High Signal-to-noise Ratio Region Research Articles

Intelligent threshold selection in fading environment of cognitive radio network: Advances in throughput and total error probability

SummaryOne of the main challenges of spectrum sensing (SS) in the cognitive radio network (CRN) is selection of threshold for captivating the sensing decision, and such an issue becomes more challenging especially at low signal‐to‐noise ratio (SNR) because it affects the sensing performance and throughput of cognitive user (CU). However, the sensing decision of individual CU may not be accurate due to fading effects in the sensing environment, and significant improvement is accomplished with the cooperation of users. Therefore, in this paper, we have investigated the performance of energy detector SS (EDSS) technique in the CRN under fading environment with cooperative and noncooperative SS scenario. Further, we have introduced the concept of critical SNR (γc) to select the appropriate threshold and based on which the algorithms are proposed to enhance the throughput and reduce the total error (sensing error) probability of CU at different SNR (γ). From the results, we have accomplished that at the low SNR region (γ ≤ γc), throughput is maximum with constant false‐alarm rate (CFAR) threshold selection approach in the cooperative scenario while in the high SNR region (γ > γc), its value is maximum with minimizing the error probability (MEP) threshold selection approach in the noncooperative scenario. Moreover, the sensing error is reduced with cooperation, and threshold selection with MEP approach outperforms CFAR approach for γ ≤ γc. Further, the proposed approach outperforms the other approaches in terms of throughput and sensing error (total error) probability in the Rayleigh and Nakagami‐m fading environments.

A Simple Evaluation for the Secrecy Outage Probability Over Generalized-K Fading Channels

A simple approximation for the secrecy outage probability (SOP) over generalized-K fading channels is developed. This approximation becomes tighter as the average signal-to-noise ratio (SNR) of the wiretap channel decreases. Based on this simple expression, we also analyze the asymptotic SOP in the high SNR region of the main channel. Besides simplifying the SOP expression significantly, this asymptotic SOP expression reveals the secrecy diversity order in a general case. Numerical results demonstrate the high accuracy of our proposed approximation results.

A new construction method of QC-LDPC codes with low error floor based on EETS and Zig-Zag

Aiming at the problem that quasi-cyclic low density parity check (QC-LDPC) codes may have the error floor in the high signal to noise ratio (SNR) region, a new construction method of the QC-LDPC codes with the low error floor is proposed. The basic matrix of the method is based on the progressive edge growth (PEG) algorithm and the improved eliminate elementary trapping sets (EETS) algorithm so as to eliminate the elementary trapping sets in the basic matrix, then the Zig-Zag method is used to construct the cyclic shift matrix which is used to extend the basic matrix in order to construct the parity check matrix. The method not only can improve the error floor in the high SNR region, but also can flexibly design the code length and code rate. The simulation results show that at the bit error rate of 10−6, the PEG-trapping-Zig-Zag (PTZZ)-QC-LDPC(3024,1512) codes with the code rate of 0.5, compared with the PEG-Zig-Zag (PZZ)-QC-LDPC(3024,1512) codes and the PEG-QC-LDPC(3024,1512) codes, can respectively improve the net coding gain of 0.1 dB and 0.16 dB. The difference among the bit error rate performance curves will become better with the increase of the SNR. In addition, the PTZZ-QC-LDPC(3024,1512) codes have no error floor above the SNR of 2.2 dB.

