1.Abstract
The potentials of massive multiple-input multipleoutput (MIMO) are all based on the available instantaneous channel state information (CSI) at the base station (BS). Therefore, the user in frequency-division duplexing (FDD) systems has to keep on feeding back the CSI to the BS, thereby occupying large uplink transmission resources. Recently, deep learning (DL) has achieved great success in the CSI feedback. However, the existing works just focus on improving the feedback accuracy and ignore the effects on the following modules, e.g., beamforming (BF). In this paper, we propose a DL-based CSI feedback framework for BF design, called CsiFBnet. The key idea of the CsiFBnet is to maximize the BF performance gain rather than the feedback accuracy. We apply it to two representative scenarios: single- and multi-cell systems. The CsiFBnet-s in the single-cell system is based on the autoencoder architecture, where the encoder at the user compresses the CSI and the decoder at the BS generates the BF vector. The CsiFBnet-m in the multi cell system has to feed back two kinds of CSI: the desired and the interfering CSI. The entire neural networks are trained by an unsupervised learning strategy. Simulation results show the great performance improvement and complexity reduction of the CsiFBnet compared with the conventional DL-based CSI feedback methods.
CSI 反馈用于beamforming，考虑了单小区和多小区两种场景
beamforming需要考虑不同的方式，包含码本的还得仔细思考思考怎么做。
2.Introduction
MASSIVE multiple-input multiple-output (MIMO) is one of the key techniques in future wireless communications [1], [2]. The massive MIMO systems, equipping base stations (BSs) with a very large number of antennas, have achieved dramatic gains in spectral and energy efficiency as well as to simplify the signal processing [3]. However, these potential benefits can be acquired only when the instantaneous and accurate channel state information (CSI) is available at the transmitter. In time-division duplexing (TDD) systems, the BSs can infer the downlink CSI from the uplink CSI utilizing the channel reciprocity. However, there is weak reciprocity between the downlink and uplink channels in frequency division duplexing (FDD) systems, which are widely employed by the existing cellular systems. Therefore, after estimating the downlink channel from the pilots sent by the BS, the user keeps on feeding CSI back to the BS. The feedback overhead in codebook-based CSI feedback methods scales linearly with the dimension of CSI matrix, which is determined by the antenna numbers of the BS and user. In massive MIMO systems, this strategy is infeasible due to the substantial antennas at the BS, which consumes many precious uplink bandwidth resources [3]. Therefore, developing a technique that can greatly reduce the feedback overhead while keeping on the feedback accuracy is urgent.
Compressive sensing (CS) has been regarded as a promising technology, which exploits the CSI sparsity in certain domain [4]. The spatial correlations among nearby antennas are utilized to compress the CSI in spatial-frequency domain for overhead reduction in [5]. The authors in [6] consider joint downlink channel estimation and feedback by exploiting the spatially joint sparsity of multiple users’ CSI matrices due to the shared local scatters. The CSI reconstruction at the BS turns into an NP-hard optimization problem and is often solved by iterative algorithms, thereby consuming substantial computing resources and time. Besides, the sparsity of CSI is the only prior information and the CS-based feedback methods can not exploit the environment information at all. These shortcomings make the CS based methods difficult to be implemented in practical systems. Codebook-based approaches are usually adopted to reduce feedback overhead. However, the feedback quantities resulting from these approaches need to be scaled linearly with the number of transmit antennas and are prohibitive in a massive MIMO regime [7]. There are some works, e.g., [8], [9], which quantize and feedback the beamformer with a codebook and use the spectrum efficiency as the optimization objective to select the codeword.
Recently, deep learning (DL) has achieved great success in physical layer communications [10], [11], e.g., channel estimation [12], joint channel estimation and signal detection [13], beamforming (BF) [14], and semantic communication [15]. The authors in [7] first apply DL to CSI feedback problem and propose an autoencoder architecture, CsiNet, where the encoder at the user compresses the CSI by fully connectedly (FC), layer and the decoder at the BS reconstructs the CSI from the feedback codeword and then uses convolutional layer to refine the initial reconstructed CSI. The existing DL-based CSI feedback methods focus on improving the feedback accuracy by introducing expert knowledge and proposing novel NN architectures [16]. Long short-term memory architecture is introduced to exploit the temporal correlation in time-varying massive MIMO channels in [17]. The work in [18] introduces an offset NN to minimize the nonuniform quantization distortion and proposes a multiple-rate feedback framework. CoCsiNet and distributed DeepCMC in [19], [20] exploit the correlation between the nearby users and propose a cooperative and distributed feedback framework. The computational complexity is considered in [21], [22] and NN quantization and pruning are adopted in [21]. The authors in [18], [23], [24] consider the feedback errors and an extra NN, called DNNet, is introduced to improve the performance of channel feedback in [24]. The work in [25] investigates the effects of adversarial attack on the DL-based CSI feedback. The practical performance of the DL-based CSI feedback is investigated in [26]. Besides, many novel NN architectures, e.g., CsiNet+ [18], ConvCsiNet [22], ConvlstmCsiNet [27], CRNet [28], and ReNet [29] are proposed to improve the feedback accuracy.
