Cascaded Rayleigh Fading Research Articles

Effective Capacity Analysis over Cascaded Rayleigh Fading Channels with Arbitrary Correlation

Effective Capacity Analysis over Cascaded Rayleigh Fading Channels with Arbitrary Correlation

Improved S-AF and S-DF Relaying Schemes Using Machine Learning Based Power Allocation Over Cascaded Rayleigh Fading Channels

We investigate the performance of a dual-hop intervehicular communications (IVC) system with relay selection strategy. We assume a generalized fading channel model, known as cascaded Rayleigh (also called n*Rayleigh), which involves the product of n independent Rayleigh random variables. This channel model provides a realistic description of IVC, in contrast to the conventional Rayleigh fading assumption, which is more suitable for cellular networks. Unlike existing works, which mainly consider double-Rayleigh fading channels (i.e, n = 2); our system model considers the general cascading order n, for which we derive an approximate analytic solution for the outage probability under the considered scenario. Also, in this study we propose a machine learning-based power allocation scheme to improve the link reliability in IVC. The analytical and simulation results show that both selective decode-and-forward (S-DF) and amplify-and-forward (S-AF) relaying schemes have the same diversity order in the high signal-to-noise ratio regime. In addition, our results indicate that machine learning algorithms can play a central role in selecting the best relay and allocation of transmission power.

Impacts of Residual Self-Interference, Hardware Impairment and Cascade Rayleigh Fading on the Performance of Full-Duplex Vehicle-to-Vehicle Relay Systems.

In practice, self-interference (SI) in full-duplex (FD) wireless communication systems cannot be completely eliminated due to imperfections in different factors, such as the SI channel estimation and hardware circuits. Therefore, residual SI (RSI) always exists in FD systems. In addition, hardware impairments (HIs) cannot be avoided in FD systems due to the non-ideal characteristics of electronic components. These issues motivate us to consider an FD-HI system with a decode-and-forward (DF) relay that is applied for vehicle-to-vehicle (V2V) communication. Unlike previous works, the performance of the proposed FD-HI-V2V system is evaluated over cascaded Rayleigh fading channels (CRFCs). We mathematically obtain the exact closed-form expressions of the outage probability (OP), system throughput (ST), and ergodic capacity (EC) of the proposed FD-HI-V2V system under the joint and crossed effects of the RSI, HIs, and CRFCs. We validate all derived expressions via Monte-Carlo simulations. Based on these expressions, the OP, ST, and EC of the proposed FD-HI-V2V system are investigated and compared with other related systems, such as ideal hardware (ID) and half-duplex (HD) systems, as well as a system over traditional Rayleigh fading channels (RFCs), to clearly show the impacts of negative factors.

Statistics of cascaded Rayleigh fading channels with arbitrary correlation

Exact expressions for the probability density function (PDF) and cumulative distribution function (CDF) of cascaded Rayleigh fading channels with arbitrary correlation but not necessarily identically distributed are derived. Furthermore, the PDF and CDF of the instantaneous signal-to-noise ratio are obtained. The cascaded channels are assumed to have slow frequency non-selective arbitrarily correlated Rayleigh fading with arbitrarily values of fading parameters. Indeed, the expressions of the outage probability and average normalised channel capacity for this channel model are derived. The average bit error probability for coherently detected binary signals in additive white Gaussian noise channel as well as in arbitrarily correlated cascaded Rayleigh fading channels is obtained. Numerical results are also provided and authenticated by Monte Carlo simulation. To the best of the authors' knowledge, the derived expressions for this channel model are new and have not been reported in the literature.

End-to-end SER of MRT/MRC and SC in multi-hop wireless sensor networks

The purpose of this study is to express analytically the end-to-end (e2e) symbol error rate (SER) in multi-hop decode-and-forward relaying in wireless sensor networks. These may occur in independently distributed cascaded Nakagami-m fading channels that may or may not be identical. In this study, all sensor terminals show mobility and this study is possibly the first one that undertakes performance analysis of maximal ratio transmission/maximum ratio combining and selection combining diversity that enables a better system performance in a multi-hop wireless sensor transmission system. In this paper, the first step undertaken was to generate a closed-form expression of the probability distribution function (PDF), the cumulative distribution function, and the moment-generating function for the system being examined. This discovery helped in the evaluation of the eventual performance of the system as far as e2e SER is concerned. It also helped in determining the upper limits of SER expressions for high signal-to-noise ratios. In the next phase, the intended system was utilized in an accurate approximation of the PDF of the cascaded Rayleigh fading channels to compare the findings acquired thus with those derived by its use in the actual PDF of the cascaded Rayleigh fading channels. These analytical findings were then validated with the help of Monte-Carlo simulations.

Improved S-AF and S-DF Relaying Schemes using Machine Learning based Power Allocation over Cascaded Rayleigh Fading Channels

Improved S-AF and S-DF Relaying Schemes using Machine Learning based Power Allocation over Cascaded Rayleigh Fading Channels

Performance Analysis for Multi-Hop Cognitive Radio Networks Over Cascaded Rayleigh Fading Channels With Imperfect Channel State Information

In this letter, we consider a cognitive radio network with imperfect channel state information where secondary users transmit signals using multi-hop relaying. When the channels between secondary users are modeled as cascaded Rayleigh fading, we derive the exact outage probability of the secondary network in an analytic form and the approximate outage probability in a closed form. Then we propose a secondary user selection scheme to minimize the outage probability. The validity of our analysis is verified through simulation.

