On Selection Combining Diversity in Dual-Hop Relaying Systems Over Double Rice Channels: Fade Statistics and Performance Analysis

This paper investigates the performance of selection combining (SC) diversity in dual-hop cooperative networks under double Rice fading channels. Expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the SC output fading processes are first investigated. The obtained quantities are in the form of finite and semi-infinite range integrals, which can be easily computed using numerical tools. For the PDF, CDF, and LCR statistics corresponding approximate solutions are determined using the Laplace method’s of integration. The PDF and CDF are then applied to derive exact and approximate solutions for the average symbol error probability (SEP) of non-coherent M-ary differential phase-shift keying (M-DPSK) modulation. Moreover, results corresponding to the special cases of mixed Rayleigh $\times $ Rice and double Rayleigh fading channels are extracted. The validity of the derived expressions and the accuracy of the approximations have been checked by using computer simulations. The results can be useful in the performance assessment of mobile-to-mobile (M2M) communications with dual-hop cooperative SC diversity and millimeter wave (mmWave) bands where, in general, the line-of-sight (LOS) propagation arises.

[1]  P. Vainikainen,et al.  Statistical Analysis of the Multiple Scattering Radio Channel , 2006, IEEE Transactions on Antennas and Propagation.

[2]  Khoa N. Le.  Comments on "Distribution Functions of Selection Combiner Output in Equally Correlated Rayleigh, Rician, and Nakagami-m Fading Channels" , 2015, IEEE Trans. Commun..

[3]  Mazen O. Hasna,et al.  A performance study of dual-hop transmissions with fixed gain relays , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[4]  Matthias Pätzold,et al.  Statistical Properties of Double Hoyt Fading With Applications to the Performance Analysis of Wireless Communication Systems , 2018, IEEE Access.

[5]  Gregory W. Wornell,et al.  Cooperative diversity in wireless networks: Efficient protocols and outage behavior , 2004, IEEE Transactions on Information Theory.

[6]  Matthias Patzold,et al.  Channel Models for Mobile-to-Mobile Cooperative Communication Systems: A State of the Art Review , 2011, IEEE Vehicular Technology Magazine.

[7]  Pornchai Supnithi,et al.  Performance of Digital Modulation in Double Nakagami-m Fading Channels with MRC Diversity , 2009, IEICE Trans. Commun..

[8]  Pornchai Supnithi,et al.  Performance of M-PSK in mobile satellite communication over combined ionospheric scintillation and flat fading channels with MRC diversity , 2009, IEEE Transactions on Wireless Communications.

[9]  Irving S. Reed,et al.  Performance of MDPSK, MPSK, and noncoherent MFSK in wireless Rician fading channels , 1999, IEEE Trans. Commun..

[10]  George P. Efthymoglou,et al.  V2V Cooperative Relaying Communications Under Interference and Outdated CSI , 2018, IEEE Transactions on Vehicular Technology.

[11]  Iain B. Collings,et al.  SER of Multiple Amplify-and-Forward Relays with Selection Diversity , 2011, IEEE Transactions on Communications.

[12]  Dhammika Jayalath,et al.  Outage performance of line of sight decode and forward relays in cooperative VANETs , 2013 .

[13]  Murat Uysal,et al.  Cooperative Diversity for Intervehicular Communication: Performance Analysis and Optimization , 2009, IEEE Transactions on Vehicular Technology.

[14]  Matthias Pätzold,et al.  On the Statistical Analysis of Equal Gain Combining over Multiple Double Rice Fading Channels in Cooperative Networks , 2010, 2010 IEEE 72nd Vehicular Technology Conference - Fall.

[15]  George K. Karagiannidis,et al.  Level crossing rate and average fade duration of the double Nakagami-m random process and application in MIMO keyhole fading channels , 2008, IEEE Communications Letters.

[16]  Yawgeng A. Chau,et al.  Channel statistics and performance of cooperative selection diversity with dual-hop amplify-and-forward relay over Rayleigh fading channels , 2008, IEEE Transactions on Wireless Communications.

[17]  Roderick Wong,et al.  Asymptotic approximations of integrals , 1989, Classics in applied mathematics.

[18]  Matthias Pätzold,et al.  On the First- and Second-Order Statistics of Selective Combining over Double Nakagami-m Fading Channels , 2014, 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall).

[20]  Matthias Pätzold,et al.  BEP analysis of M-ary PSK modulation schemes over double Rice fading channels with EGC , 2010, The 7th IEEE International Conference on Mobile Ad-hoc and Sensor Systems (IEEE MASS 2010).

[21]  Yuhao Wang,et al.  Performance Analysis of Bidirectional AF Based Cooperative Vehicular Networks , 2020, IEEE Transactions on Vehicular Technology.

