Two direct sampling correlator-type receivers for differential chaos shift keying (DCSK) communication systems under frequency non-selective fading channels are proposed. These receivers operate based on the same hardware platform with different architectures. In the first scheme, namely sum-delay-sum (SDS) receiver, the sum of all samples in a chip period is correlated with its delayed version. The correlation value obtained in each bit period is then compared with a fixed threshold to decide the binary value of recovered bit at the output. On the other hand, the second scheme, namely delay-sum-sum (DSS) receiver, calculates the correlation value of all samples with its delayed version in a chip period. The sum of correlation values in each bit period is then compared with the threshold to recover the data. The conventional DCSK transmitter, frequency non-selective Rayleigh fading channel, and two proposed receivers are mathematically modelled in discrete-time domain. The authors evaluated the bit error rate performance of the receivers by means of both theoretical analysis and numerical simulation. The performance comparison shows that the two proposed receivers can perform well under the studied channel, where the performances get better when the number of paths increases and the DSS receiver outperforms the SDS one.

An estimation method of pseudo-random (PN) codes in the periodic long code direct sequence spread spectrum signals using a pair of spreading code and scrambling code [i.e. long scrambling code direct sequence spread spectrum (LSC-DSSS)] is investigated in this study. Via the investigation of properties of triple correlation function (TCF) of m-sequences, the existence of common peaks in the TCFs of different m-sequences is proved, and the corresponding relationship between common peaks and primitive polynomials is further investigated. Four theorems are proposed as supplements of triple correlation theory and a novel estimation algorithm of the PN codes in LSC-DSSS signals is put forward on the basis of the theorems. With certain carrier frequency and chip rate of spreading code, this algorithm first eliminates the influence of information codes through delay-and-multiply operation. Then the TCF of signal is calculated, and the two PN codes in signal are successfully estimated finally by searching and using the common peak coordinates in the TCF. Simulation results show that the proposed algorithm exhibits excellent performance in estimating PN codes in LSC-DSSS signals.

Energy efficiency is a major issue in the energy-constrained wireless sensor network to ensure longer battery life. In this study, minimisation of total energy per bit for multi-hop decode-and-forward network employing M-ary quadrature amplitude modulation is considered. An average bit error rate (ABER) requirement at the destination over an independent Rayleigh fading channel is assumed. A realistic energy model is considered. The authors have proposed joint optimisation of constellation size, energy allocation per bit and relay location assuming fixed end-to-end distance. The authors have considered two scenarios: one, that each hop employs the same constellation size per hop and two, it adapts independently to take different constellation size. A novel solution is implemented following least square method to find the approximate closed-form solution of the optimal constellation size, which otherwise would not have been possible. It is observed that joint optimisation technique where the constellation size adapts independently per hop outperforms the one where the constellation size is same. Least amount of total energy is consumed per bit for balanced link. Finally, the analysis shows that for a realistic energy model, the dual hop network provides significant energy saving of 58% at 10 − 4 ABER over multi-hop network with four hops.

Selected mapping (SLM) works effectively in peak-to-average power ratio reduction for the single-carrier frequency-division multiple access (SC-FDMA) system. However, the need for side information (SI) transmission results in data rate loss and increase of the system complexity. To avoid explicit SI transmission for SLM-based SC-FDMA systems, an SI embedding and detection scheme is proposed by exploiting the block pilot symbols. Specifically, to enable SI embedding, the authors propose to represent the SI index for each data symbol in the subframe by a location set of some selected subcarriers in the block pilot symbol. For SI detection, an optimal pilot-aided maximum-likelihood SI detector is presented. As a low-complexity alternative, a suboptimal log-likelihood ratio SI detector is also proposed. In addition, the authors provide theoretical analysis of SI detection error rate and discuss the effect of the proposed scheme on channel estimation. Simulation results show that, in SLM-based SC-FDMA systems, the proposed scheme significantly outperforms existing methods in terms of both SI detection and bit error rate (BER) and achieves the same BER performance as its counterpart with perfect SI.

The authors study the performance of protograph low-density parity-check (LDPC) codes over two-dimensional (2D) intersymbol interference (ISI) channels in this study. To begin with, the authors propose a modified version of finite-length (FL) extrinsic information transfer (EXIT) algorithm so as to facilitate the convergence analysis of protograph codes. Exploiting the FL-EXIT analyses, the authors observe that the protograph codes optimised for 1D ISI channels, e.g. the 1D-ISI protograph code, cannot maintain their advantages in the 2D-ISI scenarios. To address this problem, the authors develop a simple design scheme for constructing a family of rate-compatible improved protograph (RCIP) codes particularly for 2D-ISI channels, which not only outperform the 1D-ISI protograph code, but also are superior to the regular column-weight-3 code and optimised irregular LDPC codes in terms of the convergence speed and error performance. More importantly, such RCIP codes benefit from relatively lower error-floor as well as linear encoding and fast decoding. Thanks to these advantages, the proposed RCIP codes stand out as better alternatives in comparison with other error-correction codes for ultra-high-density data storage systems.

