Asymptotic Spectral Distribution of a Second-Order Progressive Scattering Channel

This letter investigates the asymptotic spectral distribution (ASD) of a stochastic second-order progressive scattering channel (PSC), a prevalent component in radar and communication systems. Leveraging random matrix theory (RMT), we derive a precise probability density function (PDF) consist of basic algebraic structure. The accuracy of the proposed ASD is validated through rigorous Monte Carlo experiments, demonstrating a strong alignment between the theoretical distribution and its numerical representation. Subsequently, utilizing the proposed ASD, we compute the channel capacity parameters of the second-order PSC, encompassing the normalized input-output mutual information (IOMI) and the arithmetic mean over minimum mean square error (MMSE). Our results indicate superior IOMI performance and confirm that the channel capacity of the second-order PSC is markedly lower than that of the TRC. Furthermore, we anticipate the potential application of the ASD to acoustic scattering and reverberation problems at the sea surface and seabed.