AbstractThe authors consider a quantum radar which operates on the quantum illumination principle. The authors’ attention is focused on its function of target detection in a noisy environment. The role of the optical parametric amplifier (OPA) in detection is first examined by the authors, and a dual‐OPA design for more flexible combination of optimised gains is proposed, resulting in a detector substantially improved in its performance from the normally used 1‐OPA design. Then, the use of the entanglement information in the covariance matrix (CM) between the returned signal and idler beams for detection is considered, and a technique to extract such information is proposed. By employing some statistical relationships between positive definite matrices, the authors come up with a new target detection method. Numerical experiments confirm the superior detection performance of the CM detectors compared to that of the OPA detectors.

In this paper, a novel hyper-rectangle cover theory is developed. Two important concepts, the cover order and the cover length, are introduced. We construct a specific échelon form of the matrix in the same manner as that employed to determine the rank of the matrix to obtain the cover order of any given matrix. Using the properties of the cover order, we obtain the necessary and sufficient conditions for the existence and uniqueness of the solutions for linear equations system with non-negativity constraints on variables for both homogeneous and nonhomogeneous cases. In addition, we apply the cover theory to analyze some typical problems in linear algebra and optimization with non-negativity constraints on variables, including linear programming (LP) problems and non-negative least squares (NNLS) problems. For LP problems, the three possible behaviours of the solutions are studied through cover theory. On the other hand, we develop a method to obtain the cover length of the covered variable. In this process, we discover the relationship between the cover length determination problem and the NNLS problem. This enables us to obtain an analytical optimal value for the NNLS problem.

In this paper, we investigate the design of an optimal non-orthogonal multiple access (NOMA) transmission scheme with finite alphabet inputs for a typical two-user uplink wireless communication system, in which channel state information are available at both transmitters and receivers, and each terminal equips a single antenna. For such a system, two users utilize four quadrature amplitude modulation constellations to transmit their data information to a common base station and the receiver employs an optimal maximum likelihood detector for jointly estimating the two users' transmitted signals. We consider the design of a pair of scalar beamformers for these two users such that the minimum Euclidean distance of the received sum-constellation is maximized subject to each individual user power constraint. A closed-form optimal solution and the corresponding optimal sum constellation are attained. Numerical simulations verify that when signal to noise ratio is slightly high, our proposed NOMA scheme outperforms other existing NOMA designs for the same system.

Quantum illumination (QI) is a technique exploiting the quantum entanglement between the transmitted signal and the idler to enhance the detection performance of a quantum radar over the classical radar. Here, we propose the double optical parameter amplifier (OPA) detector for QI so that the effect of entanglement between the idler and the returned signal beams is maximized. We show here how even when a weak returned signal is embedded in a large background noise, the probability of detection can be significantly increased.

A design technique is developed for the probing signals of a Multi-Input Multi-Output (MIMO) radar. The concentration of the energy of the signal in its essential duration and essential bandwidth is achieved through the use of a class of time-frequency concentrated functions called the WLJ functions as the synthesizing signal set. The goal is to design a signal vector having a pre-specified desired covariance (CoV) matrix while ensuring that the side-lobes of the ambiguity functions are small. Since CoV matrices are structurally constrained, they form a manifold in the signal space. Hence, we argue that the difference between these matrices should not be measured in terms of the conventional Euclidean distance (ED); rather, the distance should be measured along the surface of the manifold, that is, in terms of a Riemannian distance (RD). In either case, the signal optimisation problem is non-convex in the design variables, involving, respectively, a quartic and a square-root objective function. An efficient algorithm based on successive convex approximation is developed in which the original non-convex problems are transformed so that they can be approximated by a convex quadratically constrained quadratic problem at each stage, resulting in good approximate solutions. Comparing the designs using ED and RD, we find that the convergence of the algorithm can be significantly faster when optimising over the manifold (RD) than when optimising over the whole space (ED). More importantly, for tight constraints, the use of RD yields solutions which satisfy the constraints far better than the use of ED.

