Expression For Error Probability Research Articles

Covert performance enhancement in NOMA enabled CoMP network with optimal RIS selection

In this paper, we consider the covert rate maximization problem for the cell edge user in a reconfigurable intelligent surface (RIS) aided downlink non-orthogonal multiple access (NOMA) network with coordinated multipoint (CoMP) transmission in the presence of channel estimation errors. We derive the analytical expression for the detection error probability (DEP) at the adversary (Willie) assuming the worst case scenario where they employ optimal detection threshold. With the derived analytical expression, we propose an optimal RIS selection scheme to boost the covert rate. To further improve the covert performance, we optimize the NOMA power allocation coefficients and phase shifts of the selected RIS subject to the target rate and covertness constraints. Simulation results demonstrate the improvement in covert rate and robustness offered by the proposed scheme in the presence of channel estimation errors over other benchmarks.

Performance analysis of FSO communications over a generalized turbulence fading channel with pointing error

SummaryQuantitatively assessing the performance of free space optical (FSO) communication systems requires an accurate description of turbulence induced fading. However, it is well known that common irradiance distributions inaccurately model intensity tail regions. Recently, a general fading model as the product of arbitrary number of Gamma with inverse Gamma was proposed and shown to accurately predict measurements, besides containing many well‐known models as special cases. This paper is concerned with analyzing the effect of discrepancies among different fading distributions on optical system performance in terms of bit error rates and capacity. Based on the general fading model a unified analysis of the channel structure effects on FSO communications in the presence of turbulence and pointing error is presented. The outage probability is investigated for both homodyne and direct detection schemes. Closed form expressions for the average probability of bit error for intensity modulation, phase shift keying and polarization shift keying, single‐input‐single‐output systems are given and verified by Monte‐Carlo simulations. Spatial diversity is also studied through single‐input‐multiple‐output systems. Also, the ergodic capacity is derived. Comparisons between the proposed distributions and other widely used distributions are carried out and show significant differences among existing fading models. This suggests possible improvements in the spectral efficiency and error performance design of optical wireless communication systems.

A Simple Design of Reconfigurable Intelligent Surface-Assisted Index Modulation: Generalized Reflected Phase Modulation

As a potential member of next generation wireless communications, the reconfigurable intelligent surface (RIS) can control the reflected elements to adjust the phase of the transmitted signal with less energy consumption. A novel RIS-assisted index modulation scheme is proposed in this paper, which is named the generalized reflected phase modulation (GRPM). In the GRPM, the transmitted bits are mapped into the reflected phase combination which is conveyed through the reflected elements on the RIS, and detected by the maximum likelihood (ML) detector. The performance analysis of the GRPM with the ML detector is presented, in which the closed form expression of pairwise error probability is derived. The simulation results show the bit error rate (BER) performance of GRPM by comparing with various RIS-assisted index modulation schemes in the conditions of various spectral efficiency and number of antennas.

Emission rate optimization in diffusion-based molecular communication among mobile bacteria

In quorum sensing (QS), bacteria exchange information by using molecular signals to work together. In this paper, we study diffusion-based molecular communication with the QS mechanism between the transmitter node and receiver node which are composed of a population of mobile bacteria in a cluster, respectively. The expression of average bit error probability (BEP) at a receiver bacterium is derived. Furthermore, we use the projected gradient descent (PGD) algorithm to solve the optimization problem whose objective is to minimize the average BEP under emission rate constraints which require that the emission rate of each transmitter bacterium has lower and upper bounds. Finally, the numerical results show the PGD algorithm has good convergence behaviors and it is more efficient in finding the optimal emission rate with fewer iterations than genetic algorithm. The obtained results are expected to provide guidance in designing QS-based molecular communication system with lower average BEP.

