As a new enchanting theory, compressed sensing (CS) demonstrates that a sparse signal can be recovered through a surprisingly small number of linear measurements by solving a problem of ℓ ₁ norm minimisation (which can be thought as a special case of the signomial diversity measures). However, the traditional CS model with ℓ ₁ norm minimisation can not fully exploit the sparsity especially when the degree of sparsity increases or the measurements number reduces. In this study, the Cauchy diversity measures is incorporated into the proposed model to deal with the above difficulties. The simulation results demonstrate that under the same condition, this new model offers a superior reconstruction precision compared with the common used signomial diversity measures.

This study extends the problem of fault detection (FD) for linear discrete-time systems with unknown input to non-linear systems. Moreover, based on physical consideration, the constraints of state are considered. A non-linear recursive filter is developed where the constrained state and the input are interconnected. Constraints which can improve the quality of estimation are imposed on individual updated sigma points as well as the updated state. The advantage of algorithm is that it is able to incorporate arbitrary constraints on the states during the estimation procedure. Unknown input which can be any signal is obtained by least-squares unbiased estimation and the state estimation problem is transformed into a standard unscented Kalman filter problem. By testing the mean of the innovation process, a real-time FD approach is proposed. Simulations are provided to demonstrate the effectiveness of the theoretical results.

This study presents a novel property of the two-dimensional DFT-modulated filter bank and an efficient algorithm for designing the filter bank with large scale (with a large number of subbands and filters of large spatial support). It is firstly shown that the overall transfer function and aliasing transfer functions can be simply represented with the multiplication of the prototype filters and their modulated filters; a new property used to remarkably reduce the calculation of these functions. On the other hand, the design problem of the filter bank is formulated into an unconstrained optimisation problem. Based on the gradient vector, the conjugate gradient method is utilised to solve the design problem. The convergence of the proposed algorithm is analysed. Numerical examples and comparisons with other methods are included to show the performance of the algorithm.

This study considers a networked system in which the measurement suffers from one-step delay and packet dropouts because of the unreliability of the network. A new model applied to describe the arrival conditions of the measurements is proposed. Based on the new model and using a state augmentation method, optimal linear filter, predictor and smoother are obtained. A sufficient condition for the convergence of the system is given. Finally, the simulation results show the effectiveness of the proposed algorithms.

As an important class of non-Gaussian statistic model, α-stable distribution has received much attention because of its generality to represent impulsive interference. Unfortunately, it does not have a closed-form probability density function (PDF) except for a few cases. For this reason, suboptimal zero-memory non-linearity (ZMNL) function has to be used as an approximation in designing locally optimal detector, such as classical Cauchy and Gaussian-tailed ZMNL (GZMNL). To enhance the performance of detectors, the authors first investigate the approximate PDFs for the symmetric α-stable. In particular, a simplified version of Cauchy–Gaussian mixture (CGM) model, called bi-parameter CGM (BCGM) model is detailed. This BCGM model has a concise closed-form, and hence is more tractable than the classical Gaussian mixture model and CGM model. Then based on the preset false alarm ratio (FAR), the test threshold is adaptively evaluated by using BCGM to maintain a constant FAR. The authors further devise an algebraic-tailed ZMNL (AZMNL) with a simplified form. Simulation results show that the detector with AZMNL outperforms the ones with classical Cauchy and GZMNL, and achieves near-optimal performance in varying impulsive interference.

Maximum-eigenvalue-detection (MED) and maximum-eigenvalue geometric-mean (ME-GM) are attractive eigenvalue-based spectrum sensing (EBSS) schemes for cognitive radio (CR). The first objective of this paper is to present an analytical probability of detection (PD) expression for MED. The evaluated expression matches the simulation results well. Many of the existing analytical results for EBSS schemes are based on the asymptotic Tracy-Widom (TW) distribution; however, for small or moderate sample length, N and secondary users, M the distribution lacks accuracy. Recently, adjusted centring and scaling parameters have been presented to improve the accuracy of the TW distribution for this practical scenario; thus, the second objective is to present the adjusted-TW expressions (probability of false alarm (PFA), threshold and PD) for MED and ME-GM. The proposed results show an improved accuracy for moderate N when M is small. To improve the accuracy for small N the authors propose to use an exact cumulative distribution function of the maximum eigenvalue. Hence the third objective of the paper is to present the exact analytical expressions for MED. The exact approach is then applied to ME-GM, where an asymptotic expression for the GM is employed. The exact analysis exhibits a higher accuracy for both MED and ME-GM.

A novel design of oversampled generalised discrete Fourier transform filter banks is proposed, with application to subband-based convolutive blind source separation (BSS), where either instantaneous BSS algorithms or joint BSS algorithms can be applied. Conventional filter banks design is usually focused on elimination of the overall aliasing error and the perfect reconstruction (PR) condition, which are required by traditional subband adaptive filtering applications. However, because of the unknown scaling factor, the traditional PR condition is not necessary in the context of subband BSS and can be relaxed in the design. Owing to the increased degrees of design freedom, the authors can introduce an additional cost function to enhance the mutual information between adjacent subband signals. Together with a reduced subband aliasing level, it leads to an improved subband permutation alignment result for instantaneous BSS and an overall better performance for the joint BSS.

