Truncated Channel Inversion With Fixed Rate Research Articles

Capacity analysis of shadowed Beaulieu-Xie fading channels

In this paper, we provide a capacity analysis for the shadowed Beaulieu-Xie (SBX) fading model, under different transmission policies. From this analysis, we derive new expressions for the channel capacity per unit bandwidth considering four adaptive transmission schemes, namely: constant power with optimal rate adaptation (ORA); optimal power and rate adaptation (OPRA); channel inversion with fixed rate (CIFR) and truncated CIFR (TCIFR). We obtain asymptotic expressions for the channel capacity. A unified ergodic capacity analysis is presented for the maximum-ratio combining (MRC), the equal gain combining (EGC) and the selection combining (SC) diversity receivers. We present capacity curves for different parameters that characterize the channel.

Effective Capacity of $L_p$ -Norm Diversity Receivers Over Generalized Fading Channels Under Adaptive Transmission Schemes

This paper presents novel moment generating function (MGF)- and characteristic function (CHF)-based frameworks for the EC performance analysis of a generic L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm diversity combining scheme under adaptive transmission policies. The considered system operates over generalized fading channels, a maximum delay constraint and under various channel state information (CSI) conditions. Depending upon the operational CSI, four policies are studied, namely: i) Constant power with optimal rate adaptation (ORA); ii) Optimal power and rate adaptation (OPRA); iii) Channel inversion with fixed rate (CIFR); and iv) Truncated CIFR (TIFR). The L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm diversity is a generic diversity structure which includes as special cases various well-known diversity schemes, such as equal gain combining (EGC), maximal ratio combining (MRC) and amplify-and-forward (AF) relaying. Under the ORA and OPRA policies, we derive single integral expressions for evaluating the EC of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm diversity reception directly from the MGF or the incomplete MGF of the Signal-to-Noise-Ratio (SNR) at the receiver, respectively. For the EC performance evaluation of the EGC and AF relaying systems operating under the OPRA policy, a CHF-based approach, which is computationally more efficient as compared to the MGF-based approach, is further presented. It is shown that the EC for the CIFR and TIFR policies can be directly evaluated from the MGF or the CHF of the SNR at the receiver, respectively. For the ORA policy, a novel analytical approach for the asymptotic EC performance analysis is also developed and evaluated, revealing how important system operation parameters affect the overall system performance. The mathematical formalism is validated with selected numerical and equivalent simulation performance evaluation results, thus confirming the correctness of the proposed analytical methodology.

Error probability and channel capacity analysis of wireless system over inverse gamma shadowed fading channel with selection diversity

SummaryIn this paper, we present an analytical framework to analyse the error probability and the channel capacity of the inverse gamma (I‐Gamma) shadowed fading channel. First, the work discusses the utility of the I‐Gamma over log‐normal (LN) and gamma fading models where the closeness of I‐Gamma with other existing shadowing models is carried out. Utilising the probability density function (PDF) of the I‐Gamma shadowed fading channel, various metrics of the communication system, namely, the average symbol error probability (SEP), the channel capacity under optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR), and truncated CIFR (TIFR) are derived. Further, the work is extended to derive a novel selection combining (SC) PDF, and the analytical results for the SEP and the channel capacity of SC diversity are presented. Furthermore, we also provide simpler asymptotic expressions for the average SEP. In addition, the simplified high and low signal‐to‐noise‐ratio (SNR) solutions to channel capacity are also provided. The derived mathematical formulations have been endorsed by comparing with Monte Carlo simulations.

Comparison of adaptive algorithms for free space optical transmission in Málaga atmospheric turbulence channel with pointing errors

