Expressions For Ergodic Capacity Research Articles

A Robust Opportunistic Relaying Strategy for Co-Operative Wireless Communications

Using outdated channel state information (CSI) in an opportunistic relaying system (ORS) leads to wrong selection of the best relay, which substantially deteriorates its performance. In this paper, therefore, we propose a robust cooperative scheme coined opportunistic space-time coding (OSTC) to deal with the outdated CSI. A predefined number (i.e., $N$ ) of relays, instead of a single relay in ORS, are opportunistically selected from $K$ cooperating relays. At the selected relays, $N$ -dimensional orthogonal space-time coding is employed to encode the regenerated signals in a distributed manner. Then, $N$ branches coded signals are simultaneously transmitted from the relays to the destination, followed by a simple maximum-likelihood decoding at the receiver. To evaluate its performance, the closed-form expressions of outage probability and ergodic capacity are derived, together with an asymptotic analysis that clarifies the achievable diversity. Analytical and numerical results reveal that a full diversity of $K$ is reaped by the proposed scheme when the knowledge of CSI is perfect. In the presence of outdated CSI, where the diversity of ORS degrades to one, the diversity of $N$ can be kept. Moreover, OSTC’s capacity is remarkably higher than that of the existing schemes based on orthogonal transmission. From the perspective of multiplexing-diversity tradeoff, the proposed scheme is the best cooperative solution until now.

A Joint Antenna and Path Selection Technique in Single-Relay-Based DF Cooperative MIMO Networks

In this paper, we consider a single-relay-based decode-and-forward (DF) cooperative multiple-input multiple-output (MIMO) system in which the source, the relay, and the destination are equipped with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{s}$</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">$N_{r}$</tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{d}$</tex-math></inline-formula> antennas, respectively. We propose a joint antenna and path selection scheme, which jointly selects the single-transmit and single-receive antenna pairs, along with the selection of either a direct path that consists of source–destination channels or a cooperative path that consists of source–relay and relay–destination channels. The proposed selection scheme is based on the maximization of minimum of maximums (max-min-max) criterion of instantaneous signal-to-noise ratio (SNR). The analysis in this paper is based on the assumptions that all the channels follow independent Rayleigh fading. A closed-form expression of the symbol error rate (SER) for the proposed scheme in a cooperative MIMO system with <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 is derived. We extract the analytical diversity order from the derived SER and show that the proposed selection scheme achieves the diversity order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{s}N_{d}+N_{r}\mathrm{min}(N_{s},N_{d})$</tex-math></inline-formula> in the considered cooperative MIMO system. Closed-form expressions of bandwidth efficiency (BE) and ergodic capacity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(C_{t})$</tex-math></inline-formula> are derived for the proposed scheme. An optimized selection parameter from the specific set of values is numerically evaluated by maximizing a heuristic utility function <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(C_{t}\times \mbox{BE}/\mbox{SER})$</tex-math></inline-formula> . By using the already-gathered information about the maximum instantaneous SNR of every hop, a power adaptation scheme that maximizes the instantaneous SNR in the cooperative path is proposed and analyzed. The proposed power adaptation scheme, which is applied only in the event of selection of a cooperative path, outperforms the uniform-power-distribution-based DF cooperative MIMO system.

Performance study of opportunistic scheduling in dual‐hop multi‐user underlay cognitive network

In this study, the authors investigate the performance of opportunistic scheduling for the dual-hop amplify-and-forward multi-user cognitive relaying network. Expressions are derived for the cumulative distribution function (CDF) and probability density function of the equivalent signal-to-noise ratio (SNR). From the derived CDF, the outage performance of the cognitive network is investigated. Then, an expression for average error probability is derived. Furthermore, simple and generic asymptotic expressions for the outage and error probabilities are obtained and discussed. In addition, a closed-form expression for the system's ergodic capacity is derived. Their asymptotic results show that opportunistic scheduling has no impact on diversity gain. It is confirmed that the array gain determines the SNR advantage of opportunistic scheduling over the single-user scenario. Moreover, they study adaptive power allocation under the total transmit power constraint in order to minimise the average error probability. As expected, the results show that optimum power allocation improves system performance compared with uniform power allocation. Finally, numerical results and Monte Carlo simulations are also provided to support the correctness of the analytical calculations.

