Beamforming question

Question

I'm working on a beamforming network. Every node in the network is half-duplex and has a linear antenna array that is capable of digital beamforming. A receiving node can be capable of forming any number of beams as long as it is within its power constraint.

My question is: when transmit beamforming are we able to form multiple simultaneous beams? For example, suppose a transmitter wants to transmit a packet to receiver #1 and then receiver #2.

Would the transmitter operation go something like this?:

1. Form a beam to receiver #1
2. Transmit
3. Form a beam to receiver #2
4. Transmit

Or are we able to do the following?:

1. Form beams to receiver #1 and #2
2. Transmit

Answer 1

I am not completely sure, but I think transmit beamforming is another name for precoding. In precoding we do the following:

1- Form the composite transmit signal as $$\sum_{i=1}^2\mathbf{w}^*_i\,s_i$$ where $\{\mathbf{w}_i\}_{i=1}^2$ are the $N$-dimensional precoding vectors, where $N$ is the number of transmit antennas.

2- The received signal at receiver 1 is $$r_1=\mathbf{h}_1^T\sum_{i=1}^2\mathbf{w}^*_i\,s_i+n_1$$

and at receiver 2 it's

$$r_2=\mathbf{h}_2^T\sum_{i=1}^2\mathbf{w}^*_i\,s_i+n_2$$

The design of the precoding vectors are such that to maximize the power of the desired signal, while minimizing the power of the interference and noise. Note that the CSIs have to be at the transmitter to design the precoding vectors.