This study investigates the signal estimation problem in noisy sensor networks with quantised communications. The sensors are subject to random sensor failures, and synchronously take noisy measurements to produce local estimates by using a Kalman filtering scheme at each sampling instant. A quantiser is considered to be embedded in each sensor, and the probabilistic quantisation strategy is adopted to reduce the energy consumption. In between two sampling instants, each sensor collects quantised local estimates from its neighbours and runs a consensus-based fusion algorithm to generate a fused estimate. The process noises and measurement noises are considered to be spatially uncorrelated, a recursive equation is presented to calculate the estimation error covariance matrix and an upper bound is derived for the estimation performance index. Moreover, a sufficient condition for the convergence of the upper bound of the estimation performance index is also presented. Two types of optimisation problems are constructed for cases of infinite and finite recursions, respectively, where the former one focuses on minimising the derived upper bound of the estimation performance index, and the latter one aims to minimise the energy consumption subject to a constraint on the estimation performance. Illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.

In this study, the authors present a novel voicing detection algorithm which employs the well-known aperiodicity measure to detect voiced speech in signals contaminated with non-stationary noise. The method computes a signal-adaptive decision threshold which takes into account the current noise level, enabling voicing detection by direct comparison with the extracted aperiodicity. This adaptive threshold is updated at each frame by making a simple estimate of the current noise power, and thus is adapted to fluctuating noise conditions. Once the aperiodicity is computed, the method only requires a small number of operations, and enables its implementation in challenging devices (such as hearing aids) if an efficient approximation of the difference function is employed to extract the aperiodicity. Evaluation over a database of speech sentences degraded by several types of noise reveals that the proposed voicing classifier is robust against different noises and signal-to-noise ratios. In addition, to evaluate the applicability of the method for speech enhancement, a simple F ₀-based speech enhancement algorithm integrating the proposed classifier is implemented. The system is shown to achieve competitive results, in terms of objective measures, when compared with other well-known speech enhancement approaches.

The issue of joint angle and array gain-phase error estimation for a bistatic multiple-input multiple-output array is discussed in this study, and an algorithm for the joint estimation with non-linear arrays is proposed. First, the estimations of the transmit and receive direction matrices can be obtained via trilinear decomposition, then the relationship between the columns of the direction matrices is utilised to eliminate the influence of the gain-phase errors, and the angles can be estimated two by two via least squares. Finally, the array gain-phase error vectors can be estimated for calibration according to the estimated angles and direction matrices. The proposed algorithm requires no eigenvalue decomposition of the received data, and can achieve automatically paired estimations of the angles. Furthermore, no information of the gain-phase error is needed. The simulation results verify the algorithmic effectiveness of the proposed algorithm.

A new detection method for data-dependent superimposed training with equi-spaced amplitude modulation or equi-spaced square quadrature amplitude modulation is presented in this study. Symbol and bit error floor of the proposed detection method is analysed. To remove the error floor, a data coding method is also proposed. Analysis and simulation results show that the proposed detection method outperforms the existing methods, and the data detection performance can be further improved via data coding.

The detection of sparse signals against background noise is difficult since the information in the signal is only carried by a small portion of it. Prior information is usually assumed to ease detection. This study considers the general unknown and arbitrary sparse signal detection problem when no prior information is available. Under a Neyman–Pearson hypothesis-testing problem model, a new detection scheme referred to as the likelihood ratio test with sparse estimation (LRT-SE) is proposed. The SE technique from the compressive sensing theory is incorporated into the LRT-SE to achieve the detection of sparse signals with unknown support sets and arbitrary non-zero entries. An analysis of the effectiveness of LRT-SE is first given in terms of the characterisation of the conditions for the Chernoff-consistent detection. A large deviation analysis is then given to characterise the error exponent of LRT-SE with respect to the signal-to-noise ratio and the angle between the sparse signal and its estimate. Numerical results demonstrate superior detection performance of the proposed scheme over existing asymptotically optimal sparse detectors for finite signal dimensions. In addition, the simulation shows that the error probability of the proposed scheme decays exponentially with the number of observations.

