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In this paper, we consider the problem of joint secure routing and transmit power optimization for a multi-hop ad-hoc network under the existence of randomly distributed eavesdroppers following a Poisson point process (PPP). Secrecy messages are delivered from a source to a destination through a multi-hop route connected by multiple legitimate relays in the network. Our goal is to minimize the end-to-end connection outage probability (COP) under the constraint of a secrecy outage probability (SOP) threshold, by optimizing the routing path and the transmit power of each hop jointly. We show that the globally optimal solution could be obtained by a two-step procedure where the optimal transmit power has a closed-form and the optimal routing path can be found by Dijkstra's algorithm. Then a friendly jammer with multiple antennas is applied to enhance the secrecy performance further, and the optimal transmit power of the jammer and each hop of the selected route is investigated. This problem can be solved optimally via an iterative outer polyblock approximation with one-dimension search algorithm. Furthermore, suboptimal transmit powers can be derived using the successive convex approximation (SCA) method with a lower complexity. Simulation results show the performance improvement of the proposed algorithms for both non-jamming and jamming scenarios, and also reveal a non-trivial trade-off between the numbers of hops and the transmit power of each hop for secure routing., Comment: 13 pages, 10 figures, to be published in IEEE Transactions on Communications

Millimeter wave offers a sensible solution to the capacity crunch faced by 5G wireless communications. This paper comprehensively studies physical layer security in a multi-input single-output (MISO) millimeter wave system where multiple single-antenna eavesdroppers are randomly located. Concerning the specific propagation characteristics of millimeter wave, we investigate two secure transmission schemes, namely maximum ratio transmitting (MRT) beamforming and artificial noise (AN) beamforming. Specifically, we first derive closed-form expressions of the connection probability for both schemes. We then analyze the secrecy outage probability (SOP) in both non-colluding eavesdroppers and colluding eavesdroppers scenarios. Also, we maximize the secrecy throughput under a SOP constraint, and obtain optimal transmission parameters, especially the power allocation between AN and the information signal for AN beamforming. Numerical results are provided to verify our theoretical analysis. We observe that the density of eavesdroppers, the spatially resolvable paths of the destination and eavesdroppers all contribute to the secrecy performance and the parameter design of millimeter wave systems., Comment: 14 pages, 12 figures, accepted by the IEEE Transactions on Wireless Communications

In the fifth generation era, the pervasive applications of Internet of Things and massive machine-type communications have initiated increasing research interests on the backscatter wireless powered communication (B-WPC) technique due to its ultra high energy efficiency and low cost. The ubiquitous B-WPC network is characterized by nodes with dynamic spatial positions and sporadic short packets, of which the performance has not been fully investigated. In this paper, we give a comprehensive analysis of a multi-antenna B-WPC network with sporadic short packets under a stochastic geometry framework. By exploiting a time-space Poisson point process model, the behavior of the network is well captured in a decentralized and asynchronous transmission way. We then analyze the energy and information outage performance in the energy harvest and backscatter modulation phases of the backscatter network, respectively. The optimal transmission slot length and division are obtained by maximizing the network-wide spatial throughput. Moreover, we find an interesting result that there exists the optimal tradeoff between the durations of the energy harvest and backscatter modulation phases for spatial throughput maximization. Numerical results are demonstrated to verify our analytical findings and show that this tradeoff region gets shrunk when the outage constraints become more stringent., Comment: 14 pages, 8 figures, accepted by the IEEE Internet of Things Journal

This work proposes a novel location-based multi-group multicast framework which is termed as non-orthogonal multiple access (NOMA) assisted multi-region geocast. This novel spectrum sharing framework exploits the NOMA technology to realize the simultaneous delivery of different messages to different user groups characterized by different geographical locations. The essence of the proposed framework is that the geographical information of user groups unites NOMA and multi-group multicast to enhance the spectral efficiency (SE) and the energy efficiency (EE) of wireless transmissions. Specifically, we investigate the downlink beamforming design of the proposed framework in multiple-input single-output (MISO) settings. The decoding strategy for NOMA is designed and guaranteed by users' geographical information and required quality of service (QoS). The majorization and minimization (MM) algorithm is exploited to solve the non-convex and intractable problems therein. Comprehensive numerical experiments are further provided to show that NOMA holds tremendous promise but also limitations in terms of SE and EE, compared with spatial division multiple access (SDMA) and orthogonal multiple access (OMA).

