In this paper, non-orthogonal multiple access (NOMA) networks assisted by multiple intelligent reflecting surfaces (IRSs) with discrete phase shifts are investigated, in which each user device (UD) is served by an IRS to improve the quality of the received signal. Two scenarios are considered according to whether there is a direct link between the base station (BS) and each UD, and the outage performance is analyzed for each of them. Specifically, the asymptotic expressions for the upper and lower bounds of the outage probability in the high signal-to-noise ratio (SNR) regime are derived. Following that, the diversity order is obtained. It is shown that the use of discrete phase shifts does not degrade diversity order. More importantly, simulation results reveal that a 3-bit resolution for discrete phase shifts is sufficient to achieve near-optimal outage performance. Simulation results also imply the superiority of IRSs over full-duplex decode-and-forward relays.

Intelligent reflecting surfaces (IRSs) are envisioned to provide reconfigurable wireless environments for future communication networks. In this paper, both downlink and uplink IRS-aided non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) networks are studied, in which an IRS is deployed to enhance the coverage by assisting a cell-edge user device (UD) to communicate with the base station (BS). To characterize system performance, new channel statistics of the BS-IRS-UD link with Nakagami-$m$fading are investigated. For each scenario, the closed-form expressions for the outage probability and ergodic rate are derived. To gain further insight, the diversity order and high signal-to-noise ratio (SNR) slope for each scenario are obtained according to asymptotic approximations in the high-SNR regime. It is demonstrated that the diversity order is affected by the number of IRS reflecting elements and Nakagami fading parameters, but the high-SNR slope is not related to these parameters. Simulation results validate our analysis and reveal the superiority of the IRS over the full-duplex decode-and-forward relay.

In this paper, a downlink non-orthogonal multiple access (NOMA) system is studied, in which an intelligent reflecting surface (IRS) is deployed to enhance the coverage by assisting a cell-edge user device (UD) to communicate with the base station (BS). To characterize system performance, new channel statistics for the BS-IRS-UD link with Nakagami-m fading are investigated. Based on the new channel statistics, the closed-form expression for the outage probability is derived. To gain further insight into the problem, the diversity order is obtained according to the asymptotic approximation in the high signal-to-noise ratio (SNR) regime. It is demonstrated that the diversity order is affected by the number of IRS elements and Nakagami fading parameters. Simulation results validate our analysis and reveal the superiority of the IRS over the full-duplex decode-and-forward relay in the high-SNR regime.

Heterogeneous cellular networks (HCNs) present an attractive solution to increased demands in mobile user capacity. Comprehensive studies have been conducted in stochastic geometric models that represent the relatively random placement of base transmitting stations (BTSs) operating at different power levels. This study considers the design of two‐tier HCNs for which picocell BTSs from the second tier are separated simultaneously from each other and from their tier‐1 macrocell counterparts. These separations, introduced in detail in the study, are termed the co‐tier and cross‐tier separations, with each parameter characterised by a minimum distance separation. Subsequently, expressions are obtained for distance distributions of BTSs from specific tiers to typical users, followed by conditional probabilities of association with each tier. We show that a minimum radius of association can be guaranteed for a tier‐2 BTS based on the values of co‐tier and cross‐tier separations. Furthermore, we analyse the Laplace transform of interference to the typical user and the resultant formulae for coverage probability, and by extension, area spectral efficiency. Numerical results demonstrating the effect of co‐tier and cross‐tier separation on these performance parameters support the analysis and provide insights into cell planning based on this concept.

A joint user clustering and subcarrier allocation scheme for downlink non-orthogonal multiple access (NOMA) systems is examined in this paper. We propose the scheme for downlink NOMA systems which maximizes the achievable diversity order. The closed-form expression of the outage probability of the worst-performance user in the worst case is derived and validated by simulations. Numerical results show that the proposed scheme can achieve the same diversity order as the exhaustive searching scheme.

Homogeneous user models have been traditionally considered in heterogeneous cellular networks (HCNs) that comprise base transmitting stations (BTSs) operating at different power levels. As small-cell BTSs are usually deployed to cater to dense user clusters in limited spaces, Poisson cluster processes (PCPs) have found application in modeling non-homogeneous user distributions, for which deployments are placed at the center of user clusters. We propose a two-tier HCN model that comprises a single potential tier-2 small-cell deployment per user cluster. The potential tier-2 BTS deployments are offset by a randomly distributed distance with respect to the centers of their corresponding clusters, which are also known as social attractors (SAs). Deployment or active transmission of a tier-2 BTS may only occur if there is sufficient separation from active tier-1 BTSs in the network, effectively creating a Poisson hole process (PHP) of tier-2 BTSs. By using variations of the PCP to model clustered users that surround SAs, distance distributions are analyzed for two situations, where the offset between an SA and a potential tier-2 BTS is modeled by using the uniform and Gaussian distributions, respectively. This result is extended to obtain the probability of association of users to their corresponding cluster deployments, and the two BTS tiers.

In this paper, we investigate physical layer security in a two-tier heterogeneous network with sub-6 GHz massive multi-input multi-output (MIMO) macro cells and millimeter wave (mmWave) small cells. By considering pilot attacks from the eavesdroppers, we analyze the coverage and secrecy performance using stochastic geometry. For the sub-6 GHz tier, we show that increasing the number of BS antennas is more effective than increasing BS density in improving the coverage performance, whereas densifying BS is more effective for security enhancement. For the mmWave tier, we first derive the success probability of beam alignment based on a beam sweeping-based channel training model. It is shown that the mmWave tier may outperform the sub-6 GHz counterpart in terms of both coverage and secrecy through densifying the base stations. Our results also reveal that the mmWave small cell can provide better coverage performance in the high transmission rate region, and can achieve higher security in the low redundant rate region, which reveals the advantage of using mmWave for secure communication. Numerical results verify the analysis.

In this paper, the impact of adaptive smarter eavesdroppers on the secrecy performance of a multi-antenna cellular network is investigated. The eavesdroppers can act as either passive eavesdroppers or active jammers based on their distance to the active base stations (BSs). To analyze the secrecy performance, the BSs, cellular users, and eavesdroppers are modeled as independent Poisson point processes. The closed-form expressions of the connection outage probability and lower bound of the secrecy outage probability are derived using the stochastic geometry approach. Following that, the conditions under which the eavesdroppers can act as active jammers are obtained. Finally, the optimal power allocation between artificial noise and information signal and the secrecy code rate at each BS, as well as the guard zone of the eavesdroppers are obtained using the Stackelberg game approach, where the eavesdroppers are modeled as the leader and the BSs as the follower. The Stackelberg equilibrium is obtained through the proposed iterative algorithm. Numerical results verify the theoretical analysis and show that the secrecy performance can be degraded severely by the adaptive eavesdroppers.

In this paper, the security issue in a multi- input-single-output (MISO) system in the presence of multiple randomly distributed eavesdroppers (Eves) is investigated. The Eves are distributed according to a Poisson Point Process (PPP) and each of them can operate in either a half-duplex (HD) or full-duplex (FD) mode. For a FD-mode Eve, it can overhear the secret information transmission and send some jamming signals simultaneously to degrade the reception of Bob. Based on the stochastic geometry method, we first derive the cumulative distribution function (cdf) expressions of the signal-to-interference-plus- noise ratio (SINR) for Bob and Eves. Following that, a lower bound of the intercept probability is obtained. Some important properties are derived, which provide very useful insights. Finally, the optimal power allocation of Alice and the optimal fraction of FD-mode Eves are solved by using a game-theoretical approach. Simulation results are shown to validate the theoretical analysis.

In this paper, the security in a device-to-device (D2D) spectrum sharing network is investigated. The cellular users and eavesdroppers are distributed according to two independent Poisson Point Processes (PPPs), and the positions of the D2D transmitters follow a hard-core point process. Based on the stochastic geometry, we first derive closed-form expressions of the connection and secrecy outage probabilities of a typical user and then analyze the impacts of different parameters. We also derive the connection probability of a D2D user, which is shown to be independent of the parameters of the base station (BS). Following that, we analyze the impact of D2D transmissions on the power allocation at the BS and derive the optimal power allocation solution for the fixed-rate transmission scheme. Simulation results validate the analysis.

In this paper, physical layer security in multi-antenna small-cell networks is investigated, where the multi-antenna base stations (BSs), cellular users, and eavesdroppers are all randomly distributed according to three independent Poisson point processes. To improve the secrecy performance, artificial noise (AN) aided transmission is adopted at each BS. Based on the stochastic geometry, we first derive the closed-form expressions of the connection and secrecy outage probabilities, and then comprehensively analyze the impact of different parameters through asymptotic analysis. It shows that in a low cell-load case, deploying more BSs will improve the connection and secrecy outage performance, and deploying more transmit antennas at each BS will only improve the connection outage performance. For a fixed-rate transmission, the condition under which AN becomes unnecessary is derived. We also derive a semi closed-form expression of the lower bound of the achievable average secrecy rate, which is numerically efficient to evaluate. Finally, we extend the study to a high cell-load case and adopt the zero-forcing beamforming scheme to support multi-user transmission. The connection and secrecy outage probabilities are also analyzed. Moreover, the optimal number of users maximizing the secrecy area spectral efficiency is discussed, and it is shown to be a fixed portion of the number of transmit antennas. Simulation results are presented to validate the theoretical analysis.

