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The operation is described mathematically below for the transmitter and receiver side.
The transmitter antenna array has <math>N_t</math> elements. The transmit signal vector is modeled as follows:
:<math> \mathbf{x} = \sum_{i=1}^K \mathbf{w}_i P_i s_i</math>
where <math>\mathbf{x}</math> is the <math>N_t \times 1</math> vector of transmitted symbols and <math>\mathbf{w}_i</math> is the <math>N_t \times 1</math> linear precoding vector. PU<sup>2</sup>RC generates <math>{\mathbf{w}_i}</math> based on the received finite channel status information, which is delivered to the base station by the user equipment (UE) using a coded look-up table index.
Every receiver has a receive antenna array with <math>N_r</math> elements. The receive signal vector at user <math>k (=1,2,\ldots,K)</math> is modeled as follows:
:<math>\mathbf{y}_k = \mathbf{H}_k\mathbf{x}+\mathbf{n}_k</math>
where <math>\mathbf{y}_k</math> and <math>\mathbf{n}_k</math> are the <math>N_r \times 1</math> received symbol and noise, respectively, and <math>\mathbf{H}_k</math> is the <math>N_r \times N_t</math> matrix with the channel coefficients.
The figure illustrates the throughput advantage of PU<sup>2</sup>RC over the conventional single-user and no scheduling scheme, assuming that the codebook size is one, i.e., <math>(G=1)</math>. For larger codebook sizes the performance can be better than the performance of the unit-size codebook. Because of codebook-based multi-user scheduling, PU<sup>2</sup>RC 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.
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