This paper concerns two-hop communication over relay-assisted Block fading channel. It is assumed there is not a direct link between the transmitter and the affiliated destination and the communication occurs in two hops through the use of a relay, where the amplify and forward (AF) strategy is employed at this node. In this case, in a Rayleigh block fading channel, the optimal weight function at the relay in terms of maximizing the received signal to noise ratio (SNR) at the destination is derived, assuming the relay is aware of channel gains associated with both hops and that the relay is subject to an average power constraint. Finally, the resulting SNR is compared to the case of having a peak power constraint at the relay which is served as a benchmark throughout the simulations.

Background: The intravoxel incoherent motion (IVIM) model extracts both functional and structural information of a tissue using motion-sensitizing gradients.Objective: The Objective of the present work is to investigate the impact of signal to noise ratio (SNR) and physiologic conditions on the validity of IVIM parameters.Material and Methods: This study is a simulation study, modeling IVIM at a voxel, and also done 10,000 times for every single simulation. Complex noises with various standard deviations were added to signal in-silico to investigate SNR effects on output validity. Besides, some blood perfusion situations for different tissues were considered based on their physiological range to explore the impacts of blood fraction at each voxel on the validity of the IVIM outputs. Coefficient variation (CV) and bias of the estimations were computed to assess the validity of the IVIM parameters.Results: This study has shown that the validity of IVIM output parameters highly depends on measurement SNR and physiologic characteristics of the studied organ.  Conclusion: IVIM imaging could be useful if imaging parameters are correctly selected for each specific organ, considering hardware limitations.