An Upper Bound on the Capacity of Distributed MIMO Systems With Rician/Lognormal Fading

In many communication environments for distributed MIMO (D-MIMO) systems, insufficient angular spread and dominant nonfading paths exist simultaneously. In such situations, a spatially correlated Rician/Lognormal channel model is appropriate. In this letter, analytic upper bound of ergodic capacity is presented for D-MIMO systems operating on Rician/Lognormal fading channels. In the analysis, it is assumed that receive correlation and transmit correlation exist simultaneously, and the rank of channel mean matrix is arbitrary. To avoid the appearance of Hayakawa polynomials, which cannot be simplified, the determinant in the expression of ergodic capacity is expanded by use of the linear sum of determinants of noncentral wishart matrices. The results of computer simulation show that the bound remains tight across the entire signal-to-noise ratio (SNR) regime.

Ergodic Capacity Analysis of Decode-and-Forward Relay-Assisted FSO Systems Over Alpha–Mu Fading Channels Considering Pointing Errors

The ergodic capacity of decode-and-forward (DF) relay-assisted free-space optical (FSO) communication systems when line of sight is available is analyzed over gamma–gamma fading channels with pointing errors. A novel closed-form approximate ergodic capacity expression is obtained in terms of the H-Fox function for a three-way FSO communications system when the $\alpha{-} \mu$ distribution to efficiently approximate the probability density function (PDF) of the sum of gamma–gamma with pointing-error variates is considered. Moreover, we present novel asymptotic expressions at high signal-to-noise ratio (SNR) , as well as low SNR for the ergodic capacity of DF relay-assisted FSO systems. The main contribution in this paper lies in an in-depth analysis about the impact of pointing errors on the ergodic capacity for cooperative FSO systems. In order to maintain the same performance in terms of capacity, it is corroborated that the presence of pointing errors requires an increase in SNR, which is related to the fraction of the collected power at the receive aperture, i.e., $A_{0} $ . Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.

Coordinated Semidirectional Distributed Antenna System with Capacity and Energy Efficiency Analyses for Cloud Cellular Network

In order to further explore the coordination gain from the cloud cellular network, the Coordinated Semidirectional Distributed Antenna System (CS-DAS) is proposed with deploying 180-degree sector antennas. Based on the CS-DAS, the coordinated cellular deployment structure is established with corresponding communication procedure designs. The handover process for CS-DAS is designed with less handover rate and signaling overheads. The system performances of ergodic capacity and Energy Efficiency are derived, with a strong focus on the downlink performances, and analyzed with comparisons of current cellular structure. The numerical expressions of ergodic capacity are obtained with improvements of coordinated gain. The Energy Efficiency with different transmission modes is also investigated. The simulation results verify the performance improvements.

Unified analysis of transmit, receive and hybrid diversity techniques over generalized‐K channels

AbstractIn this work, unified performance analysis of various transmit, receive and hybrid diversity techniques are studied over generalised‐K composite fading channels. Of transmit diversity techniques, orthogonal space‐time block coding, maximal‐ratio transmission and transmit antenna selection techniques are investigated. On the other hand, maximal‐ratio combining and selection combining are examined as receive antenna diversity techniques. In this paper, 10 different multi‐antenna techniques have been analyzed. Exact outage probability, symbol error probability, moment generating function, moments and ergodic capacity expressions are derived in closed‐form. Asymptotic expressions are also derived in order to provide deeper insight by obtaining array and diversity gains of the studied multi‐antenna scenarios. Simulations verify theoretical results. We show that the diversity orders of the investigated scenarios are the minimum of the diversity orders of the system for only small‐scale fading channel case and the shadowing parameter, and limited by the shadowing effect especially in heavy shadowing case. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Outage performance and ergodic capacity of multiuser cognitive MIMO AF relaying systems with MUS/MRT/RAS over Nakagami‐m fading channels

