From a random walk model introduced by Jakeman, Field and Tough derived the stochastic dynamics accounting for the scattering of a wavelike field from a random medium, and showed how the scattering cross-section was observable through the fluctuations of the scattered field phase. In the context of K-scattering, we pursue this strategy by deriving an explicit analytical expression of the deviation between the exact (underlying) and the inferred (observed) crosssection. We then deduce a condition to optimize the inference. Simulation results assert the viability of our theoretical formulae. Their consequences are discussed. IntroductionStochastic models, originating from electromagnetic scattering, but appropriate for more general situations (e.g., spin dynamics in nuclear magnetic resonance (NMR)) have recently encountered growing interest. In the same vein, this paper derives a new result, closely related to the previous contribution of [1], concerning the inference of the cross-section from the received amplitude. In the context of Jakeman's random walk model with step number fluctuations (cf. [2]) for a component phase diffusion model, it was shown in [1] that the scattering cross-section could be obtained from the (smoothing over a sample window of the) intensity-weighted instantaneous (squared) fluctuations of the phase. This result extended for arbitrary populations the anterior theoretical model of [3], whose pertinence had been established in [4] for anomaly detection. However, the closeness (in terms of the correlation coefficient) between the hidden population (exact cross-section) and the population obtained through the highly volatile phase decoherence (inferred cross-section) was heavily influenced by the smoothing process, i.e. over how many pulses the phase decoherence was averaged. Here lies the pertinency of our new result. Having recalled the stochastic model described in these previous papers and its experimental implications, we derive an expression for the error between the hidden and the estimated cross-sections. The concept of optimal smoothing, defined as the lower bound of this smoothing error, is then introduced. Moreover, we provide analytical formulae for the optimal window length (a value to be used for experimental situation) and for the corresponding error. Emphasis is placed on K-scattering and the extension to more general populations is discussed. The adequacy of this development is illustrated by simulation data, which compares the analytical error (derived in this

We first derive the stochastic dynamics of a Gaussiancompound model with an inverse Gamma distributed texture from Jakeman's random walk model with step number fluctuations. Following a similar approach existing for the Kdistribution, we show how the scattering cross-section may be inferred from the fluctuations of the scattered field intensity. By discussing the sources of discrepancy arising during this process, we derive an analytical expression for the inference error based on its asymptotic behaviours, together with a condition to minimize it. Simulated data enables verification of our proposed technique. The interest of this strategy is discussed in the context of radar applications.

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It is known that a random walk model yields the multiplicative representation of a coherent scattered amplitude in terms of a complex OrnsteinUhlenbeck process modulated by the square root of the cross-section. A corresponding biased random walk enables the derivation of the dynamics of a weak coherent scattered amplitude as a stochastic process in the complex plane. Strong and weak scattering patterns differ regarding the correlation structure of their radial and angular fluctuations. Investigating these geometric characteristics yields two distinct procedures to infer the scattering cross-section from the phase and intensity fluctuations of the scattered amplitude. These inference techniques generalize an earlier result demonstrated in the strong scattering case. Their significance for experimental applications, where the cross-section enables tracking of anomalies, is discussed.