In this letter, a novel Golden-Hadamard codebook (GHC) scheme is proposed to improve the performance of the traditional precoded Alamouti coding for multiple-input and single-output systems. Although the traditional discrete Fourier transform codebook (DFTC) performs satisfactorily with Alamouti coding and offers numerous benefits for the Rayleigh fading channel, this scheme inherently generates huge codeword distortion, which leads to a lower minimum chordal distance (MCD). Furthermore, the uncertain format of all prior versions of codebooks results in poorer minimum determinant (MD) values. Hence, the proposed GHC scheme successfully deals with the issues of traditional DFTC to achieve a better codebook format that completely overcome both MCD and MD problems. The effectiveness of the proposed GHC scheme is confirmed, in terms of bit-error-rate through Monte Carlo simulations., Comment: 4 pages,4 figures,2 table, Published (Early Access) in IEEE Communications Letters

This paper studies physical layer security in a wireless ad hoc network with numerous legitimate transmitter-receiver pairs and eavesdroppers. A hybrid full-/half-duplex receiver deployment strategy is proposed to secure legitimate transmissions, by letting a fraction of legitimate receivers work in the full-duplex (FD) mode sending jamming signals to confuse eavesdroppers upon their information receptions, and letting the other receivers work in the half-duplex mode just receiving their desired signals. The objective of this paper is to choose properly the fraction of FD receivers for achieving the optimal network security performance. Both accurate expressions and tractable approximations for the connection outage probability and the secrecy outage probability of an arbitrary legitimate link are derived, based on which the area secure link number, network-wide secrecy throughput and network-wide secrecy energy efficiency are optimized respectively. Various insights into the optimal fraction are further developed and its closed-form expressions are also derived under perfect self-interference cancellation or in a dense network. It is concluded that the fraction of FD receivers triggers a non-trivial trade-off between reliability and secrecy, and the proposed strategy can significantly enhance the network security performance., Comment: Journal paper, double-column 12 pages, 9 figures, accepted by IEEE Transactions on Wireless Communications, 2017

With the recent emergence of 5G era, heterogeneous cellular networks (HCNs) have invoked a popular research interest. In this paper, we provide a comprehensive analysis for multiantenna transmissions in a multi-tier downlink HCN. We first propose a reliability-oriented threshold-based mobile association policy, where each user connects to the strongest base station from which this user can obtain the largest truncated long-term received power. Under our mobile association policy, we derive analytical expressions for the exact outage probability of an arbitrary randomly located user, along with computationally convenient lower and upper bounds. Asymptotic analysis on the outage probability shows that introducing a large access threshold into mobile association significantly decreases the outage probability. We further investigate the spectrum efficiency and the energy efficiency of the HCN. Our theoretic analysis and numerical validations show that both the spectrum and energy efficiencies can be improved by properly choosing the access threshold., Comment: Journal paper, double column, 13 pages, 9 figures, accepted to appear on IEEE Transactions on Communications

In this paper, we study the benefits of full-duplex (FD) receiver jamming in enhancing the physical-layer security of a two-tier decentralized wireless network with each tier deployed with a large number of pairs of a single-antenna transmitter and a multi-antenna receiver. In the underlying tier, the transmitter sends unclassified information, and the receiver works in the halfduplex (HD) mode receiving the desired signal. In the overlaid tier, the transmitter deliveries confidential information in the presence of randomly located eavesdroppers, and the receiver works in the FD mode radiating jamming signals to confuse eavesdroppers and receiving the desired signal simultaneously. We provide a comprehensive performance analysis and network design under a stochastic geometry framework. Specifically, we consider the scenarios where each FD receiver uses single- and multi-antenna jamming, and analyze the connection probability and the secrecy outage probability of a typical FD receiver by providing accurate expressions and more tractable approximations for the two metrics. We further determine the optimal deployment of the FD-mode tier in order to maximize networkwide secrecy throughput subject to constraints including the given dual probabilities and the network-wide throughput of the HD-mode tier. Numerical results are demonstrated to verify our theoretical findings, and show that network-wide secrecy throughput is significantly improved by properly deploying the FD-mode tier., Comment: Journal paper, double column, 15 pages, 11 figures, accepted to appear on IEEE Transactions on Wireless Communications

This letter proposes a novel dual user selection scheme for uplink transmission with multiple users, where a jamming user and a served user are jointly selected to improve the secrecy performance. Specifically, the jamming user transmits jamming signal with a certain rate, so that the base station (BS) can decode the jamming signal before detecting the secret information signal. By carefully selecting the jamming user and the served user, it makes the eavesdropper decode the jamming signal with a low probability meanwhile the BS can achieve a high receive signal-to-noise ratio (SNR). Therefore, the uplink transmission achieves the dual secrecy improvement by jamming and scheduling. It is shown that the proposed scheme can significantly improve the security of the uplink transmission., Comment: journal paper, double column, 4 pages, 1 figure, accepted for publication on IEEE Communications Letters

To improve the sum-rate (SR) of the dual-hop relay system, a novel two-stage power allocation scheme with non-orthogonal multiple access (NOMA) is proposed. In this scheme, after the reception of the superposition coded symbol with a power allocation from the source, the relay node forwards a new superposition coded symbol with another power allocation to the destination. By employing the maximum ratio combination (MRC), the destination jointly decodes the information symbols from the source and the relay. Assuming Rayleigh fading channels, closed-form solution of the ergodic SR at high signal-to-noise ratio (SNR) is derived and a practical power allocation is also designed for the proposed NOMA scheme. Through numerical results, it is shown that the performance of the proposed scheme is significantly improved compared with the existing work.

