Capacity and amount of fading analysis for SIMO communications over ημ and λμ fading channels

https://doi.org/10.1016/j.dsp.2020.102921Get rights and content

Abstract

This study evaluates the performance of single-input multiple-output (SIMO) wireless networks or dual-branch (DB) SIMO scenarios over the ημ and the λμ fading links. First, the probability density functions (PDFs) of the instantaneous signal to noise ratio for a DB SIMO system in the ημ and the λμ fading conditions. Then, the closed-form expressions of the effective rate (ER or effective capacity) for a SIMO network are derived. In addition to this, asymptotic ER expressions for the considered SIMO network are proposed. The analytical capacity expressions with different transmission policies such as optimal rate adaptation with constant transmit power, optimal simultaneous power and rate adaptation, channel inversion with fixed-rate (CIFR), and truncated channel inversion with fixed-rate are obtained for the SIMO network. Furthermore, the capacity expressions with CIFR policy for DB SIMO communications over the ημ and the λμ fading channels are derived by using the proposed PDFs. Finally, the amount of fading expressions for SIMO networks over the ημ and the λμ fading links are proposed by employing the elementary functions. The proposed analytical expressions provide to establish different radio propagation scenarios by adjusting η, λ or μ parameter. To confirm the accuracy of our analysis, the proposed analytical expressions are verified via exact simulations.

Introduction

Accurate fading characterization is accepted as a crucial mission in the influential analysis for the performance of wireless communication networks. Non-homogeneous fading environments such as ημ, κμ, and λμ fading models are typically preferred in realistic wireless transmission scenarios. For this purpose, the ημ, the κμ, and the λμ distributions have been considered comparatively convenient fading types as they also contain traditional fading types which are known Hoyt, Nakagami-m, Rayleigh, Weibull, and Rice distributions [1], [2], [3], [4], [5], [6], [7], [8]. In addition to this, the ημ, the κμ, and the λμ fading channel models can also properly determine the small-scale variations of a wireless signal under non-line-of-sight circumstances [2], [4]. Undoubtedly, the high data rate is an indisputable requirement for future generation wireless communication systems. For this reason, it is predicted that high frequency bands, which are not used today, will be used to reach high data rates. With the use of higher frequencies, the wavelengths will decrease and small cell transmission architectures will come to the fore. Accurate fading characterization of channel environments in these communication architectures is a very important issue.

Due to the reasons mentioned above, the ημ, the κμ, and the λμ fading channel models are commonly employed in many realistic wireless communication applications [5], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26] (see references therein). Approximate error probability (EP) expression for dual-branch (DB) single-input multiple-output (SIMO) systems over λμ fading channels were obtained in [5]. Physical-layer security analysis for systems over the ημ and the λμ fading channels were presented in terms of average secrecy capacity and average outage probability expressions [9]. The study in [10] examined the outage and EP performance of a dual-hop (DH) communication system via amplify-and-forward (AF) relaying for different fading conditions which are subject to ημ and κμ fading links. A theoretical framework for the performance of DH decode-and-forward cooperative networks over ημ fading channels with co-channel interference (CCI) was provided [11]. As a different network model, the authors in [12] presented novel closed-form expressions for the symbol EP of rectangular quadrature amplitude modulation (QAM) with maximal-ratio combining (MRC) techniques over ημ fading conditions. For the same fading model, closed-form expressions for the exact symbol and bit EP of cross QAM constellations with MRC diversity reception were derived [13]. As a different work, in [14], the physical-layer security of a mixed radiofrequency/free-space optical DH wireless network over mixed ημ and M-distribution was investigated. As the secrecy performance of transmit antenna selection/MRC networks with CCI over ημ fading channels was presented in [15], a comprehensive performance evaluation of DH cognitive AF relaying systems under spectrum-sharing operation over ημ fading environments was provided [16]. The study in [17], the performance evaluation of L-branch MRC over ημ fading conditions in the presence of imperfect channel estimation was analyzed.

In [18], the authors studied energy detection based on spectrum sensing over κμ and κμ extreme fading environments. In [19], the effective throughput of multiple-input–single-output networks over κμ fading was analyzed with delay constraints, and they derived new expressions for the effective throughput of the considered system. As the author presented a comprehensive analytical framework for the QAM (rectangular or cross) signaling over κμ shadowed fading conditions [20], the coverage analysis in downlink cellular communication scenario over κμ shadowed fading channels was presented [21]. For SIMO networks, the studies in [22], [23], [24], [25] were presented to evaluate the different performance metrics such as secrecy analysis, secrecy outage probability, and physical-layer security for their network models. In [22], a SIMO network over generalized-K fading was considered through physical-layer security. The authors proposed the average secrecy capacity expression for a SIMO network over κμ fading conditions [23]. Likewise, exact and asymptotic secrecy outage probabilities for SIMO networks over αμ fading were presented in [24]. The other work in [25], the secrecy performance evaluation of SIMO networks over correlated κμ shadowed fading environments was examined. The study in [26], the approximate error analyses for SIMO networks in the presence of additive white generalized Gaussian noise over the ημ, the κμ, and the λμ fading channels were presented.

