# PCONet: A Trainable Feedback Scheme of Precoder for the Uplink Multi-User MIMO Systems
## 4 Experimental Evaluations
### Simulation Results and Analysis with the i.i.d. Rayleigh Channel  
#### 4.2.1 The NMSE Performance  
The NMSE performance between the recovered and the original precoding matrices utilizing the **LloydMax** scheme is depicted in Table 3. The codebooks are specially optimized over statistical datasets with various SNRs and different quantization bits. Since these codebook-based schemes are inevitably limited by the quantization error, better NMSE performance of the LloydMax scheme comes at the expense of the increased feedback overhead. Although remarkable NMSE performance can be obtained when the evaluating SNRs (i.e., \(\mathcal{SNR}_{eval}\)) match with the designing SNRs (i.e., \(\mathcal{SNR}_{design}\)) under the same quantization bits, the performance of the codebook-based scheme is not satisfactory when \(\mathcal{SNR}_{eval}\) mismatch with the \(\mathcal{SNR}_{design}\) over the i.i.d. Rayleigh channel. Thus, it needs to store multiple codebooks to combat channel variations under different channel SNRs.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Settings** \\ \hline \(K\) & The number of UEs & \(4,6,8\) \\ \(N_{k,t}\) & The number of antennas of each UE & \(4\) \\ \(N_{k,s}\) & The number of data streams of each UE & \(2\) \\ \(N_{l}\) & The total number of transmit antennas & \(16,24,32\) \\ \(N_{s}\) & The total number of independent data & \(8,12,16\) \\ \(N_{r}\) & The number of BS antennas & \(32\) \\ \(\mathcal{M}\) & The number of bits of per modulated & \(2,4\) \\  & symbol & \\ \(\mathcal{N},Rate\) & The length and code rate of the low & \(384,1/2\) \\  & density parity check code & \(384,1/2\) \\ \(\beta_{1}\) & The quantization bits of the Lloyd-Max & \(2,3\) \\ \(\beta_{2}\) & The quantization bits of the PCQNet & \(4\) \\  & The numbers of feedback Bits of the & \(16,32,48\) \\  & Lloyd-Max scheme & \(16,32,48\) \\  & The numbers of feedback Bits of the & \(4,8,16,32,48\) \\ \(m_{2}\) & PCQNet scheme & \(4,8,16,32,48\) \\ CR & The CRs of the PCQNet scheme & \(1/16,1/4,1/2\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: List of simulation parameters.  
The NMSE performance of the LloydMax scheme and the PCQNet is not correlated with SNRs. Only the generation of different test datasets is related to SNRs and the testing of NMSE performance is not necessarily related to the value of the SNRs. We provide a guideline for subsequent research of BLER performance via the visualization of NMSE performance in Figure 4.  
The codebook-based LloydMax scheme is sensitive to the number of bits, the SNRs, and the realistic channel distribution. The NMSE will significantly drop when the \(\mathcal{SNR}_{real}\) mismatches with the \(\mathcal{SNR}_{design}\). On the contrary, the CNN-based compression scheme is more SNR-adaptive and we set \(\mathcal{SNR}_{design}=0\) dB. The CRs of the PCQNet are set to \(1/16\), \(1/8\), \(1/4\), and \(1/2\) for m = 4, 8, 16, 32, respectively. The PCQNet can achieve better NMSE performance than the LloydMax scheme under the same feedback bits (e.g., \(m=16,32,48\)) as shown in Figure 4. The green dotted line with low quantization factor \(\beta=1\) is almost a straight line over the i.i.d. channel. Despite the different input precoding matrices under different SNRs, the NMSE of the recovered matrices is equally poor. Because the quantization error is so large that the precoding matrices cannot be correctly recovered.