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Joint Phase and Amplitude Modelling Using a Finite-State Markov Chain for η–µ Fading Channels

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Abstract

The η–µ fading distribution is used for better representation of small scale variations of the faded signal in Non Line-Of-Sight conditions. In this paper, first-order Finite-State Markov Chain (FSMC) model of η–µ fading channel is proposed for two cases. i.e., considering received signal amplitude only and by jointly varying amplitude and phase. FSMC model captures the essence of slowly fading channels and acts as an important tool to study the performance of wireless communication systems. The Performance parameters of η–µ fading channels like level crossing rate, steady-state probability, state-time duration and state transition probability are studied. Numerical results depicting the performance of FSMC for η–µ fading channels show that η–µ distribution (Format 2) is a severely affected fading channel as compared to η–µ distribution (Format 1) as the former generally occurs in urban areas whereas the latter occurs in suburban and rural areas.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, SRM University, Kattankulathur, Tamilnadu, 603203, India

    V. Nithya & C. Priyanka

  2. Department of Electrical and Computer Engineering, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA, 94132, USA

    Vidhyacharan Bhaskar

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  1. V. Nithya
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  2. C. Priyanka
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  3. Vidhyacharan Bhaskar
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Correspondence to Vidhyacharan Bhaskar.

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Appendix

Appendix

1.1 Algorithm to Find Level Crossing Rate (LCR), Steady State Probability (SSP), State Transition Probability (STP), and State Time Duration (STD)

Input: fm, µ and η

Output: LCR, SSP, STP, STD

1.2 η–µ Fading Distribution Format 1

Case 1: First order FSMC modeling of η–µ fading distribution (Format 1) considering the received signal amplitude only

  • 01: Divide the signal amplitude values into K states

  • 02: Set upper limit value for each state \(v_{k}\)

  • 03: Total number of states S = K

  • 04: k = State index

  • 05: for k = 1: S do

  • 06: Calculate LCR, Nk using Eq. (9)

  • 07: Calculate SSP, πk using Eq. (4)

  • 08: Calculate STP, \(t_{k,k - 1}\) for transition from present state to previous state using Eq. (12)

  • 09: Calculate STP, \(t_{k,k}\) for looping back to same state using Eq. (12)

  • 10: Calculate STP, \(t_{k,k + 1}\) for transition from present state to next state using Eq. (12)

  • 11: Calculate STD, \(\overline{\tau }_{k}\) using Eq. (14)

  • 12: end

  • 13: Plot LCR, SSP, STP and STD

Case 2: First order FSMC modeling of η–µ fading distribution (Format 1) by jointly varying both received signal amplitude and phase

  • 13: Divide the phase values into K1 states

  • 14: Set upper limit for each phase state \(v_{k1}\)

  • 15: Total number of states S = K. K1

  • 16: Repeat (04) to (13) using Eqs. (9), (5), (13) and (15)

1.3 η–µ Fading Distribution Format 2

Case 1: First order FSMC modeling of η–µ fading distribution (Format 2) considering the received signal amplitude only

  • 17: Repeat (01) to (13) using Eqs. (21), (18), (22) and (24)

Case 2: First order FSMC modeling of η–µ fading distribution (Format 2) by jointly varying both received signal amplitude and phase

  • 18: Repeat (13) to (16) using Eqs. (21), (19), (23) and (25)

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Nithya, V., Priyanka, C. & Bhaskar, V. Joint Phase and Amplitude Modelling Using a Finite-State Markov Chain for η–µ Fading Channels. Wireless Pers Commun 112, 923–940 (2020). https://doi.org/10.1007/s11277-020-07083-x

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  • DOI: https://doi.org/10.1007/s11277-020-07083-x

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