GAO Zhengguang,LI Lun,WU Hao,TU Xuezhen,HAN Bingtao
(1.State Key Laboratory of Mobile Network and Mobile Multimedia Technology,Shenzhen 518055,China；
2.The College of Computer Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)
Abstract: A unified deep learning (DL) based algorithm is proposed for channel state information (CSI) compression in massive multipleinput multiple-output (MIMO) systems.More importantly,the element filling strategy is investigated to address the problem of model redesigning and retraining for different antenna typologies in practical systems.The results show that the proposed DL-based algorithm achieves better performance than the enhanced Type Ⅱ algorithm in Release 16 of 3GPP.The proposed element filling strategy enables one-time training of a unified model to compress and reconstruct different channel state matrices in a practical MIMO system.
Keywords: deep learning;channel state information;element filling strategy
In 5G and Beyond networks,massive multiple-input multiple-output (MIMO) is considered one of the key enabling technologies to improve link capacity and energy efficiency for wireless communications[1–5].To achieve these potential advantages,simultaneous channel state information (CSI) is required to optimize the precoding for massive MIMO systems.In frequency division duplex (FDD) MIMO systems of 4G,the downlink CSI obtained at the user equipment (UE) is sent to the base station,and vector quantization or codebook-based approaches are adopted as the compression algorithms for CSI to decrease feedback overhead[6].However,the feedback overhead increases significantly in massive MIMO systems because the feedback quantity of the current methods increases linearly with the number of antennas.This challenge has inspired researchers to explore an effective algorithm to compress the CSI in massive MIMO systems.The technology of compressive sensing (CS) is exploited to address this issue[7–8].Based on the uncorrelated sparse vector transformed from the correlated CSI matrix,the CS-based methods are expected to achieve an accurate performance for CSI compression.Several CS-based algorithms have been proposed in massive MIMO systems,such as the least absolute shrinkage and selection operator (LASSO)l1-solver and approximate message passing (AMP)[9].The advanced CS-based algorithms which include TV minimization by augmented Lagrangian and alternating direction algorithms (TVAL3) as well as blockmatching and 3D filtering (BM3D)-AMP have also been proposed to improve the accuracy[10–11].Although CS-based methods have been investigated comprehensively,it still has inherent disadvantages[11].Firstly,the effectiveness of CS-based methods relies on the assumption that CSI matrices are sparse in some bases whereas channels are not always sparse in practical systems.And the random projection of CS-based methods cannot extract useful information from the channel structure of MIMO systems,which has negative impacts on the algorithm performance.Finally,the decoding process always requires iterative solving,therefore the decompression of the CS-based method is sub-optimal and time-consuming.In a word,the CSbased method cannot achieve high performance for the reason that the CSI matrix is not sparse enough under the large compression ratio,and the slow reconstruction of the CS-based method makes it difficult to adapt many real-time scenarios in practical systems.Recently,deep learning has been explored in signal detection and network planning[12–13].Motivated by the rapid progress of deep learning in computer vision (CV),in particular,the successful trial of image compression and reconstruction by the autoencoder,the researcher has explored DL-based algorithms for CSI compression comprehensively.
A novel residual neural network-based model called CsiNet is proposed in Ref.[14],which shows that the performance of CsiNet outperforms existing CS-based methods significantly,especially for low compression regions.To exploit the temporal correlations of CSI,a long-short time memory (LSTM) architecture is combined with CsiNet as CsiNet-LSTM in Ref.[15],and it shows that considering the temporal correlations benefits the accuracy of CSI reconstruction.The CsiNet is modified and redesigned as CsiNet+in Ref.[16],which improves the performance of CSI compression.More importantly,a novel quantization layer is introduced in the DL model for end-to-end training,which meets the practical requirement of CSI feedback in massive MIMO systems.Recently two novel DL-based models called CRNet and ACRNet have been proposed for better performance in Refs.[17–18].In Ref.[17],multi-resolution CRBlocks are designed in CRNet,and the warm-up aided training scheduler is implemented to achieve better performance.The result proves the effectiveness of multi-resolution CRBlocks and the novel training scheduler.In Ref.[18],a novel model called ACRNet is proposed to provide the state-of-the-art performance with network aggregation and parametric rectified linear unit (PReLU) activation.Besides,the network binarization technique is implemented to ensure the high performance and small memory cost.Most of the above works have achieved the state-of-art performance previously and outperformed CS-based methods significantly in some regions,while some problems still exist in the following aspects.Most enlightening works focus on novel designs of the DL model to improve the performance of CSI compression,but ignore the quantization of information in bit-streams for transmission in practical MIMO systems.These models should consider the quantization layer and have end-to-end training and testing to evaluate the performance of practical systems.In addition,the proposed DL-based algorithms are evaluated in the COST2100 dataset[19],which only includes data with the same shape.However,the shape of the CSI matrix changes with antenna arrangements in massive MIMO systems.Generally,misalignment problems exist between the previous model and the coming data with different shapes.To our knowledge,there are no published works discussing how to deal with this issue in practical systems.Motivated by this,a unified DL-based method for CSI feedback is proposed in massive MIMO Systems.The rest of this paper are organized as follows.
