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.

## See Also Edit

- Zero-forcing beamforming is transmit beaforming with the interference nulling algorithm at the transmitter.
- Transmit Beamformingis beamforming applied to the downlink channel.
- Smart Antennas
- MIMO