In this paper, the secure transmission strategy for a multi-input-single-output multi-eavesdropper system with coexistence of a secure user (Bob) and a normal user (NU) is investigated. The NU and Bob require normal and secure data transmissions, respectively, and thus, the stream for the NU can be exploited to confuse the eavesdroppers. To guarantee the security of Bob, artificial noise (AN) is also deliberately injected into the null space of Bob and NU. The power allocation among Bob, NU, and AN, as well as the wiretap code rates, is jointly optimized to maximize the effective secrecy throughput (EST), under the average throughput constraint of the NU and statistical channel state information (CSI) of eavesdroppers. Both non-adaptive and adaptive transmission schemes are proposed, based on the statistical and instantaneous CSI of the legitimate channels, respectively. An alternative optimization algorithm is proposed to obtain the optimal parameters. It is proved that the EST is a quasi-concave function of the secrecy rate and the power allocated to Bob, and for fixed wiretap code rates, the optimal power allocation is derived in a closed-form expression. Numerical results show that the EST increases with the increase in transmitting power and the number of transmit antennas, and decreases with the increasing throughput constraint of the NU. Improved EST can be achieved through injecting AN and concurrent transmission of Bob and NU.

The quality of energy detector is quite challenging when the system parameters are not stable. On the other hand, in a cognitive radio network, primary users are licensed to use the desired radio spectrum band(s) and the throughput of the primary network has the highest priority to be kept satisfied. Therefore, it is quite important to secure the quality of primary service to a certain level, and it is worthless to blindly improve the throughput of the secondary network without taking its possible effects on the primary throughput into account. Hence, the mentioned issues motivate us to enhance the total throughput of the system when it suffers from an unstable primary network, due to a medium-traffic rate, and a random density of the secondary users, due to a stochastic-modeled secondary network, at the same time. By introducing a 1-persistent method in a cooperative spectrum sensing scheme, we show how effectively it can improve both primary and secondary throughputs, resulting in higher total throughput of the system.

In this paper, the security of multi-input single- output (MISO) amplify-and-forward relaying network with untrustworthy relay nodes is considered, where the untrustworthy nodes can help to forward the received signal and they may also try to decode such information, which can be regarded as potential eavesdroppers (Eves). To deal with such kind of smarter Eves, relay selection is adopted and both the maximal-ratio transmission (MRT) scheme and the zero-forcing beamforming (ZFBF) scheme are used at the multi-antenna base station (BS). To achieve a positive secrecy capacity, the destination also injects intended jamming signal to confuse the decoding of the untrustworthy nodes. Either approximation or lower bound of the secrecy outage probability is derived in closed form. It is shown that the proposed partial relay selection scheme approaches the optimal relay selection scheme. In particular, for the ZFBF scheme, when the number of antennas is large enough, increasing the number of relay nodes will increase the diversity order and thus improves the secrecy performance. Simulation results validate the effectiveness of the scheme and correctness of analysis.

We formulate and study a multi-user multi-armed bandit (MAB) problem that exploits the temporal-spatial reuse of primary user (PU) channels so that secondary users (SUs) who do not interfere with each other can make use of the same PU channel. We first propose a centralized channel allocation policy that has logarithmic regret, but requires a central processor to solve a NP-complete optimization problem at exponentially increasing time intervals. To avoid the high computation complexity at the central processor and the need for SU synchronization, we propose a heuristic distributed policy that incorporates channel access rank learning in a local procedure at each SU at the cost of a higher regret. We compare the performance of our proposed policies with other distributed policies recently proposed for opportunistic spectrum access. Simulations suggest that our proposed policies significantly outperform the benchmark algorithms when spectrum temporal-spatial reuse is allowed.

We formulate and study a multi-user multi-armed bandit problem that exploits the temporal–spatial opportunistic spectrum access (OSA) of primary user (PU) channels, so that secondary users (SUs) who do not interfere with each other can make use of the same PU channel. We first propose a centralized channel allocation policy that has logarithmic regret, but requires a central processor to solve an NP-complete optimization problem at exponentially increasing time intervals. To overcome the high computation complexity at the central processor, we also propose heuristic distributed policies that, however, have linear regrets. Our first distributed policy utilizes a distributed graph coloring and consensus algorithm to determine SUs’ channel access ranks, while our second distributed policy incorporates channel access rank learning in a local procedure at each SU at the cost of a higher regret. We compare the performance of our proposed policies with other distributed policies recently proposed for temporal (but not spatial) OSA. We show that all these policies have linear regrets in our temporal–spatial OSA framework. Simulations suggest that our proposed policies have significantly smaller regrets than the other policies when spectrum temporal–spatial reuse is allowed.

In this paper, the security aspect of an amplify-and-forward relaying network with untrusted relay nodes is considered. The untrusted nodes can help to forward the received signal and they may also try to decode such information, which can be regarded as potential eavesdroppers (Eves). To deal with such a challenging issue, a successive relaying scheme is adopted, where the multi-antenna source transmits to two selected nodes alternately, and the conventional detrimental inter-relay interference is used to jam the untrusted nodes without external helpers. Considering different complexity requirements, several relay selection schemes are proposed, and the closed-form expressions of the lower bound of secrecy outage probability are derived accordingly. To obtain some insights for the network design, an asymptotic analysis is also given, which shows that the maximum secrecy diversity order of N-1 can be achieved, where N is the number of the untrusted relays. Moreover, the spectral efficiency is improved dramatically with the successive relaying scheme. Simulation results show that the proposed max-min scheme has almost the same performance as that of the optimal one, and the theoretical results match well with the simulation results.

The pilot spoofing attack is one kind of active eavesdropping activities conducted by a malicious user during the channel training phase. By transmitting the identical pilot (training) signals as those of the legal users, such an attack is able to manipulate the channel estimation outcome, which may result in a larger channel rate for the adversary but a smaller channel rate for the legitimate receiver. With the intention of detecting the pilot spoofing attack and minimizing its damages, we design a two-way training-based scheme. The effective detector exploits the intrusive component created by the adversary, followed by a secure beamforming-assisted data transmission. In addition to the solid detection performance, this scheme is also capable of obtaining the estimations of both legitimate and illegitimate channels, which allows the users to achieve secure communication in the presence of pilot spoofing attack. The detection probability is evaluated based on the derived test threshold at a given requirement on the probability of false alarming. The achievable secrecy rate is utilized to measure the security level of the data transmission. Our analysis shows that even without any pre-assumed knowledge of eavesdropper, the proposed scheme is still able to achieve the maximal secrecy rate in certain cases. Numerical results are provided to show that our scheme could achieve a high detection probability as well as secure transmission.

Status changing of the primary user and the number of secondary users (SUs) are crucial issues for designing a reliable cognitive radio network. In this paper, a medium-traffic primary network is assumed when SUs are stochastically distributed over an area around a secondary base station. By using cooperative spectrum sensing over Rayleigh-faded sensing and imperfect reporting channels, we propose an extra sensing part within the transmission phase of the secondary network in which only some SUs (called sensing SUs) participate in sensing. Although the extra sensing may suffer from interference by transmitting SUs, we show that the total transmission throughput of the system can be improved significantly due to better quality of the detection. Moreover, we reveal that involving all SUs in the extra sensing part does not necessarily increase the total throughput of the system.

In this paper, we study an energy-harvesting cognitive radio (CR) system where each secondary user (SU) harvests energy to recharge its battery. Cooperative spectrum sensing is employed to enhance the sensing performance. In this energy- constrained scenario, the SUs, as per their energy-arrival rates, can cooperate to achieve higher opportunistic spectrum utilization and improved primary user (PU) detection. For a heterogeneous CR system with different sensing environment and energy-arrival process at each SU, the optimal probability of sensing is obtained for each SU to maximize the SU network throughput while satisfying the PU collision and energy-causality constraints. SOSTOOLS is employed to solve the polynomial optimization problem, and a suboptimal scheme which can be used for larger systems is proposed. Furthermore, under a homogeneous scenario, it is shown that with a minimum number of SUs cooperating, the CR throughput performance can overcome the energy- causality and PU collision constraints.