A novel DL-based network named ACRNet+is proposed in Section 2.To improve the performance in the practical massive MIMO system,the advanced module of channel attention and spatial attention is used to enhance the ability of feature extraction.And a 3-bit uniform quantization layer is implemented in ACRNet+for end-to-end training in Section 3,which minimizes the impact of the accuracy quantization of the model.In addition,an element filling strategy is proposed to address the incompatible problem of the trained model for the CSI matrix with a different size.Section 4 shows the experimental results that ACRNet+provides better performance than the enhanced Type Ⅱ (eType Ⅱ) algorithm in the 901 dataset which focuses on outdoor scenarios with dual-polarized antennas.The element filling strategy enables the trained model to compress the diversified CSI matrices accurately without further training.Section 5 concludes the paper.
A simple single-cell downlink is adopted in massive MIMO systems withNtantennas at the base station (BS) andNrantennas at UE,whereNt≥1 andNr=1 in this paper.The system considers orthogonal frequency division multiplexing (OFDM)with subcarrierNc[20],so the received signalynat then-thsubcarrier can be expressed as:
whereFdandare DFT matrices with the shape ofNc×NcandNt×Ntrespectively.The obtained matrixHcontains only the firstNarows of useful elements whereas other rows of elements are near zero.Although the DFT can reduce the elements of the downlink channel matrix,the firstNarow of the transformed matrix calledHais still too large to be sent directly through the uplink channel.According to the inaccuracy of the large compression ratio and the slowing decoding procedure of CS-based methods,a DL-based encoder and decoder are considered for CSI compression at UE and reconstruction at the BS.An auto-encoder is a neural network-based model to reconstruct the raw data through self-supervised learning.It firstly builds the main features into a lower-dimensional representation of the input data,and then the decoder tries to reconstruct the data as similarly as possible[22].
The overview of the DL-based model for uplink feedback is shown in Fig.1.The CSI matrixHain the angular-delay domain is obtained from the DFT ofand matrix truncation.The encoder of ACRNet+compresses the input ofHainto a one-dimensional vectorvwithMelements.Therefore,the compressive ratio can be expressed as
▲Figure 1.Pipeline of ACRNet+model for channel state information (CSI) compression
In practical systems,the bitstream is required for uplink feedback,so a 3-bit uniform quantizer is used to convert the float vectorvinto a binary vectorvb.The above process is abstracted as
whereFqdenotes the function of quantization,Fenstands for the encoder of ACRNet+,andWenis the trainable parameter of the encoder.After uplink transmission,the bitstreamvbis dequantized into the float vector,and then the float feature is reconstructed into.The decoding process can be formulated as
whereFdqdenotes the function of dequantization,Fdestands for the decoder of ACRNet+,andWdeis the trainable parameter of the decoder.After the decoding process,the estimated channel matrix for the downlink can be obtained from the inverse DFT of
3.1 Design of ACRNet+
ACRNet is one of the most effective models in existing works,which provides the state-ofart performance for CSI compression in COST2100[18].Based on the network aggregation technique,a novel feedback block that contains parallel convolutional groups is implemented to extract relatively independent features[23–24].In addition,a learnable activation function of the parametric ReLU and an advanced training scheme are used to boost the performance of the model.
To inherit the advantages of ACRNet,ACREnBlock and ACRDeBlock are introduced in the proposed ACRNet+.In addition,channel attention (CA) and spatial attention (SA) are implemented to extract the useful features accurately from the CSI matrices,especially for outdoor scenarios with the randomness of multi-path fading and unpredicted interferences[25].Inspired by the design of multi-resolution networks for CSI feedback tasks in previous works[17],two independent channels with different convolution layers are built to provide more feature granularity.After the combination of the features from these two channels,CA and SA are used to make further extraction of the combined features.Different from the design of ACRNet,a quantized layer is added to convert the compressed data into bitstreams for feedback transmission on the uplink.At the BS,the bitstream is dequantized into the float features,and then the compressed vector from the dequantized layer is reconstructed intothrough one fully connected network and two ACRDeBlocks.
