Closed-form Expression For Ergodic Capacity Research Articles

Intelligent-Reflecting-Surface-Aided Bidirectional Full-Duplex Communication System With Imperfect Self-Interference Cancellation and Hardware Impairments

In this article, we combine two new technologies [full-duplex (FD) transmission and intelligent reflecting surface (IRS)] in a wireless communication system for investigation. Specifically, we evaluate the performance of an IRS-aided bidirectional FD communication system in a practical scenario where imperfect self-interference (SI) cancellation and hardware impairments (HIs) are taken into consideration. We successfully derive the closed-form expressions of ergodic capacity (EC) and symbol error rate (SER) of the IRS-aided FD-HI system over Rayleigh fading channels. We confirm the correctness of the derived expressions via Monte-Carlo simulations. To clarify the effects of residual SI and HIs, we compare the performance of the IRS-aided FD-HI system with that of the IRS-aided FD-ideal hardware (ID), half-duplex (HD)-HI, and HD-ID systems. Numerical results clarify a strong impact of residual SI and HIs on the EC and SER of the IRS-aided FD-HI system. Thus, the EC and SER of the IRS-aided FD-HI system go to the saturated values in a high signal-to-noise regime even with a large number of reflecting elements in the IRS. Therefore, depending on the residual SI and HI levels as well as the requirements about the EC and SER in practice, we can use appropriately the transmit power of terminals and number of reflecting elements in the IRS for enhancing the performance and saving the energy consumption of the IRS-aided FD-HI system.

A Three-Phase CDRT Strategy Based on Successive Relay for Smart Grid

In the vision of the future smart grid, the communication is often featured by wide range, massive connect, and low latency, which poses new requirements on the reachable distance and spectral efficiency of wireless communication. In this regard, this paper studies ergodic capacity enhancement by applying successive relay (SR) technology to a non-orthogonal multiple access (NOMA) based Coordinated Direct and Relay transmission (CDRT) system, where a base station (BS) communicates with a near user (NU) directly while communicating with a far user (FU) with the help of a group of relays. We design a novel three-phase CDRT strategy based on SR technology to overcome the half-duplex (HD) constrain without introducing additional noise. The proposed strategy can improve the spectral efficiency while expanding the communication coverage, which to some extent improves the communication quality of the edge users of the smart grid and reduces the communication delay. To analyze the performance of the proposed three-phase CDRT strategy, an exact and closed-form expression for ergodic capacity of the NU, the FU, and the whole system is derived. Finally, the numerical and simulation results validate the analysis results and show that the proposed strategy can improve the ergodic capacity of FU without reducing the capacity scaling of NU.

On the Capacity Performance of Hybrid FSO/RF System With Adaptive Combining Over Generalized Distributions

This paper investigates the ergodic capacity performance of hybrid free space optics (FSO)/ radio frequency (RF) system by employing an adaptive-combining-based switching scheme. In the adaptive combining scheme, the FSO and RF links are combined using the maximal-ratio combining (MRC) at the output, when the instantaneous signal-to-noise ratio (SNR) of the FSO link drops below a predefined threshold SNR value. The FSO link experiences the atmospheric turbulence, which is modeled using the generalized Malaga distribution, non-zero boresight misalignment or pointing errors, and atmospheric attenuation, under two types of detection techniques, i.e. heterodyne detection (HD) and intensity modulation/direct detection (IM/DD). Similarly, the fading of the RF link is characterized using the generalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> distribution. In particular, we derive the probability density function (PDF) of the instantaneous SNR of the adaptive combining scheme. Capitalizing on the SNR statistics, we obtain the unified closed-form ergodic capacity expressions for the adaptive-combining-based hybrid FSO/RF system. In addition, the asymptotic expressions for the ergodic capacity of the system at the high-SNR region are presented. All the derived analytical expressions are validated by using Monte-Carlo simulations. Numerical results and discussions are provided to compare the ergodic capacity performance of the adaptive-combining-based hybrid FSO/RF system with the existing system models such as single-link FSO, MRC-based hybrid FSO/RF, and hard-switching-based hybrid FSO/RF systems.

Multiuser Scheduling for Asymmetric FSO/RF Links in Satellite-UAV-Terrestrial Networks

This letter investigates the multiuser downlink transmission performance of an asymmetric free space optical (FSO)/radio frequency (RF) link. Here, the satellite delivers signal to the unmanned aerial vehicle (UAV) through a FSO link subject to Gamma-Gamma distributed turbulence, while the UAV forwards the decoded signal to multiple users through RF links characterzied by the correlated Rayleigh fading channel. By adopting that the selective decode-and-forward (DF) protocol at the UAV, we derive a closed-form expression for ergodic capacity (EC) of the considered system, where the RF link exploits transmit beamforming (BF) based on statistical channel state information (CSI) to obtain better performance than single antenna scenarios in existing works. Then, with the help of the derived EC and the available statistical CSI, a novel proportional fair scheduling (PFS) scheme is proposed. Finally, numerical results are conducted to verify the correctness of the theoretical analysis and the superiority of the proposed scheduling scheme.