A new, reliable and computationally efficient blind method is proposed for joint estimation of channel order and number of active users in a direct sequence code-division multiple-access system with multi-path fading channel. The proposed method (i) exploits a parametric model used for equalisation of multi-path channels in finite impulse response multi-input multi-output systems, (ii) first, estimates rank of correlation matrix of observation, by combining the subspace method and information-theoretic criteria, (iii) then, estimates simultaneously channel order and number of active users, by using the estimated rank and the model parameter, without any prior information, (iv) uses only a single antenna, in contrast to the previous methods, while having the ability to jointly estimate higher numbers of active users and channel order in lower signal-to-noise ratios. Numerical results show that the proposed method can estimate higher number of users and also has higher detection probability when using minimum mean square error algorithm.

In this study, the authors propose a speech recognition system using harmonic structure related information to detect harmonic features in noisy environment. The proposed algorithm first extracts the harmonic components contained inside the speech signals using sine function convolution. By setting the frequency of the sine function as equal to the fundamental frequency of speech signals, harmonic components can be extracted out. The reconstructed signal obtained by summing up the extracted harmonic components is found to have a high degree of correlation with the original signal. The extracted frame energy measure of the harmonic components has been further processed to become dynamic harmonic features and then used together with the European Telecommunications Standards Institute (ETSI) front-end processed mel-frequency cepstral coefficients (MFCC) feature or the perceptual linear prediction (PLP) feature in the speech recognition system. The proposed enhanced speech recognition system shows a better recognition rate over the ETSI front-end processed MFCC (or PLP)-based speech recognition system.

Time–frequency distribution (TFD) has been widely used for micro-Doppler analysis in radar signal processing. However, the spectrogram will suffer from aliasing if the maximum Doppler frequency exceeds half of the pulse repetition frequency, which may lead to false estimation of the targets' kinematic properties. In this study, by transmitting a series of random pulse repetition interval (RPRI) pulses, a concise TFD approach named short-time compressed sensing (STCS) is proposed for aliasing-free micro-Doppler analysis. In STCS, precise analysis and synthesis of the random sampling time series can be achieved by exploiting the signal's sparsity in the frequency domain. Furthermore, adaptive to the data, the widths of the particular rectangle windows are determined by sequential processing with a proper optimisation rule. To speed up the STCS procedure, the smoothed L0 algorithm is chosen for sparse recovery, where the pseudoinverse of the dictionaries can be calculated iteratively. The simulation results indicate that the proposed STCS approach can achieve both preferable TFD and acceptable computational cost. The effectiveness of the STCS is finally verified by the application for micro-Doppler estimating in RPRI radar.

Recent work in the area of compressed sensing mainly focuses on the perfect recovery of the entire support for sparse signals. However, partial support recovery, where a part of the signal support is correctly recovered, may be adequate in many practical scenarios. In this study, in the high-dimensional and noisy setting, the authors develop the probability of partial support recovery of the optimal maximum-likelihood (ML) algorithm. When a large part of the support is available, the asymptotic mean-square-error (MSE) of the reconstructed signal is further developed. The simulation results characterise the asymptotic performance of the ML algorithm for partial support recovery, and show that there exists a signal-to-noise ratio (SNR) threshold, beyond which the increase of SNR cannot bring any obvious MSE gain.

The commonly used root-mean-square error for estimation performance evaluation is easily dominated by large error terms. So many new alternative absolute metrics have been provided in X. R. Li's work. However, each of these metrics only reflects one narrow aspect of estimation performance, respectively. A comprehensive measure, error spectrum, was presented aggregating all these incomprehensive measures. However, when being applied to dynamic systems, this measure will have three dimensions over the total time span, which is not intuitive and difficult to be analysed. To overcome its drawbacks, a new metric, dynamic error spectrum (DES), is proposed in this study to extend the error spectrum measure to dynamic systems. Three forms under different application backgrounds are given, one of which is balanced taking into account both good and bad behaviour of an estimator and so can provide more impartial evaluation results. It can be applied to a variety of dynamic systems directly. Then the challenge in performance evaluation of the interacting multiple model (IMM) algorithm is considered, and the IMM algorithm is chosen as the testing case to illustrate the superiority of the DES metric. The simulation results validate its utility and effectiveness.

The modulated wideband converter (MWC) is a recently proposed compressive sampling system for acquiring sparse multiband signals. For the MWC with digital sub-channel separation block, channel gain mismatch and time delay will lead to a potential performance loss in reconstruction. These gains and delays are represented as an unknown multiplicative diagonal matrix here. The authors formulate the estimation problem as a convex optimisation problem, which can be efficiently solved by utilising least squares estimation. Then the calibrated system model is obtained and the estimates of the gains and time delays of physical channels from the estimate of this matrix are calculated. Numerical simulations verify the effectiveness of the proposed approach.