The detailed architecture of ACRNet+is shown in Fig.2.The image inputHawith the shape 2 ×Ha×Htis fed into two independent channels.The first channel includes a 5 × 5 convolution layer,and the second channel is made up of two convolution layers with a 1 × 9 kernel and a 9 × 1 kernel respectively.Then the outputs of the two channels are combined through element addition.To boost the representation power of networks,a convolutional block attention module (CBAM) is implemented to focus on important features and suppress unnecessary ones along two separate dimensions[25].After the adaptive feature refinement by CBAM,the output of CBAM passes through the two ACREnBlocks which include a 1 × 9 kernel and a 9 × 1 kernel for further feature processing,and then the flattened feature from ACREnBlock is condensed into the vector withMelements.To meet the practical requirement for transmission of wireless communication,a 3-bit uniform quantizer is implemented for quantization.The quantizer is embedded in neural networks as the quantization layer for end-to-end training,which can minimize the negative impacts on the model accuracy.At the BS,the bitstream is firstly recovered to the compressed vector through dequantization.Then the vector passes through a fully connected layer for element augmentation,the output is reshaped in the same dimension as the input.Finally,the reshaped feature passes one convolution layer with a 5 × 5 kernel and two ACRDeblocks which include a 1 × 9 kernel,a 7 × 7 kernel and a 9 × 1 kernel for the final reconstruction.
▲Figure 2.Proposed ACRNet+architecture
3.2 Generalization Scheme for CSI Compression
One of the main concerns for DL-based methods is the generalization problem.For data with the same shape,we can evaluate the model through the performance of cross validation and testing.DL-based methods for CSI compression have been proven effective in most previous works.However,the generalization of the DL-based model has never been discussed for data with different shapes.In practical MIMO systems,the shape of the downlink channel matrix changes with the arrangement of antennas.The misalignment problem happens in this scenario.The direct method is to get several models trained for different antenna typologies,but it requires huge computation resources for several well-trained models as well as the corresponding switching strategy.Therefore,the element filling strategy is proposed to support the training of a unified model for different scenarios covering several antenna combinations.At first,the dataset with the largest size is selected as the benchmark.Then the dataset with other shapes is filled by the constant elements with the same shape as the benchmark.Finally,a unified DL-based model is trained on the hybrid dataset covering the data from several antenna combinations in massive MIMO systems.Considering the fact that most elements inHaare close to 0.5,the padding element is set to 0.5,which can decrease the disturbance of the padding elements for the compression and reconstruction of the actual elements.
In this paper,we consider three scenarios including 4 × 4 MIMO,2 × 4 MIMO,and 1 × 8 MIMO with dual-polarized antennas,and the corresponding datasets are represented as data1,data2 and data3.During the training process,the real and imaginary parts of the data are represented as the third dimension,and the shapes for these datasets are 2 × 32 × 32,2 × 16 × 32,and 2 × 16 × 32 respectively.According to the element filling strategy,we perform the padding operation to data2 and data3,which reshapes them as the size of 2 × 32 × 32.After the same shape for these scenarios is obtained,a unified model is trained on the dataset which randomly samples from data1,data2 and data3.We compare the performance of the model trained on the hybrid dataset with the model trained separately on one of the three datasets.
Most previous works are based on COST2100,which deploys a uniform linear array with 32 antennas at the BS and 1 024 subcarriers.In this paper,more complicated scenarios are considered to evaluate the effectiveness of the DL-based model.To evaluate the practical performance of ACRNet+,we first compare the performance of ACRNet+with eType2 algorithm of Release 16 (R16) from 3GPP in two outdoor scenarios with dual-polarized antennas and two antenna topologies.The shape of the two datasets is 2 × 32 × 32.In addition,a unified model is trained on three datasets with different shapes through the element filling strategy.The performance of ACRNet+trained on the hybrid dataset is compared with ACRNet+trained separately on one of these datasets.
