Investigating Noise Immunity of Signal-Code Constructions Employing Trellis Coded Modulation under Impulsive Noise

Ensuring the noise immunity of radio engineering systems operating under severe power and spectral constraints constitutes a pressing scientific and technical problem, particularly in the presence of impulsive noise with a non-Gaussian distribution. This paper considers the application of signal-code constructions based on Trellis Coded Modulation as an effective solution for enhancing noise immunity without bandwidth expansion.

The objective of this research is a comprehensive evaluation of the impact of statistical parameters of channels described by Bernoulli – Gaussian and Middleton Class A models on the system's Bit Error Rate, as well as the establishment of an analytical relationship between these models across various operating regimes.

The research methodology is based on theoretical analysis utilizing the apparatus of mathematical statistics, with result verification performed via simulation in the MATLAB environment.

The scientific novelty lies in conducting a generalized stability analysis of the Trellis Coded Modulation system under a wide variation of noise parameters and, specifically, in the development of a methodology for determining model equivalence boundaries. The proposed approach enables a justifiable transition from the computationally complex Middleton model to simpler approximations (Bernoulli – Gaussian or Gaussian), thereby ensuring the simplification of the system's mathematical description while maintaining the required accuracy of the results.

Simulation results demonstrate that increasing the power ratio between the Gaussian and impulsive components consistently improves the system's noise immunity for both modulation types: 8-Phase Shift Keying and 16-Quadrature Amplitude Modulation. Regarding the verification of model equivalence boundaries, it has been established that approximation by the Bernoulli – Gaussian model is valid at an impulsive index value of  for both for both modulation types. At the same time, convergence to the Gaussian model is achieved at different threshold values:  for 8-Phase Shift Keying and  for 16-Quadrature Amplitude Modulation, which is attributed to the difference in signal constellation density.

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