Showing papers in "Iet Signal Processing in 2016"

Distributed estimation over sensor networks based on distributed conjugate gradient strategies

Abstract: This study presents distributed conjugate gradient (CG) algorithms for distributed parameter estimation and spectrum estimation over wireless sensor networks. In particular, distributed conventional CG (CCG) and modified CG (MCG) algorithms are developed with incremental and diffusion adaptive cooperation strategies. The distributed CCG and MCG algorithms have an improved performance in terms of mean square error as compared with least-mean square-based algorithms and a performance that is close to recursive least-squares algorithms. In comparison with existing centralised or distributed estimation strategies, key features of the proposed algorithms are: (i) more accurate estimates and faster convergence speed can be obtained and (ii) the design of preconditioners for CG algorithms, which can improve the performance of the proposed CG algorithms is presented. Simulations show the performance of the proposed CG algorithms against previously reported techniques for distributed parameter estimation and distributed spectrum estimation applications.

Compressive sensing for cluster structured sparse signals: variational Bayes approach

Abstract: Compressive sensing (CS) provides a new paradigm of sub-Nyquist sampling which can be considered as an alternative to Nyquist sampling theorem. In particular, providing that signals are with sparse representations in some domain, information can be perfectly preserved even with small amount of measurements captured by random projections. Besides sparsity prior of signals, the inherent structure property behind some specific signals is often exploited to enhance the reconstruction accuracy. In this study, the authors are aiming to take into account the cluster structure property of sparse signals, of which the non-zero coefficients appear in clustered blocks. By modelling simultaneously both sparsity and cluster prior within a hierarchical statistical Bayesian framework, a non-parametric algorithm can be obtained through variational Bayes approach to recover original sparse signals. The proposed algorithm could be slightly considered as a generalisation of Bayesian CS (BCS), but with a consideration on cluster property. Consequently, the performance of the proposed algorithm is at least as good as BCS, which is verified by the experimental results.

Convolution and correlation theorems for the two-dimensional linear canonical transform and its applications

Abstract: Convolution and correlation operations are very important in signal processing community, as well as in sampling, filter design and applications. In this study, the authors derive the convolution and correlation theorems for the two-dimensional linear canonical transform (2D LCT). Moreover, they utilise the convolution theorem to investigate the sampling theorem for the band limited signal in the 2D LCT domain. They also discuss multiplicative filter for the band limited signal in the 2D LCT domain which has much lower computational load than the method in the 2D LCT domain.

Knowledge-aided STAP with sparse-recovery by exploiting spatio-temporal sparsity

Abstract: In this paper, novel knowledge-aided space-time adaptive processing (KA-STAP) algorithms using sparse representation/recovery (SR) techniques by exploiting the spatio-temporal sparsity are proposed to suppress the clutter for airborne pulsed Doppler radar. The proposed algorithms are not simple combinations of KA and SR techniques. Unlike the existing sparsity-based STAP algorithms, they reduce the dimension of the sparse signal by using prior knowledge resulting in a lower computational complexity. Different from the KA parametric covariance estimation (KAPE) scheme, they estimate the covariance matrix using SR techniques that avoids complex selections of the Doppler shift and the covariance matrix taper. The details of the selection of potential clutter array manifold vectors according to prior knowledge are discussed and compared with the KAPE scheme. Moreover, the implementation issues and the computational complexity analysis for the proposed algorithms are also considered. Simulation results show that our proposed algorithms obtain a better performance and a lower complexity compared with the sparsity-based STAP algorithms and outperform the KAPE scheme in presence of errors in prior knowledge.

Image super-resolution reconstruction using the high-order derivative interpolation associated with fractional filter functions

Abstract: In this stydy, the authors present a single image super-resolution (SISR) reconstruction based on high-order derivative interpolation (HDI) in the fractional Fourier transform (FRFT) domain. First, the HDI formula is derived using a simple technique, which is based on the relationship between the fractional band-limited signal and the traditional band-limited signal. This interpolation formula contains the derivative information of the image and the FRFT domain filter functions (FDFF). Moreover, the advantages of the FDFF are also analysed. Second, the new SISR reconstruction is presented via the HDI. The main advantage is that the presented method involves the derivatives of an image in the resizing process. Moreover, the authors take advantage of the FDFF to resize the image. Furthermore, three evaluation criteria and some simulations are presented to validate the effectiveness of the proposed method. Last, the proposed method is applied to colour image processing. For a colour image case, the RGB colour space is chosen for super-resolution reconstruction. In addition to peak signal-to-noise ratio, the authors have also used the correlation to assess the quality of the reconstruction. Compared with many methods, extensive experimental results validate that the proposed method can obtain the better-edge characteristic, less blur and less aliasing.

