MU-MIMO Beamforming by Constructive Interference
Wireless telecommunication technology has developed practical multiple-user multiple-input multiple-output (MU-MIMO) antenna configurations. This Demonstration shows a plot of energy density for 2D beamforming of an antenna array (red dots) and two receivers (locators) exhibiting constructive interference. You can choose relative phases to strengthen the signal at selected points, preferably using different frequencies. For a triangular array, select Δ.
Assume that the antenna array transmits a signal at two frequencies to two receivers by choosing phase differences optimized for their locations. A 2D map of the resulting energy density is shown. For simplicity, and to prevent infinities at the antennas, we neglect reduction of power with the distance from the antennas. In 3D, the energy density decreases as the square of the distance.
Drag either of the two locators to change the positions of the receivers. The first two controls let you choose the wavelengths, such that 1 is the lattice constant of the antenna array. The next two controls let you change the number of antennas in the array in the horizontal and vertical directions. You can also switch to a triangular array, indicated by "Δ". Finally, the last two controls let you choose the viewing distance and the resolution (MaxRecursion for the DensityPlot).
 Wikipedia. "Multi-user MIMO." (Aug 2, 2016) en.wikipedia.org/wiki/Multi-user_MIMO.
 Wikipedia. "Beamforming." (Aug 2, 2016) en.wikipedia.org/wiki/Beamforming.
 Wikipedia. "Interference (Wave Propagation)." (Aug 2, 2016) en.wikipedia.org/wiki/Interference_(wave_propagation).