On Performance of Low-Power Wide-Area Networks With the Combining of Reconfigurable Intelligent Surfaces and Relay

This article proposes an integration of multiple reconfigurable intelligent surfaces (RISs) with a relay to enhance the performance of a low-power wide-area (LPWA) network. Specifically, besides using the traditional relaying approach to assist the transmission between an Internet of Things (IoT) sensor and a gateway, multiple RISs are also utilized to boost the intermediate links between the IoT sensor and the relay and between the relay and the gateway. We mathematically derive the analytical expressions of average outage probability (AOP) and average symbol error probability (ASEP) of this multiple-RIS-relay aided LPWA network over Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading channels. The performance of the proposed network is also compared with the performance of the relay-aided LPWA network without using RISs. The analytical results show that the exploitation of RISs can greatly enhances the performance of the LPWA network. Thus, the multiple-RIS-relay aided LPWA network can operate at the high frequency band for long range transmission. Moreover, the effect of various important factors such as the location of the RISs, the Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> parameters, the data transmission rate, and the modulation scheme on the performance of the multiple-RIS-relay aided LPWA network are also investigated in practical scenarios.

A Game-Theoretic Approach to Achieve Covert Communication in Cognitive Radio Systems

In this paper, we investigate a covert cooperative cognitive radio (CCCR) system, where multiple primary transmitters (PTs) transmit information with the aid of multiple secondary transmitters (STs) in order to conserve power consumption. In return, by opportunistically accessing PT's spectrum, STs send confidential information to a secondary receiver (SR) in the presence of external eavesdropper (Eve). Aiming to maximize covert rate, we model our CCCR framework as an evolutionary game in which each PT and ST make decisions based on their utility histories. By introducing the evolutionary game, we propose a game-oriented secondary user scheduling (G-SUS) scheme to find when multiple STs determine to access PTs' spectrum. Moreover, we analyze covert performance of the proposed scheme and obtain a closed-form expression for Eve's detection error probability. Numerical results show that, the minimal detection error probability at Eve can be effectively impacted by creating channel uncertainty and noise uncertainty. Furthermore, the results also demonstrate the proposed scheme can converge quickly, which stimulates its practical implementation.

Joint Code Index Modulation Aided Enhanced Spatial Modulation for High-Rate MIMO Systems

In this paper, a novel scheme, which introduces the technology of the code index modulation (CIM) into the realm of enhanced spatial modulation (ESM), named CIM-ESM, is proposed to achieve high spectral efficiency and high energy efficiency in multiple-input multiple-output (MIMO) systems. In the CIM-ESM scheme, information bits are conveyed not only by modulated symbols and spreading code indices, but also by the indices of the active antenna and constellation combinations. Meanwhile, the mathematical expressions for the average bit error probability (ABEP) in the presence of channel estimation errors, data rate, energy efficiency, and complexity of the CIM-ESM scheme are deduced. To achieve a higher transmission rate and code utilization, we further propose an enhanced scheme, named joint CIM-ESM (JCIM-ESM) scheme. In the JCIM-ESM scheme, spreading codes are jointly selected to form spreading code pairs and the matching indices of the spreading code pairs are utilized to convey extra information bits. Finally, Monte Carlo simulation results corroborate the tightness of the derived ABEP expression in the high signal-to-noise ratio region and reveal that both the CIM-ESM and JCIM-ESM schemes can provide better performance than CIM spread spectrum (CIM-SS), generalized CIM-aided spatial modulation (GCIM-SM), generalized space CIM (GSCIM), and CIM-aided QSM (CIM-QSM) schemes.

Performance Analysis of Uplink Non-Orthogonal Multiple Access in the Presence of Co-Channel Interference

In sixth generation (6 G) networks, a massive number of users and devices must be connected, necessitating flexible resource allocation. In this context, non-orthogonal multiple access (NOMA) has been proposed as a promising technique to enable mass connectivity. This study presents a performance analysis for the impact of co-channel interference (CCI) on uplink NOMA networks. More specifically, it is considered that CCI is introduced by randomly deployed terminals within the cellular coverage area, affecting the reception of the base station (BS) in the uplink. In this network, fading conditions follow the Rayleigh distribution and two cases are examined for the CCI statistics, i.e. independent and identically distributed, and independent but not identically distributed. A thorough performance analysis is conducted to derive the outage probability, ergodic rate, error probability, achievable sum-rate, and throughput expressions, highlighting the adverse effects of CCI on the uplink NOMA network. Furthermore, an asymptotic analysis is provided, shedding light on the derived analytical results. Towards improving the performance of uplink NOMA, power allocation is formulated as an optimization problem, and solved to derive the power allocation coefficient of the users. Our analytical and asymptotic derivations are verified through Monte-Carlo-based computer simulations and it is revealed that the proposed power allocation method achieves significant performance gains, facilitating uplink NOMA.