Two-dimensional DOA estimation for L-shaped array with nested subarrays without pair matching

Abstract: Non-uniform L-shaped array consisting of two nested arrays and its computationally efficient two-dimensional direction-of-arrival (DOA) estimation method are developed in this study. The basic idea of the proposed method is to utilise the property of nested arrays and the conjugate symmetry property of the signal auto-correlation function for different time lags to construct a conjugate augmented spatial–temporal cross-correlation matrix (CAST-CCM) and form joint diagonalisation structure from the signal subspace corresponding to the CAST-CCM. Hence, the DOAs are estimated and paired automatically via signal subspace joint diagonalisation technique. The proposed method can handle underdetermined DOA estimation with automatic matching and deal with the angle ambiguity problem when multiple sources have the same azimuth or elevation angles. Meanwhile, the proposed method is computationally efficient without multidimensional search. The effectiveness of the proposed method is verified through computer simulations.

Optimal design of wideband infinite impulse response fractional order digital integrators using colliding bodies optimisation algorithm

Abstract: This study presents a novel approach to design wideband infinite impulse response fractional order digital integrators (FODIs) for the half and one-fourth order integrators based on a parameter independent metaheuristic algorithm called colliding bodies optimisation (CBO). The performance of CBO-based FODIs have been compared with the designs based on three well-known benchmark evolutionary optimisation algorithms namely, real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) in terms of robustness, consistency, parameter sensitivity, convergence speed, and computational time. Simulations results confirm that the proposed CBO-based designed FODIs achieve consistently superior magnitude responses in a computationally efficient manner as compared with the designs based on RGA, PSO, and DE. The proposed CBO-based FODIs also significantly outperform all state-of-the-art designs reported in literature in terms of two different magnitude response error metrics. This research work underlines the potential of CBO as an efficient optimisation tool for the design of accurate digital approximations to the fractional order integrators.

Efficient methodology for electrocardiogram beat classification

Abstract: Electrocardiogram (ECG) beat behaves as a non-linear and non-stationary signal. Since most of the existing data processing tools are poor alternatives for processing such signals, Hilbert–Huang transform (HHT) proves to be an efficient method as it deals with a time-varying frequency spectrum. In this study, a new and efficient methodology is proposed using HHT for feature selection which includes a set of essential features such as weighted mean frequency, Kolmogorov complexity and other statistical features (median, standard deviation, kurtosis, skewness and central moment) computed from the intrinsic mode functions extracted using the empirical mode decomposition (EMD) algorithm. Further, one-against-one multi-class support vector machine is employed for the classification of six generic ECG beats, namely: normal, left bundle branch block, right bundle branch block, premature ventricular contraction, paced beat and atrial premature beat. The classification process in this study yields better results than existing methodologies in terms of classification accuracy equal to 99.51% along with sensitivity, specificity and positive predictivity of 98.64, 99.77 and 98.17%, respectively.

N -phase logistic chaotic sequence and its application for image encryption

Abstract: In this study, the authors use a non-symmetric partition to generate N-phase pseudorandom sequences using the logistic maps. The theoretical analysis shows that this N-phase logistic sequence is with uniform distribution, as well as independent and identically distributed. Numerical experiments show that these N-phase logistic sequences have high complexity and are with good randomness. A fast algorithm with its time complexity be O(M) is proposed to generate these N-phase sequences. Furthermore, they propose a new image encryption algorithm based on the N-phase logistic sequence, which is combined with both shuffling and substitution algorithms. Several security tests are carried out to demonstrate that the authors’ new algorithm is with a high security level, and can resist various attacks, which can be competitive with some other recently proposed image encryption algorithms.

Spread spectrum audio watermarking based on perceptual characteristic aware extraction

Abstract: This study presents a high-performance audio watermarking scheme using spread spectrum modulation. Unlike conventional extractors which use simple correlation, this watermarking scheme exploits the perceptual characteristic of the watermarked audio before correlation. It is noted that although the watermark extractor works blindly neither which the original audio signal nor the embedded watermark signal is available, however, the spectral power structure of embedded watermark can be estimated using perceptual analysis methods. With this information, the watermark performance is improved by introducing an estimation-equalisation-correlation based extraction mechanism. The pre-equaliser at the extractor is carefully designed to obtain optimised extraction performance. Moreover, the perceptual analysis and shaping method are improved to make sure the watermark estimation is accurate. The perceptual characteristic aware extraction-based watermarking scheme achieves high embedding capacity up to 43 bps/channels, with low perceptual distortion to the host audio. Experiments on real audio signals show that the proposed watermarking scheme achieves high performance and is robust against various types of attacks.