We study a spoofing attack happened in the physical layer of a multiple-antenna system, where an adversary tries to spoof the transmitter by sending the identical pilot (training) signal as that of a legitimate receiver in the uplink channel estimation phase. This attack, named as pilot spoofing attack, could lead to a secrecy information leakage to the adversary and information rate decrease at the legitimate receiver. Due to the serious results caused by the pilot spoofing attack, we propose an energy-ratio detector (ERD) to protect the legitimate components. The ERD makes the decision by exploiting the asymmetry of the received signal strength (RSS) between the transmitter and the legitimate receiver when the system is under the pilot spoofing attack. Numerical results are presented to illustrate the effectiveness of our proposed detector.

In a time-division duplex (TDD) based multi-input single-output (MISO) system, the channel state information (CSI) can be obtained during the channel estimation phase in which the receiver transmits the pilot symbols to the transmitter. This scheme may suffer from a so-called pilot spoofing attack, i.e., an adversary may send identical pilot signals as those of the legitimate receiver to spoof the transmitter. The resultant channel estimate may then contain the CSI of both legitimate and illegitimate receivers, and if such estimated channel is used for transmit beamforming, the information dedicated for legitimate receiver will leak to the illegitimate receiver. In this paper, we study the detection and defending strategies for such pilot spoofing attack. A two-way training based scheme is proposed. The durations of the training periods are also designed to optimize the secrecy rate. Finally, numerical results are presented to show the performance of our proposed method.

Over the past few decades, frequency hopping (FH) techniques have attracted considerable interest in both military and commercial communications. However, fading and interference can significantly degrade the performance of an FH system. One method commonly employed to overcome the degradation in performance because of the fading is the use of diversity. Furthermore, fast FH (FFH) systems can enjoy both time and frequency diversity and hence FFH systems employed in conjunction with diversity‐combining techniques are effective for combating fading and interference effects. In this study, the authors provide a comprehensive survey on the past and current research work on diversity‐combining techniques for suppressing different types of interference in FFH M ‐ary frequency‐shift‐keying systems over various fading channels. Some commonly used theoretical approaches for analysing performance of FFH systems are also presented. In addition to the survey, they will also discuss some interesting areas of future work in this research topic.

The pilot spoofing attack is one kind of active eavesdropping conducted by a malicious user during the channel estimation phase of the legitimate transmission. In this attack, an intelligent adversary spoofs the transmitter on the estimation of channel state information (CSI) by sending the identical pilot signal as the legitimate receiver, in order to obtain a larger information rate in the data transmission phase. The pilot spoofing attack could also drastically weaken the strength of the received signal at the legitimate receiver if the adversary utilizes large enough power. Motivated by the serious problems the pilot spoofing attack could cause, we propose an efficient detector, named energy ratio detector (ERD), by exploring the asymmetry of received signal power levels at the transmitter and the legitimate receiver when there exists a pilot spoofing attack. Our analysis shows that by setting the ratio of received signal power levels at the transmitter and the legitimate receiver as the test statistic, the detecting threshold is derived without using the knowledge of the CSI of the legitimate channel as well as the illegitimate channel. Furthermore, we study the performance of the proposed ERD in various special cases in order to obtain useful insights. Numerical results are presented to further demonstrate the performance of our proposed ERD.

The status of a primary user (PU) within sensing time is one of the important parameters, which is considered to be fixed in many studies of spectrum sensing in cognitive radio networks. In this paper, we consider a medium traffic of a primary network, in which the PU changes its state (either idle or active) at most once during the sensing period of the secondary user (SU). This situation degrades the detection performance of the secondary network. We first try to find a suitable distribution for observed energy levels by SUs, and then evaluate the detection performance of the both single- and double-threshold methods in terms of the total error probability using cooperative spectrum sensing over imperfect reporting channels. The results show that the double-threshold scheme outperforms the single one.

The authors consider the problem of energy consumption in a multiband cognitive radio network, in which a secondary user can sense multiple frequency bands authorised to the primary user (PU) before it decides to access some frequency bands and keep the interference introduced to the PU under a certain threshold. The sensing time and power allocation need to be designed carefully to reduce the energy consumption. Therefore they identify the optimal sensing time and accessing power to minimise the energy consumption of the cognitive radio that simultaneously senses and accesses multiple bands under the multiband sensing‐based spectrum sharing scheme. To obtain the optimal solution, they transform the original problem formulated as the ratio of two functions into another parametric formulation. The interference power is considered as one of constraints in the author's scheme in order to protect the PU. The algorithm of optimal sensing time and power allocation is proposed for the multiband cognitive radio system. Furthermore, they discuss the effect of channel number, interference power and gain estimation of channels on energy consumption and optimal sensing time and validate their schemes and analysis by simulation results.

A novel limited feedback strategy based on a compressive sensing technique is proposed for the downlink large‐scale multiple‐input single‐output (MISO) system. The effectiveness of transmit beamformers relies on the feedback quality of channel state information (CSI). The instantaneous CSI is compressed and sent back to the base station (BS) by receivers. An efficient recovery algorithm is applied at the BS in the presence of measurement noise and feedback link noise. The proposed feedback strategy can provide the BS with much more precise CSI as compared with some conventional vector quantisation schemes. The proposed scheme also has lower‐computational complexity. Furthermore, the authors derive a tight lower bound on the user sum rate, assuming that zero‐forcing beamforming is applied at the BS, and that active users are semi‐orthogonal to each other. Numerical results show that the proposed compressive sensing‐based limited feedback scheme yields better performance gain than the conventional channel quantisation approaches.

In a cognitive radio network, a primary user (PU) shares its spectrum with secondary users (SUs) temporally and spatially, while allowing for some interference. We consider the problem of estimating the no-talk region of the PU, i.e., the region outside which SUs may utilize the PU's spectrum regardless of whether the PU is transmitting or not. We propose a distributed boundary estimation algorithm that allows SUs to estimate the boundary of the no-talk region collaboratively through message passing between SUs, and analyze the trade-offs between estimation error, communication cost, setup complexity, throughput and robustness. Simulations suggest that our proposed scheme has better estimation performance and communication cost trade-off compared to several other alternative benchmark methods, and is more robust to SU sensing errors, except when compared to the least squares support vector machine approach, which however incurs a much higher communication cost.

In this paper, we propose a novel coordinated downlink beamforming strategy based on the semidefinite relaxation (SDR) approach for a clustered multicell cellular system. As base station (BS) cooperation can provide significant performance improvement for the system capacity and interference suppression, we divide the whole network into a number of clusters. In each cluster, several BSs share the common user data and cooperatively design their signaling strategies. In this system, maximizing the sum-rate requires solving a global nonconvex optimization problem. We apply the semidefinite programming (SDP) relaxation to convert the original problem into distributed convex SDP which can be solved efficiently and optimally with convex optimization techniques. Numerical results show that the proposed beamforming algorithm provides a remarkable sum-rate enhancement and outperforms some existing schemes.

In a cognitive radio network, a primary user (PU) shares its spectrum with secondary users (SUs) temporally and spatially, while allowing for some interference. We consider the problem of estimating the interference coverage region of the PU, i.e., the region outside of which SUs may utilize the PU's spectrum regardless of whether the PU is transmitting or not. We propose a distributed boundary estimation algorithm that allows SUs to estimate the boundary of the coverage region collaboratively through message passing between SUs. We also propose a spatial spectrum sensing scheme based on the estimated boundary. Simulation results suggest that our proposed scheme has better estimation performance and communication cost trade-offs compared to centralized boundary estimation methods, and has better weighted throughputs than traditional fusion center based collaborative spectrum sensing methods.

In this study, the authors present an algorithm to detect unknown interference in slow frequency‐hopped quadrature phase‐shift‐keying systems. Both partial‐band noise interference and multitone interference are considered. The algorithm is developed based on the correlator outputs over one hop. A suitable threshold level is derived for detection. The authors formulate the analytical expressions for probability of detection for both interference models. Numerical results reveal that the proposed algorithm can detect both interference types even at low interference power.

A low‐complexity channel estimation algorithm is proposed to improve performance of two high frequency standardised waveforms: MIL‐STD‐188‐110B Appendix C standard and STANAG 4285. In the proposed estimation algorithm, the channel impulse response is modelled as a linear‐time function within a frame and the least square criterion is adopted. With the estimated CIRs, the authors study and compare bit‐error‐rate (BER) performance and complexity of three turbo equalisation (TEQ) schemes, including the minimum mean‐square error (MMSE), the MMSE with decision feedback equalisation (DFE) (MMSE‐DFE) and the soft‐feedback interference‐cancellation (SFIC) turbo receivers. The authors then propose a hybrid TEQ scheme that uses the MMSE‐DFE equaliser for the first iteration and the SFIC equaliser for the rest. Simulation results show that the proposed channel estimation algorithm performs well and the TEQ schemes realise a significant performance improvement as compared with a non‐iterative receiver. Moreover, the proposed hybrid TEQ scheme achieves the best trade‐off between BER and complexity for the MIL‐STD‐188‐110B Appendix C standard, whereas the SFIC‐TEQ scheme is optimal for the STANAG 4285 standard.