Symbol error probability of mmWave communications with transmit antenna selection and RISs under the impacts of hardware impairments

SummaryIn practice, hardware impairments (HIs) often exist in wireless devices, especially in low‐cost device systems. However, previous reports usually ignored HIs due to the computational complexity in mathematical derivations, particularly in millimeter‐wave (mmWave) communications. This article proposes the usage of transmit antenna selection (TAS) and multiple reconfigurable intelligent surfaces (RISs) to address HIs in mmWave communications. In particular, TAS is utilized at the source to increase the received signal power at the destination and reduce the effects of HIs. Multiple channel gains from RISs are combined with the classical source‐destination channel gain at the destination. The symbol error probability (SEP) expression of the mmWave communications with TAS and RISs under the effects of HIs (shortened as the TAS‐RISs‐HIs communications) is formulated over Nakagami‐ channels and verified through Monte Carlo simulations. The effects of HIs on the SEP of TAS‐RISs‐HIs communications are demonstrated through numerical illustrations. Specifically, the SEP of the TAS‐RISs‐HIs communications is significantly higher than the SEP of the ideal hardware communications with TAS and RISs, especially in the high transmit power regime. As a result, ignoring HIs when evaluating the SEP of the mmWave communications can result in some inappropriate conclusions. Moreover, the joint and separate advantages of TAS and RISs are thoroughly analyzed when comparing the SEPs in the cases with and without TAS, with and without RISs.

A New Approach to Deriving Closed-Form Bit Error Probability Expressions of MPSK Signals

In conventional approach, the bit error probability (BEP) expressions of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary phase-shift keying (MPSK) signals over additive white Gaussian noise (AWGN) channel are derived by averaging error probabilities for all bits of MPSK symbol. The closed-form BEP expressions of MPSK signals over AWGN channel can also be derived by using the weighted conditional symbol error probability (SEP) expressions, which has not been reported. In this paper, we derive the conditional SEP expressions of MPSK signals in terms of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions by changing the domain of integration from a plane bounded by two rays into a quadrant. By weighting the conditional SEP expressions according to average distance spectrum, the closed-form BEP expressions of MPSK signals over AWGN channel are obtained. Only two summations involving two parameters are required. The closed-form BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are derived by using the BEP expressions over AWGN channel and the moment generating function-based approach. The approximate BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are obtained by using elementary functions-based approximations of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions. The conciseness and computational complexity of our BEP expressions are verified by the comparison with existing results.

Average bit error probability performance of intelligent reflecting surface‐aided wireless communications over Hoyt fading

SummaryIn this article, the performance of a wireless communication system with an intelligent reflecting surface (IRS) panel installed between the transmitter and receiver is studied. The channel is considered to be the Hoyt faded and additive white Gaussian noise. Closed‐form expressions for average bit error probability (ABEP) for both coherent Gray‐coded rectangular quadrature amplitude modulation and non‐coherent modulation schemes are presented. We apply the moment‐generating function‐based method for the derivation. In addition, asymptotic ABEP expressions are also obtained. Using asymptotic ABEP expressions, we obtained diversity order which is a function of the number of IRS elements. The effect of the number of IRS elements and fading parameters on the ABEP is studied. The ABEP performance improves with an increase in the number of reflecting elements but degrades with an increase in the fading severity. The accuracy of each analytical ABEP expression is verified by the simulation of the system considered herewith.