A fundamental design problem for massive machine-type communication (mMTC) networks is efficient data collection from the machine-type communication devices (MTCDs), which is the subject of investigation in this paper. An unmanned aerial vehicle (UAV) being deployed to facilitate data collection from MTCDs is considered. Taking into account the limited energy for both the UAV and MTCDs, a problem of minimizing the total energy consumption subject to completion of the data collection tasks by planning the UAV trajectory is formulated. A Global Optimum (GOP) trajectory can be obtained for a UAV serving all the MTCDs simultaneously if the UAV’s flying altitude is larger than $\sqrt {3}$ times its maximum service radius. However, communication energy efficiency drops as the UAV’s altitude increases. Clustering-based service strategies and dynamic trajectory planning algorithms, namely clustered GOP (C-GOP) and clustered particle swarm optimization (C-PSO), are proposed to overcome the above issue. The data collection efficiency is maximized by locating the optimal UAV hovering point for each serving MTCD cluster, which is dynamically adjusted with the UAV hovering position until all MTCDs are served. It is shown that the GOP is the optimal strategy for a small number of MTCDs concentrated in a small area. While for large number of MTCDs or task area, the clustered algorithms are more favorable from energy efficiency, complexity and scalability perspectives.

In this paper, we are interested in a noncoherent MIMO system with a single transmitter having two antennas communicating with a receiver having at least two antennas over a Rayleigh fading channel. It is assumed that the channel coefficients keep constant during four successive time slots, after which they become new independent value. For such a system, we propose a novel parameterized coding method to systematically and efficiently design an optimal unitary constellation by optimizing both noncoherent diversity and coding gains with the maximum likelihood (ML) receiver. We first characterize the optimal structure for each parameter when the number of bits allocated for each parameter space is fixed and then, find an optimal bit allocation for each parameter space subject to a total transmission bits constraint by further maximizing the coding gain. Computer simulations demonstrate that our proposed coding scheme significantly outperforms the traditional methods in literature for the same noncoherent system.

In this paper, user-centric clustering for uplink coordinated multi-point (CoMP) processing in a multi-cell environment is investigated such that the inter-cell interference (ICI) within cluster can be effectively eliminated. Although full cooperation among all cells in the network can achieve the highest cooperative gain in terms of ICI cancellation, such scheme consumes too much cooperation resources in the form of backhaul and processing power. In addition, from the quality-of-service (QoS) provisioning perspective, different users may have different demand for CoMP processing to guarantee its QoS. By considering the tradeoff between cooperative gain and cost, a cluster size minimization problem subject to QoS constraints is formulated to achieve dynamic user-centric clustering for uplink CoMP. As the constrained 0-1 integer programming problem depends largely on the intra-cluster interference weight, we propose a subgradient-based algorithm to solve the relaxed problem. Simulation results demonstrate that the proposed clustering algorithm achieves both the smallest cluster size and the best QoS provisioning for cell-edge users in terms of outage probability in the comparison with existing clustering algorithms.

We propose to use the power spectral density (PSD) matrices of the received signals of a multi-sensor system as the feature of processing. PSD matrices have structural constraints and they form a manifold in signal space. We introduce two new Riemannian distance (RD) measures on the PSD matrix manifold and developed algorithms to locate the means and medians of PSD matrices in terms of these RD. These concepts are then applied to the detection of narrow-band sonar signals in noise and the results are encouraging.

We consider the problem of designing probing signals for a Multi-Input Multi-Output (MIMO) radar. The goal is to design a signal vector with a desired covariance while ensuring the side-lobes of the ambiguity functions are small. We will also consider cases in which a bandwidth constraint is placed on the signal. Since covariance matrices are structurally constrained, they form a manifold in the signal space. Hence, we argue that the difference between these matrices should not be in terms of the conventional Euclidean distance (ED), rather, the distance should be measured along the surface of the manifold, i.e., in terms of Riemannian distance (RD). In either case, the optimization problem is quartic in the design variables. An efficient algorithm based on iterative convex quadratic optimization is developed and is effective in producing good solutions. In addition, we show that by optimizing over the manifold, the number of iterations can be significantly reduced in comparison to optimizing in the Euclidean space. Several orthonormal signal sets, including the Walsh functions, the cosine functions and the WLJ functions, are employed to design the transmission signal vector, giving us different feasible regions in the optimization. It is observed that the WLJ othornormal basis yields feasible solutions under tight time-frequency constraints.

