# PCONet: A Trainable Feedback Scheme of Precoder for the Uplink Multi-User MIMO Systems
## 1 Introduction
By contrast, the non-codebook-based centralized scheme has enormous throughput advantages compared to the codebook approaches but with relatively high cost of the feedback of precoding matrices. Recently, as the success of deep learning reaches more fields, the neural-network-based auto-encoder has been recently applied to enhance the performance of MU-MIMO systems in [16; 17; 18]. It is worth noting that the auto-encoder is well suited to tackling the vector compression problem because of its robustness to the unstable wireless channel conditions. The deep neural network (DNN) in [19] takes the place of the conventional zero-forcing detection and offers near-optimal transmission quality with much less computational complexity than the optimal scheme. Motivated by the convolutional neural network (CNN)-based deep learning compression approaches of channel state information (CSI) [20; 21; 22], we propose a novel compression and quantization network architecture named PCQNet for the joint transceiver optimization. The proposed PCQNet compresses the high-dimensional precoding matrices to the low-dimensional vectors. Considering that only bitstreams can be transmitted in a practical digital system, we also introduce a quantization module to convert the floating-point vector into bitstreams. Our proposed PCQNet can flexibly adjust the compression ratios compared with the codebook scheme in [13]. These CNN-based methods considerably improve the compression performance of the precoding matrices. At the same time, the data-bearing bitstreams are directly produced during the offline training. Thus, the robustness of the network for practical deployment is effectively improved on the basis of the compression network in [19]. Moreover, we extend the CNN-based compression network in [20; 21] to the precoding design of the uplink MU-MIMO scenarios. Multiple works of the transceiver optimization are limited to single-user scenarios or the particular MU multiple-input single-output (MISO) systems [23; 24]. We focus on the more general MU-MIMO scenarios considering both the interference of multiple users and the interference from multiple data streams of the same UE. We aim to design a trainable compression architecture for the offline implementation of the centralized precoding with the MMSE receiver. In summary, the major contributions are summarized as follows:We propose a CNN-based architecture named PCQNet to produce the data-bearing bitstreams for each UE to recover the precoding matrices. It can achieve near-optimal performance and further reduce the feedback overhead compared with the existing 3 GPP codebook scheme in certain scenarios. 2. We develop a general trainable compression and quantization framework for the precoding matrices in the uplink MU-MIMO systems. The proposed PCQNet architecture as well as the Lloyd-Max quantization scheme can flexibly adjust the feedback overhead by training an auto-encoder. 3. The precoding matrices with different compression ratios (CRs) are evaluated on the performance of the centralized implementation with an optimal MMSE transceiver. As far as we know, the effect of the feedback accuracy on the performance has not been investigated before. Specifically, we explore the trade-off between the block error rates (BLER) and the CRs of the precoding matrices. The remainder of this article is organized as follows: Section 2 introduces the system model and the joint transceiver optimization. Section 3 describes the network architecture and the training strategy of the PCQNet. Three baseline methods are also presented to provide a benchmark for our proposed PCQNet. In Section 4, experimental evaluations and performance analysis are provided to demonstrate the efficiency of our trainable CNN-based PCQNet. Finally, the concluding statements are given in Section 5. **Notations**: Symbols for matrices (vectors) are denoted by boldface upper (lower) case letters. \(\mathbb{R}\), \(\mathbb{C}\) and \(\mathbb{N}\) denote the real set, the complex set, and the positive integers, respectively.