Closed-Form Expressions of Ergodic Capacity and MMSE Achievable Sum Rate for MIMO Jacobi and Rayleigh Fading Channels

Multimode/multicore fibers are expected to provide an attractive solution to overcome the capacity limit of the current optical communication system. In the presence of strong crosstalk between modes and/or cores, the squared singular values of the input/output transfer matrix follow the law of the Jacobi ensemble of random matrices. Assuming that the channel state information is only available at the receiver, we derive a new expression for the ergodic capacity of the MIMO Jacobi fading channel. The proposed expression involves double integrals which can be easily evaluated for a high-dimensional MIMO scenario. Moreover, the method used in deriving this expression does not appeal to the classical one-point correlation function of the random matrix model. Using a limiting transition between Jacobi and associated Laguerre polynomials, we derive a similar formula for the ergodic capacity of the MIMO Rayleigh fading channel. Moreover, we derive a new exact closed-form expressions for the achievable sum rate of MIMO Jacobi and Rayleigh fading channels employing linear minimum mean squared error (MMSE) receivers. The analytical results are compared to the results obtained by Monte Carlo simulations and the related results available in the literature, which shows perfect agreement.

SER and throughput analysis of space–time analog network coded relaying system over shadowed Rician fading channels

This research article presents an innovative approach based on analog network coding (ANC) in conjunction with space time block coding (STBC) which is termed as space time analog network coding (STANC). The STANC investigated as an affective network coding strategy to combat the effects of shadowing and path loss in wireless networks. The another objective of this research work is to evaluate the impact of relay location on system performance in increasing shadowing effect due to increasing tall structure like multistory building in metropolitan area. The performance of the proposed system is analyzed in terms of symbol error rate (SER), STANC gain and ergodic capacity using analytical expressions. Moment generating function approach is used to drive the SER for M-PSK modulated signals. The approximate closed-form expression of ergodic capacity is presented using the derived mean and second moment for STANC based cooperative system. Rician shadowed model is used which efficiently evaluate the effect of shadowing as compared to other fading models given in the literature which is the main advantage of this model. Numerical results signify that the approximated analytical expressions derived can be effectively used for performance improvement under path loss and shadowing effect as compared to simple ANC based system.

A closed-form ergodic capacity expression for a generic cooperative diversity network in Rayleigh fading channels

In this paper, we derive a closed-form ergodic capacity expression for a generic cooperative diversity network (GCDN) in Rayleigh fading channels. We first derive a closed-form probability density function (pdf) of the instantaneous diversity-combined signal-to-noise ratio, and then a closed-form ergodic capacity expression for the GCDN by using the derived closed-form pdf. Through numerical analyses, we analyze the ergodic capacities according to the number of cooperative nodes (CNs), respective numbers of CN antennas, and respective channel qualities between a set of the CNs and a user terminal, and also characterize the resulting ergodic capacity behaviors.

Performance Analysis of Collaborative Beamforming With Outdated CSI for Multi-Relay Spectrum Sharing Networks

Prior works on performance analysis for cognitive radio networks often assume perfect channel state information (CSI), which may not be readily available. This paper investigates the effects of the outdated CSI on the performance of a dual-hop multi-antenna multi-relay spectrum sharing system. To exploit the benefits of available multiple antennas, collaborative zero-forcing beamforming is considered at the secondary user (SU) source node with the outdated CSI and maximum ratio combining diversity reception at the destination node. The $N$ th best relay selection strategy is adopted at the relays. Analytical outage probability and bit-error rate expressions are derived for the SU. Moreover, we examine the high signal-to-noise ratio regime and present closed-form expressions for the asymptotic outage probability and asymptotic bit-error rate with and without feedback delay. In addition, we derive the closed-form ergodic capacity expression for the special case of our considered system, and analyze the effects of delay on the capacity. Furthermore, the closed-form outage probability expression for the primary user is obtained and the impact of delay on the interference on the primary user is investigated. Monte Carlo simulations are carried out to verify our analysis.

