A spatial beam is formed to the desired direction depending on the level of beamforming capability. For example, the number of elements determines the width of a beam. When the element array consist of omni direction elements, the beam width is given as in average where is the number of the antennas equipped in the antenna array.
Beamforming for wireless communication systems Edit
Consider a wireless device which is equipped with antennas. Beamforming can be used for both transmission and reception.
In the transmission case, the beam-formed signal at the front end point of the transmit wireless device is modeled as
where is the message signal (chosen from a complex Gaussian alphabet with power ) intended for the th receiver and is the corresponding beamforming vector.
If multiple beams are used, the transmission spatial signal model can be extended as
where is the message signal vector and is the corresponding beamforming transform matrix.