Per-user unitary rate control

It is assumed that the base station employs ${\displaystyle N_{t}}$ transmission antennas. The ${\displaystyle N_{t}\times 1}$ transmission signal vector is given by

${\displaystyle \mathbf {x} =\sum _{i=1}^{K}\mathbf {w} _{i}P_{i}s_{i}}$

where ${\displaystyle \mathbf {w} _{i}}$ is the ${\displaystyle N_{t}\times 1}$ linear precoding vector. PU²RC generates ${\displaystyle \mathbf {w} _{i}}$ based on the received finite channel status information, which is delivered to the base station from the user equipment (UE) through uplink feedback signaling. The feedback signal consists of index in a look-up table of a precoding codebook.

Every receiver has a receive antenna array with ${\displaystyle N_{r}}$ elements. The receive signal vector at user ${\displaystyle k(=1,2,\ldots ,K)}$ is modeled as follows:

${\displaystyle \mathbf {y} _{k}=\mathbf {H} _{k}\mathbf {x} +\mathbf {n} _{k}}$

where ${\displaystyle \mathbf {y} _{k}}$ and ${\displaystyle \mathbf {n} _{k}}$ are the ${\displaystyle N_{r}\times 1}$ received symbol and noise, respectively, and ${\displaystyle \mathbf {H} _{k}}$ is the ${\displaystyle N_{r}\times N_{t}}$ matrix with the channel coefficients.

The figure illustrates the throughput advantage of PU²RC over the conventional single-user and no scheduling scheme, assuming that the codebook size is one, i.e., ${\displaystyle (G=1)}$. For larger codebook sizes the performance can be better than the performance of the unit-size codebook. Because of codebook-based multi-user scheduling, PU²RC outperforms the conventional single-user and no scheduling scheme when the number of users is larger than one. Note that the performance plotted in the figure for the two systems were obtained assuming linear receiver.