On the Capacity of Gaussian MIMO Channels with Memory

• Main Authors: Charalambous, C.D (Author), Loyka, S. (Author)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers Inc. 2022
• Subjects: Antennas; Channel capacity; Channel modelling; Channel models; Channel's capacity; Channels with memory; Covariance matrices; Covariance matrix; Eigenvalue and eigenfunctions; Eigenvalues and eigenfunctions; Electric power transmission; Energy harvesting; Gaussians; Impulse response; Interference; memory; Memory management; Memory-management; MIMO; MIMO communication; OFDM; Orthogonal frequency division multiplexing; Spectral density
• Online Access: View Fulltext in Publisher
• ISBN: 10897798 (ISSN)
• DOI: 10.1109/LCOMM.2022.3174774

The operational capacity of Gaussian MIMO channels with memory was obtained by Brandenburg and Wyner in [9] under certain mild assumptions on the channel impulse response and its noise covariance matrix, which essentuially require channel memory to be not too strong. This channel was also considered by Tsybakov in [10] and its information capacity was obtained in some cases. It was further conjectured, based on numerical evidence, that these capacities are the same in all cases. This conjecture is proved here. An explicit closed-form expression for the optimal input power spectral density matrix is also given. The obtained result is further extended to the case of joint constraints, including per-antenna and interference power constraints as well as energy harvesting constraints. These results imply the information-theoretic optimality of OFDM-type transmission systems for such channels with memory. Crown