AbstractTo improve the performance of cognitive spectrum‐sharing systems and to reduce the implementation complexity of multiple antenna systems, a cognitive multiple‐input multiple‐output (MIMO) amplify‐and‐forward relay cooperation (C‐MIMO AF‐RC) multiuser system is considered over Nakagami‐m fading channels by integrating maximum ratio transmission (MRT), multiuser selection (MUS) and receive antenna selection (RAS) techniques. In the C‐MIMO AF‐RC multiuser systems, all secondary users (SUs) are equipped with multiple antennas while the primary users (PUs), single antenna. The interested cognitive systems are investigated under the case where the systems have perfect or imperfect channel state information (CSI) of both the SUs–SUs and SUs–PUs links so that the effect of outdated CSI can be achieved. Specially, we first obtain the exact closed‐form expressions of the cumulative distribution function of end‐to‐end signal‐to‐noise ratio. Secondly, we perform a comprehensive comparison investigation on outage probability and ergodic capacity. Specially, based on moment generating function, the exact closed‐form expression of ergodic capacity is achieved. Finally, to highlight the insight of the effect of key system parameters, the high signal‐to‐noise ratio asymptotic analysis of outage probability is performed as well as diversity and coding gains, by considering the two cases where the systems have perfect or imperfect CSI of both the SUs–SUs and SUs–PUs links. The derivations clearly show that the CSI concerning SUs–PUs links only affects the coding gain, but not the diversity order. However, the CSI concerning the SUs–SUs links plays a key role on the achievable diversity order. In particular, when the CSI of SUs–SUs links is perfect, the C‐MIMO AF‐RC multiuser systems achieve the full diversity including not only MRT diversity but also MUS and RAS diversities. In contrast, when the CSI concerning secondary links is outdated, the MUS and RAS diversities disappear, and the MUS and RAS only improve coding gain. The remaining diversity is achieved through MRT.

Performance analyses of decode‐and‐forward multi‐hop relay network scenarios with multiple antenna techniques over Nakagami‐ m fading channels

In this study, unified performance analysis of many decode-and-forward multi-antenna multi-hop relay network scenarios is studied over flat Nakagami-m fading channels. The investigated multi-hop relay network scenarios include maximal-ratio transmission, transmit antenna selection and orthogonal space–time block coding techniques as transmit diversity techniques and maximal-ratio combining and selection combining as receive diversity techniques. Performance analysis consists of derivation of outage probability, symbol error probability, moments of end-to-end signal-to-noise ratio and ergodic capacity expressions. In addition, derivation of asymptotic outage probability and symbol error probability expressions is also presented to provide further insight to the performance analysis by quantifying the asymptotic diversity order and array gain. The theoretical performance results are validated by Monte Carlo simulations.

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.

Capacity Bounds for Rayleigh/Lognormal MIMO Channels With Double-Sided Correlation

In this letter, both analytic upper bound and lower bound of ergodic capacity are presented for distributed multiple-input multiple-output (D-MIMO) systems operating on Rayleigh/Lognormal fading channels. In the analysis, it is assumed that receive correlation and transmit correlation exist simultaneously, and the numbers of receive and transmit antennas both are arbitrary. The determinant in the expression of ergodic capacity is expanded as a linear sum of determinants of quadratic forms. Then the moments of the determinants are determined. Thereby upper and lower bounds on the ergodic capacity are obtained. The bounds remain tight across the entire Signal-to-Noise ratio (SNR) regime. The validity of above conclusion is verified by computer simulation.

