## FANDOM

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Beamforming is a signal processing technique which can generate a spatial beam to enhance signal transmission and reception.

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 $\Omega = 2 pi / N$ in average where $N$ 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 $M$ 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

$\mathbf{x} = \mathbf{w}_i s_i$

where $s_i$ is the message signal (chosen from a complex Gaussian alphabet with power $P/M$) intended for the $i$th receiver and $\mathbf{w}_i$ is the corresponding beamforming vector.

If multiple beams are used, the transmission spatial signal model can be extended as

$\mathbf{x} = \sum_{i=1}^K \mathbf{w}_i s_i = \mathbf{W} \mathbf{s}$

where $\mathbf{s} = [s_1, s_2, \ldots, s_K]$ is the message signal vector and $\mathbf{W} = [\mathbf{w}_1, \mathbf{w}_2, \ldots, \mathbf{w}_M]$ is the corresponding beamforming transform matrix.