Constrained Riemannian Noncoherent Constellations for the MIMO Multiple Access Channel

We consider the design of multiuser constellations for a multiple access channel (MAC) with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> users, with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antennas each, that transmit simultaneously to a receiver equipped with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antennas through a Rayleigh block-fading channel when no channel state information (CSI) is available to either the transmitter or the receiver. In full-diversity scenarios where the coherence time is at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ≥ ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> + 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> , the proposed constellation design criterion is based on the asymptotic expression of the multiuser pairwise error probability (PEP) derived by Brehler and Varanasi (2001). In non-full diversity scenarios, for which the previous PEP expression is no longer valid, the proposed design criteria are based on proxies of the PEP recently proposed by Ngo and Yang (2021). Although both the PEP expression and its bounds or proxies were previously considered intractable for optimization, in this work we derive their respective unconstrained gradients. These gradients are in turn used in the optimization of the proposed cost functions in different Riemannian manifolds representing different power constraints. In particular, in addition to the standard unitary space-time modulation (USTM) leading to optimization on the Grassmann manifold, we consider a more relaxed percodeword power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">oblique manifold</i> , and an average power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trace manifold</i> . Equipped with these theoretical tools, we design multiuser constellations for the MIMO MAC in full-diversity and non-full-diversity scenarios with state-of-the-art performance in terms of symbol error rate (SER).

Error Probability Analysis of Intelligent Reflecting Surface-Enabled Non-Orthogonal Multiple Access Systems

We analyze the error performance of intelligent reflecting surface (IRS)-aided non-orthogonal multiple access (NOMA) systems. We deduce novel approximate analytical expressions for average symbol error probability (SEP) for PAM and QAM. We also analyze the multi-user scenario by deriving the novel approximate analytical expressions for (i) the average SEP for multicast transmission and (ii) the average pairwise error probability (PEP) for unicast transmission. We consider Rayleigh fading direct path and independently Rician fading reflected paths from access point to users via IRS. We also formulate and solve a constrained optimization problem to determine the fraction of elements to be activated at any IRS in order to guarantee near-identical SEP performance for both the users. We present results to elucidate that adding few extra IRS elements yields SNR gain for both users, requires allocation of lower power to weaker user and supports communication with higher-order constellation without significant increase in SEP/PEP. Furthermore, a 3-bit programmable IRS yields near-identical performance as an IRS with infinite precision phase-shift. Impact of estimation error on average SEP is also investigated.

Criteria for the deployment of a heterogeneous linear WSN: Operability vs energy efficiency

Linear Wireless Sensor Networks (LWSN) are typically used for monitoring infrastructure systems extending over several kilometers, where propagation conditions can be inhomogeneous in different sections of the network. Obstacles and reflecting objects contribute to bit errors in data packets, which take extra time and energy to recover. However, the impact of the inhomogeneities across LWSN sections on the time and energy performance of the entire network remains underreported. In addition, conventional methods of building LWSN by distributing relay nodes among inhomogeneous sections have failed to balance operability and energy efficiency criteria. This article examines the models of time and energy loss in LWSN sections showing different signal fading, represented by the Rician K-factor in the expressions for the bit error probability. On the basis of the dependences of time losses on inter-node distances, algorithms for deploying a heterogeneous LWSN are proposed according to the criterion of minimizing end-to-end network delay without restrictions on hardware and energy resources or when distributing a limited number of nodes. As an alternative to the efficiency criterion, we propose algorithms for balancing power consumption in a heterogeneous LWSN at an acceptable level of power loss without limiting the number of nodes or at the lowest level of power loss with a limit on the number of nodes. Experiments were carried out on CC2500 TI node transceivers in five inhomogeneous LWSN sections, where K-factor ranges from 5 to 100, in order to demonstrate the efficiency of the proposed algorithms. Results showed that the end-to-end delay and energy loss can be reduced by 1.36 and 2.4 times, respectively, compared to those in networks with uniformly distributed nodes. To further assess the operability and energy efficiency of the algorithms, a scheme is proposed based on the ratio of normalized concessions in the Pareto region. Additionally, the optimal number of nodes is determined when selecting a rational algorithm for deploying a heterogeneous LWSN.