In this study, the authors investigate average capacity of free space optics communication over Málaga atmospheric turbulence channel with pointing errors and path loss, for intensity modulated/direct detection (IM/DD) and heterodyne detection. Various algorithms which use adaptive transmission with both types of detection are considered, such as: optimal rate adaption (ORA), optimal power and rate adaption (OPRA), channel inversion with fixed rate (CIFR) and truncated channel inversion with fixed rate (TIFR). Analytical closed-form expressions for channel capacities of ORA, OPRA and TIFR adaptive transmission are presented, and the authors prove that CIFR transmission is not feasible in the strict sense for the conditions considered. Obtained analytical results are numerically evaluated and graphically presented for different strengths of atmospheric turbulence (in weak, moderate and strong turbulence regime) for both types of detection (IM/DD and heterodyne), and for considered algorithms of adaptive transmission (ORA, OPRA and TIFR). The authors have developed expressions suitable for approximating high signal-to-noise ratio channel capacity, and they graphically present and compare the asymptotic approximations with the obtained analytical results for different strengths of turbulence for both types of detection. Also, obtained analytical results were confirmed by Monte-Carlo simulations, and graphically compared for different strengths of turbulence regimes.

Asymptotic capacity analysis under different adaptive transmission for TAS/MRC MIMO scheme subject to Weibull fading channels

This paper investigates a unified average channel capacity (ACC) analysis under different adaptive transmission of multiple-input multiple-output (MIMO) system, combining single transmit antenna selection (TAS) and maximal-ratio combining (MRC) receiver operating under independent flat Weibull multipath fading channels (WFCs). Based on a tight approximate probability density function expression of the signal-to-noise ratio (SNR) at the considered receiver output, we derive new accurate closed-form expressions of ACC for TAS/MRC system employing several rate adaptation techniques, namely optimal rate adaptation, optimal simultaneous power and rate adaptation, channel inversion with fixed rate (CIFR), truncated CIFR (TCIFR), and continuous power TCIFR (CTCIFR). Further, asymptotic expressions, in both high and low-SNR regimes, are investigated. The results show high accuracy for significant values of Lt×Lr TAS/MRC system. Indeed, the smaller Lt×Lr, the better the PDF’s accuracy, therefore, the better are the capacities. Numerical outcomes have been assessed by utilizing Mathematica and Matlab Software and corroborated via Monte-Carlo simulations.

Average SEP and channel capacity analysis over Generic/IG composite fading channels: A unified approach

This paper develops an analytical framework to analyse important performance metrics of the wireless communication system over generic fading channels characterized by α−μ/Inverse Gaussian (IG), η−μ/IG, and κ−μ/IG distributions. The important performance metrics, namely, the outage probability (OP), the amount of fading (AOF), the average symbol error probability (SEP) of coherent and non-coherent schemes, the channel capacity under optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR), and truncated CIFR (TCIFR) policy are analysed. Further, low and high signal-to-noise-ratio (SNR) approximations for channel capacity are presented. Furthermore, for asymptotic analysis the approximate composite probability density function (PDF) at the origin was developed and utilized to derive the closed-form expressions for the average SEP of both coherent and non-coherent modulation schemes with maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) diversity schemes. The proposed asymptotic solutions are simple and can be easily used to describe the system behaviour at high SNR. The correctness of the derived results has been verified by comparing them with Monte Carlo simulations.

A tight approximate analytical framework for performance analysis of equal gain combining receiver over independent Weibull fading channels

In this paper, a method for approximating the probability distribution of sum of independent and identical Weibull random variables is adopted to analyze the performance of equal gain combiner (EGC) receiver over non-identical Weibull fading channel (WFC). Our main result is to derive a generalized expression of the probability density function (PDF) of the signal-to-noise ratio (SNR) at the EGC output in the case of non-identical WFC. Based on this PDF, accurate approximation of significant performance criteria, such as outage probability (OP), the amount of fading (AoF), and average symbol/bit error probability (ASEP/ABEP), are derived. In addition, we derived the analytical expressions for channel capacities under various adaptation policies such as optimal rate adaptation (ORA), optimal simultaneous power and rate adaptation (OPRA), channel inversion with fixed rate (CIFR), and truncated channel inversion with fixed rate (TCIFR). The proposed mathematical analysis is complemented by several numerical results and validated using Monte Carlo simulation method.