Antenna Selection Method of Maximizing Secrecy Rate for Green Secure Spatial Modulation

In secure spatial modulation systems, an active antenna-group (AAG) selection of maximizing the average secrecy rate (SR) is proposed to avoid the disadvantage that conventional AAG selection scheme of minimizing bit error ratio at desired receiver may lead to a substantial SR loss. However, due to the limited active antenna pattern and finite-alphabet inputs, it is very hard for us to optimize the SR without closed-form expression. To address the two issues, first, by exploiting the relationship between minimum mean-square error and mutual information, the expression of SR in the low signal-to-noise ratio (SNR) region is derived. Using the expression, the problem of maximizing SR (Max-SR), called Max-SR I, is converted to integer programming problem. In the high SNR region, we derive an asymptotical lower bound for SR, and find the fact that the Max-SR can be reduced to maximizing the difference of Bob’s minimum Euclidean distance and Eve’s one, called Max-SR II. Through this conclusion, we can find the relationship between SR and bit-error rate. Furthermore, Max-SR III is proposed to overcome the disadvantage of the SR performance loss for the above two asymptotical algorithms in the moderate SNR region, where an approximate expression is exploited as the efficient metric to design AAG. Numerical results show that the SR performance of the proposed Max-SR III is close to that of optimal exhaustive search method, and the Max-SR I and Max-SR II can achieve acceptable SR performance with extremely low complexity.

Further Results on the Cramér–Rao Bound for Sparse Linear Arrays

Sparse linear arrays, such as co-prime and nested arrays, can identify up $O(M^2)$ uncorrelated sources with only $O(M)$ sensors by utilizing their difference coarray model. In our previous work, we derived closed-form asymptotic mean-squared error (MSE) expressions for two coarray based MUSIC algorithms and analyzed the Cramer-Rao bound (CRB) in high signal-to-noise ratio (SNR) regions, under the assumption of uncorrelated sources. In this paper, we provide further analysis of the CRB presented in our previous work. We first establish the connection between two CRBs, the CRB derived with the assumption that the sources are uncorrelated, and the classical stochastic CRB derived without this assumption. We show that they are asymptotically equal in high SNR regions for uncorrelated sources. Next, we analyze the behavior of the former CRB for co-prime and nested arrays with a large number of sensors. We investigate the effect of configuration parameters on this CRB. We show that, for co-prime and nested arrays, this CRB can decrease at a rate of $O(M^{-5})$ for large values of $M$ , while this rate is only $O(M^{-3})$ for an $M$ -sensor ULA. This finding analytically demonstrates that co-prime and nested arrays can achieve better asymptotic estimation performance when the number of sensors is a limiting factor. We also show that for a fixed aperture, co-prime and nested arrays require more snapshots to achieve the same performance as ULAs, showing the trade-off between the number of spatial samples and the number of temporal samples. Finally, we demonstrate our analytical results with numerical experiments.

Analysis and Design of SCMA-Based Hybrid Unicast-Multicast Relay-Assisted Networks.

This paper studies a multi-user network model based on sparse code multiple access (SCMA), where both unicast and multicast services are considered. In the direct transmission scheme, the communication between the base station (BS) and the users is completed with one stage, in which the relay is inexistent. In the two-stage cooperative transmission scheme, any number of relays are placed to improve the reliability of wireless communication system. The BS broadcasts the requested message to users and relays in the first stage, and the successful relays forward the message to unsuccessful users in the second stage. To characterize the performance of these two schemes, we derive the exact and approximate expressions of average outage probability. Furthermore, to take full advantage of the cooperative diversity, an optimal power allocation and relay location strategy in the high signal-to-noise ratio (SNR) regime is studied. The outage probability reaches the minimum value when the first stage occupies half of the total energy consumed. Simulation and analysis results are presented to demonstrate the performance of these two schemes. The results show that the two-stage cooperative scheme effectively reduce the average outage probability in SCMA network, especially in the high SNR region.

Automatic contour extraction algorithm for swept-source optical coherence tomography cornea image

In a swept source-optical coherence tomography system, the telecentric scanning mode gives rise to central saturation artifacts,partial structural loss, and low SNR (signal-to-noise ratio) area in the corneal image, which affects the accuracy of corneal contour extraction. In order to solve this problem, in this paper we propose an automatic extraction algorithm for corneal image of low quality. This algorithm divides the image into high and low SNR region according to the standard deviation distribution of the cornea image. For the high SNR region, we localize the peak point to extract the contour. For the low SNR region, image enhancement is achieved by the registration and superposition of successive frames, which provides reference contour points for low SNR areas. Then corneal contour localization is achieved by weighing the advantages and disadvantages of reference contour points and local line fitting results. Finally, global polynomial fitting is used to achieve the whole corneal contour information. Experiments on the optical eye model show that comparing with the existing algorithms, the accuracy of corneal contour extraction is improved by 4.9% on average.

