Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  derive new closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the two-user multiple access channel (MAC). The derived relations generalize the fundamental relation beten the derivative of the mutual information and the minimum mean squared error (MMSE) to multiuser setups.  prove that the derivative of the mutual information with respect to the signal to noise ratio (SNR) is equal to the MMSE plus a covariance induced due to the interference, quantified by a term with respect to the cross correlation of the multiuser input estimates, the channels and the precoding matrices.  also derive new relations for the gradient of the conditional and non-conditional mutual information with respect to the MMSE. Capitalizing on the new fundamental relations,  investigate the linear precoding and por allocation policies that maximize the mutual information for the two-user MAC Gaussian channels with arbitrary input distributions.  show that the optimal design of linear precoders may satisfy a fixed-point equation as a function of the channel and the input constellation under specific setups.  show also that the non-mutual interference in a multiuser setup introduces a term to the gradient of the mutual information which plays a fundamental role in the design of optimal transmission strategies, particularly the optimal precoding and por allocation, and explains the losses in the data rates. Therefore,  provide a novel interpretation of the interference with respect to the channel, por, and input estimates of the main user and the interferer.
['Samah A. M. Ghanem']
I am writing a research paper on a idea Multiple Access Gaussian Channels with Arbitrary Inputs: Optimal Precoding and Power Allocation
[{"from": "human", "value": "I am writing a research paper on a idea Multiple Access Gaussian Channels with Arbitrary Inputs: Optimal Precoding and Power Allocation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  derive new closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the two-user multiple access channel (MAC). The derived relations generalize the fundamental relation beten the derivative of the mutual information and the minimum mean squared error (MMSE) to multiuser setups.  prove that the derivative of the mutual information with respect to the signal to noise ratio (SNR) is equal to the MMSE plus a covariance induced due to the interference, quantified by a term with respect to the cross correlation of the multiuser input estimates, the channels and the precoding matrices.  also derive new relations for the gradient of the conditional and non-conditional mutual information with respect to the MMSE. Capitalizing on the new fundamental relations,  investigate the linear precoding and por allocation policies that maximize the mutual information for the two-user MAC Gaussian channels with arbitrary input distributions.  show that the optimal design of linear precoders may satisfy a fixed-point equation as a function of the channel and the input constellation under specific setups.  show also that the non-mutual interference in a multiuser setup introduces a term to the gradient of the mutual information which plays a fundamental role in the design of optimal transmission strategies, particularly the optimal precoding and por allocation, and explains the losses in the data rates. Therefore,  provide a novel interpretation of the interference with respect to the channel, por, and input estimates of the main user and the interferer."}]