On the other hand, various researches about effective capacity and capacity analysis with different power adaption policies for composite fading channels are existed in the literature [27], [28], [29], [30], [31], [32], [33]. In [27], the channel capacity under different transmission policies over αλημ/gamma fading channels was examined by employing a mixture of the gamma distribution. While the capacity analysis was presented for single-input single-output (SISO) networks over ημ fading channels in [28], the different capacity analyses of a SISO network over composite ημ/gamma fading channel were analyzed in [29]. Besides, a comprehensive study of effective capacity analysis for a SISO network over generalized composite fading channels was presented in [30]. Similarly, the achievable channel capacity for F composite fading channels was comprehensively investigated in [31]. For capacity analysis with different power adaption techniques, the analysis for a SISO network in [32], [33] was carried out over fluctuating two-ray and Fisher–Snedecor F fading channels, respectively. However, none of the above-cited studies (see [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33]) has analyzed the effective rate (ER, also known as effective capacity), capacity performance with different transmission policies, and amount of fading (AoF) analysis of SIMO network or DB SIMO scenario in either ημ or λμ channels. In addition, in real and practical communication applications, one of the important factors affecting the channel capacity is the average transmission power limitation in the transmitter. This can be handled by performing power adjustment according to the instantaneous channel status to improve channel capacity. For these reasons, channel capacities with different transmission power adaption methods emerge as an important issue. Furthermore, the examination of ER and AoF for the considered network models is one of the most important contributions of the presented study. It is important that the presented works will be also apprehensible in terms of the complexity and simplicity of the considered networks. In this context, the core aim of this paper is to provide the ER, capacity and AoF expressions which have necessary simplicity, insightful or less complexity for the considered SIMO networks over the ημ and the λμ fading channels.

To the best of the authors' knowledge, the ER, capacity with different transmission policies and AoF performances of SIMO wireless communication networks over the ημ and the λμ fading channels remain substantially undiscovered. Besides, the DB SIMO communications over the ημ and the λμ fading channels have not been reported yet. Motivated by these explanations, our paper conducts research into the ER, capacity with different transmission policies and AoF of SIMO networks or DB SIMO scenario in the ημ, and the λμ fading conditions. The contributions of this paper are summarized next.

In this paper, we propose some novel expressions of ER, capacity with different power adaption techniques, and AoF for a SIMO and DB SIMO networks over the ημ and the λμ fading channels. Our contributions are summarized as follows:

  • Based on the MRC technique, new probability density function (PDF) expressions for DB SIMO network over ημ and the λμ fading channels are obtained.

  • Novel analytical expressions for the ER of the considered SIMO networks are derived. These expressions include elementary mathematical functions for the calculations. Also, the asymptotic ER expressions for SIMO networks over the ημ and the λμ fading channels are presented.

  • The capacity expressions (optimal rate adaptation with constant transmit power (ORA), optimal simultaneous power and rate adaptation (OPRA), channel inversion with fixed-rate (CIFR), truncated channel inversion with fixed-rate (TCIFR)) of the considered SIMO networks with different transmission policies are obtained under both the ημ and the λμ fading channels.

  • In addition to this, for the DB SIMO network, the capacity expression with CIFR policy is proposed.

  • AoF expression for the SIMO system over the ημ and the λμ fading conditions is also derived with the help of rth order moment expressions.

  • The accuracy of the proposed results for ER, capacity, or AoF is corroborated through comparisons with exact numerical simulations.

The remainder of the paper is organized as follows: Section 2 defines the considered networks and channel models, while Section 3 describes the ER analysis. Likewise, the capacity analyses with different transmission policies and AoF for SIMO networks are also presented in Section 3. Section 4 focuses on the numerical results and discussions. Finally, conclusions are presented in Section 5.

Section snippets

SIMO networks and channel models

As in Fig. 1a, we consider a SIMO network in which the transmitter sends information messages to the receiver with a single antenna, while the destination receives it with N receiver antennas through the ημ or the λμ fading channels. Here, the reason why SIMO network systems are considered can be said to be traditional uplink communication or any communication from a single antenna transmission relay to a multi-antenna receiver. On the other hand, for practical scenarios, the versatile ημ

Capacity and AoF analyses

This section presents ER analysis, four different capacity derivations with different transmission polices, the AoF analysis by using rth order moment expressions are obtained and the asymptotic ER analysis for the considered SIMO networks over the ημ and the λμ fading channels.