[22]  Mohamed-Slim Alouini,et al.  Level crossing rate over multiple independent random processes-an extension of the applicability of the rice formula , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[23]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[24]  Sergey Loyka,et al.  From Multi-Keyholes to Measure of Correlation and Power Imbalance in MIMO Channels: Outage Capacity Analysis , 2008, IEEE Transactions on Information Theory.

[25]  Ertugrul Basar,et al.  Impact of I/Q Imbalance on Amplify-and-Forward Relaying: Optimal Detector Design and Error Performance , 2019, IEEE Transactions on Communications.

[26]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[27]  Young Jin Chun,et al.  On the Product of Two κ – μ Random Variables and its Application to Double and Composite Fading Channels , 2018 .

[28]  Samuel Pierre,et al.  On the Performance of Multihop-Intervehicular Communications Systems Over n*Rayleigh Fading Channels , 2016, IEEE Wireless Communications Letters.

[29]  Sergey Loyka,et al.  Diversity-multiplexing tradeoff and outage probability in MIMO relay channels , 2010, ISIT.

[30]  Matti Latva-aho,et al.  Performance Analysis of Optimal Beamforming in Fixed-Gain AF MIMO Relaying over Asymmetric Fading Channels , 2014, IEEE Transactions on Communications.

[31]  R. M. A. P. Rajatheva,et al.  Noncoherent Amplify-and-Forward MIMO Relaying With OSTBC Over Rayleigh–Rician Fading Channels , 2013, IEEE Transactions on Vehicular Technology.

[32]  George K. Karagiannidis,et al.  On the second order statistics of the multihop rayleigh fading channel , 2009, IEEE Transactions on Communications.

[33]  Patrick Claus F. Eggers,et al.  Investigations of outdoor-to-indoor mobile-to-mobile radio communication channels , 2002, Proceedings IEEE 56th Vehicular Technology Conference.

[34]  Nazih Hajri,et al.  On the statistical properties of selection combining cooperative diversity over double Rice fading channels , 2014, 2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt).

[35]  George P. Efthymoglou,et al.  Approximations to the Distribution of the Sum of Generalized Normal RVs Using the Moments Matching Method and its Applications in Performance Analysis of Equal Gain Diversity Receivers , 2018, IEEE Transactions on Vehicular Technology.

[36]  Philip Schniter,et al.  On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels , 2005, IEEE Transactions on Information Theory.

[37]  Helmut Bölcskei,et al.  Outdoor MIMO wireless channels: models and performance prediction , 2002, IEEE Trans. Commun..

[38]  Daniel Benevides da Costa,et al.  On the Double-Generalized Gamma Statistics and Their Application to the Performance Analysis of V2V Communications , 2018, IEEE Transactions on Communications.

[39]  Gordon L. Stüber,et al.  Outage probability for cooperative diversity with selective combining in cellular networks , 2010, Wirel. Commun. Mob. Comput..

[40]  S. Rice.  Mathematical analysis of random noise , 1944 .

[41]  H. Hashemi,et al.  The indoor radio propagation channel , 1993, Proc. IEEE.

[42]  Nazih Hajri,et al.  On the performance analysis of binary non-coherent modulations with selection combining in double rice fading channels , 2016, 2016 IEEE 27th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC).

[43]  Matthias Pätzold,et al.  On the Statistical Properties of Equal Gain Combining over Mobile-to-Mobile Fading Channels in Cooperative Networks , 2010, 2010 IEEE International Conference on Communications.

[44]  Talha Batool,et al.  Dual-Hop Amplify-and-Forward Relay Systems with EGC over M2M Fading Channels Under LOS Conditions: Channel Statistics and System Performance Analysis , 2013 .

[45]  Haci Ilhan,et al.  Performance analysis of AF relaying cooperative systems with relay selection over double Rayleigh fading channels , 2012, 2012 6th International Conference on Signal Processing and Communication Systems.

[46]  Yazid M. Khattabi.  New Analytical Approach in the SER Evaluation of CSIN-Assisted AF Dual-Hop Wireless Systems , 2019, IEEE Wireless Communications Letters.

[47]  Helmut Bölcskei,et al.  Fading relay channels: performance limits and space-time signal design , 2004, IEEE Journal on Selected Areas in Communications.

[48]  Gordon L. Stüber,et al.  Statistical properties of amplify and forward relay fading channels , 2006, IEEE Transactions on Vehicular Technology.

[49]  Bayan S. Sharif,et al.  Solutions to Integrals Involving the Marcum $Q$-Function and Applications , 2015, IEEE Signal Processing Letters.