[Paper Review] Performance Analysis of M-QAM Multihop Relaying over mmWave Weibull Fading Channels.

Abdelaziz Soulimani, Mustapha Benjillali+2 more|arXiv (Cornell University)|Oct 26, 2016

Cooperative Communication and Network Coding16 references19 citations

TL;DR

This paper presents an exact closed-form performance analysis of M-QAM multihop relaying over millimeter-wave Weibull fading channels, using generalized hypergeometric functions to model outage probability, BER, SER, BLER, ergodic capacity, and energy efficiency. It derives optimal power allocation strategies that improve BER and energy efficiency, validated via Monte Carlo simulations and new computational codes for special functions.

ABSTRACT

The paper presents a comprehensive closed-form performance analysis framework for multihop communications over Weibull fading channels. The analyzed scheme consists basically of multiple regenerative relays with generalized high-order quadrature amplitude modulation (M-QAM) transmissions. To take into consideration the channel fading in the mmWave range, we adopt the advocated Weibull model for its flexible ability to cover different channel conditions. The end-to-end performance is evaluated in terms of outage probability, bit error probability (BER), symbol error probability (SER), block error rate (BLER), ergodic capacity, and energy efficiency (EE). For all the metrics, we present exact closed-form expressions along with their asymptotic behavior, some in terms of generalized hypergeometric functions. Based on the obtained analytical results, we also present a practical application, we derive two BER- and EE-optimal transmit power allocation strategies, and we discuss the resulting performance gains. The exactness of our analysis is illustrated by numerical examples, and assessed via Monte-Carlo simulations for different system and channel parameters. Finally, as a secondary contribution, noting the increasing popularity of Fox's H and bivariate H functions, we provide new and generalized codes for computing these functions which are of practical utility in different contexts.

Motivation & Objective

• To develop a comprehensive analytical framework for multihop M-QAM systems over millimeter-wave Weibull fading channels.
• To evaluate key performance metrics including outage probability, BER, SER, BLER, ergodic capacity, and energy efficiency.
• To derive optimal transmit power allocation strategies that minimize BER and maximize energy efficiency.
• To provide new computational tools for Fox's H and bivariate H functions for broader applicability in signal processing and communications.
• To validate analytical results through Monte Carlo simulations across diverse system and channel parameters.

Proposed method

• Adopts the Weibull fading model to accurately represent millimeter-wave channel conditions with flexible fading severity.
• Derives exact closed-form expressions for outage probability, BER, SER, BLER, ergodic capacity, and energy efficiency using generalized hypergeometric functions.
• Analyzes asymptotic behavior of performance metrics to understand system behavior at high SNR.
• Proposes two transmit power allocation strategies—BER-optimal and EE-optimal—based on analytical optimization of performance metrics.
• Introduces generalized computational codes for Fox's H and bivariate H functions to support future research in special function computation.
• Validates analytical results through extensive Monte Carlo simulations across varying channel and system parameters.

Experimental results

Research questions

• RQ1 What are the exact closed-form expressions for key performance metrics (outage, BER, SER, BLER, ergodic capacity, EE) in multihop M-QAM systems over Weibull fading mmWave channels?
• RQ2 How do the asymptotic behaviors of these performance metrics scale with signal-to-noise ratio and fading parameters?
• RQ3 What are the optimal power allocation strategies that minimize BER and maximize energy efficiency in such systems?
• RQ4 How accurate are the derived analytical expressions compared to practical simulations across different system configurations?
• RQ5 What practical computational tools can be developed for evaluating Fox's H and bivariate H functions in wireless communication analysis?

Key findings

• The paper derives exact closed-form expressions for outage probability, BER, SER, BLER, ergodic capacity, and energy efficiency using generalized hypergeometric functions.
• Asymptotic analysis reveals the diversity gain and coding gain behavior of the system under high SNR conditions.
• The BER-optimal power allocation strategy significantly reduces bit error rates across all hops compared to uniform power allocation.
• The EE-optimal power allocation strategy achieves higher spectral and energy efficiency, particularly in low-to-mid SNR regimes.
• Monte Carlo simulations confirm the accuracy of the analytical expressions across a wide range of fading parameters and system configurations.
• New generalized computational codes for Fox's H and bivariate H functions are provided, enabling efficient evaluation in future research and applications.