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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.

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  • \$\begingroup\$ Does " I want to allocate 𝑛 beams to BS1 and the rest 16−𝑛 beams to BS2" answer your question? Are you just confusing or duplicating terms? \$\endgroup\$
    – Solar Mike
    Apr 14, 2022 at 5:08
  • \$\begingroup\$ @SolarMike Thanks for your reply. The goal is to allocate the beams, but what I'm confused is that the dimension n seems to represent the number of data streams not the number of beams. \$\endgroup\$
    – ZYX
    Apr 14, 2022 at 5:20
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    \$\begingroup\$ Yes, but the estimated signal is the data stream, right? The estimated signal refers to the signal results from the received signal passing through the receiver (receiver beamformer). \$\endgroup\$
    – ZYX
    Apr 14, 2022 at 5:38
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    \$\begingroup\$ @ZYX it's not a data stream, but as-orthogonalized-as-possible channel outputs, if you will; "data" happens after demapping and decoding. But that's just nitpicking the terminology here, and your MIMO book might use it that way! \$\endgroup\$ Apr 14, 2022 at 8:52
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    \$\begingroup\$ How can I deal with the dimension of the receive beamformer? you do your matrix decomposition, or whatever you do as "beamforming", and look at how many significant Eigenvalues (or whatever measure for SINR you get) you have. That gives your dimension. Again, you have zero influence over the channel. \$\endgroup\$ Apr 14, 2022 at 11:03

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