The goal of the feedback is to acquire the CSI as accurate as possible and the physical meaning of CSI is ignored. The feedback mechanism of the CS- or DL-based methods is to drop the redundant or unimportant information, which is sometimes based on the sparsity assumption [18]. Reducing the feedback mean-squared error (MSE) has been the direct optimization goal of the most works [7], [17]–[22]. However, the MSE sometimes can not really measure the signal fidelity [30]. In massive MIMO, the most important information in CSI is the phase and magnitude of the paths. Unfortunately, the MSE function equally treats all information and sometimes even keeps on secondary information at the expense of useful information. Therefore, although the MSE is lower, the total communication system may perform worse. This also occurs in the computer vision domain, where how to assess the quality of the reconstructed images is a great challenge. Signal-to-noise ratio (SNR) and structural similarity (SSIM) are the most widely used assessment metrics. But, they can not well predict the subjective human perception of image fidelity and quality [30], [31]. Subjective assessment is the most reliable and accurate. However, subjective test cannot be directly used as the optimization metric and is expensive and time-consuming. Fortunately, in the CSI feedback domain, subjective metrics are not needed and we can assess the effects of feedback accuracy on the subsequent communication modules, which require accurate CSI. Meanwhile, the performance of subsequent communication modules, e.g., BF, can be the optimization goal of the feedback, which can be also regarded as joint feedback and BF design.
这相当于给目前的CSI feedback提出了更高的要求，之前只管反馈的全不全，现在还要考虑反馈的好不好。怎么评价反馈的好不好呢？将反馈的信道用在Beamforming中，看看它的性能，能从某种程度上反映出信道信息反馈的质量。
Besides, the existing DL-based CSI feedback works only consider some simple massive MIMO systems and extending the DL techniques to more complicated scenarios, e.g., multi-cell systems [32], is necessary. In the single-cell FDD systems, only the downlink channel between the BS and user needs to be fed back. In the multi-cell systems, the user has to feed back the desired and the interfering channels, respectively, to combat co-channel interference [33]. Extending DL-based CSI feedback and BF to this complicated scenario is a challenge.
从单小区拓展到多小区，将来自于其他小区的干扰也考虑在内。
In this paper, we propose a DL-based implicit CSI feedback NN framework for BF, called CsiFBnet, in massive MIMO systems. First, we consider a simple scenario, i.e., a single-user and single-cell massive MIMO system. The proposed framework, called CsiFBnet-s, replaces an end-to-end procedure including CSI compression, quantization, generating BF vectors satisfying the constant modulus constraint. This framework is based on the autoencoder architecture, in which a uniform quantization is embedded between the encoder and decoder. Then, we consider a more complicated multi-cell scenario and develop an NN framework, called CsiBFnet-m, to realize CSI feedback for maximizing the sum-rates (at high SNR), adopting a soft hand-off model [34]. Different from the single-cell, the desired and the interference CSI should be fed back to the BS and taken into consideration during BF vector design. Our contributions in this paper are summarized as follows:
- We propose an implicit CSI feedback strategy, CsiFBnet, which aims at improving the performance of BF rather than the CSI feedback accuracy, i.e., the MSE.
- A single-user and single-cell scenario is taken into consideration. In the proposed CsiFBnet-s, the encoder at the user side compresses and quantizes the downlink CSI and the decoder at the BS generates the BF vectors satisfying the constant modulus constraint from the feedback measurements. This method shows great performance improvement especially when the number of feedback bits is extremely constrained.
- Then, we extend the proposed framework to a more complicated scenario, i.e., the multi-cell massive MIMO system, and adopt the soft hand-off model with a single interferer. In the multi-cell systems, both of the desired and interference CSI should be fed back to the BS. In
the conventional BS cooperation, the interference CSI is exchanged among the nearby BSs but the backhaul links among BSs are capacity-limited. In the proposed CsiFBnet-m, only the compressed and quantized CSI is exchanged among the nearby BSs, thereby reducing the overhead of backhaul.
- To maximize the sum-rate of the multi-cell systems, the decoder at the BS generates the BF vectors locally from the compressed feedback measurements, which outperforms the methods of feeding back accurate CSI and designing BF vectors separately.