Analysis and Optimization for Weighted Sum Rate in Energy Harvesting Cooperative NOMA Systems

We consider a cooperative non-orthogonal multiple access system with radio frequency energy harvesting, in which a user with good channel harvests energy from its received signal and serves as a decode-and-forward relay for enhancing the performance of a user with poor channel. We here aim at maximizing the weighted sum rate of the system by optimizing the power allocation coefficient used at the source and the power splitting coefficient used at the user with good channel. By exploiting the specific structure of the considered problem, we propose a low-complexity one-dimensional search algorithm which can provide optimal solution to the problem. As a benchmark comparison, we derive analytic expressions and simple high signal-to-noise ratio (SNR) approximations of the ergodic rates achieved at two users and their weighted sum with fixed values of the power allocation and the power splitting coefficients, from which the scaling of the weighted sum in the high SNR region is revealed. Finally, we provided numerical results to demonstrate the validity of the optimized scheme. Index Terms-Cooperative NOMA, RF-energy harvesting, weighted sum rate analysis and optimization.

Decode-and-Forward Relaying for Cooperative NOMA Systems With Direct Links

This paper investigates a cooperative non-orthogonal multiple access system, in which a base station communicates with two far users with the aid of a decode-and-forward (DF) relay. Three cooperative relaying schemes, namely, the fixed relaying (FR), the selective DF with coordinated direct and relay transmission (SDF-CDRT), and the incremental-selective DF (ISDF) relaying are proposed to enhance the outage performance for the two far users by utilizing both the direct and relay links. Taking into account the received signal-to-noise ratio (SNR) events at the relay, the SDF-CDRT scheme adaptively forms an orthogonal transmission branch with respect to the direct link or keeps silent to reduce error propagation. Besides considering the relay detection results, the ISDF scheme further exploits the limited feedback of the received SNR events from two users, so that error propagation can be avoided and unnecessary relaying can be reduced. Analytical expressions for the outage probabilities and average throughputs of the paired users are derived in closed-form for the three cooperative relaying schemes. Asymptotic expressions for the outage probabilities are derived in the high SNR region. It is shown that the FR and SDF-CDRT schemes achieve a diversity order of one for both users, while the ISDF scheme achieves a diversity order of two for both users. The superior system performance achieved by the proposed schemes over those of the existing methods is verified by Monte Carlo simulations.

Outage probability of scheduled MRT scheme in cognitive MISO networks with imperfect CSI

In this study, the authors assess the performance of a cognitive multiple-input single-output (MISO) network, where the secondary base station schedules a secondary destination D k ∗ to communicate from K candidates, by employing scheduled maximal ratio transmission (MRT) scheme. A practical scenario is considered where imperfect channel state information (CSI) is taken into account. Specially, assuming Rayleigh fading channels, the exact expression for the cumulative distribution function of the received signal-to-noise ratio (SNR) at D k ∗ is derived, from which the outage probability (OP) at D k ∗ is obtained. An asymptotic expression for the OP at high SNR region is also presented, indicating the diversity gain that the scheduled MRT scheme can achieve. Furthermore, the interference OP at the primary receiver is discussed due to imperfect CSI in the link from base station to primary receiver link. Finally, extensive performance evaluation results accompanied with equivalent ones obtained by computer simulations are presented to corroborate the proposed analysis.