A very tight approximate results of MRC receivers over independent Weibull fading channels

In this paper, we study the performance of L-branch maximal-ratio combining (MRC) receivers operating over independent Weibull-fading channels. Our main result is a very tight approximation of the probability density function (PDF) of the signal-to-noise ratio (SNR) at the output of the combiner. Based on this result, accurate approximation of significant performance criteria, such as outage probability and average symbol error rate (ASER) are derived. We also evaluate the average bit error rate (ABER) for several coherent and non-coherent modulation schemes, using a closed-form expression for the moment-generating function (MGF) of the output SNR for MRC receivers. In addition, we derive some analytical expressions for channel capacity under various adaptation policies such as optimal rate adaptation (ORA), Optimal simultaneous power and rate adaptation (OPRA), Channel inversion with fixed rate (CIFR), and Truncated channel inversion with fixed rate (TCIFR). The proposed mathematical analysis is complemented by numerous numerical results, which point out the effects of fading severity on the overall system performance. Computer simulations are also performed to verify the validity and the accuracy of the proposed theoretical approach.

Spectrum efficiency evaluation of LMF channels under various adaptation policies with hybrid diversity schemes

A single-input multiple-output (SIMO) system with lognormal multipath fading (LMF) channel is considered in this paper. The spectrum efficiency (capacity per unit bandwidth) of a LMF channel for various adaptation policies is studied. We obtain the closed-form expressions for various adaptation policies such as (i) optimal power and rate adaptation (OPRA) policy, (ii) channel inversion with fixed rate (CIFR) policy, and (iii) truncated channel inversion with fixed rate (TIFR) policy with hybrid diversity combining techniques like hybrid maximal ratio combining (MRC)-equal gain combining (EGC), hybrid EGC-MRC, and hybrid MRC-selection combining (SC) diversity. Numerical results show that the use of hybrid diversity combining techniques improves the spectrum efficiency over stand-alone diversity combining techniques. OPRA policy that provides the highest spectrum efficiency when compared to other policies is also shown.

Average Channel Capacity of Correlated Dual-Branch Maximal Ratio Combining Under Worst Case of Fading Scenario

The channel capacity and probability of outage results for optimum power and rate adaptation (OPRA) and truncated channel inversion with fixed rate (TIFR) schemes over correlated diversity branch obtained so far in literature are applicable only for m ? 1. This paper derived closed-form expressions for the average channel capacity and probability of outage of dual-branch maximal ratio combining (MRC) over correlated Nakagami-0.5 (m < 1) fading channels. This channel capacity and probability of outage are evaluated under OPRA and TIFR schemes. Since, the capacity and probability of outage expressions of dual-branch MRC under OPRA and TIFR schemes contain an infinite series; bounds on the errors resulting from truncating the infinite series have been derived for both average channel capacity and probability of outage. The corresponding expressions for Nakagami-0.5 fading are called expressions under worst fading condition with severe fading. Finally, numerical results are presented, which are then compared to the capacity and probability of outage results that previously published for OPRA and TIFR schemes. It has been observed that OPRA provides improved average channel capacity and probability of outage, as compared to TIFR under worst case of fading. It is also observed that probability of outage under TIFR scheme is not improved adequately than the probability of outage under OPRA even as employing diversity.

Effective Capacity of Statistical Delay QoS Guarantees with Imperfect Channel Information in Spectrum-Sharing Networks

This paper considers a spectrum-sharing cognitive network in which a secondary user shares spectrum with an existing primary user as long as the interference caused by the secondary user to the primary user is below permissible levels. We investigate the delay quality-of-service (QoS) guaranteed capacity gains with imperfect channel state information (CSI) between the secondary transmitter and the primary receiver in Rayleigh fading environments. In particular, we quantify the relation between the secondary link effective capacity and the interference inflicted on the primary user. The impacts of channel estimation error on the performance of the secondary link are studied. We further evaluate and compare the capacity gains using proposed power allocation policies and truncated channel inversion with fixed rate (TIFR) transmission policies under different constraint conditions. Our results indicate channel estimation errors, especially in the smaller value range, lead to considerably degradation of capacity gains for the looser delay QoS requirements. Numerical simulations are conducted to corroborate our theoretical analysis. 

