Cutset Bounds on the Capacity of MIMO Relay Channels

• Main Authors: Youngmin Jeong, Dung Phuong Trinh, Hyundong Shin
• Format: Article
• Language: English
• Published: IEEE 2017-01-01
• Series: IEEE Access
• Subjects: Cooperative relaying; cutset bound; ergodic capacity; hyper-Wishart matrix; multiple-input multiple-output (MIMO); Rayleigh fading
• Online Access: https://ieeexplore.ieee.org/document/8037973/
• ISSN: 2169-3536

We analyze the ergodic capacity of multiple-input multiple-output (MIMO) Rayleigh-fading relay channels. We first derive the probability density function of a sum of independent complex central Wishart matrices-called the central hyper-Wishart matrix-and its joint eigenvalue density. We then derive a trace representation for the max-flow min-cut upper bound on the ergodic capacity of general full-duplex MIMO relay channels where each communicating node is equipped with N antennas and has access only to respective receive channel state information. We also establish the Schur monotonicity theorem for this cutset bound as a functional of the signal-to-noise ratios (SNRs) of three communication links. We further characterize the exact ergodic capacity in the regularity SNR regime where the upper and lower bounds coincide.