Numerical results

For the aim of illustration and to approve the proposed analytical studies, we provide some simulations and numerical examples by using the MATHEMATICA and MATLAB software packages. Since the proposed final expressions contain infinite series, it is sufficient to employ 20 terms in these series to obtain precise results. For example, Table 1 demonstrates the truncation evaluation of the ER expressions for a SIMO network over ημ and λμ fading channels. From Table 1, it can be seen that the

Conclusion

In this paper, ER performance, capacity performance with different transmission polices and AoF performance of SIMO wireless communication networks over both the ημ fading and the λμ fading has been addressed. First, the PDF expressions of DB SIMO networks over the ημ and the λμ fading channels were obtained. Then, novel analytical expressions for a SIMO network were derived for the ER, capacity, and AoF, which have been validated through comparisons with respective results from exact

CRediT authorship contribution statement

Mehmet Bilim: Conceptualization, Investigation, Methodology, Software, Visualization, Writing – original draft.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Mehmet Bilim was born in Gaziantep, Turkey. He received the B.Sc., M.Sc. and Ph.D. degrees in Electrical and Electronics Engineering from Erciyes University, Turkey, in 2010, 2012 and 2018, respectively. From 2011 to 2018, he was a Research Assistant in the Department of Electrical and Electronics Engineering at Erciyes University. Currently, he is an assistant professor in the department of Electrical and Electronics Engineering at Nuh Naci Yazgan University. He teaches courses in wireless

References (38)

  • M. Bilim

    QAM signaling over κμ shadowed fading channels

    Phys. Commun.

    (2019)
  • M. Bilim

    Uplink communications with AWGGN over non-homogeneous fading channels

    Phys. Commun.

    (2020)
  • M. Bilim

    A performance study on diversity receivers over κμ shadowed fading channels

    AEÜ, Int. J. Electron. Commun.

    (2019)
  • N.Y. Ermolova et al.

    The ημ fading distribution with integer values of μ

    IEEE Trans. Wirel. Commun.

    (Jun. 2011)
  • M.D. Yacoub

    The κμ distribution and the ημ distribution

    IEEE Antennas Propag. Mag.

    (Feb. 2007)
  • P.C. Sofotasios et al.

    The ημ/gamma and the λμ/gamma multipath/shadowing distributions

  • G. Fraidenraich et al.

    The λμ general fading distribution

  • M. Bilim et al.

    Error analysis of dual-branch SIMO systems over λμ fading channels

  • J.F. Paris, P.C. Sofotasios, T.A. Tsiftsis, Special issue on advances in statistical channel modeling for wireless...
  • P.C. Sofotasios et al.

    Entropy and channel capacity under optimum power and rate adaptation over generalized fading conditions

    IEEE Signal Process. Lett.

    (Nov. 2015)
  • M. Bilim

    Capacity analysis of ακμ fading channels for different adaptive transmission schemes

  • J.M. Moualeu et al.

    Physical-layer security of SIMO communications systems over multipath fading conditions

    IEEE Trans. Sustain. Comput.

    (2019)
  • K.P. Peppas et al.

    Performance analysis of dual-hop AF relaying systems over mixed ημ and κμ fading channels

    IEEE Trans. Veh. Technol.

    (Sep. 2013)
  • K. Peppas

    Dual-hop relaying communications with cochannel interference over ημ fading channels

    IEEE Trans. Veh. Technol.

    (Oct. 2013)
  • H. Yu et al.

    On the error probability of cross QAM with MRC reception over generalized ημ fading channels

    IEEE Trans. Veh. Technol.

    (July 2011)
  • V. Asghari et al.

    Symbol error probability of rectangular QAM in MRC systems with correlated ημ fading channels

    IEEE Trans. Veh. Technol.

    (Mar. 2010)
  • L. Yang et al.

    Physical-layer security for mixed ημ and M-distribution dual-hop RF/FSO systems

    IEEE Trans. Veh. Technol.

    (Dec. 2018)
  • L. Yang et al.

    Physical layer security for TAS/MRC systems with and without co-channel interference over ημ fading channels

    IEEE Trans. Veh. Technol.

    (Dec. 2018)
  • J. Yang et al.

    Dual-hop cognitive amplify-and-forward relaying networks over ημ fading channels

    IEEE Trans. Veh. Technol.

    (Aug. 2015)
  • Cited by (0)

    Mehmet Bilim was born in Gaziantep, Turkey. He received the B.Sc., M.Sc. and Ph.D. degrees in Electrical and Electronics Engineering from Erciyes University, Turkey, in 2010, 2012 and 2018, respectively. From 2011 to 2018, he was a Research Assistant in the Department of Electrical and Electronics Engineering at Erciyes University. Currently, he is an assistant professor in the department of Electrical and Electronics Engineering at Nuh Naci Yazgan University. He teaches courses in wireless communications and his current research interests are in spread spectrum communications, multiuser communications, multiple access techniques, wireless networks, millimeter wave communications, digital communications, fading channels, cooperative diversity and applications of neural networks to communication systems. He was a recipient of the Ph.D. Research Fellowships from the Scientific and Technological Research Council of Turkey (TUBITAK). He was the recipient of Best Presenter Award and Best Paper Award from the ICAT International Conferences 2016 and 2019, respectively. He is also the author of more than 30 papers in major conferences and journals. He is a reviewer for IEEE, Elsevier, Wiley, Springer, and IET journals.

    View full text