Capacity analysis of Rayleigh fading channels in low signal‐to‐noise ratio regime for maximal ratio combining diversity because of combining errors

In this research work, the authors derive closed-form expressions for capacity per unit bandwidth (spectrum efficiency) of correlated Rayleigh fading channels under maximal ratio combining diversity at low signal-to-noise ratios (SNRs). Spectrum efficiency expressions are derived for M diversity branches under adaptation policies, such as: (i) optimal power and rate adaptation (OPRA) policy, (ii) optimal rate adaptation (ORA) policy and (iii) truncated channel inversion with fixed rate (TIFR) policy. Even at low SNRs, if space diversity is exercised using a single-input multiple-output system, spectrum efficiency achieved is higher compared with that achieved when signals are uncorrelated and have no diversity. This forms the focal point of this study. Analytical results show accurately that OPRA policy provides highest capacity over other adaptation policies. The spectrum efficiency for the three policies and outage probability for the low SNR case are derived, plotted and analysed in detail in this work.

Impact of partial relay selection on the capacity of communications systems with outdated CSI and adaptive transmission techniques

AbstractThe impact of outdated channel state information (CSI) on the capacity of amplify-and-forward (AF) partial relay selection systems is studied in this article. The closed-form expressions for the distribution of received signal-to-noise ratio (SNR) in a multi-relay cooperative communications system is first derived, with independent and identically distributed (i.i.d.) Rayleigh fading channels being assumed in each wireless link. After that, the theoretical closed-form expressions for both outage probability and channel capacity of partial relay selection are derived, with four classical adaptive transmission techniques, including the constant power with optimal rate adaption (ORA), the optimal power and rate adaption (OPRA), the channel inversion with fixed rate (CIFR) and truncated channel inversion with fixed rate (TIFR), being considered. Numerical analysis proves that the channel capacity of partial relay selection is impacted considerably by some critical parameters, including the number of relays, the channel correlation coefficient and the end-to-end SNR, etc. It’s also exhibited in the numerical results that among the four adaptive transmission techniques, the diversity order of OPRA is larger than that of TIFR, and the OPRA outperforms TIFR with about 0.15 bits/s/Hz in terms of average channel capacity.

Effective capacity of delay quality-of-service constrained spectrum sharing cognitive radio with outdated channel feedback

In this paper, we consider a spectrum sharing cognitive radio network coexisting with a primary network. Particularly, the channel state information (CSI) between the secondary transmitter and the primary receiver is assumed to be outdated due to channel feedback latency. The secondary user (SU) is assumed to satisfy a given delay quality-of-service (QoS) constraint as well as the average interference power constraint. We aim to derive the maximum arrival rate of the SU under aforementioned constraints with the outdated CSI. In this respect, we derive the optimal power allocation to achieve the maximum effective capacity, and further derive the effective capacity. The closed-form expressions for the lower and upper bounds on the effective capacity are also derived. In addition, we obtain the effective capacities under two widely adopted adaptive transmission schemes, i.e., optimal power and rate allocation (OPRA) and truncated channel inversion with fixed rate (TIFR). Numerical results are conducted to corroborate our studies. It is shown that the effective capacities of the SU under various transmission schemes are insensitive to the channel correlation coefficient especially under low channel correlation coefficient. It is also shown that the lower and upper bounds on the effective capacity are significantly tight under stringent delay QoS constraint.

Adaptive transmission in MIMO AF relay networks with orthogonal space-time block codes over Nakagami-m fading

In this article, we apply different adaptive transmission techniques to dual-hop multiple-input multiple-output amplify-and-forward relay networks using orthogonal space-time block coding over independent Nakagami-m fading channels. The adaptive techniques investigated are optimal simultaneous power and rate (OSPR), optimal rate with constant power (ORCP), and truncated channel inversion with fixed rate (TCIFR). The expressions for the channel capacity of OSPR, ORCP, and TCIFR, and the outage probability of OSPR, and TCIFR are derived based on the characteristic function of the reciprocal of the instantaneous signal-to-noise ratio (SNR) at the destination. For sufficiently high SNR, the channel capacity of ORCP asymptotically converges to OSPR while OSPR and ORCP achieve higher channel capacity compared to TCIFR. Although TCIFR suffers from an increase in the outage probability relative to OSPR, it provides the lowest implementation complexity among the considered schemes. Along with analytical results, we further adopt Monte Carlo simulations to validate the theoretical analysis.