Outage capacity evaluation of extended generalized-[formula omitted] fading channel in the presence of random blockage

In this paper, we analyse the outage and ergodic capacity performance of the extended generalized-K fading channel in the presence of possible temporary physical blockage between the source and the destination. Presented outage capacity analysis is general and can be used in analysis of wireless radio frequency or free-space optics systems. We establish the novel relation among significant parameters as outage capacity, probability of outage, probability of blockage, as well as severity and shaping parameters of multipath fading and shadowing. The theoretical results are expressed in terms of special Fox׳s H functions. The work clearly illustrates the usefulness of Fox׳s H and Meijer׳s G functions in analysing wireless communication systems. The analytical expression derived here enables us to determine the maximum error free data transmission rate for fixed value of outage probability under particular channel conditions. Using expressions for ergodic capacity previously reported in literature, we briefly analyse the impact of blockage on ergodic capacity, too. The numerical results show that the shadowing shaping factor has the considerable effect on outage capacity and is pronounced more extensively when probability of outage is lower. In addition, the results show that the effect of shadowing shaping factor is stronger for outage than ergodic capacity. The effect of multipath fading severity on outage capacity is stronger for lower values of shadowing spread. The link blockage causes significant decreasing of ergodic capacity and appearance of outage floor.

Ergodic Capacity of SIM-Based DF Relayed Optical Wireless Communication Systems

In this letter, we consider a dual-hop, subcarrier intensity modulation-based relayed optical wireless communication system under the combined influence of atmospheric turbulence and pointing error impairments. The turbulence-induced fading is modeled by independent but not necessarily identically distributed Gamma–Gamma fading statistics with misalignment fading. The relaying protocol followed by the relay is decode and forward. We first, derive the statistics of instantaneous signal-to-noise ratio at the destination, followed by the novel and exact analytical expressions for ergodic capacity of the system in terms of mathematically tractable Meijer’s G-function and extended generalized bivariate Meijer’s G-function.

Performance Analysis of Coherent Free-Space Optical Systems With Multiple Receivers

In this letter, we investigate the performance of a coherent free-space optical (FSO) communication system with multiple receive apertures over atmospheric turbulence fading channels. In particular, we derive the average error probability and the ergodic capacity of the coherent FSO system with multiple receive apertures in series representations. To mitigate the atmospheric turbulence-induced amplitude fluctuations and phase aberrations, we use, at the receive apertures, the modal compensation technique. Numerical results confirm the derived average error probability and ergodic capacity expressions.

Ergodic Capacity Analysis of Full-duplex Mimo Relay Channel using Tracy-Widom Distribution with Processing Delay

We explore a full-duplex technique in wireless communication particularly for relay networks. We consider the relay to operate in full-duplex, which occurs when transmission and reception are conducted in the same channel. We investigate potential benefits of full-duplex technique in relay networks, which uses multiple antennas for transmission and reception combined with the Amplify-Forward (AF) scenario. We study the effects of multiple antennas in terms of relay capacity. We derive an ergodic capacity expression using the Tracy-Widom distribution. Using Singular Value Decomposition (SVD) and perfect Channel State Information (CSI), we investigate these three scenarios: First, we consider the relay to have an antenna larger than that of both source and destination. Second, we consider both relay and destination to have an antenna larger than that of the source. Third, we consider both relay and source to have antenna larger than that of the destination. We show the results that the capacity of the relay with a fullduplex technique is almost twice the capacity of an half-duplex. We show that increasing the number of destination antennas is not help much when one of the source antennas is small. Moreover, the capacity decreases due to a channel hardening effect, when the number of destination antennas is larger than that of the source.

Performance analysis of ad-hoc routing in heterogeneous clustered multi-hop wireless networks

This paper analyzes the performance of clustered decode-and-forward multi-hop relaying (CDFMR) wireless Rayleigh fading networks, and sheds light on their design principles for energy and spectral efficiency. The focus is on a general performance analysis (over all SNR range) of heterogeneous wireless networks with possibly different numbers of relays in clusters of various separations. For clustered multi-hop relaying systems, hop-by-hop routing is known as an efficient decentralized routing algorithm which selects the best relay node in each hop using local channel state information. In this article, we combine hop-by-hop routing and cooperative diversity in CDFMR systems, and we derive (i) a closed-form expression for the probability distribution of the end-to-end SNR at the destination node; (ii) the system symbol error rate (SER) performance for a wide class of modulation schemes; and (iii) exact analytical expressions for the system ergodic capacity, the outage probability and the achievable probability of the SNR (power) gain. We also provide simple analytical asymptotic expressions for SER and the outage probability in high SNR regime. Numerical results are provided to validate the correctness of the presented analyses.

