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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 ith 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

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