Generalized Index Modulation for MIMO-OTFS Transmission

Recently, the combination of multiple-input multiple-output technology with orthogonal time frequency space modulation (MIMO-OTFS) has drawn extensive attention with the advantage of exploring the additional transmit diversity or spatial multiplexing of the MIMO scheme. Motivated by the potential spectral efficiency of multi-domain index modulation, in this paper, we propose a generalized index modulation based MIMO-OTFS (GIM-MIMO-OTFS) to convey extra information with the aid of the spatial and delay-Doppler indices. To reduce the supreme complexity of maximum likelihood (ML) detection with a large size of look-up table in GIM-MIMO-OTFS, a two stage index detector based on power information is presented. Furthermore, the analytical expression of average bit error probability (ABEP) is derived to evaluate the performance of the proposed scheme. Simulation results demonstrate the enhanced performance of the proposed scheme in high-mobility scenarios, and highlight the complexity and outperformance of the proposed detector compared to ML detector.

Quadrature Spatial Scattering Modulation for mmWave Transmission

In this letter, we investigate a novel quadrature spatial scattering modulation (QSSM) transmission technique based on millimeter wave (mmWave) systems, in which the transmitter generates two orthogonal beams targeting candidate scatterers in the channel to carry the real and imaginary parts of the conventional signal, respectively. Meanwhile, the maximum likelihood (ML) detector is adopted at the receiver to recover the received beams and signals. Based on the ML detector, we derive the closed-form average bit error probability (ABEP) expression of the QSSM scheme. Furthermore, we evaluate the asymptotic ABEP expression of the proposed scheme. Monte Carlo simulations verify the exactness and tightness of the derivation results. It is shown that the ABEP performance of QSSM is better than that of traditional spatial scattering modulation.

Generalized Closed-Form Expression for the Bit Error Probability of MPSK with Phase Noise

Generalized Closed-Form Expression for the Bit Error Probability of MPSK with Phase Noise

On the Exact Closed-Form ABEP Analysis of Downlink NOMA Over mmWave TWDP Fading

This paper presents the performance analysis of two users’ downlink non-orthogonal multiple access (NOMA) over a millimeter-wave two-wave with diffuse power (TWDP) fading model for successive interference cancellation errors. The new closed-form expressions of average bit error probability (ABEP) for both users are derived for quadrature phase-shift-keying and binary phase-shift-keying modulation pairs. Further, the asymptotic ABEP expressions are derived to provide better insights into the performance analysis. The diversity order of each user is also derived with the aid of asymptotic ABEP expression. The obtained expressions over TWDP fading channels are generalized ABEP expressions as it also shows ABEP expressions for both Rician and Rayleigh fading channels as special cases. Simulation results support the correctness of each analytical ABEP expression.

Optimal Rotated M-PSK Signaling for Multi-User Receive Diversity System Over Correlated Rician Fading Channels

In this letter, a two-user receive diversity non-orthogonal multiple-access (NOMA) wireless communication system is considered with the transmitter utilizing a rotated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary phase-shift keying ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -PSK) modulation for data modulation over correlated Rician fading channels. A maximum ratio combining scheme followed by an optimum maximum-likelihood rule is employed for received data detection at each user end. Further, a simple separation scheme is proposed to eliminate the use of successive interference cancellation at the receiver end of the NOMA system. The receiver structure is utilized to derive a closed-form expression for the symbol error probability which is minimized by obtaining the optimal rotation angle of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -PSK constellation. The variations of the optimal rotation angle with system parameters are studied by numerical results which lead to novel modulation schemes for the considered system.

Channel Estimation and Performance Analysis of a Wide-FOV Visible Light Communication System With Random Receiver Orientation and Location

A practical visible light communications (VLC) system accounting for the effect of the random orientation and the random location of the photo-detector receiver is considered in this paper. The characterizations of the random orientation of the receiver, modeled as the receiver employing wide field of view (FOV) for data detection, and the random location of the receiver are utilized to derive the statistics for the scenarios in which (i) only the orientation of the receiver is random, (ii) only the location of the receiver is random, and (iii) both the orientation and location of the receiver are random. Furthermore, the receiver structures for a fully coherent VLC system and a VLC system employing the least-squares technique for channel estimation are proposed. Employing the receiver structures, the closed/series-form expressions for the symbol error probabilities are derived for all three scenarios of practical VLC channel models. The numerical results particularly show the crucial role of the ratio of the distance of the location of the receiver from the center of the receiving plane to the distance from the light-emitting diode (LED) to the center of the receiving plane in the performance of all the considered VLC systems.