This paper develops a power allocation strategy for multiple networks of Poisson-distributed single-antenna nodes that share the available spectrum in a spectrum underlay scenario. This strategy aims to maximize the overall throughput obtained by sharing the spectrum while limiting the degradation of the successful transmission probability of each network. In its original form, this joint power allocation problem is difficult to solve. However, we demonstrate that the problem can be transformed into a convex optimization formulation, which can be efficiently solved. Furthermore, we obtain a quasi-closed-form solution that has a water-filling interpretation by analyzing the optimality conditions. Numerical results indicate that, when a spectrum-sharing scheme employs the proposed optimal strategy of power allocation, the throughput substantially improves over that obtained by exclusively allocating the spectrum to the primary network. Moreover, when the number of spectrum-sharing networks increases, the enhancement is significant, being up to the limit imposed by the maximum allowable degradation in the performance of each network.

In this paper, joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation for bistatic multiple-input-multi-output (MIMO) radar in an unknown spatially correlated noise environment is investigated. The signal model is based on the assumption that the waveforms are transmitted by two separated subarrays having M 1 and M 2 sensors and received by two separated subarrays having N 1 and N2 sensors, respectively. The received data are pulse-compressed using a matching matrix consisting of M=M 1 +M 2 orthogonally transmitted waveforms. The joint covariance matrix of unknown correlated noise is analyzed. A novel algorithm is proposed by jointly estimating the DOD and DOA with transmitter and receiver subarrays in unknown noise. The joint estimation algorithm is based on the canonical correlation decomposition (CCD) and exploits the shift-invariance properties in the Kronecker product structure of each column of the various steering matrices. The estimated DOA and DOD can be automatically paired correspondingly. In addition, the formulas of stochastic Cramer-Rao bounds (CRB) for DOD and DOA estimation are derived. Simulations show that our method can effectively improve the performance of estimation in unknown correlated noise environments and is insensitive to having different noise environments in the two subarrays.

Estimation of covariance matrices is a common problem in signal processing applications. Commonly applied techniques based on the cost optimization (e.g. maximum likelihood estimation) result in an unconstrained estimation in which the positive definite nature of covariance matrices is ignored. Consequently this may result in accurate estimation of the covariance matrix which may affect overall performance of the system. In this paper we propose to estimate the covariance matrix using Frechet mean which ensures that the estimate also has positive definite structure. We demonstrate the applicability of the proposed technique on both estimation and classification accuracy using numerical simulations. In addition we discuss some of the preliminary results we obtained by applying our techniques to high content cell imaging data set.

We consider the problem of narrow-band signal detection in a passive sonar environment. The classical method employs a fast Fourier Transform (FFT) delay-sum beamformer in which the feature used in detection is the output of the FFT spectrum analyser in each frequency bin. This is compared to a locally estimated mean noise power to establish a likelihood ratio test (LRT). In this paper, we suggest to use the power spectral density (PSD) matrix of the spectrum analyser output as the feature for detection due to the additional cross-correlation information contained in such matrices. However, PSD matrices have structural constraints and describe a manifold in the signal space. Thus, instead of the widely used Euclidean distance (ED), we must use the Riemannian distance (RD) on the manifold for measuring the similarity between such features. Here, we develop methods for measuring the Fréchet mean of noise PSD matrices and optimum weighting matrices for measuring similarity of noise and signal PSD matrices. These are then used to develop a decision rule for the detection of narrow-band sonar signals using PSD matrices. The results yielded by the new detection method are very encouraging.

