Performace Evaluation of Maximum A-Posteriori Estimator in the Nakagami-m Fading MIMO Channels for m<1

Subject Areas : Majlesi Journal of Telecommunication Devices

Hamid Nooralizadeh ¹ , Mahyar Shirvanimoghaddam ²

1 - Faculty member of Islamshahr Branch, Islamic Azad University
2 - School of Electrical and Computer Engineering, The University of Sydney, Australia

Received: 2024-01-17 Accepted : 2024-04-25 Published : 2024-06-11

Keywords: Nakagami-m fading, One-sided Gaussian fading, Rayleigh fading, Maximum A-Posteriori estimator,

Abstract :

The Nakagami-m model has garnered significant attention in the literature as a versatile channel model suitable for describing channels experiencing varying degrees of fading, from severe to moderate. This model aligns closely with the characteristics observed in the majority of measured fading radio channels. The estimation of Nakagami-m fading in a multiple-input multiple-output (MIMO) channel poses a crucial challenge. Deriving the probability density function (pdf) for a Nakagami distribution random vector with correlated entries and developing closed-form classical and/or Bayesian estimators for a linear MIMO channel proves to be impractical. We simplify the analysis by assuming that the entries of the Nakagami fading random vector are uncorrelated. Consequently, the joint distribution of the channel vector entries is computed by multiplying the pdfs of the individual entries. Subsequently, the maximum a-posteriori (MAP) estimation of the channel entries is determined. Under the assumption of orthogonal training symbols, the obtained results lead to second-order nonlinear equations. To evaluate the performance of MAP channel estimator in MIMO Nakagami-m frequency-flat fading channels, these nonlinear complex equations are solved numerically. The findings indicate that one-sided Gaussian fading represents the worst-case scenario, yet the channel estimation results surpass those of the least squares (LS) estimation. Additionally, fewer errors are observed in Rayleigh fading channel estimation. Furthermore, it is demonstrated that the performance of MAP estimator improves with an increase in the Nakagami shape parameter. The numerical results affirm that the proposed estimator serves as a suitable method for estimating Nakagami-m fading in uncorrelated MIMO channels with m<1.

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