2018/11/12 by Walid Hachem, Hachem, Walid, Adrien Hardy +3
Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1811.04734
openalex publication_date 2018/11/12 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28
Shannon's mutual information of a random multiple antenna and multipath\nchannel is studied in the general case where the channel impulse response is an\nergodic and stationary process which is assumed to be available at the\nreceiver. From this viewpoint, the channel is represented by an ergodic\nself-adjoint block-Jacobi operator, which is close in many aspects to a block\nversion of a random Schr "odinger operator. The mutual information is then\nrelated to the so-called density of states of this operator. In this paper, it\nis shown that under the weakest assumptions on the channel, the mutual\ninformation can be expressed in terms of a matrix-valued stochastic process\ncoupled with the channel process. This allows numerical approximations of the\nmutual information in this general setting. Moreover, assuming further that the\nchannel impulse response is a Markov process, a representation for the mutual\ninformation offset in the large Signal to Noise Ratio regime is obtained in\nterms of another related Markov process. This generalizes previous results from\nLevy~\et.al.. It is also illustrated how the mutual information\nexpressions that are closely related to those predicted by the random matrix\ntheory can be recovered in the large dimensional regime.\n