The multiple-input and multiple-output (MIMO) channel model is very useful for the presentation of a wide range of wireless communication systems. This paper addresses the joint design of a precoder and a receiver for a point-to-point MIMO channel model in a scenario in which perfect channel state information (CSI) is available at both ends. We develop a novel framework for the dual transmission-reception process. Under the proposed framework, the receiver decomposes the channel matrix by using a block QR decomposition, where Q is a unitary matrix and R is a block upper triangular matrix. The optimal maximum likelihood (ML) detec- tion process is employed within each diagonal block of R. Then, the detected block of symbols is substituted and subtracted sequentially according to the block QR decomposition based successive cancellation. On the transmitting end, the expression of probability of error based on ML detection is chosen as the design criterion to formulate the precoder design problem. This paper presents a design of MIMO transceivers in the particular case of having 4 transmitting and 4 receiving antennas with full CSI knowledge on both sides. In addition, a closed-form expression for the optimal precoder matrix is obtained for channels satisfying certain conditions.

The direct application of orthogonal space-time block coding (OSTBC) for multiple input and multiple output (MIMO) systems to distributed cooperative relay networks makes the equivalent channel matrix for maximum likelihood (ML) detection lose its orthogonality. Hence, this paper proposes a new design that makes the channel matrix be orthogonally distributed (OD) for a suboptimal symbol-by-symbol detector (SBSD). Using ODSTBC, an asymptotic symbol error probability (SEP) formula with SBSD is derived, showing the optimal diversity gain function is achieved. In addition, two kinds of ODSTBC designs for the distributed relay networks are presented, which interestingly renders that SBSD is equivalent to the ML detector. Numerical results verify the diversity analysis and indicate competitive error performance to currently available orthogonal distributed STBC designs with much simpler complexity.

This paper develops a power control strategy for multiple spectrum-sharing networks of single antenna nodes in a spectrum underlay scenario. A distinguishing feature of the proposed strategy is that it requires only knowledge of the spatial distribution of the nodes, rather than instantaneous channel state information. The strategy seeks to maximize a weighted sum of the throughput of each network while guaranteeing specified successful transmission probabilities. In its native form, this joint power allocation problem is difficult to solve. However, we show that the problem can be transformed into a convex optimization formulation that can be efficiently solved using general purpose tools. Furthermore, we analyze the optimality conditions and obtain a quasi-closed form solution reminiscent of waterfilling. Numerical results demonstrate that spectrum sharing employing the proposed optimal power yields a substantial throughput gain over allocating the spectrum to a single network.

Signal classification is an important issue in many branches of science and engineering. In signal classification, a feature of the signals is often selected for similarity comparison. A distance metric must then be established to measure the dissimilarities between different signal features. Due to the natural characteristics of dynamic systems, the power spectral density (PSD) of a signal is often used as a feature to facilitate classification. We reason in this paper that PSD matrices have structural constraints and that they describe a manifold in the signal space. Thus, instead of the widely used Euclidean distance (ED), a more appropriate measure is the Riemannian distance (RD) on the manifold. Here, we develop closed-form expressions of the RD between two PSD matrices on the manifold and study some of the properties. We further show how an optimum weighting matrix can be developed for the application of RD to signal classification. These new distance measures are then applied to the classification of electroencephalogram (EEG) signals for the determination of sleep states and the results are highly encouraging.

We examine the robust downlink beamforming design from the point of outage probability constraint. We further reason that since the estimated downlink channel correlation (DCC) matrices form a manifold in the signal space, the estimation error should be measured in terms of Riemannian distance (RD) instead of the commonly used Euclidean distance (ED). Applying this concept of measure to our design constraint, we transform the design problem into a convex optimization which can be solved efficiently by standard methods. Simulation results show that the performance of our design is superior to those of other robust beamformers recently developed.

In this paper we take a new perspective on the worst case robust multiuser downlink beamforming problem with imperfect second order channel state information at the transmitter. Recognizing that all channel covariance matrices form a Riemannian manifold, we propose to use a measure properly defined along this manifold in order to model the set of mismatched channel covariance matrices for which robustness shall be guaranteed. This leads to a new robust beamforming problem formulation for which a convex approximation is derived. Simulation results show a dramatically improved performance of the proposed scheme, both in terms of transmission power and constraint satisfaction, as compared to the previous methods.