In this study, the authors focus on energy efficiency of a cognitive radio (CR) system, in which a secondary user (SU) senses periodically and accesses opportunistically a specific band authorised to a primary user (PU). Based on a generalised expression of energy consumption, we jointly optimise sensing, transmission and frame durations to maximise the energy efficiency for a CR system and investigate the performance of the proposed design over Rayleigh fading channels. The problem of energy efficiency is formulated as a function of sensing and transmission durations with the constraints on the interference to the PU. To protect the PU, we limit the detection probability as well as restrict the interference caused by the SU because of the re‐occupancy of the PU. In a generalised model, energy consumptions of sensing, transmission and idling state need to be considered for the SU. The optimal sensing and transmission durations are obtained by a sub‐optimal iterative algorithm. The performance of energy efficiency and duration of the SU over a Rayleigh‐faded channel is investigated. Numerical results show that the proposed reduced‐complexity approach performs comparably with that of the exhaustive search algorithm.

In this study, the authors propose a diversity‐combining scheme with transmit antenna selection (TAS) and output‐threshold generalised selection combining (OT‐GSC) receiver. It is shown that the proposed TAS/OT‐GSC can achieve similar performance as compared to the TAS/GSC with a reduced number of channel estimates when the predetermined signal‐to‐noise ratio (SNR) threshold is optimised. The outage probability, average output SNR, and symbol‐error rate (SER) expressions of the proposed TAS/OT‐GSC scheme are derived and presented over independent and non‐identically distributed Rayleigh‐fading channels. The analytical expressions are validated by simulation results. The trade‐off comparisons in terms of the SER and number of channel estimates between the TAS/OT‐GSC and TAS/GSC are discussed. Lastly, the capacity between the TAS/OT‐GSC and TAS/GSC is compared.

The composite effect of hostile multitone jamming and partial-band noise jamming on bit-error rate (BER) performance of a fast frequency-hoppedM-ary frequency-shift-keying system is studied over Rayleigh fading channels in the presence of timing and frequency offsets. The maximum-likelihood (ML) diversity-combining method is employed to improve BER performance of the system. Analytical BER expression of the proposed ML receiver is derived. The analytical results, validated by computer simulation, show that the proposed ML receiver can suppress the composite hostile jamming more effectively than some existing conventional diversity-combining receivers. The ML receiver is also found to be robust against inaccurate estimation of the required side information.

In this paper, we propose a detection algorithm to detect unknown partial-band noise interference (PBNI) which is frequently encountered in slow frequency-hopped spread spectrum (SFH-SS) systems. The algorithm utilizes a simple hypothesis testing to decide presence of PBNI in any particular hop after dehopping. A suitable threshold level is first derived to detect the PBNI by analyzing the statistical property of the outputs of two correlators used for quadrature phase-shift-keying (QPSK) demodulation. Then, the proposed detector is developed by summing the outputs of the correlators over one hop duration. We also formulate an expression for probability of detection (PD) and use it as a performance measure for detection. Analytical and simulation results show that the proposed detector is able to detect the PBNI very well even at low interference power (8 dB lower than signal power). In addition, numerical results reveal that the proposed algorithm can also be used to detect multitone interference (MTI) encountered in slow FH-SS systems.

Iterative equalization techniques are effective in mitigating inter-symbol interference (ISI). In this paper, we first study and compare three low-complexity adaptive-channel-estimation-based turbo equalization (ACE-based TEQ) algorithms over high-frequency (HF) waveform channels based on the STANAG 4285 standard. These reduced-complexity equalization algorithms include the minimum mean-square error (MMSE), the MMSE decision feedback equalization (MMSE-DFE) and the soft feedback interference cancellation (SFIC). To address the issue of the HF channel time-variation, an explicit adaptive channel estimator is used to determine the unknown channel coefficients. In addition, we have also proposed a hybrid ACE TEQ algorithm. Numerical results show that the ACE-SFIC-based TEQ scheme is the best in terms of trade-off between bit-error rate (BER) and implementation complexity for the STANAG 4285 military waveforms.

Bit-error rate (BER) expressions of a suboptimum maximum-likelihood (ML) receiver with the composite effect of partial-band noise jamming and multitone jamming are derived for fast frequency-hopped systems employing M-ary frequency-shift-keying modulation over Rician-fading channels. These BER expressions can be used to study the system performance under Rayleigh fading as a special case. Owing to the fact that the computation of the logarithm of the modified Bessel function is non-linear in nature, one of the existing approximations is required to derive the BER expressions for the analysed system. A suboptimum ML receiver structure is therefore proposed and analysed. The analytical results are compared with simulation results. Under various jamming and fading conditions, the proposed suboptimum ML receiver is found to be able to suppress interference effectively.

In this study, the performance of a synchronous fast frequency-hopped multiple-access (MA) M-ary frequency-shift-keying system employing maximum-likelihood (ML) method over either frequency-selective Rician- or Rayleigh-fading channels is investigated. The ML receiver structures are derived and analysed. It is assumed that all the signals arrive at a receiver with the same power strength and all the users operating in the system undergo independent frequency-selective fading. The performance of the ML receivers is compared with that of the linear-combining and the product-combining receivers. The bit-error rate results of the two conventional receivers are obtained via simulation. The proposed analysis, validated by simulation results, shows that the proposed ML receivers can suppress the MA interference more effectively than other existing receivers under different fading conditions. Moreover, the proposed ML receivers are shown to be robust against the inaccuracy in estimation of the required side information.

Bit-error rate (BER) expressions of generalised selection combining with low-density parity-check (LDPC) codes, using binary phase-shift keying signals, over an independent and identically distributed Rayleigh-fading channel are derived using the Gaussian approximation (GA) approach. BER results for both selection combining and maximum-ratio combining can be computed from this BER expression as special cases. The symmetry and stability conditions of both density evolution (DE) and GA analysis are also studied. The degree distribution for irregular LDPC codes is optimised using differential evolution. The theoretical results are compared with both simulation results and DE thresholds. These BER expressions allow us to achieve a significant reduction in computational complexity for analysing the system performance as compared to simulation and DE.

The two wave with diffused power (TWDP) fading model is a very useful fading model characterised by two specular waves in the presence of other diffused waves and is applicable to both the Rayleigh and Rician fading channels as special cases. The performance of switch diversity with binary modulation schemes over the TWDP fading channel is examined. The four types of switch diversity investigated in this study comprise of the switch-and-stay combining, switch-and-examine combining, switch-and-examine combining with post-selection and scan-and-wait combining. The expressions of the average output signal-to-noise ratio (SNR) at the receiver and bit-error rate (BER) are derived and presented. The pre-determined SNR thresholds of the switch diversity over the TWDP fading channel are optimised to obtain the minimum BER. Analytical results are validated by simulation.

In this paper, we propose a joint iterative detection/decoding scheme for a generalized discrete two-dimensional (2D) interference channel with low-density parity-check (LDPC) codes. A reduced-state form of the channel detector is also proposed to further reduce the system complexity. To achieve better performance, iterations are introduced between the two constituent channel detectors and among the two constituent detectors with the LDPC decoder. The computational complexity and performance of different iteration schemes are analyzed. Simulation results show that the proposed detection scheme can mitigate the 2D interference effectively and the LDPC codes can be well integrated to the 2D iterative detector to further improve the system performance significantly.

We propose an efficient successive relaying (SR) transmission protocol for multiple-relay cooperative systems under the half-duplex constraint. In this protocol, the process of relay selection is conducted once the instantaneous channel state information changes. During each channel coherent interval, the source keeps transmitting newly generated messages, and two selected relays successively decode and forward the source's information to the destination. In particular, in one time slot, a selected relay jointly decodes both signals transmitted from the source and the other selected relay. In the next time slot, this relay forwards the superposition of these two decoded signals. The destination jointly decodes messages at the end of each interval. The lower bound of outage probability is derived in a closed-form expression and the diversity-multiplexing trade-off (DMT) performance is characterized as well. It is demonstrated by the numerical results that the proposed SR protocol is capable of achieving both full diversity gain and high multiplexing gain.

In this paper, we propose a detection algorithm to detect unknown multitone interference (MTI) encountered in frequency-hopped spread spectrum (FH-SS) systems over a Rayleigh fading channel and additive white Gaussian noise by using autoregressive (AR) spectral estimation method. The proposed algorithm is performed in the AR coefficient domain. The incoming received data is separated into non-overlapping data segments, and the Yule-Walker (YW) AR method is applied on each data segment to obtain the AR coefficient vector. The resultant coefficient vectors are used in the averaging process to obtain the spectrum estimate of the MTI. Computer simulations are conducted in order to investigate detection performance of the proposed AR spectral averaging technique and comparisons are made between the proposed scheme and the fast Fourier transform (FFT) based scheme. Numerical results show that the proposed technique is able to detect the MTI accurately under such a channel environment even at low signal-to-noise power ratio (SNR) condition. The comparisons reveal that the proposed AR detection technique is promising to be employed in slow FH-SS systems to detect the MTI due to higher estimation accuracy and better reliability as compared to the FFT- detection technique.

