# Beamforming 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

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 $$r_1=\mathbf{h}_1^T\sum_{i=1}^2\mathbf{w}^*_i\,s_i+n_1$$
$$r_2=\mathbf{h}_2^T\sum_{i=1}^2\mathbf{w}^*_i\,s_i+n_2$$