Energy-efficient interference management in LTE-D2D communication

Abstract: This paper focuses on one of the key enabling technology that will compose future 5G network, the Direct-LTE communication underlying a cellular infrastructure, also commonly known as Device-to-Device (D2D). Energy efficiency algorithms are proposed for the communication between D2D users and cellular users (CUs) and, following the Lagrangian duality theory, an optimal power and rate control solution is given for D2D users, while satisfying the interference limits related to CUs. Finally, the new algorithm is used to achieve proportional fairness between D2D users and CUs and to show with numerical results that the interference to CUs can be limited to always be under a predefined threshold.

Sequential quasi-convex-based algorithm for waveform design in colocated multiple-input multiple-output radars

Abstract: This study considers the problem of waveform design for colocated multiple-input multiple-output (MIMO) radars for multiple targets in the presence of multiple interferences in white Gaussian noise. Here, the authors jointly design the transmit waveform and receive beamforming by a sequential algorithm. The proposed sequential algorithm maximises the minimum signal-to-interference-plus-noise ratio (SINR) to design both continuous and finite alphabet phase waveforms. In the case of continuous phase, all phases can be chosen in the waveform space, while in finite alphabet case, phases are only chosen from a confine set. Two important practical constraints of ‘constant envelope’ and ‘similarity’ are considered as well. The authors also have converted the waveform design problem into a quasi-convex optimisation problem which can be effectively solved by using convex optimisation toolbox (CVX). They have evaluated the performance of the matched filter output, beampattern and peak-to-average power ratio via numerical simulations and shown that the proposed sequential method achieves better SINR performance compared with existing MIMO radar transmit waveform design methods, for both single and multiple target scenarios.

Distributed fusion estimator for multi-sensor asynchronous sampling systems with missing measurements

Abstract: The fusion estimation problem for a class of multi-sensor asynchronous sampling linear stochastic systems with missing measurements is considered, where the state is updated uniformly and each sensor non-uniformly samples one measurement at most within a state update period. Based on the sampled measurement data of each sensor, the optimal local state estimators are designed at the state and measurement points by using the projection theory. The cross-covariance matrices between estimation errors of any two local estimators are derived. Based on the obtained local estimators and cross-covariance matrices, the distributed optimal fusion estimator is given by using matrix-weighted fusion estimation algorithm in the linear minimum variance sense. A simulation example verifies the effectiveness of the algorithms.

Comparison of centralised scaled unscented Kalman filter and extended Kalman filter for multisensor data fusion architectures

Abstract: This study presents three non-linear centralised scaled unscented Kalman filter (SUKF) for multisensor data fusion algorithms, which are augmented measurements, measurements weighted and sequential filtering fusion. First, the accuracy analysis of extended Kalman filter (EKF) and SUKF is investigated in detail. Second, through comparing the error covariance traces and the absolute mean estimation errors of X and Y directions of centralised SUKF for multisensor data fusion algorithms with that of centralised EKF for multisensor data fusion algorithms, it can be remarked that the performance of centralised augmented measurements SUKF for multisensor data fusion algorithm is the best one among the six algorithms, which is to say that Algorithm (Iu) shows the best performance in accuracy. Finally, combining and synthetically analysing the running time of six algorithms, it illustrates that Algorithm (Iu) is optimal in comprehensive aspects among six algorithms.

Improved single channel phase-aware speech enhancement technique for low signal-to-noise ratio signal

Abstract: In the state-of-the-art single channel speech enhancement techniques, the short-time spectral amplitude is modified while the effect of the phase corruption due to the contamination of additive noise is neglected. This study introduces an improved speech enhancement algorithm based on a phase-aware multi-band spectral subtraction technique which estimates the spectral amplitude of the clean speech signal by considering the phase of the speech and noise signal components, and uses the estimated phase of the clean speech signal for signal reconstruction in the time domain. Experimental results show that the proposed algorithm yields better performance in terms of various objective and composite quality measures and other intelligibility assessment metrics while compared with other existing spectral subtraction methods. Using the composite objective measure quality evaluation technique, it is observed that the overall signal quality of the enhanced speech signal is improved on an average by 70% at 0 dB global input signal-to-noise ratio by using the proposed approach.

