A dual-band 10-port multiple input multiple output (MIMO) antenna array for 5G smartphone is proposed. Each antenna in the MIMO system can work from 3.4 to 3.6 GHz and 5 to 6 GHz with 10 dB (2:1 VSWR) impedance bandwidth. Nevertheless, for a 3:1 VSWR, the antenna operates from 3.3 to 3.8 GHz and 4.67 to 6.24 GHz. The MIMO system is formed by making 10 seven-shaped coupled fed slot antenna elements excited at two different resonant modes and integrated into the system circuit board. By implementing the spatial and polarization diversity techniques, high isolation better than 28 dB between any pair of antenna elements is achieved. The proposed 10-port MIMO antenna array is fabricated and measured. Significant radiation efficiency is obtained, ranging from 65 to 82% for both bands. The antenna gain in the required operating band is substantial, around 3–3.8 dBi. Further, the MIMO parameters such as envelope correlation co-efficient, channel capacity, and total active reflection co-efficient are calculated. The antenna's robustness is estimated by analyzing the user hand effects and specific absorption rate (SAR). The measured results are well agreed with the simulated results.

Fix a bivariate distribution F on X × Y, considered as a pair (α, {Fx}), where α is a marginal distribution on X and {Fx} is a collection of conditional distributions on Y. For essentially every (β,{Gx}) satisfying a certain pair of moment conditions determined by (α, {Fx}), J(β, {Fx}) ≦ J(α, {Fx}) ≦ J(α, {Gx}), where J is mutual information. This relates to two sorts of extremizations of mutual information of relevance to communication theory and statistics.