Impact of Outdated Relay Selection on the Capacity of AF Opportunistic Relaying Systems with Adaptive Transmission over Non-Identically Distributed Links

In this paper, we derive probability density function (PDF) and cumulative distribution function (CDF) expressions for the end-to-end signal-to-noise ratio (SNR) of an opportunistic relaying amplify-and-forward (AF) cooperative diversity system over independent and non-identically distributed (i.ni.d.) Rayleigh fading links where outdated channel state information (CSI) is used for relay selection. Based on these expressions, we derive the analytical capacity and outage probability expressions for four classical adaptive transmission techniques, namely, optimal power and rate adaptation (OPRA), constant power with optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR) and truncated channel inversion with fixed rate (TIFR). Numerical evaluations results are presented showing the impact of relay selection with outdated CSI and i.ni.d. links on the performance of each adaptive transmission technique in AF opportunistic relaying systems.

On the Outage Capacity of Sensing-Enhanced Spectrum Sharing Cognitive Radio Systems in Fading Channels

Spectrum sharing has received an increasing amount of attention in cognitive radio over the past few years as an effective method of alleviating the spectrum scarcity problem in wireless communications by allowing unlicensed users to use the same spectrum as the licensed users under the condition of protecting the latter from harmful interference using a received interference power constraint at the licensed receivers. In this paper, we study the outage capacity and the truncated channel inversion with fixed rate (TIFR) capacity of a sensing-enhanced spectrum sharing cognitive radio system under two different scenarios, namely with and without missed-detection interference power constraints for the protection of the primary users, for both Rayleigh and Nakagami-m fading channels. In our analysis, we consider various constraints on the capacity that include: (i) average transmit power constraints, (ii) peak interference power constraints, (iii) average interference power constraints and (iv) target detection probability constraints, and derive the power allocation strategy, as well as the TIFR and outage capacity for each scenario. Finally, we provide simulation results, which indicate that the sensing-enhanced spectrum sharing cognitive radio system can achieve higher outage and TIFR capacity compared to the conventional non-sensing spectrum sharing cognitive radio system.

Capacity Analysis of Opportunistic Cooperative Networks under Adaptive Transmission over Rayleigh Fading Channels

In this paper, opportunistic cooperative amplify-and-forward networks in conjunction with three different adaptive policies, namely optimal simultaneous power and rate adaptation (OPRA), constant power with optimal rate adaptation (OPA) and truncated channel inversion with fixed rate (TIFR), are investigated and compared in terms of Rayleigh channel capacity where the source adapts its rate and/or power level according to channel conditions while the best relay simply amplifies and then forwards the received signals. Furthermore, the effect of diversity combining on the network is studied by investigating two cases of maximal ratio combining (MRC) and selection combining (SC) equipped at the destination. To this end, the mathematically tractable form of the upper and lower bound of the end-to-end effective signal-to-noise ratio (SNR) is provided and then used to derive the closed-form expression of the Shannon capacity. Our results are verified through comparison with Monte Carlo simulations in some representative scenarios where we also illustrate that, among them, for an arbitrary number of cooperative relays, OPRA slightly outperforms ORA, which, in turn, outperforms TIFR.

Capacity of Correlated Generalized Gamma Fading With Dual-Branch Selection Diversity

The capacity of correlated generalized gamma (GG) fading channels with dual-branch selection diversity (SD) reception and channel side information (CSI) available at both the transmitter and the receiver is studied and analyzed. In particular, the capacity is evaluated under four adaptive transmission policies defined according to the operational CSI: 1) optimal power and rate adaptation (OPRA); 2) constant power with optimal rate adaptation (ORA); 3) channel inversion with fixed rate (CIFR); and 4) truncated CIFR (TIFR). Under these four adaptation policies, fast converging infinite series expressions for the capacity are derived and evaluated. Furthermore, for the simplifying cases of independent GG fading channels and/or single-channel reception (i.e., no diversity), closed-form expressions have been obtained. Previously published expressions are shown to be special cases of the derived expressions. Performance evaluation results obtained by means of numerical analysis clearly demonstrate the usefulness and accuracy of the analysis.