[Paper Review] Effective throughput of MISO systems over $\kappa-\mu$ shadowed fading channels: MGF based analysis

Hussien Al‐Hmood, Hamed Al‐Raweshidy|arXiv (Cornell University)|Apr 29, 2018

Advanced MIMO Systems Optimization4 references3 citations

TL;DR

This paper presents an exact closed-form expression for the effective throughput of MISO systems over i.i.d. κ−μ shadowed fading channels using the moment generating function (MGF) of the instantaneous SNR. The analysis yields a result in terms of the extended generalized bivariate Meijer's G-function, which is further simplified for integer μ and m, and asymptotic behavior at high SNR is derived for system insight.

ABSTRACT

The effective throughput of multiple-input single-output (MISO) wireless communication systems over $\kappa-\mu$ shadowed fading channels is analysed. To obtain exact closed-from expression, the moment generating function (MGF) of the instantaneous signal to noise ratio (SNR) with independent and identically distributed (i.i.d.) transmit antennas is employed. In addition, a special case of integer values for the fading parameter is performed to simplify the derived expression. The asymptotic behaviour of the effective throughput at high values of SNR is also studied. The Monte Carlo simulations and the numerical results are presented to verify the validation of our analysis.

Motivation & Objective

• To derive an exact closed-form expression for effective throughput in MISO systems over κ−μ shadowed fading channels.
• To employ the moment generating function (MGF) of the instantaneous SNR to enable precise performance evaluation.
• To simplify the derived expression for practical implementation by assuming integer values of μ and m.
• To analyze the asymptotic behavior of effective throughput at high SNR for system design insights.
• To validate the analytical results through Monte Carlo simulations and numerical comparisons.

Proposed method

• Utilizes the MGF of the instantaneous SNR over i.i.d. κ−μ shadowed fading channels, derived from the composite distribution of κ−μ and Nakagami-m fading.
• Applies the MGF-based effective capacity formulation using the integral representation involving the Meijer's G-function.
• Expresses the effective throughput in terms of the extended generalized bivariate Meijer's G-function (EGBMGF), a special function not natively supported in MATLAB or Mathematica.
• Derives a simplified closed-form expression under the condition that μ and m are positive integers with m ≥ μ, using binomial expansion and hypergeometric functions.
• Performs asymptotic analysis at high SNR by evaluating the limit of the effective capacity expression as ρ → ∞.
• Validates the analytical results via Monte Carlo simulations and numerical evaluation across varying SNR, number of antennas, and fading parameters.

Experimental results

Research questions

• RQ1 What is the exact closed-form expression for the effective throughput of MISO systems over i.i.d. κ−μ shadowed fading channels?
• RQ2 How can the MGF-based approach be used to derive a more accurate and simplified expression compared to existing approximations?
• RQ3 What is the asymptotic behavior of effective throughput at high SNR, and how does it reflect system performance trends?
• RQ4 How does the effective throughput scale with the number of transmit antennas, μ, and m under different fading conditions?
• RQ5 To what extent do the simplified expressions for integer μ and m preserve accuracy while enabling practical implementation?

Key findings

• The exact effective throughput is derived in closed-form using the MGF and expressed as an extended generalized bivariate Meijer's G-function (EGBMGF), which is not natively available in MATLAB or Mathematica but can be computed via existing codes.
• For integer values of μ and m with m ≥ μ, the expression simplifies to a finite sum involving Pochhammer symbols and the Tricomi hypergeometric function U.
• The asymptotic expression at high SNR reveals a power-law decay in effective throughput, dependent on Lμ and Lm, providing insight into system scaling at high SNR.
• Simulations confirm the analytical accuracy, showing perfect agreement between theoretical results and Monte Carlo simulations across varying SNR and antenna configurations.
• Effective throughput increases with higher μ (more multipath clusters) and higher m (reduced shadowing severity), and improves significantly with more transmit antennas.
• The performance gain from increasing L is more pronounced when μ and m are large, indicating that diversity combining effectively combats fading in rich scattering environments.