Assume there are 2 Base Stations (BSs) each is equipped with \$M\$ antennas serving 1 User Terminal (UT) simultaneously. Say if the UT has 4\$\times\$4 Uniform Planar antenna array, which means it can generate 16 beams to receive the signal from the 2 BSs.
If I want to allocate \$n\$ beams to BS1 and the rest \$16-n\$ beams to BS2, based on the SINR maximization. First, the received signal at the UT can be expressed as $$ \mathbf{y} = \sum_{b=1}^{2}\mathbf{H}_b \mathbf{x}_b+\mathbf{n} \in\mathbb{C}^{16\times 1} $$ where \$\mathbf{H}_b\in\mathbb{C}^{16\times M}\$ is the channel from \$b\$-th BS to the UT, and \$\mathbf{x}_b\in\mathbb{C}^{M\times 1}\$ is the transmit signal of \$b\$-th BS.
The spacial beamformer to UT1 can be set as \$\mathbf{U}_1\in\mathbb{C}^{16\times n}\$, and \$\mathbf{U}_1^H\mathbf{y}\$ results the dimension \$n\times 1\$. Does the \$n\$ in the dimension represent the \$n\$ beams? However, \$n\$ seems to represent the number of data streams.
I'm confused that how to use spacial beamformer at UT side to allocate \$n\$ beams to BS1 and the rest \$16-n\$ beams to BS2 for example based on SINR maximization.