Energy-efficient design has become increasingly important to battery-powered wireless devices. In this paper, we focus on the energy efficiency of a cognitive radio network, in which a secondary user senses the channels licensed to some primary users sequentially before it decides to transmit. Energy is consumed in both the channel sensing and transmission processes. The energy-efficient design calls for a careful design in the sensing-access strategies and the sensing order, with the sensing strategy specifying when to stop sensing and start transmission, the access strategy specifying the power level to be used upon transmission, and the sensing order specifying the sequence of channel sensing. Hence, the objective of this paper is to identify the sensing-access strategies and the sensing order that achieve the maximum energy efficiency. We first investigate the design when the channel sensing order is given and formulate the above design problem as a stochastic sequential decision-making problem. To solve it, we study another parametric formulation of the original problem, which rewards transmission throughput and penalizes energy consumption. Dynamic programming can be applied to identify the optimal strategy for the parametric problem. Then, by exploring the relationship between the two formulations and making use of the monotonicity property of the parametric formulation, we develop an algorithm to find the optimal sensing-access strategies for the original problem. Furthermore, we study the joint design of the channel sensing order and the sensing-access strategies. Lastly, the performance of the proposed designs is evaluated through numerical results.

A maximum-likelihood (ML) receiver structure is proposed for fast frequency-hopped M-ary frequency-shift keying communication systems over Rayleigh-fading channels with the composite effects of multitone jamming (MTJ) and partial-band noise jamming (PBNJ). The corresponding semi-analytical bit-error rate (BER) expressions of the proposed ML receiver are also presented and validated by simulation results. Numerical results show that the BER performance with both MTJ and PBNJ is bounded by the two extreme cases, where only MTJ or PBNJ is present. It is also found that the proposed ML receiver can better counteract MTJ than PBNJ.

In this paper, we investigate the diversity-multiplexing tradeoff (DMT) of a multiple-input-multiple-output (MIMO) full-duplex single-user multihop relay channel, where a pair of source and destination communicates via multiple layers of relays. All communication terminals could be equipped with multiple antennas. The relays operate in a full-duplex mode. By incorporating time-domain linear transformation into amplify-and-forward (AF) based relaying, we propose an AF-based space-time relay scheme and show that the DMT upper bound of the channel can be achieved by properly designing space-time (ST) codes at the source.

In this paper, diversity-multiplexing tradeoff (DMT) of the delay-limited symmetric two-user single-antenna fading interference channel (IFC) with source cooperation is evaluated under both full-duplex and half-duplex cooperation constraints. The interference signal and the desired signal received by each destination node are assumed to be of comparable strength. Under each cooperation constraint, DMT upper and lower bounds are derived and shown to be tight, i.e., the lower bound meets the upper bound. A full characterization of the DMT of the channel is thus established. The upper bounds are evaluated using the capacity upper bounds and the lower bounds are obtained based on our proposed transmission schemes. The proposed transmission schemes only require partial channel state information at transmitter side (CSIT), making them suitable for practical applications. Specifically, for the transmission scheme designed under the full-duplex constraint, the partial CSIT is obtained by letting each destination represent the fading magnitude of each of its incoming links using 1 bit of information and feed back this information to the sources. In the half-duplex case, the proposed transmission scheme requires no more than 3 bits of feedback information to represent the fading magnitude of each link. Our DMT results show that source cooperation can notably improve the system diversity performance over the whole multiplexing gain region even under the half-duplex constraint.

As one of the key technologies for future wireless communication systems, user cooperation has a great potential in improving the system performance. In this paper, the diversity benefit of user cooperation is evaluated using diversity-multiplexing tradeoff (DMT) as the performance metric. Ways of exploiting the diversity benefit are devised. We investigate two typical channel models, namely, the multiple-access channel (MAC) and the interference channel (IFC). For the MAC, all the terminals are equipped with multiple antennas and theK(K≥ 2) sources cooperate in a full-duplex mode. We determine the optimal DMT of the channel and propose a compressed-and-forward (CF) based cooperation scheme to achieve the optimal DMT. For the IFC, we consider a two-user channel with single-antenna terminals and full-duplex source cooperation. A DMT upper bound and two DMT lower bounds are derived. The upper bound is derived based on a channel capacity upper bound, and the lower bounds are derived using decode-and-forward (DF) based cooperation schemes. In most channel scenarios, the bounds are found to be tight. This implies that under certain channel scenarios, the optimal DMT of the channel can be achieved by DF-based cooperation schemes.

In this paper, we propose a transmission scheme for the two-user symmetric multiple antenna interference channel (IFC) and show that the proposed transmission scheme can achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. The proposed transmission scheme requires only limited channel state information at the transmitter (CSIT) and is suitable for practical implementation. The limited CSIT is obtained by letting the destinations quantize the required information and feed back to the sources. Rules for implementing the quantization are proposed and the number of bits needed to represent the quantization is calculated. It is shown that for the proposed transmission scheme to be DMT optimal, the number of feedback bits should increase in log scale with respect to signal-to-noise ratio.

Low-density parity-check (LDPC) codes combined with cascade combining are able to achieve excellent bit-error rate (BER) performance over multipath fading channels. Cascade combining, which involves two stages of diversity combining, is very useful for situations where site diversity exists and it can reduce the complexity of the combiner when the number of diversity branches increases. The average output signal-to-noise ratio and the uncoded BER expressions of cascade combining over independent and identically distributed (i.i.d.) Nakagami-m fading channels are derived. The BER expressions of cascade combining with LDPC codes over i.i.d. Nakagami-m fading channels are derived based on the Gaussian approximation (GA) approach. These expressions include selection combining and maximum-ratio combining as special cases. The signal-to-noise ratio (SNR) thresholds for error-free decoding are obtained using density evolution (DE). Comparisons among GA analysis, DE analysis, and simulations show that they are in good agreement. The expressions obtained from the GA analysis provide better theoretical understanding of the system performance and allow us to compute the BER and SNR threshold more efficiently as compared to DE and simulations. Lastly, the stability conditions for GA and DE analyses, which are found to be exactly the same, are also presented.

Abstract In this paper, we derive the upper bound of bit‐error rate (BER) performance and diversity gain for a decode‐and‐forward (DF) cooperative system. Either maximal‐ratio combining (MRC) or cooperative MRC (C‐MRC) is employed at the receiver in the presence of independent, non‐identical Nakagami‐m fading. Both analytical and simulation results show that C‐MRC takes advantage of spatial diversity more efficiently and thus achieves the same or better performance and diversity order as compared to MRC. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we investigate the diversity-multiplexing tradeoff (DMT) of the delay-limited symmetric two-user fading interference channel (IFC) with full-duplex source cooperation. Upper and lower bounds on the channel DMT are derived and shown to be tight, i.e., the lower bound meets the upper bound. The DMT behavior of the channel is thus fully determined. The upper bound is derived based on a channel capacity upper bound. The lower bound is derived based on a proposed transmission scheme which requires only limited CSIT obtained from destination feedback. Specifically, the magnitude of each of the fading links is represented by the destinations using one bit of information and fed back to the sources. The DMT result shows that source cooperation can notably improve the system diversity performance over the whole multiplexing rate region.

In this paper, we investigate the optimal transmitter design, under the restriction of Gaussian signalling without preprocessing of information, for a secure multiple-input single-output (MISO) cognitive radio network (CRN), which consists of four terminals: a pair of secondary user transmitter (SU-Tx) and receiver, an eavesdropper and a primary user (PU). It is assumed that all the channel state information is not perfectly known at the SU-Tx due to the channel estimation errors and the loose cooperation between the SU and the PU. The design involves a nonconvex semi-infinite optimization problem, which maximizes the rate of the secondary link while avoiding harmful interference to the PU and preventing the eavesdropper from decoding the messages sent regardless of the uncertainties in the CSI. For this challenging optimization problem, we relate it with a sequence of semi-infinite capacity-achieving transmitter design problems in an auxiliary CRN without any eavesdropper, which can then be solved through transformations and using convex semidefinite programs. Finally, numerical examples are presented to evaluate the performance of the proposed algorithm.

