On Performance of Hexagonal, Cross, and Rectangular QAM for Multi-Relay Systems

Error performance is considered as one of the most important performance measures, and deriving the closed-form expressions for efficient modulation techniques over generalized fading channels is important for future cellular systems. In this paper, the performance of a dual-hop amplify-and-forward multi-relay system with best relay selection is analyzed over independent and non-identically distributed (i.n.i.d.) Nakagami-m fading links with both integer and non-integer fading parameters. The impact of practical constraints of imperfect channel state information (CSI) and non-linear power amplifier (NLPA) at each of the relays are considered. Closed-form expressions for the outage probability are derived for both integer and non-integer fading parameters, and asymptotic analysis on the outage probability is performed to obtain the diversity order of the considered multi-relay system. Based on the cumulative distribution function approach, average symbol error rate (ASER) expressions for general order hexagonal QAM, general order rectangular QAM, and 32-cross QAM schemes are also derived. The comparative analysis of ASER for various QAM schemes with different constellations is also illustrated. Furthermore, the impact of the number of relays, fading parameter, channel estimation error, and non-linear distortion on the system performance is also highlighted. Finally, the derived analytical results are validated through Monte-Carlo simulations.

[1]  Natasa Neskovic,et al.  Performance of fixed‐gain amplify‐and‐forward nonlinear relaying with hardware impairments , 2017, Int. J. Commun. Syst..

[2]  Mohsen Guizani,et al.  Mixed RF/FSO Relaying Systems with Hardware Impairments , 2017, GLOBECOM 2017 - 2017 IEEE Global Communications Conference.

[3]  André Lima Férrer de Almeida,et al.  Performance analysis of cooperative amplify-and-forward orthogonal frequency division multiplexing systems with power amplifier non-linearity , 2014, IET Commun..

[4]  Nagendra Kumar,et al.  Mitigating NLD for Wireless Networks: Effect of Nonlinear Power Amplifiers on Future Wireless Communication Networks , 2017, IEEE Microwave Magazine.

[5]  T. Aaron Gulliver,et al.  Triangular Constellations for Adaptive Modulation , 2018, IEEE Transactions on Communications.

[6]  Chin-Liang Wang,et al.  Power Allocation and Relay Selection for AF Cooperative Relay Systems With Imperfect Channel Estimation , 2016, IEEE Transactions on Vehicular Technology.

[7]  P. R. Sahu,et al.  Performance of dual‐hop DF relaying systems with QAM schemes over mixed η‐μ and κ‐μ fading channels , 2017, Trans. Emerg. Telecommun. Technol..

[8]  Vimal Bhatia,et al.  Performance Analysis of OFDM-Based Nonlinear AF Multiple-Relay Systems , 2017, IEEE Wireless Communications Letters.

[9]  Sooyoung Kim,et al.  Performance Enhancement in Future Mobile Satellite Broadcasting Services , 2008, IEEE Communications Magazine.

[10]  Vimal Bhatia,et al.  Impact of Imperfect CSI on ASER of Hexagonal and Rectangular QAM for AF Relaying Network , 2018, IEEE Communications Letters.

[11]  Xiaodai Dong,et al.  Impact of Channel Estimation Error on the Performance of Amplify-and-Forward Two-Way Relaying , 2012, IEEE Transactions on Vehicular Technology.

[12]  Michail Matthaiou,et al.  Multi-relay MIMO Systems With OSTBC Over Nakagami-$m$ Fading Channels , 2013, IEEE Transactions on Vehicular Technology.

[13]  Mohamed-Slim Alouini,et al.  Performance Analysis of Amplify-and-Forward Two-Way Relaying with Co-Channel Interference and Channel Estimation Error , 2013, IEEE Transactions on Communications.

[14]  Justin P. Coon,et al.  Two-Way OFDM-Based Nonlinear Amplify-and-Forward Relay Systems , 2016, IEEE Transactions on Vehicular Technology.