Multi-target trackers using cubature Kalman filter for Doppler radar tracking in clutter

Abstract: A major feature of the Gaussian mixture probability hypothesis density (GM-PHD) filter is that it does not require any measurement-to-track association to complete its update step. This, according to the authors, should constitute significant advantage over conventional data-association based methods, especially in presence of high false-alarm rate, frequent miss-detections and targets in close proximity. To test this hypothesis, a multi-target tracking (MTT) problem using Doppler radar is considered, where the performance of GM-PHD algorithm is compared against six data-association based MTT filters in aforementioned adverse tracking conditions. To handle the non-linearity due to Doppler, cubature Kalman filter (CKF) is used in the framework of all MTT algorithms. Detailed mathematical framework of a new non-linear variant of GM-PHD using CKF has been derived using fundamental principles of non-linear Bayesian filtering. It is named as CK-GM-PHD. CK-GM-PHD is formulated using approximated Gaussian mixture assumption and follows track-oriented approach. Cubature integration method is used to numerically compute mean and covariance of components in the Gaussian mixture. Simulation results support the hypothesis by revealing substantial performance improvement of CK-GM-PHD algorithm over conventional data-association based approaches while tested in moderate to heavy clutter rate with lower detection probability and closely spaced target scenarios.

Ensemble empirical mode decomposition-based optimised power line interference removal algorithm for electrocardiogram signal

Abstract: This study proposes an optimised algorithm to remove power line interference (PLI) from electrocardiogram (ECG) signal based on ensemble empirical mode decomposition (EEMD). A computationally efficient algorithm is one of the important requirements for real-time monitoring of cardio activities and diagnosis of arrhythmias. Computational complexity in EEMD is significantly reduced by using the EMD as the preprocessing stage. The noisy ECG signal is decomposed into intrinsic mode functions (IMFs) using EMD. ECG signals which are affected by PLI are automatically identified based on the simple ratio of the zero crossing number of IMF components. EEMD is used to decompose only ECG segments constructed from the noisy IMF components. The proposed algorithm is evaluated by real ECG signals available in MIT-BIH arrhythmia database in terms of signal-to-noise ratio and root mean square error. The computational efficiency of this new framework is measured using MATLAB profiling functions and compared with EMD, EEMD, sign-based adaptive and EMD with wavelet-based methods. Results show that the proposed algorithm performs better than the EMD, EEMD, sign-based adaptive and EMD with wavelet-based methods and it is computationally more efficient than EMD and EEMD methods.

Artificial bandwidth extension using deep neural network-based spectral envelope estimation and enhanced excitation estimation

Abstract: The authors propose a robust artificial bandwidth extension (ABE) technique to improve narrowband (NB) speech signal quality using an enhanced spectrum envelope and excitation estimation. For envelope estimation, they propose an enhanced envelope estimation method using a deep neural network with multiple layers. For excitation estimation, they use a whitened NB excitation signal that is generated by passing the excitation signal through a whitening filter. An adaptive spectral double shifting method is introduced to obtain an enhanced wideband (WB) excitation signal. The proposed ABE system is applied to the decoded output of an adaptive multi-rate (AMR) codec at 12.2 kbps. They evaluate its performance using log spectral distortion, a WB perceptual evaluation of speech quality, and a formal listening test. The objective and subjective evaluations confirm that the proposed ABE system provides better speech quality than AMR at the same bit rate.

Voiced/unvoiced speech classification-based adaptive filtering of decomposed empirical modes for speech enhancement

Abstract: This study presents a speech filtering method exploiting the combined effects of the empirical mode decomposition (EMD) and the local statistics of the speech signal using the adaptive centre weighted average (ACWA) filter. The novelty lies in incorporating the frame class (voiced/unvoiced) in the conventional filtering using the EMD and the ACWA filter. The speech signal is segmented into frames and each one is broken down by the EMD into a finite number of intrinsic mode functions (IMFs). The number of filtered IMFs depends on whether the frame is voiced or unvoiced. An energy criterion is used to identify voiced frames while a stationarity index distinguishes between unvoiced and transient sequences. Reported results obtained on signals corrupted by additive noise (white, F16, factory) show that the proposed filtering in line with the frame class is very effective in removing noise components from noisy speech signal. Compared with filtering results of the wavelet, the ACWA, and the EMD-ACWA methods, the proposed technique gives much better results in terms of average segmental signal-to-noise ratio and listening quality based on perceptual evaluation speech quality score.

