# 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
#### 4.2.2 The BLER Performance  
We compare the PCQNet with the aforementioned baselines as depicted in Figures 5 and 6. The comparisons of feedback overhead between the PCQNet and three baselines (i.e., the 3 GPP  
Figure 4: The NMSE performance of comparison between the Lloyd-Max scheme and the CNN-based PCQNet scheme over the i.i.d. channel. ( The x-coordinate represents the SNRs for the generation of the testing dataset, which are not directly correlated with the NMSE performance).  
\begin{table}
\begin{tabular}{c|c c c|c c c} \hline \hline \multicolumn{2}{c|}{**Quantization Factor**} & \multicolumn{2}{c|}{\(\beta\) = 2 (\(m\) = 32)} & \multicolumn{3}{c}{\(\beta\) = 3 (\(m\) = 48)} \\ \hline \multicolumn{2}{c|}{**NMSE (dB) SNR\({}_{design}\) (dB)**} & \multicolumn{2}{c|}{**1**} & \multicolumn{1}{c|}{**9**} & \multicolumn{1}{c|}{**17**} & \multicolumn{1}{c}{**1**} & \multicolumn{1}{c}{**9**} & \multicolumn{1}{c}{**17**} \\ \hline
1 & \(-16.16\) & \(-15.23\) & \(-11.98\) & \(-21.93\) & \(-21.14\) & \(-17.61\) \\
9 & \(-15.93\) & \(-16.60\) & \(-16.23\) & \(-21.67\) & \(-22.37\) & \(-20.20\) \\
17 & \(-15.37\) & \(-17.79\) & \(-20.08\) & \(-20.07\) & \(-23.01\) & \(-25.27\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The NMSE performance of the Lloyd-Max quantization scheme with different quantization factors over the i.i.d. channel.  
codebook scheme, the w/o compression scheme, and the LloydMax scheme) are provided in Table 4. The performance upper bound is the ideal centralized iterative scheme w/o compression which is not appropriate for practical transmission. The protocol codebook-based precoding scheme is tailored for a specific number of users or transmit antennas. To provide a benchmark for our proposed method, we consider the precoding matrices \(\mathbf{F}_{k}\in\mathbb{C}^{4\times 2},k\in\{1,2,3,4\}\) which is to be fed back to the \(k\)-th UE. The number of the feedback bits for the 3 GPP codebook scheme is \(m=5\). The LloydMax scheme separately quantizes the real and the imaginary parts of the precoding matrices, which respectively takes at least 16 bits and 32 bits to quantize a \(\mathbb{R}^{2\times 4\times 2}\) matrix with \(\beta=1\) and \(2\) (\(m=16\times\beta=16,32\)).  
The proposed PCQNet can dramatically decrease the feedback overhead and exhibit a slight BLER degradation with the further reduction of feedback bits (i.e., \(m=4,8\)). Note that the change of the CRs can be achieved by adjusting the number of feedback bits. Near-optimal performance can be derived when the number of the feedback bits is beyond 16, where the feedback overhead can be further reduced. When \(m=4\), the PCQNet significantly enhances the BLER performance of the 3 GPP codebook scheme with \(m=5\). Naturally, as we increase the number of feedback bits to 32, the performance of the PCQNet scheme as well as the LloydMax scheme will approach that of the ideal w/o compression scheme.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multirow{2}{*}{**Methods**} & **The Feedback Overhead (Number of** \\  & **Feedback Bits)** \\ \hline The 3 GPP protocol codebook & 5 \\ The LloydMax scheme & 16, 32 \\ \({}^{*}\) The PCQNet scheme & 4, 8, 16, 32 \\ w/o compression (ideal) & a complex matrix with size (4, 2) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The comparison of feedback overhead between the PCQNet and three baselines.  
Figure 5: The BLER performance comparison over the i.i.d. Rayleigh channel with QPSK and K = 4.