In this study, the authors focus on the downlink resource allocation to optimise energy-efficiency (EE) of orthogonal frequency division multiplexing-based cognitive heterogeneous network (HetNet), where network service providers operate multi-radio access technologies. A more practical case is considered, in which imperfect channel state information (CSI) is available for wireless channels between secondary base stations and secondary users (SUs), primary users (PUs). Since imperfect CSI may result in outage in secondary networks and make collision occur in primary networks, a joint subcarrier and power allocation scheme for the cognitive HetNet is proposed to guarantee quality of service requirements for both SUs and PUs in probabilistic manners. Then the probabilistic EE optimisation scheme is approximated into a deterministic convex form, and the optimal solutions for the scheme are derived by double-loop iteration method. Afterwards, the authors develop a low-complexity algorithm in the presence of imperfect CSI with a small reduction of system performance. Simulation results are provided to show the impact of channel estimation error on the EE optimisation problem and to highlight the performance improvement from considering channel estimation error in the joint subcarrier and power allocation scheme for the cognitive HetNet system.

Multiuser cooperative communications represent a research area of great interest constituting a key technology for future wireless networks. In this study, the authors consider a scenario of multi-user, single-relay network, where each user employs a part of the relay's transmission power taking into account the constraint of the total transmission power of the relay. The problem of relay power allocation to individual users with a view to optimising the long-term network performance is investigated. An adequate utility function is defined, in terms of outage probability, evaluating the cooperative network's performance due to the relay's cooperation. Taking into consideration the distributed nature of cooperative networks along with the coupled constraint of relay's total transmission power, the specific problem is transformed from a network-level to a user-level optimisation problem using a modern game-theoretic tool. More specifically, the initial power allocation problem is formulated as a state-based potential game for which the corresponding Nash equilibrium exists. Finally, a gradient learning mechanism is proposed to achieve the stationary state Nash equilibrium of the game that constitutes also the global optimal solution of the initial problem. The performance of the new proposed scheme is investigated through numerical simulations for various network parameters.

In this study, the parameter of a symmetric α-stable (SαS) noise sequence is modulated by the binary message sequence to achieve a secure communication system. The characteristic exponent ‘α’ of an SαS noise sequence carries the binary information. In order to recover the binary message sequence at the receiver, the authors propose a logarithmic moments estimator to estimate the characteristic exponent ‘α’ of the transmitted noise sequence. The optimal decision threshold and the minimum theoretical bit error ratio are derived. It is shown that the simulation results of the presented logarithmic moments estimator are consistent with the analytical results. Moreover, this estimator shows better performance and lower computational complexity than the conventional SINC estimator based on the fractional low-order moment method.

Attacks detection is an important issue in collaborative spectrum sensing (CSS) system of cognitive radio networks. Many approaches are proposed to cope with the malicious behaviour of attackers. In existing works, spectrum sensing data (SSD) received by the fusion centre is generally assumed to be integrated. However, in practical scenarios, the received SSD may be incomplete due to the imperfect reporting channel or specific CSS schemes. The performance of existing attacks detection approaches may degrade especially when the probability of missing data is large. To alleviate this challenge, the authors focus on pre-processing of incomplete SSD and propose a practical imputation algorithm, which is derived from the maximum a posteriori probability criterion, to fill in the missing values. Simulation results indicate that the proposed algorithm restores the characteristics of the SSD, and mitigate the impacts of missing value on existing attacks detection algorithm effectively.

In this study, the authors propose a moment-based estimator of the signal-to-noise ratio (SNR) over time-variant Rayleigh fading single-input multiple-output channels. The correlated time-variant channel is modelled with the well-known Jakes’ model. The authors’ approach uses the fourth-order cross-moments of the received signal to estimate the SNR with the presence of an additive white Gaussian noise which is uncorrelated between antenna elements. The SNR is deduced by estimating, respectively, the powers of the useful signals and the noise. The proposed SNR estimator is a non-data-aided (NDA) method since it does not require a training sequence. The performances of this algorithm are investigated in terms of normalised mean square error over a wide range of scenarios. Simulation results show that the proposed algorithm outperforms the NDA maximum-likelihood-based estimators and the moment-based estimators.

Herein the authors consider throughput maximisation for a secondary user (SU) in a full-duplex cognitive radio network (FD-CRN) when the SU has two separate antennas and a self-interference suppression capability. In the FD-CRN, the SU can simultaneously sense the spectrum throughout the whole time slot and transmit data. They propose algorithms based on brute-force search and particle swarm optimisation methods to help the SU achieve optimal detection thresholds for spectrum sensing in two different FD-CRN scenarios. In the first scenario, the SU individually performs spectrum sensing, whereas in the second scenario the SU's sensing results are improved by means of cooperative spectrum sensing. Theoretical and simulation results herein show that, for certain values of the system parameters in the above two scenarios, the system under consideration provides much higher throughput than previously proposed systems in conditions of high-transmission power or low signal-to-noise ratio of the primary signal.