Performance of antenna selection schemes in dual hop full-duplex decode-and-forward relaying over Nakagami-m fading channels

In this paper, we investigate the outage performance of several antenna selection (AS) schemes in dual hop full-duplex (FD) multiple-input multiple-output (MIMO) relay networks in which the relay adopts decode-and-forward (DF) protocol over Nakagami-m fading channels. In the network, the source (S), destination (D) and relay (R) are assumed to be equipped with multiple antennas. We assume that the line-of-sight component between S and D cannot be established due to the poor fading environment conditions. For signal transmission-reception during the training period, only a single antenna at each node is selected according to selection techniques, and then with the help of an error-free feedback channel the selected antenna index is sent to the related node. Outage probability (OP) expressions related to AS schemes are obtained in closed forms and asymptotic OPs are also derived in order to get more meaningful insights into OP and diversity behaviour. The theoretical results are verified by Monte Carlo simulations. We show that performance of the FD relay can be significantly improved by using selection techniques compared to half-duplex (HD), especially at low signal-to-noise ratio (SNR) region. In addition, results show that the performance floor level meaning zero diversity at high SNR region, which is also confirmed by asymptotic analysis and is an inherent disadvantage of FD relay, can be decreased. Moreover, it is shown that the FD relay with AS schemes outperforms HD as the target rate increases for a certain value of SNR and residual self-interference power.

Power Allocation Strategy of Maximizing Secrecy Rate for Secure Directional Modulation Networks

In this paper, given the beamforming vector of confidential messages and artificial noise (AN) projection matrix and total power constraint, a power allocation (PA) strategy of maximizing secrecy rate (Max-SR) is proposed for secure directional modulation (DM) networks. By the method of Lagrange multiplier, the analytic expression of the proposed PA strategy is derived. To confirm the benefit from the Max-SR-based PA strategy, we take the null-space projection (NSP) beamforming scheme as an example and derive its closed-form expression of optimal PA strategy. From simulation results, we find the following facts: in the medium and high signal-to-noise-ratio (SNR) regions, compared with three typical PA parameters such $\beta=0.1, 0.5$, and $0.9$, the optimal PA shows a substantial SR performance gain with maximum gain percent up to more than $60\%$. Additionally, as the PA factor increases from 0 to 1, the achievable SR increases accordingly in the low SNR region whereas it first increases and then decreases in the medium and high SNR regions, where the SR can be approximately viewed as a convex function of the PA factor. Finally, as the number of antennas increases, the optimal PA factor becomes large and tends to one in the medium and high SNR region. In other words, the contribution of AN to SR can be trivial in such a situation.

An SNR-adaptive relaying algorithm for multi-antenna cooperative networks

Multiple-input multiple-output (MIMO) and cooperative communications have been attracted great attention for the improvements of communication capacity, power consumption, and transmission coverage. The conventional fixed relaying protocols, amplify-and-forward (AF) and decode-and-forward (DF), have their own advantages and disadvantages, i.e. AF performs better than DF for low signal-to-noise ratio (SNR) region, while the reverse is true for high SNR region. Therefore, this paper proposes an SNR-adaptive forward (SAF) relaying scheme obtaining the advantages of both AF and DF. Furthermore, the proposed SAF does not need to switch between AF and DF when SNR changes. The main idea is to adaptively derive the soft information at the cooperative relay nodes based on the information of the received signal and the SNR. Besides, based on the theoretical analysis and the simulation results, it is affirmed that the proposed SAF achieves superior performance than both AF and DF for all SNRs. Moreover, the performance gain would be improved with the increasing number of parallel cooperative relay nodes.