In order to evaluate the proposed model in more practical scenarios,901data is generated according to the 3GPP Long Term Evolution (LTE) structure,in which parameters of channel models are specified in TR38: 901[26].We compare ACRNet+and eType2 algorithms on 901data containing two datasets,in which 16×1 MIMO and 8×2 MIMO with dualpolarized antennas are used.The generalized cosine similarity(GCS) of these two methods is presented in Figs.3 and 4.The figures show that ACRNet+outperforms eType Ⅱ in terms of GCS when consuming similar bits.For the scenario in Fig.3,the GCS of eType Ⅱ is 0.745 4 under 410 bits.The corresponding GCS of ACRNet+is 0.758 9 under 408 bits.It should be noted that it is difficult to completely match the number of bits for the two algorithms on thex-axis.The number of bits for eType Ⅱ is 410,636,770,1 220,and 1 668,and the consumed bits for ACRNet+are 408,511,768,1 024,and 1 536.We can see that the GCS of ACRNet+is better than that of eType Ⅱ although the ACRNet+requires fewer bits.For the scenario in Fig.4,the advantage of ACRNet+is more obvious.The closest performance for ACRNet+and eType Ⅱ occurs when the number of bits is about 770.The corresponding GCS for eType Ⅱ is about 0.793 9 where the GCS of ACRNet+under 768 bits is about 0.845 8.Finally,it can be seen from Fig.3 that the GCSs of the algorithms are not linearly related to the consumed bits.The GCS cannot be significantly improved when the used bit is below some threshold,and the improvement is also unobvious when the consumed bit is enough for the eType Ⅱ algorithm.These results provide a useful reference for the actual deployment of these algorithms.
▲Figure 3.GCS of ACRNet+and eType Ⅱ for the scenario with 1×16 multiple-input multiple-output (MIMO)
▲Figure 4.GCS of ACRNet+and eType Ⅱ for the scenario with 2×8 multiple-input multiple-output (MIMO)
One of the main concerns for DL-based CSI compression methods is the generalization of the model.When the topology of antennas changes,the coming data of the channel matrix are incompatible with the original DL-based model.The retraining of the model requires huge computation resources and training time.Therefore,an element filling strategy is proposed to unify the input shape.Then a unified model is trained on the datasets which cover several scenarios with different typologies.In the experiment,three datasets including 4×4 MIMO,2×4 MIMO,and 1×8 MIMO with dual-polarized antennas are generated in outdoor scenarios,and the corresponding datasets are represented as data1,data2 and data3.The training,validation,and testing sets for each dataset contain 85 000,5 000,and 10 000 samples.The shapes of these datasets are 2 × 32 × 32,2 × 16 × 32,and2 × 16 × 32 respectively.At first,data2 and data3 are reshaped into 2 ×32 × 32,where the padding element is 0.5 for all the places.We mix the reshaped datasets and randomly sample one-third of the mixed data as the training set.Therefore,the mixed training dataset also contains 85 000 samples.Finally,the performance of ACRNet+trained on the mixed dataset is compared with the model trained on the original dataset to evaluate the effectiveness of the element filling strategy.
The results of ACRNet+trained on the mixed dataset and the original dataset are presented in Table 1,in which ACRNetH represents the performance of the model trained on a mixed dataset and ACRNet+stands for the model trained separately on the original dataset.We can see from the table that the performance of ACRNetH which needs to be trained once is only slightly lower than ACRNet+which needs retraining for data with different antenna topologies.For example,the GCS of ACRNet+under 15 times compression ratio is 0.746 2,0.875 4 and 0.844 9,and the performance of ACRNetH that only requires one-time training reaches a similar performance as 0.722 8,0.850 9 and 0.810 5.The results show that the proposed element filling strategy enables the unified training of the model for the dataset which contains the samples with different sizes,and the corresponding performance reaches a similar performance trained separately.
▼Table 1.Comparison between ACRNet+and ACRNetH under the same compression ratio
One thing that should be noted is that the proposed model as well as the mentioned models in the paper addresses the CSI compression in low-speed scenarios within 3 km/h,while unknown and complex factors on the performance of the CSI feedback still exist in high-speed scenarios,which we plan to analyze in future works.
In this paper,a unified DL-based model called ACRNet+has been proposed to compress the CSI in massive MIMO systems.The proposed model outperforms eType Ⅱ algorithms in R16 of 3GPP in two outdoor scenarios.More importantly,the element filling strategy allows a unified training of the model on the dataset containing samples with different shapes,which enables the one-time training of DL-based model to address the CSI compression for different antenna typologies.The experimental results show that the performance of a unified model can reach a similar performance of the DL-based model trained separately for the dataset of a certain scenario.
Acknowledgement
Our gratitude goes to WANG Yongcheng,YANG Xikun and LUO Qingkai for the technical advices and the linguistic assistance.