In this study, the authors introduce an efficient secure channel coding (joint cryptography-channel coding) scheme based on Latin square low-density lattice codes (Latin square LDLCs) over unconstrained power additive white Gaussian noise channel. They benefit the properties of Latin square LDLCs to dramatically reduce the key size of the proposed scheme while having an acceptable level of security compared with previous similar schemes. To reduce the key size, they consider two approaches: (i) saving the generating sequence of parity-check matrix of used Latin square LDLC as the part of secret key set; (ii) employing the Hermite normal form of the generator matrix of used Latin square LDLC as the encryption matrix. To provide an acceptable level of security, they consider three other strategies: (i) applying two hard problems related to lattices, i.e. shortest basis problem and closest vector problem; (ii) using a random rational vector as the perturbation (error) vector; (iii) exploiting the special joint encryption/LDLC encoding and joint decryption/LDLC decoding algorithms. Besides, the study discusses other efficiency analysis results consisting error performance and computational complexity of the proposed scheme.

In this study, the spectrum trading problem in a self-organised and two-tier heterogeneous cellular network is studied and the bandwidth sharing problem incorporated with cell range expansion technique is formulated as a Stackelberg game. Maximising the revenue of macro eNodeB (MeNB), affording minimum required bandwidth for each home eNodeB (HeNB), enhancing per femto-user throughput, and providing better quality of service for macro-users nearby each femto-cell are the main objectives of this investigation. The authors propose an iterative scheme in which MeNB and HeNBs make decisions autonomously. The MeNB as the spectrum provider decides on the unit-bandwidth price with the objective to maximise its revenue. Each HeNB, on the other side, decides on the amount of requested bandwidth as well as the number of possible nearby macro-users which will support to take advantage of MeNB discounting. The designed discounting strategy is applied for the extra bandwidth request of HeNBs to encourage them in supporting nearby macro-users. It is shown analytically that the proposed scheme converges to a unique Nash equilibrium which is Pareto optimal. Evaluating the authors’ game through different simulations demonstrates that it is all beneficial for both MeNB and HeNBs and the social welfare is maximised in the network.

Physical layer security has received considerable attentions in recent years. Moreover, cooperative communications using some nodes of network as relays make use of the benefit of multi-antenna systems such as increasing the secrecy capacity. This study studies a communication network incorporating some multi-input–multi-output amplify and forward relays in the presence of some eavesdroppers. The objective persuaded in the current work is to find the beamforming matrices at the relays to maximise the achievable secrecy rate under either individual or total power constraint at these nodes. Accordingly, three main approaches including general rank beamforming (GRBF), rank-1 beamforming (RBF) and null-space beamforming (NSBF) are developed. For the NSBF under the total power constraint, a closed-form solution is obtained, while for the remaining scenarios the corresponding optimisation problem is expressed as a semi-definite programming problem. Numerical results indicate that the RBF and NSBF methods follow GRBF in some cases and degraded from GRBF in the others. However, it is shown that these two methods have much lower complexity than GRBF.

For iterative detection and decoding (IDD) in multiple-input multiple-output systems, the maximum a posteriori probability (MAP) detector would be ideal in terms of the performance. However, due to its high computational complexity, various suboptimal low-complexity approximate MAP detectors have been studied. In this study, a lattice reduction (LR)-based detector is considered for a near-optimal performance for IDD. The authors improve further the performance by employing a partial bit-wise minimum mean square error (MMSE) approach with randomised sampling, which has a lower complexity than that of the full bit-wise MMSE method. Moreover, the list of candidate vectors obtained by randomised sampling is extended using a MAP-aided integer perturbation algorithm for a better performance with low additional complexity. Through simulation results, it is shown that a near-optimal performance can be obtained which is better than that of the LR-based randomised successive interference cancellation and the full bit-wise MMSE methods.

An overly multiple-input–multiple-output cognitive radio femtocell network consisting of P macrocell users equipments (MUEs), known as primary users (PUs), and K femtocell access points (FAPs), known as secondary users is considered in which femtocell user equipments (FUEs) operate in the closed access mode. Each FAP is equipped with a CR device to perform the local channel state information. The main objective is to maximise the average sum-rate of the macrocell base station (MBS), as well as significantly increase in the FUE’s rate with negligible reduction in the PU’s rate for moderate-to-high signal-to-noise ratio regimes. This goal is achieved by proposing an opportunistic interference alignment (OIA) technique using the threshold-based beamforming (TBF) algorithm. Assuming that the receiver and the transmitter of the PU have perfect knowledge of their own channel matrices, the authors use the maximum eigenmode beamforming algorithm for the transmission between the MBS and its MUEs, where the PU releases some of its eigenmodes for the FAPs, in order to transmit signals for their corresponding FUEs over them. To decide on the presence or absence of MUEs, they use the generalised likelihood ratio test detector which is more robust to the noise uncertainty than the energy detector. The proposed OIA-TBF protocol allows the opportunistic FAPs to send data for FUEs and use the same frequency band of a preexisting MUE to guarantee that no interference is imposed on the MUE’s performance for such a network.