A robust minimum variance (MV) beamforming approach is proposed for improving the robustness of multiple-input multiple-output (MIMO) radar against the mismatches of the steering vector and the finite sample effects. In contrast to existing robust MV beamformers (RMVBs), the proposed RMVB utilises a specific structured model of virtual steering vector (also named transmit–receive steering vector) of MIMO radar rather than the commonly used unstructured model in phased-array radar. The basic idea of the proposed RMVB is to estimate the desired transmit and receive steering vectors under two quadratic constraints. To solve this problem, an iterative algorithm is developed. Simulations are provided to confirm the effectiveness of the proposed method.

In applying Shannon's sampling theorem, evaluation of the sampled signal Fourier spectrum is based on the fact that sampling the continuous-time signal is the result of multiplying the signal by distributions. If the signal has discontinuities, a multiplication of distributions – an undefined operation – is encountered. Such undefined operation has led to errors in the literature which to date accompany the formulation of sampling of signals containing discontinuities. This paper presents an approach to evaluating the product of distributions as a means of sampling discontinuous signals, eliminating such errors. It is shown that the value of the product of distributions may be found by invoking the Mittag–Leffler expansion. As an illustration of errors that have existed for decades and still exist in the digital signal processing literature whenever discontinuous signals are sampled the approach of impulse invariance provides a case in point. It was already noted that this approach has an inherent error. Yet, impulse invariance is still considered as one of the two main approaches for converting analogue to digital filters. In this study, the true spectra of sampled discontinuous signals are evaluated, and a new approach to the transformations between continuous-time and discrete-time systems eliminating the error, is proposed.

In this study, the authors look into digital predistortion and its combination with the peak-to-average power ratio (PAPR) reduction technique in the case of orthogonal frequency division multiplexing (OFDM)-based systems. First of all, the authors propose a new predistortion methodology which uses the addition of signals. Two different algorithms are investigated for the predistortion signals generation. The first one is based on the traditional predistortion method, where an estimation of the power amplifiers (PAs) characteristics is needed in the first place. The second algorithm to generate the predistortion signal does not need a priori PA estimation. It is based on an iterative compensation of the error between the amplified signal and the OFDM signal. Then, the authors combine this latter algorithm with the tone reservation PAPR reduction method in order to have a global adding signal expression. Two combination scenarios of PAPR reduction and predistortion obtained by means of adding a signal are proposed. The first one combines both of them in series while the second one is parallel. Performances of the proposed predistortion algorithms and the combination scenarios are compared thanks to simulations based on IEEE802.il a/g standards for a memoryless solid state PA.

This study considers linear filtering methods for minimising the end-to-end average distortion of a fixed-rate source quantisation system. For the source encoder, both scalar and vector quantisation are considered. The codebook index output by the encoder is sent over a noisy discrete memoryless channel whose statistics could be unknown at the transmitter. At the receiver, the code vector corresponding to the received index is passed through a linear receive filter, whose output is an estimate of the source instantiation. Under this setup, an approximate expression for the average weighted mean-square error (WMSE) between the source instantiation and the reconstructed vector at the receiver is derived using high-resolution quantisation theory. Also, a closed-form expression for the linear receive filter that minimises the approximate average WMSE is derived. The generality of framework developed is further demonstrated by theoretically analysing the performance of other adaptation techniques that can be employed when the channel statistics are available at the transmitter also, such as joint transmit–receive linear filtering and codebook scaling. Monte Carlo simulation results validate the theoretical expressions, and illustrate the improvement in the average distortion that can be obtained using linear filtering techniques.

Space time coding plays quite an important role in the design of multi-input multi-output (MIMO) radar. It has been shown that the correlation characteristics of waveform set have a great impact on the performance of target detection and localisation for MIMO radar. In this study, the target detection and localisation performance of co-located MIMO radar is analysed theoretically and experimentally, when correlated (not ideally orthogonal or fully coherent) waveforms are transmitted. The relationship between transmit–receive beam pattern improvement and correlation coefficients of transmitted waveforms is investigated. The signal to interference and noise ratio varying with correlation coefficients in range-Doppler matched processing is defined and analysed. Furthermore, Cramer–Rao bound for target direction of arrival estimation and target detection probability in the Neyman–Pearson criteria are derived when transmitting correlated waveforms. It is shown that the MIMO radar detection and localisation performance is much dependent with the correlation level of transmitted waveforms, which can be quite useful for MIMO radar orthogonal waveform design. Numerical simulation validates the theoretical analysis.

This study considers the minimum mean square error estimation problem for a class of jump Markov linear systems with unknown mode-dependent state delays. In order to show the difficulties caused by the unknown delays, the online Bayesian equation of the investigated system is firstly developed by incorporating the time-delay estimation into the recursion of system states. However, computing such optimal estimation causes an exponential increase in the requirement of computation and storage load. Therefore two different approximation techniques: interacting multiple-model approximation and detection–estimation method are utilised to obtain two suboptimal but executable filtering algorithms, respectively. Simulation results of the proposed methods for a system are presented to illustrate the effectiveness.