Closed-Form Expressions of Ergodic Capacity in Cloud Radio Access Networks With Nakagami-m Fading

We investigate a C-RAN model based on single nearest RRH association with Nakagami- m fading and path-loss fading. In the analysis the parameter $mL$ is not restricted to be an integer, where L is the number of antennas per RRH. We derive several closed-form expressions for the ergodic capacity, not restricted to the high SNR regime, for two classes of power path loss exponents. Moreover, the closed-form expression of a tight lower bound is provided for general scenarios. Finally, the results of simulation and numerical integration are provided to show the cross-verification.

Performance analysis of incremental hybrid decode-amplify-forward cooperative relaying with relay selection in Nakagami-m fading channels

In this paper, we investigate the performance of incremental hybrid decode-amplify-forward relaying (IHDAF) protocol for the dual-hop cooperative multi-relay networks. We deduce a tight closed-form expression for the outage probability (OP) by employing opportunistic relay selection (ORS) under Nakagami-m fading channels. We further derive an asymptotic outage expression in the high signal-to-noise ratio (SNR) regime, from which the diversity order is examined. Based on the asymptotic results, we also present an optimal relay location to minimize the overall system outage. In addition, we derive new tight closed-form expressions of ergodic capacity and asymptotic ergodic capacity for the considered system. Finally, numerical and simulation results show the correctness of our analytical findings and the performance enhancement of the considered system with ORS-IHDAF scheme compared with the other incremental ORS-based cooperative schemes.

On the capacity of MISO FSO systems over gamma-gamma and misalignment fading channels.

In this work, the ergodic capacity performance for multiple-input/single-output (MISO) free-space optical (FSO) communications system with equal gain combining (EGC) reception is analyzed over gamma-gamma and misalignment fading channels, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.). Novel and analytical closed-form ergodic capacity expression is obtained in terms of H-Fox function by using the well-known inequality between arithmetic and geometric mean of positive random variables (RV) in order to obtain an approximate closed-form expression of the distribution of the sum of M gamma-gamma with pointing errors variates. In addition, we present an asymptotic ergodic capacity expression at high signal-to-noise ratio (SNR) for the ergodic capacity of MISO FSO systems. It can be concluded that the use of MISO technique can significantly reduce the effect of the atmospheric turbulence as well as pointing errors and, hence, provide significant capacity gain over the direct path link (DL). The impact of pointing errors on the MISO FSO system is also analyzed, which only depends on the number of laser sources and pointing error parameters. Moreover, it can be also concluded that the ergodic capacity performance is dramatically reduced as a consequence of the severity of pointing error effects. Simulation results are further demonstrated to confirm the analytical results.

Downlink Performance of Distributed Antenna Systems in MIMO Composite Fading Channel

In this paper, the capacity and BER performance of downlink distributed antenna systems (DAS) with transmit antenna selection and multiple receive antennas are investigated in MIMO composite channel, where path loss, Rayleigh fading and lognormal shadowing are all considered. Based on the performance analysis, using the probability density function (PDF) of the effective SNR and numerical integrations, tightly-approximate closed-form expressions of ergodic capacity and average BER of DAS are derived, respectively. These expressions have more accuracy than the existing expressions, and can match the simulation well. Besides, the outage capacity of DAS is also analyzed, and a tightly-approximate closed-form expression of outage capacity probability is derived. Moreover, a practical iterative algorithm based on Newton’s method for finding the outage capacity is proposed. To avoid iterative calculation, another approximate closed-form outage capacity is also derived by utilizing the Gaussian distribution approximation. With these theoretical expressions, the downlink capacity and BER performance of DAS can be effectively evaluated. Simulation results show that the theoretical analysis is valid, and consistent with the corresponding simulation.

Novel Closed-Form Expressions for Ergodic Capacity of MIMO-OSFBC-OFDM Systems Over Channel Adaptation Policies

In this work, closed-form expressions for capacities per unit bandwidth for MIMO-OFDM systems employing Orthogonal Space-Frequency Block Coding over multipath frequency-selective fading channels are derived for adaptation policies like optimal power and rate adaptation, optimal rate adaptation with constant transmit power, channel inversion with fixed rate, and truncated channel inversion polices. A Signal-to-Noise Ratio based user selection scheme is considered. Optimal power and rate adaptation policy provides the highest capacity over other adaptation policies. Capacity penalty is the highest for optimal rate adaptation with constant transmit power policy, while the performance of channel inversion with fixed rate policy and truncated channel inversion policy lie between that of OPRA and ORA policies.

On the capacity of ℳ-distributed atmospheric optical channels

In this Letter, closed-form expressions of ergodic capacity, outage probability, and outage rate are derived for an atmospheric optical communication link using intensity modulation and direct detection with unbounded optical wavefront propagating through a homogeneous and isotropic turbulent medium. The optical scintillation of the received signal is modeled with the recently proposed Málaga or M turbulence distribution. By taking advantage of this unifying statistical model, the expressions here presented are valid for all possible irradiance fluctuation conditions, leading to direct relationships between turbulence parameters and link capacity performance.