Computing the proximity operator of the ℓ p norm with 0 < p < 1

Abstract: Sparse modelling with the l p norm of 0 ≤ p ≤ 1 requires the availability of the proximity operator of the l p norm. The proximity operators of the l0 and l1 norms are the well-known hard- and soft-thresholding estimators, respectively. In this study, the authors give a complete study on the properties of the proximity operator of the l p norm. Based on these properties, explicit formulas of the proximity operators of the l1/2 norm and l2/3 norm are derived with simple proofs; for other values of p, an iterative Newton's method is developed to compute the proximity operator of the l p norm by fully exploring the available proximity operators of the l0, l1/2, l2/3, and l1 norms. As applications, the proximity operator of the l p norm with 0 ≤ p ≤ 1 is applied to the l p -regularisation for compressive sensing and image restoration.

Diffusion LMS with component-wise variable step-size over sensor networks

Abstract: In this study, the authors propose a novel component - wise variable step-size (CVSS) diffusion distributed algorithm for estimating a specific parameter over sensor networks. The novelty of the CVSS algorithm is that step-sizes vary from each other on different components at each iteration. They derive the steady-state value of global mean-square deviation (MSD) and relative MSD (RMSD). In the numerical simulations, they compare the proposed CVSS algorithm with several other least mean square (LMS) algorithms. Results show that, when compared with these other algorithms, the CVSS algorithm can effectively reduce steady-state value and speed up convergence rate of RMSD while not sacrificing the convergence rate of MSD. Results also reveal that the proposed CVSS algorithm can achieve reduced difference of steady-state values of relative estimation error on various components.

Introducing new algorithms for realising an FIR filter with less hardware in order to eliminate power line interference from the ECG signal

Abstract: Power line interference (PLI) corrupts biomedical recordings. A notch filter is one of the filters that has been suggested to suppress the fundamental PLI and its harmonics in electrocardiographic recordings. Using finite impulse response (FIR) filters are one of the interesting ways to filter this interference in order to receive a rather pure signal. The frequent use of FIR filters create a field which studies realising an FIR filter and its various methods, which directly deals with the amount of hardware of the filter. In this study, the authors introduce new algorithms to realise FIR filters using less amount of hardware. By authors' definition, the filter is a black box and the authors focus on the quality of the output signal rather than focusing on the quality of frequency response of the filter. The simulation results show that the proposed algorithms remarkably reduces the hardware complexity of the FIR filter for eliminating PLI from the electrocardiogram (ECG) signal.

Polarisation smoothing for coherent source direction finding with multiple-input and multiple-output electromagnetic vector sensor array

Abstract: This study proposes a new polarisation smoothing algorithm with multiple-input and multiple-output (MIMO) electromagnetic vector sensor array to address the problem of coherent source angle estimation in MIMO radar. This algorithm can be summarised as follows: (i) matched filtering for echoes is performed to get virtual MIMO array; (ii) the virtual array is divided into six spatially identical subarrays according to polarisation information offered by electromagnetic vector sensor; and (iii) the six subarrays covariance matrices are processed with weighted smoothing to obtain polarisation smoothing covariance matrix, which can restore the rank loss of the covariance matrix of coherent sources. When compared with spatial smoothing, the proposed algorithm is suitable for spatially arbitrary array configuration, without the price of reducing effective array aperture. Simulation results show that the proposed algorithm substantially outperforms the spatial smoothing algorithm.

Zak transform and uncertainty principles associated with the linear canonical transform

Abstract: Several new results about Zak transform and uncertainty principles in the linear canonical transform (LCT) domains are presented. The results obtained rely mainly on relationship between the LCT and the classical Fourier transform. The findings will likely have potential applications in optics and signal processing.

Two-dimensional autofocus technique for high-resolution spotlight synthetic aperture radar

Abstract: Motion errors are inevitably introduced when data is acquired and considerably degrade the image quality in terms of geometric resolution, radiometric accuracy and image contrast, especially in high-resolution spotlight synthetic aperture radar (SAR) imagery. In this study, the authors present a novel two-dimensional (2D) autofocus algorithm directly inserted into polar format algorithm, which compensates the envelop error and the phase error sequentially. A coarse error correction is first performed by global positioning system or inertial navigation system in the range-compressed domain, then a new envelop compensation strategy, stage-by-stage approach, is designed, obtaining promising results for removing range cell migration after 2D interpolation. Additionally, a weighed contrast enhancement autofocus algorithm based on spatially variant model is developed to compensate for the residual phase error, which remarkably improves the estimation accuracy. The presented algorithm is very robust to deal with substantial errors over a variety of scenes even in conditions of homogenous areas with no prominent point scatterers and enables the utilisation of fast Fourier transform. The experimental results obtained by the proposed algorithm confirm that the analysis extends well to realistic situations.

