The main working principle between the beamforming (or analog beamforming) is to maximize the signal strength in a particular direction towards the receiver. For example, you can steer the antenna manually towards the transmitter to maximize the signal strength, like dish antennas. However, the approach could be more practical for mobile communications. With the help of a phase shifter, we do it electronically. On the other hand, for example, a dish antenna has an aperture that adds some gain to the received signal.Similarly, placing many antennas at a particular space instant creates a beam in a specific direction, minimizing signal strength in the rest of the directions. Here, a combination of antennas creates virtual apertures. On the transmitter side, it transmits a more robust signal toward the receiver. Oppositely, it makes a virtual aperture at the receiver and captures the signal more efficiently.
The main advantage of beamforming is maximizing the signal strength by increasing the number of antenna elements, not the total power.
In the case of analog beamforming, there is only one transmitter and one receiver, and only a single data stream is possible between them.
In the case of digital beamforming, multiple data streams are possible between transmitter and receiver or receivers. The number of users may be one or many.
If there is only one number of users, then multiple data streams between the transmitter and receiver will increase data rates through spatial multiplexing. Similarly, if multiple users exist, each data stream may be allocated to a single user. The various users communicate with the transmitter by deploying spatial multiplexing.
For Single User Digital Beamforming
The received signal vector y at receiver side,
y= √ρHDs + n
Here, D = digital beamforming matrix
ρ = average received power
H =channel matrix ( Nr X Nt)
n = additive white Gaussian noise vector
Nr and Nt are the number of antenna elements at the receiver and transmitter side respectively.
For Multi-user Digital Beamforming
D= [D1, D2, …, DU], & Du denotes the u th user, a digital precoder (size of NBS X NMS)
NBS and NMS are the number of antenna elements at the transmitter and receiver side respectively