For numerous applications in the field of signal processing, it is desired to design a compact window that can simultaneously concentrate maximum energy in finite time interval and frequency band. Although zero‐order discrete prolate spheroidal sequence (DPSS) meets this requirement, it is of infinite support. Limiting this sequence to finite support no longer guarantees the optimality property. This study aims at designing a discrete finite length window that can maximise the energy simultaneously in narrow time interval and frequency band. A multi‐objective optimisation approach is adopted to obtain the upper bound of maximum achievable time and frequency domain energy concentrations for finite length sequences. The optimal sequence thus obtained is termed as the optimal window with finite support (OWFS), and its various associated properties are discussed. It is shown analytically that as the support of OWFS approaches infinity, it converges to zero‐order DPSS. In order to illustrate its optimality, the compactness of the proposed OWFS is compared with those of various window functions. Extending the proposed OWFS, this study also discusses the formulation and associated properties of the zero‐order periodic DPSS. Further, the closed form expression for the upper bound of achievable time and frequency domain energy concentrations is also derived.

This study presents a simple technique, which is used to estimate both channel state and carrier frequency offset (CFO) in decode-and-forward relay systems, where coded orthogonal frequency division multiplexing is employed without cyclic prefix. On the basis of the least-square criterion, we derive the estimate of CFO and channel with the aids of consecutive blocks of pilot symbols. The initially proposed estimation technique achieves a distinguished performance by using a two-dimensional complete search approach; however, the computation becomes more and more intensive when the search granularity becomes finer and finer. For this reason, we further present an iterative approach as an alternative solution, which provides a performance comparable with that of the complete search method, while greatly reducing the implementation complexity. Besides, we also derive a closed-form expression of the CFO estimate for the considered system, which allows us to avoid the exhaustive search during the estimation processing. Computer simulations have been conducted to verify the efficiency of the proposed schemes.

Source localisation using time difference of arrival (TDOA) measurements has drawn considerable attention in the past few decades. The presence of outliers in TDOAs could deteriorate the localisation performance significantly. Under the reasonable assumption that outliers are sparse and they do not dominate in the raw measurement set, a computationally efficient outlier‐robust TDOA localisation method is proposed in this study. It integrates the half‐quadratic minimisation and reweighted least absolute shrinkage and selection operator to iteratively identify the outliers and find the source location estimate using the TDOA inliers only. Both additive and multiplicative forms of the proposed method are established. Simulation results demonstrate the computational efficiency and effectiveness of the developed algorithms.

In this study, an improved square root adaptive cubature Kalman filter (ISRACKF) is proposed to improve the filter performance in terms of accuracy, computation efficiency, and robustness. Through the evaluated measure of non-linearity value, the cubature rule under different accuracy levels can be adaptively selected in the dynamic process or measurement model. In this way, high accuracy can be maintained without sacrificing computation efficiency. Furthermore, the maximum correntropy criterion cost function can help improve the robustness of ISRACKF. The measure of non-Gaussianity value is utilised to control the computation complexity of the robust iterative process as well. The stability proof of estimated state error and covariance is given. The comparison results of the target tracking problem and integrated navigation system demonstrate the superior performance of the proposed ISRACKF in this study.

A new algorithm for denoising electrocardiogram (ECG) signals contaminated by additive white Gaussian noise is proposed in this study. In the proposed algorithm, a clean ECG signal is modelled as a combination of a smooth signal representing the P-wave and the T-wave, and a group-sparse (GS) signal representing the QRS-complex, where a GS signal is a sparse signal in which its non-zero entries tend to concentrate in groups. Accordingly, the proposed approach consists of two stages. In the first stage, an algorithm previously developed by the author is adapted to extract the GS signal representing the QRS-complex, while in the second stage a new algorithm is developed to smooth the remaining signal. Each one of these two algorithms depends on a regularisation parameter, which is selected automatically in the proposed algorithms. Simulation results on real and simulated ECG data show that the proposed algorithm can be successfully utilised to denoise ECG data. In addition, the proposed algorithm is also shown to produce significantly improved results compared to existing techniques used for performing similar tasks.

In device-to-device (D2D) communication underlaying cellular networks, the D2D user equipments (DUEs) can communicate by sharing the radio resources assigned to cellular user equipments. D2D communication is expected to improve the network throughput and save more energy for the user equipments. However, D2D communication causes severe interference to both the cellular users and other DUEs which is a challenge to radio resource allocation. The authors propose joint channel and power allocation algorithm to maximise the network achievable throughput, control the interference from the DUEs transmissions to cellular users and improve the energy efficiency of the user equipments. The authors formulate the problem and solve it using convex optimisation methods to select DUEs and set their powers in each channel. Simulation results show that the proposed algorithm can offer near-optimal performance and outperforms the comparable algorithms especially in terms of achievable throughput even with markedly reduced complexity levels.

Adaptive beamforming methods are sensitive to underlying assumptions on the environment, sources, or sensor array violation, especially when interferences are moving fast. In this study, the non-stationary interference source is estimated during the period in which snapshots are taken. Then, a new interference-plus-noise covariance matrix reconstruction is introduced which is derived from a simplified power spectral density function that can be used to shape the directional response of the beamformer. Finally, the beamformer is designed to impose nulls towards the regions of the moving interference based on the reconstructed covariance matrix. The essence of the proposed method is to express the inverse of the reconstructed covariance matrix which needs less computational complexity calculation. The effectiveness of the proposed method is demonstrated by numerical results.

This study investigates the problem of low probability of intercept (LPI)-based distributed multiple-input multiple-output (MIMO) radar waveform design against barrage jamming in signal-dependent clutter and coloured noise. Given the priori knowledge of the extended target impulse response, signal-dependent clutter, barrage jamming signals and coloured noise, the LPI-based scheme for optimal radar waveform design is proposed to minimise the total power consumption of the MIMO radar system by optimising the transmitted waveforms of different transmitters with a predetermined mutual information (MI) constraint for target characterisation performance. Firstly, the MI between the received echoes from the target at each receiver and the target impulse response is derived as a practical metric to characterise the parameter estimation performance of a target. Then, the LPI-based distributed MIMO radar waveform design strategy is developed. The resulting radar waveform optimisation problem is convex and solved analytically, whose solutions represent the optimum power allocation for each transmitter in the MIMO radar system. With the aid of numerical simulations, it is illustrated that to minimise the total transmission power, the optimal waveform should match with the target, clutter, jamming and coloured noise. In addition, it is also demonstrated that the LPI performance of the MIMO radar system can be significantly improved by employing the proposed radar waveform design scheme.

Advances in digital image processing and communications have created a great demand for real‐time secure image transmission over the networks. However, the development of effective, fast and secure dependent image compression‐encryption systems are still a research problem as the intrinsic features of images. A new approach is suggested in this study for partial image encryption‐compression that adopts chaotic three‐dimensional (3D) cat map to de‐correlate relations among pixels in conjunction with an adaptive thresholding technique that is utilised as a lossy compression technique instead of using complex quantisation techniques and also as a substitution technique to increase the security of the cipher image. The proposed scheme is based on employing both of lossless compression with encryption on the most significant part of the image after contourlet transform. However, the least significant parts are lossy compressed by employing a simple thresholding rule and arithmetic coding to render the image totally unrecognisable. Due to the weakness of 3D cat map to chosen plain text attack, the suggested scheme incorporates a mechanism to generate random key depending on the contents of the image (context key). Several experiments were done on benchmark images to insure the validity of the proposed technique.