The heterogeneous cellular network (HCN) is a promising approach to the deployment of 5G cellular networks. This paper comprehensively studies physical layer security in a multi-tier HCN where base stations (BSs), authorized users and eavesdroppers are all randomly located. We first propose an access threshold based secrecy mobile association policy that associates each user with the BS providing the maximum \emph{truncated average received signal power} beyond a threshold. Under the proposed policy, we investigate the connection probability and secrecy probability of a randomly located user, and provide tractable expressions for the two metrics. Asymptotic analysis reveals that setting a larger access threshold increases the connection probability while decreases the secrecy probability. We further evaluate the network-wide secrecy throughput and the minimum secrecy throughput per user with both connection and secrecy probability constraints. We show that introducing a properly chosen access threshold significantly enhances the secrecy throughput performance of a HCN., Comment: two-column 15 pages, 12 figures, accepted for publication in IEEE Transactions on Communications

This study investigates the mean capacity of multiple-input multiple-output (MIMO) systems for spatially semi-correlated flat fading channels. In reality, the capacity degrades dramatic due to the channel covariance (CC) when correlations exist at the transmitter or receiver or on both sides. Most existing works have so far considered the traditional channel covariance matrices that have not been entirely constructed. Thus, we propose an iterative channel covariance (ICC) matrix using a matrix splitting (MS) technique with a guaranteed zero correlations coefficient in the case of the downlink correlated MIMO channel, to maximize the mean capacity. Our numerical results show that the proposed ICC method achieves the maximum channel gains with high signal-to-noise ratio (SNR) scenarios., Comment: 4

Differential spatial modulation (DSM) was recently proposed to overcome the challenge of channel estimation in spatial modulation (SM). In this letter, we propose a gray code order of antenna index permutations for DSM. To facilitate the implementation, the well-known Trotter-Johnson ranking and unranking algorithms are adopted, which results in similar computational complexity to the existing DSM that uses the lexicographic order. The coding gain achieved by the proposed gray code order over the existing lexicographic order is also analyzed and verified via simulations, which reveals a maximum of about 1.2dB for the case of four transmit antennas. Based on the gray coding framework, we further propose a diversity-enhancing scheme named intersected gray (I-gray) code order for DSM, where the permutations of active antenna indices are selected directly from the odd (even) positions of the full permutations in the gray code order. From analysis and simulations, it is shown that the I-gray code order can harvests an additional diversity order at the expense of only one information bit loss for each transmission with respect to the gray code order., Comment: This paper has been withdrawn by the author due to a error in equation 2

In this paper, we investigate the optimization problem of joint source and relay beamforming matrices for a twoway amplify-and-forward (AF) multi-input multi-output (MIMO) relay system. The system consisting of two source nodes and two relay nodes is considered and the linear minimum meansquare- error (MMSE) is employed at both receivers. We assume individual relay power constraints and study an important design problem, a so-called determinant maximization (DM) problem. Since this DM problem is nonconvex, we consider an efficient iterative algorithm by using an MSE balancing result to obtain at least a locally optimal solution. The proposed algorithm is developed based on QL, QR and Choleskey decompositions which differ in the complexity and performance. Analytical and simulation results show that the proposed algorithm can significantly reduce computational complexity compared with their existing two-way relay systems and have equivalent bit-error-rate (BER) performance to the singular value decomposition (SVD) based on a regular block diagonal (RBD) scheme.