Closed-Form Capacity Result for Interference-Limited Environments With Mixed Fading

We study a multinode network, where a multi-antenna transmitter Tx communicates with its desired receiver Rx, whereas a cluster P ≡̂ {P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x,n</sub> , n = 1, . .. ,N} of unintended nodes is disturbed by the Tx-Rx (TR) communication. To prevent severe performance degradation, we impose a constraint on the total interference that is inflicted at the nodes of P. The TR link contains a line-of-sight component, whereas the propagation environment for each Tx-Px,n link is shadowed. The Tx node is preprocessing the information sequence by means of a precoding matrix that is optimized to achieve the ergodic capacity under a constraint on the maximum admissible ergodic interference power, arriving on P. In this paper, we show that the optimum precoding strategy involves the transmission of a single stream over the precoding direction, i.e., the eigenvector of the precoding matrix, which corresponds to beamforming along the instantaneous direction of the TR-link channel. The solution of the remaining power allocation problem yields the optimal precoding matrix. For this setup, we provide an efficient stochastic characterization of the network, which allows us to obtain an analytical expression for the TR-link ergodic capacity; this problem has been previously open, even for the case of a single-antenna node Tx and a single-element set P. We complement the analysis by deriving the TR-link signal-to-noise ratio and the average bit error rate, which are associated with our transmission scheme. Numerical results corroborate the theoretical analysis and reveal an interplay between the network parameters and their impact on the TR-link performance.

Performance Improvement of Dual-Hop OFDM Decode-and-Forward Relay System

Ergodic capacity of dual-hop orthogonal frequency division multiplexing (OFDM) based decode-and-forward (DF) relay system may be significantly enhanced if ordered subcarrier mapping (SCM) is implemented at relay station (R). We proved earlier that this SCM scheme also brings certain bit error rate (BER) performance improvement to assumed system. However, the level of the achieved BER reduction is very small, with no reduction at all for the high signal-to-noise ratios (SNRs) on both hops. Therefore, in this paper we propose a modification of the SCM scheme where one or more subcarriers with the lowest SNRs from both hops are omitted before ordered SCM is performed at the relay station of an OFDM DF relay system. For the scenario with Rayleigh fading statistics on both hops, and no direct communication between the source of information (S) and destination (D), we derived a closed form BER relation of the assumed uncoded BPSK modulated relay system. The analytically obtained BER results, which are verified through simulations, show that the proposed modified SCM scheme brings significant BER performance improvements for all SNR values on both hops. Additionally, in order to provide analytical tool for the assessment of ergodic capacity enhancement achieved through ordered SCM, we derived ergodic capacity expression of the dual-hop OFDM DF relay system with ordered SCM.

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.

Capacity and Error Probability Analysis of Diversity Reception Schemes Over Generalized- &lt;named-content content-type="math" xlink:type="simple"&gt;&lt;inline-formula&gt;&lt;tex-math notation="TeX"&gt;$K$&lt;/tex-math&gt;&lt;/inline-formula&gt;&lt;/named-content&gt; Fading Channels Using a Mixture Gamma Distribution

In this paper, we analyze the error probability and ergodic capacity performance for diversity reception schemes over generalized-K fading channels using a mixture gamma (MG) distribution. With high accuracy, the MG distribution can approximate a variety of composite fading channel models and provide mathematically tractable properties. In contrast to previous analysis approaches that require complicated signal-to-noise ratio (SNR) statistics, it is shown that a distribution of the received SNR for diversity reception schemes is composed of a weighted sum of gamma distributions by exploiting the properties of the MG distribution. Then, based on this result, we can derive the exact average symbol error probability and simple closed-form expressions of diversity and array gains for maximal ratio combining and selection combining. In addition, an expression of the ergodic capacity for these schemes is obtained in independent and identically distributed fading channels. Our results lead to meaningful insights for determining the system performance with parameters of the MG distribution. We show that our analysis can be expressed with any number of receiver branches over various fading conditions. Numerical results confirm that the derived error probability and ergodic capacity expressions match well with the empirical results.