In this study, the authors analyse the bit-error rate (BER) performance of band-limited direct-sequence code-division multiple-access (DS-CDMA) systems employing two types of multiuser detectors, namely, linear decorrelator with whitening (LDW) and linear minimum mean-squared error (MMSE) detector over frequency-selective multipath channels with multitone jamming (MTJ). The authors consider the generalised-K distribution in order to include both shadowing and small-scale fading effects. Generalised-K distribution is generic and versatile as it can incorporate various composite fading and shadowing effects observed in wireless communication channels with mathematical tractability. The authors derive analytical BER expressions that are functions of band-limited pulse shapes, MTJ parameters and shadowing and fading parameters of the wireless channel. The system incorporates either a Nyquist pulse or a cosine band-limited pulse shape. Numerical results show that the systems with cosine pulse demonstrate better BER performance than the ones with Nyquist pulse in the presence of MTJ. Furthermore, in the presence of MTJ, MMSE-based systems demonstrate improved BER performance as compared to LDW-based systems. The authors also observe that the systems employing two-dimensional scheme, that is, the combination of space and multipath diversity, outperform the ones with multipath diversity scheme.

In this study, the effects of timing and frequency offsets on bit-error rate (BER) performance of fast frequency-hopped M-ary frequency-shift keying communication systems over Rician-fading channels with both multitone jamming (MTJ) and partial-band noise jamming (PBNJ) are investigated. Analytical BER expressions are derived for both linear-combining and product-combining receivers. Numerical results show that under both MTJ and PBNJ conditions, the BER performance falls between the two extreme cases, in which either MTJ or PBNJ presents. It is found that the BER performance is severely degraded as the timing or frequency offset increases. The product-combining receiver is found to be more sensitive to the timing and frequency offsets than the linear-combining receiver. It is also observed that for the linear-combining receiver, the optimum diversity order increases as the timing and frequency offset increases over both Rician-fading and Rayleigh-fading channels; however, the reverse is true for the product-combining receiver.

In this paper, we address the physical-layer security issue of a secondary user (SU) in a spectrum-sharing cognitive radio network (CRN) from an information-theoretic perspective. Specially, we consider a secure multiple-input single-output (MISO) cognitive radio channel, where a multi-antenna SU transmitter (SU-Tx) sends confidential information to a legitimate SU receiver (SU-Rx) in the presence of an eavesdropper and on the licensed band of a primary user (PU). The secrecy capacity of the channel is characterized, which is a quasiconvex optimization problem of finding the capacity-achieving transmit covariance matrix under the joint transmit power and interference power constraints. Two numerical approaches are proposed to derive the optimal transmit covariance matrix. The first approach recasts the original quasiconvex problem into a single convex semidefinite program (SDP) by exploring its inherent convexity; while the second one explores the relationship between the secure CRN and the conventional CRN and transforms the original problem into a sequence of optimization problems associated with the conventional CRN, which helps to prove that beamforming is the optimal strategy for the secure MISO CR channel. In addition, to reduce the computational complexity, three suboptimal schemes are presented, namely, scaled secret beamforming (SSB), projected secret beamforming (PSB) and projected cognitive beamforming (PCB). Lastly, computer simulation results show that the three suboptimal schemes can approach the secrecy capacity well under certain conditions.

Interleaving, which is commonly used to combat bursts of errors, is an important technique in digital communications systems. The blind detection of interleaving parameters has been studied by many researchers for forward-error-correction (FEC) encoded binary data streams. In this paper, we use finite field Gauss elimination with pivoting to blindly estimate interleaving period of non-binary data streams. To be specific, the data streams are encoded by Reed Solomon codes. Suppose the percentage of zeros in each column of the analytical matrix block is denoted as phi0. Numerical results show that both the variance and the mean of phi0can be used as the evaluation parameter to detect the interleaving parameters. However, the former approach provides a 1-dB gain over the latter.

In this paper, we study the sensing-throughput tradeoff problem for a multiple-channel cognitive radio (CR) network. In particular, using the sensing-throughput tradeoff metric, we investigate the design of the optimal spectrum sensing time and power allocation schemes so as to maximize the aggregate ergodic throughput of the cognitive radio network to guarantee the quality of service (QoS) of the primary users (PUs) without exceeding the power limit of the secondary transmitter. The optimal sensing time and power allocation strategies are developed under the average power constraint. Finally, numerical results show that, for a CR network with 3 channels, whose signal-to-noise ratio of PUs are -12dB, -15dB and -20dB, respectively, there is an optimal sensing time, and the optimal sensing time is almost insensitive to the total transmit power.

To improve the spectrum utilization efficiency, cognitive radio (CR) has been proposed by allowing a cognitive radio network (CRN) to coexist with a licensed primary network. The security issues, although critical, have been less explored in the literature of CRN. In this paper, we consider a secure CRN in which a multi-antenna secondary user (SU) transmitter sends confidential information to a SU receiver on the same frequency band with a primary user (PU) in the presence of an eavesdropper. All receive terminals are equipped with a single antenna. The capacity-achieving transmitter design is formulated as a quasiconvex optimization problem to maximize the rate of the secondary link while avoiding harmful interference to the PU and preventing the eavesdropper from decoding the messages sent. By exploring the inherent convexity, the original problem is solved efficiently by a single semidefinite program (SDP). Besides, two suboptimal algorithms are proposed to reduce the computational complexity, namely, scaled secret beamforming (SSB) and projected secret beamforming (PSB). It is shown through computer simulations that the two suboptimal algorithms can achieve close-to-optimal secrecy capacity under certain conditions.

The authors studied bit-error rate (BER) performance of asynchronous band-limited direct-sequence code-division multiple-access (DS-CDMA) systems with various diversity-combining receivers over Generalised-K fading channels. The effects of band-limited pulse shapes, multitone jamming, multiple-access interference as well as both flat and frequency-selective fading are considered. The Generalised-K model is adopted in order to include the effects of shadowing and fading of a wireless channel. The authors consider binary phase-shift keying as the modulation technique. The analytical expressions are valid for any arbitrary value of Generalised-K distribution parameters. Two types of band-limited pulses, namely spectrum raised cosine and Beaulieu–Tan–Damen (BTD) pulses, are incorporated in the analysis. Numerical results show that the system with BTD pulse outperforms the one with SRC pulse for various diversity-combining receivers under various channel conditions. Furthermore, by incorporating a minimum mean-square error stage in the multipath diversity receiver, the BER performance can be further improved.

In this letter, we propose a vector state-scalar observation (VSSO) Kalman filter for channel estimation in doubly-selective orthogonal frequency division multiplexing (OFDM) systems. Vector state-vector observation (VSVO) Kalman filters have been reported before in the literature for this purpose. The proposed VSSO Kalman filter achieves the same performance as the VSVO Kalman filter and results in 92% complexity savings. The Kalman filter outperforms a recently proposed linear minimum mean square error (LMMSE) estimator and achieves a high spectral efficiency of 93% as compared to the LMMSE estimator of 68%. A key aspect of this paper is that we show how the observed pilot symbol vector can be decorrelated or decoupled into uncorrelated multipath scalars. This aspect (and the proposed Kalman filter) is similar in spirit to that of a quasi-static channel.

An optimum maximum-likelihood (ML) receiver structure for a fast frequency-hopped M-ary frequency-shift keying system over frequency-selective Rician-fading channels against partial-band-noise jamming and additive white Gaussian noise is proposed. In addition, we propose two suboptimum ML receivers and derive their corresponding analytical bit-error rate expressions.

In this paper, we consider a wideband cognitive radio network (CRN) which can simultaneously sense multiple narrowband channels and thus aggregate the perceived available channels for transmission. We study the problem of designing the optimal spectrum sensing time and power allocation schemes so as to maximize the average achievable throughput of the CRN subject to the constraints of probability of detection and the total transmit power. The optimal sensing time and power allocation strategies are developed under two different total power constraints, namely, instantaneous power constraint and average power constraint. Finally, numerical results show that, under both cases, for a CRN with three 6 MHz channels, if the frame duration is 100 ms and the target probability of detection is 90% for the worst case signal-to-noise ratio of primary users being -12 dB, -15 dB and -20 dB, respectively, the optimal sensing time is around 6 ms and it is almost insensitive to the total transmit power.

Abstract In this paper, we propose a receiver structure for transmitted‐reference ultra‐wideband (TR‐‐UWB) systems with both narrowband interference (NBI) and inter‐pulse interference (IPI) mitigation capabilities. The effects of additive white Gaussian noise (AWGN) and the IEEE 802.15.4a fading channel are also taken into consideration. We adopt band‐stop filtering to suppress the NBI. For IPI, it is statistically removed by a sum‐and‐average process. Theoretical analysis is carried out to study the lower bound of the bit‐error rate (BER) performance of the proposed receiver. Numerical results show that the proposed receiver is able to provide satisfactory performance and is robust to variations in the system design parameters. It is also observed that the proposed receiver is able to deliver good performance even when there is zero delay between the reference and data pulses, which can effectively double the system throughput. Copyright © 2008 John Wiley & Sons, Ltd.

