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This paper introduces a novel line-of-sight (LoS) $\beta-\gamma$ terahertz(THz) channel model that closely mirrors physical reality by consideringradiation trapping. Our channel model provides an exhaustive modeling of thephysical phenomena including the amount of re-radiation available at thereceiver, parametrized by $\beta$, and the balance between scattering and noisecontributions, parametrized by $\gamma$, respectively. Our findings indicate anontrivial relationship between average limiting received signal-to-noise ratio(SNR) and distance emphasizing the significance of $\gamma$ in THz systemdesign. We further propose new maximum likelihood (ML) thresholds for pulseamplitude modulation (PAM) and quadrature amplitude modulation (QAM) schemes,resulting in analytical symbol error rate (SER) expressions that account fordifferent noise variances across constellation points. The results confirm thatthe analytical SER closely matches the true simulated SER when using an optimaldetector. As expected, under maximum molecular re-radiation, the true SER isshown to be lower than that produced by a suboptimal detector that assumesequal noise variances.

Novel LoS $\beta-\gamma$ THz Channel Unifying Molecular Re-radiation Manifestations