Serially concatenated belief propagation decoder for low‐density parity‐check codes

A new decoding strategy of belief propagation (BP) for low-density parity-check codes is presented by serially concatenating the traditional simultaneous decoding (also known as flooding) and the informed dynamic decoding (IDD) (e.g. node-wise residual belief propagation (NW RBP) or informed variable-to-check (IVC) RBP). The frame error rates (FER) and bit error rates (BER) of the concatenated BP decoder outperform that of the non-concatenated single decoder. In addition, as the signal-to-noise ratio (SNR) increases, the average number of decoding iterations required for the concatenated BP decoder decreases, and tends to merge with that of the first sub-decoder in the high SNR region. Moreover, since the IDD strategies concerned in this paper require extra effort for the residual computation, and the sequential updating of IDD is much more time consuming than the simultaneous updating of flooding. Therefore, compared with using a single IDD, serially concatenating flooding and IDD reduces both the approximate decoding complexity and the decoding latency because the concatenated decoder is still dominated by the sub-decoder flooding.

Power allocation scheme and spectral efficiency analysis for downlink non‐orthogonal multiple access systems

In this study, the authors investigate the power allocation (PA) problem and spectral efficiency (SE) analysis for the single antenna downlink non-orthogonal multiple access (NOMA) system under the sum rate maximising criteria with minimum rate constraints (SRMC-MRC). For the PA problem, they propose the duality scheme for SRMC-MRC which is considered as the optimal solution for the PA problem on one orthogonal subband in the single antenna NOMA system. They propose the specific user rate maximising criteria with minimum rate constraints (SURMC-MRC) scheme to decrease the computational complexity of SRMC-MRC. The PA problem on one subband under SURMC-MRC is proved to be equivalent to SRMC-MRC. Numerical results show that both the SE and fairness performance for SURMC-MRC can strictly approach to those of the duality scheme in the whole signal-to-noise ratio (SNR) region. They prove that NOMA under SRMC-MRC can obtain SE performance advantage in the high SNR region but accompany with some disadvantages in the low SNR region over the orthogonal multiple access system. This conclusion is verified through numerical results under different parameter conditions.

Outage analysis of TAS/MRC in dual hop full-duplex MIMO relay networks with co-channel interferences

In this paper, we investigate the outage performance of transmit antenna selection (TAS) and maximal-ratio combining (MRC) in dual hop full-duplex (FD) amplify-and-forward (AF) relay network over Rayleigh fading channels. In the analysis, Rayleigh faded multiple co-channel interferers (CCIs) are also taken into account at the relay. In the network, source and destination are equipped with multiple antennas, and relay is equipped with one receive and one transmit antennas, respectively and source-destination link is not available. While the TAS is applied at the source without considering residual self-interference (RSI) effect, received signals at the destination are combined based on the MRC technique. For the analysis, we consider three approaches at the relay. In the first, we consider the received signal at the relay is corrupted by faded RSI and noise, in the second one, the RSI is considered as non-fading. In the last one, the noise is neglected. In all cases, the relay suffers from multiple Rayleigh faded CCIs. Outage probability (OP) expression related to all the cases is derived and obtained in single integral forms in case of the faded/non-fading RSI and in closed form in case of the noise neglected approach. Moreover, we also find asymptotic OPs and conduct effective diversity order analysis. The analytical results are verified by the Monte Carlo simulations. Results show that TAS decreases error floor at high signal-to-noise ratio (SNR) region and MRC provides diversity gain at low SNR region. In addition, approaches II and III are good approximations to approach I at low and high SNR regions, respectively.

Ergodic secrecy capacity of MRC/SC in single-input multiple-output wiretap systems with imperfect channel state information

This paper investigates the secrecy performance of maximal ratio combining (MRC) and selection combining (SC) with imperfect channel state information (CSI) in the physical layer. In a single-input multipleoutput (SIMO) wiretap channel, a source transmits confidential messages to the destination equipped with M antennas using the MRC/SC scheme to process the received multiple signals. An eavesdropper equipped with N antennas also adopts the MRC/SC scheme to promote successful eavesdropping. We derive the exact and asymptotic closed-form expressions for the ergodic secrecy capacity (ESC) in two cases: (1) MRC with weighting errors, and (2) SC with outdated CSI. Moreover, two important indicators, namely high signal-to-noise ratio (SNR) slope and high SNR power offset, which govern ESC at the high SNR region, are derived. Finally, simulations are conducted to validate the accuracy of our proposed analytical models. Results indicate that ESC rises with the increase of the number of antennas and the received SNR at the destination, and fades with the increase of those at the eavesdropper. Another finding is that the high SNR slope is constant, while the high SNR power offset is correlated with the number of antennas at both the destination and the eavesdropper.