In this paper we introduce modular symmetric designs and use them to study the existence of Hadamard matrices modulo 5. We prove that there exist 5-modular Hadamard matrices of order n if and only if n != 3, 7 (mod 10) or n != 6, 11. In particular, this solves the 5-modular version of the Hadamard conjecture., Comment: 7 pages, submitted to JCD

In this paper, after analyzing the reasons of poor generalization and overfitting in neural networks, we consider some noise data as a singular value of a continuous function - jump discontinuity point. The continuous part can be approximated with the simplest neural networks, which have good generalization performance and optimal network architecture, by traditional algorithms such as constructive algorithm for feed-forward neural networks with incremental training, BP algorithm, ELM algorithm, various constructive algorithm, RBF approximation and SVM. At the same time, we will construct RBF neural networks to fit the singular value with every error in, and we prove that a function with jumping discontinuity points can be approximated by the simplest neural networks with a decay RBF neural networks in by each error, and a function with jumping discontinuity point can be constructively approximated by a decay RBF neural networks in by each error and the constructive part have no generalization influence to the whole machine learning system which will optimize neural network architecture and generalization performance, reduce the overfitting phenomenon by avoid fitting the noisy data.

The partial interference cancellation (PIC) group decoding has recently been proposed to deal with the decoding complexity and code rate trade-off on the basis of space-time block code (STBC) design criterion when full diversity is achieved. It provides a framework to arrange the rate-complexity-performance tradeoff by choosing a suitable size of information symbol groups. In this paper, a simple design of a linear dispersive space-time-frequency (STF) code is proposed with a design criterion to achieve high rate for frequency-selective channels in terms of multipath when the PIC group decoding is applied at receiver. With an appropriate grouping scheme as well as the PIC group decoding, the proposed STF code is shown to obtain the similar diversity gain as the maximum likelihood (ML) decoding, namely full-dimensional sphere decoding, but have a low decoding complexity. It seems as an intermediate decoding between the ML receiver and zero-forcing (ZF) receiver. The proposed grouping design criterion for the PIC group decoding to achieve full diversity deploying the orthogonal-frequency-division multiplexing (OFDM) technique is also an intermediate condition between the loosest ML full rank criterion of codewords and the strongest ZF linear independence condition of the column vectors for the equivalent frequency-selective channel matrix. It can achieves full diversity with the PIC group decoding for any number of sub-carriers and the data rate can be made high. Several code design examples are illustrated for the feasibility of this coding scheme. Simulation results show that the proposed STF code can well address the rate-performance-complexity tradeoff of the multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) communication system., Comment: This paper has been withdrawn by the author due to a crucial sign error

The average conditional entropy of the key given the message and its corresponding cryptogram, H(K|M,C), which is reffer as a key appearance equivocation, was proposed as a theoretical measure of the strength of the cipher system under a known-plaintext attack by Dunham in 1980. In the same work (among other things), lower and upper bounds for H(S}_{M}|M^L,C^L) are found and its asymptotic behaviour as a function of cryptogram length L is described for simple substitution ciphers i.e. when the key space S_{M} is the symmetric group acting on a discrete alphabet M. In the present paper we consider the same problem when the key space is an arbitrary subgroup K of S_{M} and generalize Dunham's result., Comment: 3 pages, typos corrected, submitted to IEEE Transactions on Information Theory

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

By making use of the generalized concept of orthogonality in Latin squares, certain t-partite graphs have been constructed and a suggestion for a net work system and some applications have been made.

Some binary matrices like (1,-1) and (1,0) were studied by many authors like Cohn, Wang, Ehlich and Ehlich and Zeller, and Mohan, Kageyama, Lee, and Gao. In this recent paper by Mohan et al considered the M-matrices of Type I and II by studying some of their properties and applications. In the present paper they discussed the M-matrices of Type III, and studied their properties and applications. They gave some constructions of SPBIB designs and some corresponding M-graphs, which are being constructed by it. This is the continuation of our earlier research work in this direction, and these papers establish the importance of non-orthogonal matrices as well., Comment: 12 pages, one figure

An arrangement of s elements in s rows and s columns, such that no element repeats more than once in each row and each column is called a Latin square of order s. If two Latin squares of the same order superimposed one on the other and in the resultant array if each ordered pair occurs once and only once then they are called othogonal Latin Squares. A frequency square is an nxn matrix, such that each element from the list of n elements, occurs t times in each row and in each column. These two concepts lead to a new third concept called as t orthogonal latin squares, where from a set of m orthogonal Latin squares, if t orthogonal Latin squares are superimposed and each ordered t tuple in the resultant array occurs once and only once then it is t othogonal Latin square. In this paper it is proposed to construct such t othogonal latin squares, Comment: 29 pages

The Mn-matrix was defined by Mohan [20] in which he has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [5],Wang [33], Ehrlich [8] and Ehrlich and Zeller[9]. But in this paper, while giving some resemblances of this matrix with Hadamard matrix, and by naming it as M-matrix, we show how to construct partially balanced incomplete block (PBIB) designs and some regular bipartite graphs by it. We have considered two types of these M- matrices. Also we will make a mention of certain applications of these M-matrices in signal and communication processing, and network systems and end with some open problems., Comment: 21 pages,3 figures