Analysis of STC-GFDM with Walsh Hadamard in generalized η−μ fading channel

ABSTRACT

This manuscript presents a comprehensive analytical framework for Walsh-Hadamard Transform (WHT) precoding in Space-Time Coded Generalized Frequency Division Multiplexing (STC-GFDM) systems. The investigation specifically targets the $\mathit{\eta }$-$\mathit{\mu }$ fading channel and employs the moment generating function (MGF) approach to establish an exact closed-form expression for the Symbol Error Rate (SER). The derived expression enables the examination of one-sided Gaussian, Rayleigh, Nakagami-m and Hoyt-q fading channels as specific cases of the $\mathit{\eta }$-$\mathit{\mu }$ fading channel. Additionally, the paper also delves into the impact of crucial system parameters, including modulation order, channel fading parameters ($\mathit{\eta }$ and $\mathit{\mu }$) and the number of transmit and receive antennas, on the WHT-STC-GFDM system’s performance. Furthermore, the paper conducts an in-depth complexity analysis of the WHT precoder, shedding light on the computational demands associated with its implementation. In summary, this research enhances the understanding of WHT precoding in STC-GFDM systems operating in $\mathit{\eta }$-$\mathit{\mu }$ fading channels, providing valuable insights for the design and optimisation of future communication systems. The numerical results are validated through Monte-Carlo simulations.

KEYWORDS:

• Generalised frequency division multiplexing (GFDM)
• space time coding (STC)
• symbol error rate (SER)
• Walsh Hadamard Transform (WHT)
• $\mathit{\eta }-\mathit{\mu }$ fading channel

Acknowledgements

No funds provided for this research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data Sharing is not applicable as no datasets are generated for this article.