Capacity Bounds and Degrees of Freedom for MIMO Antennas Constrained by Q-Factor

The optimal spectral efficiency and the number of independent channels for multiple-input-multiple-output (MIMO) antennas in isotropic multipath channels are investigated when bandwidth requirements are placed on the antenna. By posing the problem as a convex optimization problem restricted by the port Q-factor, a semianalytical expression is formed for its solution. The antennas are simulated by method of moments, and the solution is formulated both for structures fed by discrete ports and for design regions characterized by an equivalent current. It is shown that the solution is solely dependent on the eigenvalues of the so-called energy modes of the antenna. The magnitude of these eigenvalues is analyzed for a linear dipole array and a plate with embedded antenna regions. The energy modes are also compared to the characteristic modes to validate characteristic modes as a design strategy for MIMO antennas. The antenna performance is illustrated through spectral efficiency over the Q-factor, a quantity that is connected to the capacity. It is proposed that the number of energy modes below a given Q-factor can be used to estimate the degrees of freedom for that Q-factor.