Multiplicative filtering in the linear canonical transform domain

Abstract: As a generalisation of fractional Fourier transform, Fresnel transform and Fourier transform, the linear canonical transform (LCT) is a four parameter class of integral transform and has been used in many fields of optics and signal processing. In this study, the authors present a model of multiplicative filtering for the band-limited signals in the LCT domain by using the convolution theorem given in the literature. Finally, practical applications of filtering in LCT domain are discussed based on the presented model of multiplicative filtering and results are compared with that of frequency domain filtering and fractional domain filtering. It is found from the simulation results that mean square error is minimum for different values of signal-to-noise ratio in case of LCT domain filtering.

Modified artificial bee colony optimisation based FIR filter design with experimental validation using field-programmable gate array

Abstract: Optimisation based design of finite impulse response (FIR) filters has been an active area of research for quite some time. The various algorithms proposed for FIR filter design aim at meeting a set of desired specifications in the frequency domain. Evolutionary algorithms have been found to be very effective for FIR filter design because of the non-linear, non-differentiable and non-convex nature of the associated optimisation problem. The present work proposes two modified versions of a recently developed evolutionary technique i.e. artificial bee colony (ABC) algorithm for design of FIR filters. The applicability of the proposed approach has been evaluated by comparing its response with conventional reported filter design techniques. The proposed variants of ABC are found to outperform other non-convex algorithms in achieving the desired specifications. In addition to the simulation results, the designed filters have been implemented in hardware using Xilinx-xc7vx330t-3ffg1157 (Virtex-7) field programmable gate array. The hardware implementation allows validation of the proposed techniques for practical filtering applications by considering real time operation parameters.

Kullback–Leibler divergence for interacting multiple model estimation with random matrices

Abstract: The problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance is studied. The system state and the unknown covariance are jointly estimated, where the unknown covariance is modelled as a random matrix according to an inverse-Wishart distribution. For the IMM estimation with random matrices, one difficulty encountered is the combination of a set of weighted inverse-Wishart distributions. Instead of using the moment matching approach, this difficulty is overcome by minimising the weighted Kullback–Leibler divergence for inverse-Wishart distributions. It is shown that a closed-form solution can be derived for the optimisation problem and the resulting solution coincides with an inverse-Wishart distribution. Simulation results show that the proposed filter outperforms the previous work using the moment matching approach.

Outage analysis of OFDM based cognitive radio network with full duplex relay selection

Abstract: In this study, outage performance of orthogonal frequency division multiplexing (OFDM) based underlay cognitive radio (CR) network is analysed. By incorporating full duplex relay selection with amplify and forward relaying strategy, the CR network improves the throughput in the presence of primary user interference. The best relay selection per subcarrier is performed based on the maximum of minimum signal to interference plus noise ratio between source to relay node and relay to destination node. The primary interference signal is modelled as a sparse vector whose non-zero elements follow the Gaussian distribution. Closed form analytical expressions are derived for the end-to-end outage probability of the proposed network and compared with the network operates in half duplex relay selection. It is investigated that the OFDM based CR network with full duplex relay selection achieves higher data rates than the existing CR network. Simulation results are given to validate the derived analytical expressions.

Cramér–Rao bound analysis for joint target location and velocity estimation in frequency modulation based passive radar networks

Abstract: With the wide spread availability and the favourable Doppler resolution, the frequency modulation (FM) commercial radio signals have become attractive for passive radar applications. Passive radar networks using multiple illuminators of opportunity and multichannel receivers have been shown to offer significant performance improvement owing to their advantage of signal and spatial diversities. In this study, the authors compute the joint Cramer–Rao lower bound (CRLB) for the target parameter (delay and Doppler) estimation error utilising FM commercial radio signals as illuminators of opportunity for passive radar network systems, where the non-coherent and coherent processing scenarios are considered. The numerical simulations are provided to show that the joint CRLB is not only a function of the transmitted waveforms but also of the relative geometry between the target and the passive radar networks for both non-coherent and coherent cases. The expressions for joint CRLB are an important performance metric for target parameter estimation in FM-based passive radar networks.