In this paper, we propose a noncoherent space-frequency (SF) code for multiple-input-multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) systems for broadband wireless communications. The proposed noncoherent SF code matrix is constructed as a combination of a noncoherent SF code matrix and a differential modulation matrix. Comparing to noncoherent SF codes and differential SF codes in the literature, the advantages of our proposed code are higher spectrum efficiency, no error floor and more suitable for broadband communication systems. Taking advantage of the codeword structure of the proposed SF code, we devise a two-stage decoding scheme, in which the decoding process is implemented in two steps by decoding the component noncoherent codeword matrix and the component differential codeword matrix sequentially. Accordingly, the decoding scheme efficiently reduces decoding complexity. Simulation results show that our proposed scheme with two-stage decoding yields better performance than the noncoherent SF codes and frequency-domain differential codes proposed in the literature.

In this paper, we focus on noncoherent space-frequency (SF) coded multiple-input-multiple-output orthogonal-frequency-division-multiplexing (MIMO-OFDM) systems. Based on OFDM subcarrier grouping, a group-based unitary space- frequency code is proposed and the effect of grouping on system performance is studied. Comparing to the coding scheme without grouping, which implements SF coding among all the OFDM tones, the proposed group-based coding scheme can greatly reduce the decoding complexity, making the noncoherent SF codes more applicable to practical use. By relating the noncoherent SF codes with packings in Grassmann manifold, we propose an efficient decoding method by restricting the implementation of decoding within a subset of the codebook. Numerical results are presented to demonstrate and verify our proposals.

Time-selective channels in orthogonal frequency division multiplexing (OFDM) systems introduce intercarrier interference (ICI) which destroys the orthogonality among the subcarriers. Equalisation techniques are needed to mitigate ICI, requiring high computational complexity for large values of Doppler spread. In this paper, we propose low-complexity equalisation methods that result in 75% savings in computations over some of the conventional methods. The savings are achieved without any loss in performance. One of the methods is to apply the one-tap equaliser on selected subcarriers to detect the corresponding symbols. We develop a criterion to determine the eligible subcarriers.

Analytical expressions of bit-error rate (BER) are derived for a fast-frequency-hopping M-ary frequency-shift- keying (FFH/MFSK) spread-spectrum communication system over frequency-selective Rayleigh-fading channels with multitone jamming (MTJ) and additive white Gaussian noise. The FFH/MFSK systems employing a linear-combining receiver (LCR) and a product-combining receiver (PCR) are studied. The desired signal and MTJ are assumed to undergo independent fading. The characteristic function approach is used to derive the analytical BER expressions for higher diversity levels. The analytical BER expressions are validated by simulation results and the PCR is found to outperform the LCR when the jamming power is relatively strong.

Since the standard union bound for space–time codes may diverge in quasi-static fading channels, the limit-before-average (LBA) technique has been exploited to derive tight performance bounds. However, it suffers from the computational burden arising from a multidimensional integral. In this paper, efficient bounding techniques for space–time codes are developed in the framework of Gallager bounds. Two closed-form upper bounds, the ellipsoidal bound and the spherical bound, are proposed that come close to simulation results within a few tenths of a decibel. In addition, two novel methods of weight enumeration operating on a further reduced state diagram are presented, which, in conjunction with the bounding techniques, give a thorough treatment of performance bounds for space–time codes.

In this paper, an adaptive window length estimation for channel estimation in direct-sequence (DS) code-division multiple-access (CDMA) receivers is presented. The estimated optimum window length is derived based on autocovariance analysis of the estimated channel coefficients. As the propagation channel changes over time, an adaptive algorithm for updating the window length is proposed through Doppler and signal-to-noise ratio (SNR) estimations. The proposed system improves the performance by adaptively selecting and continuously updating the window lengths over a wide-range of velocities (5 to 400 kmph).

The knowledge of Doppler spread is very important in many channel estimation (tracking) algorithms for flat fading channels. Recently, doppler spread estimators based on the profile of the power spectral density (psd) have been published. They make use of the fact that there is an abrupt change in the psd around the maximum Doppler frequency. However, this assumption is invalid in low signal-to-noise ratios (SNRs). In this paper, we introduce an iterative Kalman autoregressive (IKAR) estimator which overcomes this drawback. In doing so, we also study the excellent detection properties of the IKAR detector and demonstrate its superiority over some of the conventional detectors. The IKAR estimator performance is studied for two low SNR scenarios.

Recently, Gallager's bounding techniques have been used to derive tight performance bounds for coded systems in fading channels. Most works in this field have thus far dealt with coherent decoding. This paper develops Gallager bounds for noncoherent systems in fading channels. Unlike coherent decoding, the exact error probability of a noncoherent decoder/detector conditioned on the fading coefficients does not admit a closed-form expression. This difficulty is overcome in this paper by employing the Chernoff technique. Although it weakens the bounds to some extent, the Chernoff technique enables the derivations of the limit-before-average (LBA) bound and Gallager bounds in closed form for noncoherent fading channels. Numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound.

The bit-error rate (BER) analysis for BPSK pre-detection maximal ratio combining (MRC) systems in two-wave with diffuse power (TWDP) fading is presented. In TWDP fading, the received signal is composed of two specular components in addition to the diffuse signal. The analysis shows that in TWDP fading, the BER of the MRC system is given by the weighted sum of the BERs of a number of MRC systems in Rician fading. The methodology used in the analysis is verified through simulation.

We present improved differential lattice decoding (DLD) for multi-antenna differential modulation by exploiting both basis reduction and sphere decoding. The extra complexity of DLD is shown to be worthwhile in terms of the obtained performance gain over Clarkson et al.'s decoding scheme. With roughly another fold of complexity of basis reduction, DLD augmented by a local search practically attains the maximum-likelihood decoding performance.

In this paper, we propose a frequency-domain approach to estimate carrier frequency offset in a third-generation wideband code-division multiple-access (3G-WCDMA) system. The frequency-offset estimator, which is designed to operate in a multipath fading environment, does not require any prior knowledge about the correlation function of the fading process. The nature of the estimator is very conducive for the usage of binary search that greatly accelerates the estimation procedure. The algorithm has a low computational complexity in the order of O(N) and the dual features of estimating frequency offset and Doppler spread simultaneously. It is shown to have a wide estimation range. The performance is good even in low SNR, especially when selection diversity combining is used. It meets the Third Generation Partnership Project (3GPP) requirement of 0.1 ppm for the frequency-offset estimation even for short observation intervals.

From a lattice viewpoint, Clarkson, Sweldens and Zheng significantly reduced the complexity of multiantenna differential decoding. Their approximate decoding algorithm, however, has not unleashed the full potential of lattice decoding. In this paper, we present several improved algorithms, generally referred to as differential lattice decoding (DLD), for multiantenna communication. We first analyze two distinct approximate DLD algorithms, and then develop an algorithm that exactly finds the closest lattice point in the Euclidean space. This exact DLD is subsequently augmented by local search to compensate for the remaining approximation. The small amount of extra complexity of the exact or augmented DLD is rewarded by a clear performance gain. We find that employing basis reduction is very effective to reduce the overall decoding complexity for high lattice dimensions. Moreover, the dimension of the lattice defined in this paper is independent of the number of receive antennas, which results in not only lower complexity, but also better performance for a multiantenna receiver.

This letter presents the bit error rate (BER) performance analysis for an uncoded binary phase-shift keying (BPSK) system in two-wave with diffused power (TWDP) fading channels. Simulation results of receiver performance, with or without maximal-ratio combining (MRC), are also presented. These performance studies quantitatively reveal that TWDP fading can produce a link worse than Rayleigh fading when the two direct waves are equal in strength and have a combined power of /spl ges/ 6 dB higher than the diffused power. These results point to using TWDP fading rather than Rayleigh fading as a worst case scenario in designing communication systems, especially in situations where TWDP fading is likely, such as when directional antennas or arrays and when wideband signals are used.

We show that linear prediction (LP)-based decision-feedback detection (DFD) for nondiagonal differential space-time modulation (DSTM) may suffer from a severe performance degradation in continuously fading channels. DSTM constellations that incur no degradation in LP-DFD are identified as those with a diagonal generator. To cater to other constellations, we propose a low-complexity DFD scheme by inserting decision-feedback symbols into the metric of multiple-symbol differential detection.

Linear prediction (LP)-based decision-feedback differential detection (DFDD) only works for diagonal differential space-time modulation (DSTM) when fading is changing fast and continuously. For other constellations, it suffers bad performance. We propose DFDD based on multiple-symbol differential detection (MSDD) for DSTM to cope with continuous fading. A key observation is that the correlation matrix of the received signal can be expressed in terms of DSTM matrices corresponding to the sent information symbols. In this way, decision feedback can be inserted into the MSDD metric, yielding a DF-MSDD receiver while maintaining almost the same performance as MSDD.