Adaptive Multi-Node Multiple Input and Multiple Output (MIMO) Transmission for Mobile Wireless Multimedia Sensor Networks

Mobile wireless multimedia sensor networks (WMSNs), which consist of mobile sink or sensor nodes and use rich sensing information, require much faster and more reliable wireless links than static wireless sensor networks (WSNs). This paper proposes an adaptive multi-node (MN) multiple input and multiple output (MIMO) transmission to improve the transmission reliability and capacity of mobile sink nodes when they experience spatial correlation. Unlike conventional single-node (SN) MIMO transmission, the proposed scheme considers the use of transmission antennas from more than two sensor nodes. To find an optimal antenna set and a MIMO transmission scheme, a MN MIMO channel model is introduced first, followed by derivation of closed-form ergodic capacity expressions with different MIMO transmission schemes, such as space-time transmit diversity coding and spatial multiplexing. The capacity varies according to the antenna correlation and the path gain from multiple sensor nodes. Based on these statistical results, we propose an adaptive MIMO mode and antenna set switching algorithm that maximizes the ergodic capacity of mobile sink nodes. The ergodic capacity of the proposed scheme is compared with conventional SN MIMO schemes, where the gain increases as the antenna correlation and path gain ratio increase.

Transmit Antenna Selection OFDM Systems With Transceiver I/Q Imbalance

One of the serious imperfections affecting orthogonal frequency-division multiplexing (OFDM) systems is transceiver in-phase/quadrature-phase (I/Q) imbalance. In this paper, the effect of I/Q imbalances on the transmit antenna selection (TAS) OFDM system is studied. The optimum antenna selection in presence of transmit and receive I/Q imbalances are proposed. We derive closed-form expressions for ergodic capacity of the system with transmit and receive I/Q imbalances. Moreover, some tight and simple lower and upper bounds for the ergodic capacity of the TAS OFDM system are derived. The simplicity of the proposed formula gives insight into the performance and optimization of the system. Finally, the analytical results are confirmed by simulations.

Capacity of multiuser multiple input multiple output-orthogonal frequency division multiplexing systems with doubly correlated channels for various fading distributions

In this article, the capacity of multiuser multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) system is analysed under Rayleigh, Rician, Lognormal and Weibull fading channels, and compared with each other under both semi- and doubly correlated channels. The distribution of the complex Wishart matrix is utilised to derive closed-form expressions of ergodic capacity of MIMO-OFDM systems under doubly correlated channels when the transmitter has no channel state information (CSI) and the receiver has perfect CSI. The capacity of MIMO-OFDM systems is plotted for various fading channels under different system specifications, such as number of transmit and receive antennas, number of subcarriers and different power levels. The obtained results are used to study the impact of channel correlation on capacity.

Exact Closed-Form Expression for Ergodic Capacity of Amplify-and-Forward Relaying in Channel-Noise-Assisted Cooperative Networks with Relay Selection

In this letter, an exact closed-form expression is derived for the ergodic capacity of dual-hop channel-noise-assisted amplify-and-forward cooperative networks with relay selection considered by Costa and Aïssa. Simulation results corroborate the theoretical analysis.

Advances in Relay Networks: Performance and Capacity Analysis of Space-Time Analog Network Coding

We propose modified space-time-coding-based analog network coding (ANC) for multiple-relay network, termed space-time analog network coding (STANC). We present the performance and capacity analysis of the proposed network in terms of SER and ergodic capacity. We derive the closed-form expressions for the moment-generating function (MGF) of the equivalent signal-to-noise ratio (SNR) of the multiple-relay STANC network over independent and identically distributed (i.i.d.) Rayleigh, Nakagami, and Rician channels. Average SER of the system is evaluated using MGF-based approach. We further derive the approximate closed-form expressions of ergodic capacity. These expressions are simple and enable effective evaluation of the performance and capacity of STANC system.

Introducing Space into MIMO Capacity Calculations

The large spectral efficiencies promised for multiple-input multiple-output (MIMO) wireless fading channels are derived under certain conditions which do not fully take into account the spatial aspects of the channel. Spatial correlation, due to limited angular spread or insufficient antenna spacing, significantly reduces the performance of MIMO systems. In this paper we explore the effects of spatially selective channels on the capacity of MIMO systems via a new capacity expression which is more general and realistic than previous expressions. By including spatial information we derive a closed-form expression for ergodic capacity which uses the physics of signal propagation combined with the statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and leads to valuable insights into the factors determining capacity for a wide range of scattering models.