Compressed sensing-based time-domain channel estimator for full-duplex OFDM systems with IQ-imbalances

In full-duplex orthogonal frequency-division multiplexing (OFDM) systems with in-phase and quadrature (IQ) imbalances, a time-domain least squares (TD-LS) channel estimator is proposed for estimating both the source-to-destination (intended) and the destination-to-destination (self-interference) channels. To further improve the performance, an adaptive orthogonal matching pursuit (OMP) is proposed and its sparsity is estimated by a threshold method. Finally, the full-duplex interference is removed using serial interference cancellation and sphere decoding is used to complete the maximum likelihood detection. Simulation results demonstrate that in terms of both the mean square error (MSE) and the bit error rate (BER), the proposed adaptive OMP performs better than the TD-LS by exploiting the sparse property of the channel. Additionally, compared to the gradient projection, the proposed adaptive OMP is better in the low and medium signal-to-noise ratio (SNR) regions and marginally worse in the high SNR region.

On the Multiband Carrier Aggregated Nonlinear LTE-A System

This paper analyzes the impact of nonlinear high power amplifiers (HPAs) on the multiband carrier aggregated (CA) long-term evolution-advanced (LTE-A) system. It is assumed that the LTE-A system consists of a multi-input-multioutput (MIMO) orthogonal frequency-division multiplexing (OFDM)-based downlink physical-layer architecture. It has been shown that the nonlinear distortion caused by HPAs can be represented in terms of a complex attenuation factor and additive zero mean Gaussian “nonlinear” noise. The closed-form generalized expressions of complex attenuation factor and variance of additive Gaussian nonlinear noise are derived that are applicable to any number of aggregated bands with any nonlinearity order and memory depth. From these expressions, the overall performance of a multiband CA-MIMO-OFDM system in terms of symbol error rate and error vector magnitude for M-ary quadrature amplitude modulation (M-QAM) has been evaluated. We also investigate the combined effect of a number of aggregated bands, input-back off, and diversity gain on the performance of a CA-MIMO-OFDM system. It is observed that diversity gain can improve the performance of CA-MIMO-OFDM in low signal-to-noise ratio (SNR) region. However, in the high SNR region, there is no substantial effect of increasing diversity on the performance. A good agreement between the analytical and simulation results in the multipath Rayleigh fading channel validates the theoretical results obtained in this paper.

Analysis and Optimization of Caching and Multicasting in Large-Scale Cache-Enabled Heterogeneous Wireless Networks

Heterogeneous wireless networks (HetNets) provide a powerful approach to meeting the dramatic mobile traffic growth, but also impose a significant challenge on backhaul. Caching and multicasting at macro and pico base stations (BSs) are two promising methods to support massive content delivery and reduce backhaul load in HetNets. In this paper, we jointly consider caching and multicasting in a large-scale cache-enabled HetNet with backhaul constraints. We propose a hybrid caching design consisting of identical caching in the macro-tier and random caching in the pico-tier, and a corresponding multicasting design. By carefully handling different types of interferers and adopting appropriate approximations, we derive tractable expressions for the successful transmission probability in the general signal-to-noise ratio (SNR) and user density region as well as the high SNR and user density region, utilizing tools from stochastic geometry. Then, we consider the successful transmission probability maximization by optimizing design parameters, which is a very challenging mixed discrete-continuous optimization problem. By exploring structural properties, we obtain a near optimal solution with superior performance and manageable complexity. This solution achieves better performance in the general region than any asymptotically optimal solution, under a mild condition. The analysis and optimization results provide valuable design insights for practical cache-enabled HetNets.