Outage performance analysis for a $K$th-best wireless-powered relaying SIMO system with non-linear energy harvester

This paper examines the outage performance of a wireless-powered relaying single-input, multiple-output system with non-linear energy harvesters over double cascaded Rayleigh fading channels. In particular, a source node with a single antenna transmits information to a destination node with multiple antennas through $N (N \\ge 1)$ single-antenna wireless-powered relays. The destination node adopts maximal ratio combining in order to process the multiple signal copies. Each relay is conducted with a non-linear energy harvester, in which the harvested power is limited by a threshold. The relays employ power-splitting receivers to deal with the information receiving and energy harvesting, and broadcast the processed information using a decode-and-forward protocol. A $K$th-best relay in terms of outage probability (OP) is selected to assist with source-relay-destination transmission. An analytical expression is derived for the OP, and verified using Monte Carlo simulation results.

Finite‐SNR diversity‐multiplexing trade‐off of inter‐vehicular cooperative diversity protocols

The finite-signal-to-noise ratio (SNR) diversity-multiplexing trade-off (DMT) of cooperative diversity protocols are investigated in vehicular networks based on cascaded Rayleigh fading. Lower bounds of DMT at finite SNR for orthogonal and non-orthogonal protocols are derived. The results showcase the first look into the achievable DMT trade-off of cooperative diversity in volatile vehicular environments. It is shown that the diversity gains are significantly suboptimal at realistic SNRs.

On the Second-Order Statistics of Correlated Cascaded Rayleigh Fading Channels

The second-order statistics of two correlated cascaded (double) Rayleigh fading channels are analyzed, where different relevant second-order cross-correlation functions of in-phase and quadrature components of the cascaded Rayleigh channels are derived. The level crossing rate (LCR) and average fade duration (AFD) of the cascaded channels are evaluated, and a single-integral form of the LCR is derived. Numerical results of the LCR and AFD are presented, and the effect of the correlation is illustrated.

Relay Selection in Dual-Hop Vehicular Networks

In this letter, we investigate cooperative diversity with relay selection over cascaded Rayleigh fading channels. In particular, we analyze the performance of a relay selection scheme for cooperative vehicular networks with the decode-and-forward (DF) protocol. Only the “best” relay, which satisfies an index of merit, is selected. We ignore the direct transmission between the source ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> ) and its destination ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> ), and assume that the destination has perfect knowledge of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> → <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> → <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> channel gains. We study the performance of the underlying scheme in terms of outage probability and investigate its achievable diversity order.

Novel Distributed Space-Time Trellis Codes for Relay Systems over Cascaded Rayleigh Fading

In this letter, we consider the deployment of distributed space-time trellis codes (STTCs) for user cooperation. We derive a pairwise error probability (PEP) expression for distributed STTCs over cascaded Rayleigh fading channels. Using the derived PEP expression, we determine a code design criterion and propose novel 4-/8-/16-state 4-PSK and 8-/16-state 8-PSK distributed STTCs through a systematic code search. We confirm the superiority of the proposed codes through extensive Monte-Carlo simulations.

Unified BER and optimum threshold analysis of binary modulations in simple and cascaded Rayleigh fading channels with switched combining

Following a unified analytical framework, the bit error rate (BER) of several coherent and non-coherent binary modulation schemes is derived for a switched diversity system. The two variants of switched combining that have been investigated are switch and stay combining and switch and examine combining. For channel modelling, at first a simple slow flat fading channel is assumed, where the amplitude attenuation obeys the Rayleigh distribution. Later the BER calculations are repeated for cascaded Rayleigh fading channel case. Rayleigh fading is the most popular model for electromagnetic signal propagation in wireless media when both or either of the transmitter/receiver is fixed. On the other hand, when both the transmitter and the receiver are mobile, a cascaded (or double) Rayleigh fading model is better suited. The applicability of these two models, namely simple and cascaded Rayleigh model, has been indicated by several theoretical studies and their suitability is established by various field measurements. In our paper, simple closed-form BER expressions as a function of switching threshold have been found and optimum switching thresholds have been computed for both these models as well as for both types of diversity combining described earlier. The results presented in this paper can be very useful for communication system designers to analyze link quality of switched diversity assisted systems in various wireless environments. Copyright © 2010 John Wiley & Sons, Ltd.

BICM-ID with signal space diversity over cascaded rayleigh fading channels [transactions letters

Bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) is considered for cascaded Rayleigh fading channels. A tight bound on the asymptotic error probability is derived to determine the optimal rotation matrix for SSD design and to identify the key parameters that influence the system performance. It is shown that, for small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the conventional and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. Illustrative simulation results for various scenarios are in a good agreement with analytical derivations.

Performance Bounds of Orthogonal Space-Time Block Codes Over Keyhole Nakagami-$m$ Channels

The application of Bonferroni-type bounds is investigated for orthogonal space-time block codes over a keyhole Nakagami-m fading channel, which includes a cascaded Rayleigh fading channel as a special case. In particular, upper and lower bounds on the symbol error rate and bit error rate are derived and shown to be very tight at any signal-to-noise ratio. The developed bounds are applicable for arbitrary signal constellations and mappings and can be accurately computed with single finite-range integrals.

Diversity analysis of space-time coding in cascaded Rayleigh fading channels

Cascaded Rayleigh distribution is used to model multipath fading in mobile-to-mobile communication scenarios and provides a better fit to experimental data in such scenarios compared to the conventional Rayleigh channel model. In this letter, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the cascaded Rayleigh fading channel, which is in the form of a simple single finite-range integral. Through the derived PEP expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels. Monte-Carlo simulations are further demonstrated to confirm the analytical results.

Maximum achievable diversity order for cascaded Rayleigh fading channels

In this Letter, we investigate the error rate performance of coherent M-ary phase shift keying (M-PSK) modulation over cascaded Rayleigh fading with receive antenna diversity. Through the derived symbol error rate (SER) expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degredation in comparison to conventional Rayleigh channels.