[15]  Mohsen Guizani,et al.  Impact of Non-Linear High-Power Amplifiers on Cooperative Relaying Systems , 2017, IEEE Transactions on Communications.

[16]  Xi-chun Zhang,et al.  Exact Symbol Error Probability of Cross-QAM in AWGN and Fading Channels , 2010, EURASIP J. Wirel. Commun. Netw..

[17]  Vimal Bhatia,et al.  Performance analysis of AF OFDM system using multiple relay in presence of nonlinear-PA over inid Nakagami-m fading , 2018, Int. J. Commun. Syst..

[18]  George K. Karagiannidis,et al.  θ-QAM: A parametric quadrature amplitude modulation family and its performance in AWGN and fading channels , 2010, IEEE Transactions on Communications.

[19]  Sami Muhaidat,et al.  Amplify-and-Forward Selection Cooperation over Rayleigh Fading Channels with Imperfect CSI , 2012, IEEE Transactions on Wireless Communications.

[20]  Tharmalingam Ratnarajah,et al.  Performance Analysis of IA Techniques in the MIMO IBC With Imperfect CSI , 2015, IEEE Transactions on Communications.

[21]  Vimal Bhatia,et al.  ASER Analysis of Hexagonal and Rectangular QAM Schemes in Multiple-Relay Networks , 2018, IEEE Transactions on Vehicular Technology.

[22]  Neelesh B. Mehta,et al.  Accurate Performance Analysis of Single and Opportunistic AF Relay Cooperation with Imperfect Cascaded Channel Estimates , 2013, IEEE Transactions on Communications.

[23]  P. R. Sahu,et al.  Performance Analysis of Rectangular QAM With SC Receiver Over Nakagami- $m$ Fading Channels , 2014, IEEE Communications Letters.

[24]  Yueming Cai,et al.  On the Finite-SNR DMT of Two-Way AF Relaying with Imperfect CSI , 2012, IEEE Wireless Communications Letters.

[25]  Mohamed-Slim Alouini,et al.  Adaptive Modulation over Nakagami Fading Channels , 2000, Wirel. Pers. Commun..

[26]  Sung-Joon Park,et al.  Performance Analysis of Triangular Quadrature Amplitude Modulation in AWGN Channel , 2012, IEEE Communications Letters.

[27]  Luca Rugini,et al.  Symbol Error Probability of Hexagonal QAM , 2016, IEEE Communications Letters.

[28]  Yang Yang,et al.  Relay technologies for WiMax and LTE-advanced mobile systems , 2009, IEEE Communications Magazine.

[29]  Mohamed-Slim Alouini,et al.  Exact BER computation for cross QAM constellations , 2005, IEEE Transactions on Wireless Communications.

[30]  Mohamed-Slim Alouini,et al.  BER computation of 4/M-QAM hierarchical constellations , 2001, 12th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. PIMRC 2001. Proceedings (Cat. No.01TH8598).

[31]  Vimal Bhatia,et al.  Exact ASER Analysis of Rectangular QAM in Two-Way Relaying Networks Over Nakagami- $m$ Fading Channels , 2016, IEEE Wireless Communications Letters.

[32]  Vimal Bhatia,et al.  Performance analysis of OFDM based 3-hop AF relaying network over mixed Rician/Rayleigh fading channels , 2018, AEU - International Journal of Electronics and Communications.

[33]  Davide Dardari,et al.  A theoretical characterization of nonlinear distortion effects in OFDM systems , 2000, IEEE Trans. Commun..

[34]  Vimal Bhatia,et al.  Performance analysis of orthogonal frequency division multiplexing-based cooperative amplify-and-forward networks with non-linear power amplifier over independently but not necessarily identically distributed Nakagami-m fading channels , 2017, IET Commun..

[35]  Juan Manuel Romero-Jerez,et al.  Performance of Selection Combining Diversity in $\eta{-}\mu$ Fading Channels With Integer Values of $\mu$ , 2015, IEEE Transactions on Vehicular Technology.