Existing work on decision feedback detection (DFD) of differential space-time modulation (DTSM) were largely confined to diagonal constellations. In other works considering nondiagonal constellations, the temporal variation of fading in the DTSM supersymbol duration was ignored. In this paper, we take a close look at the DFD receiver structure for nondiagonal DSTM in temporally correlated fading. We identify the constellations of which the error performance is not influenced by ignorance of fading variation. In addition, by analyzing the error performance, we demonstrate that existing DFD, is however, fundamentally mismatched to other constellations in fast fading. A major conclusion is that diagonal design still plays an important role for the efficacy of DFD for nondiagonal constellation in fast fading.

Novel decision-feedback (DF) linear prediction (LP) receivers, which process multiple samples per symbol interval in conjunction with optimal sample combining, are proposed for differential space-time modulation (DSTM) over Rayleigh fast-fading channels. Performance analysis demonstrates that multisampling DF-LP receivers outperform their symbol-rate sampling counterpart in fast fading substantially. In addition, an asymptotically tight upper bound on the pairwise error probability is derived. In view of this bound, the design criterion of DSTM for fast fading is the same as that for block-wise static fading. To avoid the estimation of the second-order statistics of the channel, a polynomial-model-based DF-LP receiver is proposed. It can approach the performance of the optimum DF-LP receiver at high signal-to noise ratios, provided fading is moderate.

Approximate maximum-likelihood noncoherent sequence detection (NSD) for differential space-time modulation (DSTM) in time-selective fading channels is proposed. The starting point is the optimum multiple-symbol differential detection for DSTM that is characterized by exponential complexity. By truncating the memory of the incremental metric, a finite-state trellis is obtained so that a Viterbi algorithm can be implemented to perform sequence detection. Compared to existing linear predictive receivers, a distinguished feature of NSD is that it can accommodate nondiagonal constellations in continuous fading. Error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers. By incorporating the reduced-state sequence detection techniques, performance and complexity tradeoffs can be controlled by the branch memory and trellis size. Numerical results show that most of the performance gain can be achieved by using an L-state trellis, where L is the size of the DSTM constellation.

In previous years, the MUSIC timing estimator were proposed for direct-sequence code-division multiple access (DS-CDMA) signals. It has been generally assumed that the channel noise is temporally white. However it may be invalid in practice due to, for instance, the presence of some narrowband interference or the lumping of secondary users into with the noise. We consider blind code timing in unknown colored noise by using the matrix decomposition technique. A subspace-based code timing estimation algorithm is presented and its performance is evaluated by computer simulation and compared with the MUSIC method. It is proved that the proposed timing estimation algorithm provides better performance than the MUSIC method in colored noise.

We consider the propagation delay estimation of a direct-sequence code-division multiple-access (DS-CDMA) system in unknown correlated noise. The new propagation delay estimation method proposed here is based on generalized correlation decomposition (GCD). First, the received signal with a dual-antenna through a flat-fading channel is modeled. Then, two GCD-based propagation delay estimators: dual-antenna singular value decomposition (SVD) and dual-antenna canonical correlation decomposition (CCD) estimators are presented and compared with common MUSIC estimator. Simulation results show that the proposed estimators, especially the dual-antenna CCD estimator, are robust against the near-far problem and outperform the common MUSIC estimator in unknown correlated noise.

A new recursive technique for the excision of FM interference in DS spread-spectrum communication system is introduced. The proposed algorithm tabulates the jammer-corrupted received samples as a matrix to model a time-varying process. Input vectors are sent into the matrix to produce upon multiplication output vectors from which the frequency information in the matrix is deduced. The scheme resembles the familiar closed-loop frequency response estimation procedures in classical control theories. The estimated frequency then tunes an adaptive notch filter for interference suppression. The method provides more accurate IF estimates than given by the Wigner-Ville distribution and a performance close to notch filtering at the exact IF at a significantly lower computational requirement.

We derive the analytical bit-error rate (BER) expressions for a fast frequency-hopped binary frequency-shift keying self-normalizing receiver over a fading channel with the worst-case band multitone jamming (MTJ) and additive white Gaussian noise (AWGN). The desired signal and MTJ are assumed to undergo independent Rician fading and our analyses, validated with simulation results, show that the system performance is not sensitive to different types of MTJ fading conditions. The self-normalizing receiver is found to be superior to the linear-combining receiver when the signal amplitude does not experience severe fading, while the converse is true under Rayleigh fading signal conditions. Under a Rician fading channel and AWGN conditions, the worst-case MTJ and the worst-case partial-band noise jamming are shown to have similar effects on the BER performance of the self-normalizing receiver with diversity.

This paper studies the bit-error rate (BER) performance of a fast frequency-hopped (FFH) binary frequency-shift-keying (BFSK) clipper receiver in the presence of multitone jamming (MTJ) and additive white Gaussian noise (AWGN). By using the Taylor-series expansion and the quantization approach, the BER expressions for higher diversity levels can be obtained without much extra computational complexity. The analytical BER results, validated by simulations, show that there is an optimum diversity level for the clipper receiver. Performance comparisons among various receivers demonstrate that the BER performance of the clipper receiver is significantly better than that of the linear-combining receiver. In addition, the clipper receiver also outperforms the product-combining receiver and the self-normalizing receiver provided that the clipping threshold is set at the desired signal power level.

We study the bit-error rate performance of a fast frequency-hopped binary frequency-shift-keying (FFH/BFSK) spread spectrum (SS) communication system over fading channels with the worst-case band multitone jamming (MTJ) and additive white Gaussian noise (AWGN). The FFH system employing a clipper receiver is investigated and the corresponding bit-error expressions are obtained using the quantization approach. The desired signal and MTJ are assumed to undergo independent fading and our analysis, validated with simulation results, shows that the performance of the system is not sensitive to a particular type of MTJ fading model.

We derive the optimum structure of a maximum-likelihood (ML) receiver for a fast frequency-hopped binary frequency-shift-keying (FFH/BFSK) spread-spectrum (SS) communication system operating in the presence of multitone jamming (MTJ) and additive white Gaussian noise (AWGN). It is shown that the side information of noise variance, signal tone amplitude, and multiple interfering tone amplitude at each hop, as well as the computation of nonlinear modified Bessel function are required to implement the optimum ML receiver. We have also derived and analyzed two suboptimum receivers-namely, the ML-I and ML-II receivers-for large and small signal-to-noise ratio (SNR), respectively. Performance comparisons among various receivers show that the ML receiver gives the best performance, while the ML-I and ML-II receivers also outperform the other existing methods under both high and low SNR conditions.

The bit-error rate (BER) analysis of an asynchronous cellular direct-sequence code-division multiple-access (DS-CDMA) system over Rician fading channels often results in a complicated multi-integral expression even though Gaussian approximation is applied. As a result, saddlepoint integration (SPI) is introduced to evaluate the BER performance efficiently and accurately. The computational effort of this method grows only linearly with the number of interfering cells in the system, regardless of the number of active mobiles in each cell. The probability density function (pdf) for multiple Rayleigh interferers is compared to that obtained through the combined pdf (c-pdf) approach. Finally, the analysis for the Rician fading channel is evaluated using the SPI technique. The results obtained are accurate compared to the simulation data.

Analytical expressions for bit-error probability are derived for a fast frequency-hopping binary frequency-shift keying (FFH/BFSK) spread-spectrum communication system over a fading channel with worst-case band multitone jamming (MTJ) and additive white Gaussian noise (AWGN). An FFH system employing either a linear-combining receiver or a clipper receiver is investigated. The desired signal and MTJ are assumed to undergo independent fading, and our analysis, validated with simulation results, shows that the performance of the system is slightly improved as the severity of the MTJ fading is increased. The clipper receiver is found to be superior to the linear-combining receiver when the jamming power is strong. The worst-case MTJ is shown to be more harmful than the corresponding worst-case partial-band noise jamming over a fading channel with AWGN.

The performance of a compressive receiver is compared to that of a wideband radiometer in order to determine if there is any significant loss in detection performance that accompanies the added feature of frequency estimation in the compressive receiver. The waveforms to be detected are either sine waves or phase-shift keyed signals, where the latter waveforms can represent either narrow-band binary phase-shift keyed (PSK) signals or direct sequence spread spectrum waveforms. It is shown that the compressive receiver outperforms the radiometer in detecting the presence of a sine wave. The compressive receiver is also shown to exhibit superior performance when the input contains a binary PSK signal and the system is operating under the conditions of low input signal-to-noise power ratio and low probability of false alarm.>

The optimization between the processing gain and the coding gain of a constant-bandwidth direct-sequence spread-spectrum communication system operating in the presence of either a tone jammer or a Gaussian jammer such that the bit-error rate (BER) is minimized is presented. Both bipolar phase-shift keyed pseudo-noise (PN) modulation and quaternary phase-shift keyed PN modulation are considered. Binary BCH codes are used to illustrate the techniques for optimization. The exact BER and its Gaussian approximation are derived and compared. During the optimization, two different approaches are used to obtain the indicator functions of the optimum code. These indicators are tested and shown to yield good results.>