response (IIR) digital are presented. The FIR filter structure is optimized in the sense that for a given clock rate, both the utilization efficiency and average throughput are maximized. The IIR filter structure has approximately the same utilization efficiency and throughput rate as previous related techniques for processing a single data stream (channel), but it allows two data streams to be processed concurrently to double the performance. This feature makes the IIR system attractive for use in applications where multiple filtering and particularly bandpass analysis are required     

The SQUOD: A versatile and accurate scheme for measuring signal strengths

The SQUOD (selected quantile output device) is a simple scheme using rank-order statistics for estimating received signal strength, even following detection in a nonlinear (e.g., logarithmic) receiver. Numerical results are presented that show that for any number of steady sinusoids having incommensurable frequencies or randomly distributed mutually independent phases plus additive Gaussian noise, the populationp-quantile of the envelope can be used for estimating the rms value of the envelope with a maximum error of 0.797 dB for p = 0.5650. Analysis and numerical examples show the effects of using a finite-samplep-quantile.     

Image estimation using fast modified reduced update Kalman filter

The authors have proposed some modifications of the reduced update Kalman filter (RUKF) as applied to filtering of images corrupted by additive noise. They have reduced the computational complexity by reducing the state dimensionality. By doing so, it is shown that the computational requirement is reduced by an order of magnitude while the loss of performance is only marginal. Next, the RUKF is modified using the score function based approach to accommodate non-Gaussian noise. The image is modeled as a nonstationary mean and stationary variance autoregressive Gaussian process. It is shown that the stationary variance assumption is reasonable if the nonstationary mean is computed by an edge and detail preserving efficient estimator of local nonstationary mean. Such an estimator, called the hybrid multistage medium D (HMSMD) filter, is also described. Detailed experimental results are provided which indicate the success of the new filtering scheme     

Structural characterization of locally optimum detectors in terms of locally optimum estimators and correlators

Explicit formulas for locally (SNRrightarrow 0)optimum (MMSE) signal estimators (smoother, filter, and predictor) for discrete-time observations of a random signal in additive random noise are derived and used to characterize the locally optimum (likelihood ratio) signal detector for on-off signaling. The characterizations are canonical (distribution-free) detector structures involving estimator-correlators. These structural characterizations provide new interpretations of known detectors for various special cases. If the one-step signal predictor is recursive and the noise is white (possibly non-Gaussian or nonstationary), there is a canonical structure that admits recursive computation. The primary motivation for these structural characterizations is to render the estimator-correlator design philosophy applicable for the purpose of simplifying implementations and enhancing adaptability. Unlike the known esfimator-correlator structural characterizations for continuous-time globally optimum detectors, the new characterizations apply for non-Gaussian as well as Gaussian noise, and the estimators are explicit rather than implicit.     

Applications of cumulants to array processing. II. Non-Gaussiannoise suppression

The main motivation of using higher order statistics in signal processing applications has been their insensitivity to additive colored Gaussian noise. The main objection to those methods is their possible vulnerability to non-Gaussian noise. The authors investigate the effects of non-Gaussian ambient noise on cumulant-based direction-finding systems using the interpretation for the information provided by cumulants for array processing applications described in Dogan and Mendek. they first demonstrate the suppression of uncorrelated non-Gaussian noise that has spatially varying statistics. Then, they indicate methods to suppress spatially colored non-Gaussian noise using cumulants and an additional sensor whose measurement noise component is independent of the noise components of the original array measurements. They also indicate the noise suppression properties of the virtual-ESPRIT algorithm proposed in Dogan and Mendel. In addition, they propose a method that combines second- and fourth-order statistics together in order to suppress spatially colored non-Gaussian noise. Finally, they also illustrate how to suppress spatially colored non-Gaussian noise when the additional sensor measurement is not available. Simulations are presented to verify the results     

Adaptive alpha-trimmed mean filters under deviations from assumed noise model

Alpha-trimmed mean filters are widely used for the restoration of signals and images corrupted by additive non-Gaussian noise. They are especially preferred if the underlying noise deviates from Gaussian with the impulsive noise components. The key design issue of these filters is to select its only parameter, alpha, optimally for a given noise type. In image restoration, adaptive filters utilize the flexibility of selecting alpha according to some local noise statistics. In the present paper, we first review the existing adaptive alpha-trimmed mean filter schemes. We then analyze the performance of these filters when the underlying noise distribution deviates from the Gaussian and does not satisfy the assumptions such as symmetry. Specifically, the clipping effect and the mixed noise cases are analyzed. We also present a new adaptive alpha-trimmed filter implementation that detects the nonsymmetry points locally and applies alpha-trimmed mean filter that trims out the outlier pixels such as edges or impulsive noise according to this local decision. Comparisons of the speed and filtering performances under deviations from symmetry and Gaussian assumptions show that the proposed filter is a very good alternative to the existing schemes.     

Parametric cumulant based phase estimation of 1-D and 2-Dnonminimum phase systems by allpass filtering

This paper proposes a parametric cumulant-based phase-estimation method for one-dimensional (1-D) and two-dimensional (2-D) linear time-invariant (LTI) systems with only non-Gaussian measurements corrupted by additive Gaussian noise. The given measurements are processed by an optimum allpass filter such that a single Mth-order (M⩾3) cumulant of the allpass filter output is maximum in absolute value. It can be shown that the phase of the unknown system of interest is equal to the negative of the phase of the optimum allpass filter except for a linear phase term (a time delay). For the phase estimation of 1-D LTI systems, an iterative 1-D algorithm is proposed to find the optimum allpass filter modeled either by an autoregressive moving average (ARMA) model or by a Fourier series-based model. For the phase estimation of 2-D LTI systems, an iterative 2-D algorithm is proposed that only uses the Fourier series-based allpass model. A performance analysis is then presented for the proposed cumulant-based 1-D and 2-D phase estimation algorithms followed by some simulation results and experimental results with real speech data to justify their efficacy and the analytic results on their performance. Finally, the paper concludes with a discussion and some conclusions