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• Published: 21 February 2024

Non-orthogonal optical multiplexing empowered by deep learning

• Tuqiang Pan   ORCID: orcid.org/0000-0002-1376-2106 1 , 2   na1 ,
• Jianwei Ye 1 , 2   na1 ,
• Haotian Liu 1 , 2 ,
• Fan Zhang 1 , 2 ,
• Pengbai Xu 1 , 2 ,
• Ou Xu 1 , 2 ,
• Yi Xu   ORCID: orcid.org/0000-0003-1679-3271 1 , 2 &
• Yuwen Qin   ORCID: orcid.org/0000-0001-9879-1514 1 , 2  

Nature Communications volume  15 , Article number:  1580 ( 2024 ) Cite this article

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• Optical techniques
• Optics and photonics

Orthogonality among channels is a canonical basis for optical multiplexing featured with division multiplexing, which substantially reduce the complexity of signal post-processing in demultiplexing. However, it inevitably imposes an upper limit of capacity for multiplexing. Herein, we report on non-orthogonal optical multiplexing over a multimode fiber (MMF) leveraged by a deep neural network, termed speckle light field retrieval network (SLRnet), where it can learn the complicated mapping relation between multiple non-orthogonal input light field encoded with information and their corresponding single intensity output. As a proof-of-principle experimental demonstration, it is shown that the SLRnet can effectively solve the ill-posed problem of non-orthogonal optical multiplexing over an MMF, where multiple non-orthogonal input signals mediated by the same polarization, wavelength and spatial position can be explicitly retrieved utilizing a single-shot speckle output with fidelity as high as ~ 98%. Our results resemble an important step for harnessing non-orthogonal channels for high capacity optical multiplexing.

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Introduction.

Multiplexing is a cornerstone for optical communication, where physical orthogonality among multiplexing channels is a prerequisite for massively-encoded transmission of information 1 , 2 . For example, division multiplexing becomes a canonical form for increasing the capacity of fiber communication, such as space division multiplexing 1 , 3 , 4 , wavelength division multiplexing 1 , 5 , polarization division multiplexing 6 , 7 and mode division multiplexing 5 , 8 . However, the division nature and the orthogonal paradigm of these multiplexing mechanisms inevitably impose an upper limit of multiplexing capacity 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 . If the orthogonal paradigm of optical multiplexing can be broken, it could be a step forward for realizing non-orthogonal optical multiplexing, which will become a promising way to meet the challenge of information capacity crunch. Considering the demultiplexing of multiple orthogonal signals, the transmission matrix method 11 , 12 , 13 , 14 , 15 can tackle this issue even over a strongly scattering medium, such an MMF. While non-orthogonal optical multiplexing over an MMF can be referred to multiplexing input channels possessing non-orthogonal polarizations, the same wavelength, and the same spatial position, where their polarizations are even the same for the typical non-orthogonal scenario. In this case, the inverse transmission matrix method fails to decode the multiplexing signals with the same polarization and wavelength using a single-shot intensity detection, as schematically shown in Fig.  1 a.

a The non-orthogonal multiplexing information cannot be retrieved by the inverse transmission matrix method using a single-shot intensity detection. b Schematic of deep learning-based non-orthogonal multiplexing under multiple scattering of an MMF. As long as the neural network is well trained, the information of each channel can be retrieved utilizing the single-shot intensity output.

Recently, deep learning has been widely used in optics and photonics for inverse design of optical devices 16 , 17 and computational optics 18 , 19 , 20 , 21 . Specifically, deep neural network has been utilized to improve the performance of orthogonal multiplexing over a multiple scattering medium 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 . To date, however, all the reported multiplexing scenarios strictly rely on the physical orthogonality among multiplexing channels 11 , 12 , 13 , 14 , 15 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 . There is no attempt to leverage the nonlinear modelling capability of deep learning to achieve the non-orthogonal optical multiplexing over an MMF, resembling an alluring but still open question. Unfortunately, even multiplexing of non-orthogonal channels mediated by the same polarization or wavelength in a single mode fiber remains very challenging, which is due to the lack of effective demultiplexing method or overburdened digital signal processing 1 . Therefore, developing a new methodology for decoding information encoded in non-orthogonal input channels is of vital importance for the ultimate optical multiplexing.

In this work, we show that preliminary non-orthogonal optical multiplexing through an MMF can be achieved empowered by the SLRnet. As a proof-of-concept demonstration, multiplexing transmission of information through an MMF, including general natural scene images, uncorrelated random binary data and images not belong to the same type of training dataset, can be realized utilizing non-orthogonal input channels, as schematically shown in Fig.  1 b, facilitating the realization of non-orthogonal multiplexing transmission of optical information. Building a complicated relationship between the non-orthogonal input channels and the output through the data-driven technology, a well-trained deep neural network can retrieve the encoded information of the non-orthogonal channels merely using a single-shot output intensity. Even non-orthogonal multiplexing channels sharing the same polarization, wavelength and input spatial region can be effectively decoded. It is anticipated that our results would not only stimulate various potential applications in optics and photonics, but also inspire explorations in more broader disciplines of information science and technology.

The single channel input-output relationship of an MMF can be described by a transmission matrix, as shown by the following equation:

Here, T is the transmission matrix for a multiplexing channel through the MMF with a given input polarization and \({\overrightarrow{E}}_{out}\) and \({\overrightarrow{E}}_{in}\) are the output and input light fields, respectively. Notably, \({\overrightarrow{E}}_{in/out}\) is a complex number that contains both amplitude and phase information encoded in space (i.e. X and Y dimensions), which can be expressed as:

In this equation, A ( x ,  y ) and φ ( x ,  y ) represent the amplitude and phase distributions of the incident light field, respectively. a indicates the unit vector of electric field. If there is only an input field, the transmission matrix can be calibrated and the scrambled input wavefront can be retrieved 11 , 14 , 15 .

If the incident wavefront is a superposition of multiple non-orthogonal light fields, it becomes:

where \({\overrightarrow{E}}_{i}\) is the i t h incident light field. As shown in Fig.  1 a, multiple amplitude and phase encoded wavefronts with the same polarization states are superimposed and coupled to the proximal end of the MMF, resulting in a single speckle output at the distal end of the MMF. The output speckle intensity recorded by the CMOS camera can be expressed as follows:

where H (  ⋅  ) represents the mapping relationship between multiple input light fields C n and the single output speckle I of the MMF. Here, C n indicates n combinations of information encoded input amplitude and phase. It should be pointed out that the transmission matrix T i is different even for the multiplexing channels with parallel polarization because of the residual optical asymmetry during multiplexing and coupling to the MMF, such as slightly different k-vectors of the multiplexed beams. According to Eq. ( 4 ), the inverse transmission matrix method cannot retrieve each \({\overrightarrow{E}}_{i}\) using a single-shot intensity detection, as shown in Fig.  1 a. In order to realize demultiplexing of non-orthogonal signals through the MMF from a single-shot output speckle, the inverse mapping H −1 of the above equation

should be obtained. There is no physics-based theory reported so far, which can effectively obtain H −1 when n  > 1.

In this case, data-driven deep learning methods become an effective means to solve this problem where multiple input \({\overrightarrow{E}}_{i}\) are non-orthogonal light fields with non-orthogonal polarizations, the same wavelength, and the same spatial position. A typical supervised learning method relies on a sequence of labelled data, ( C n k ,  I k ),  k  = 1, 2, . . . ,  K , to obtain the mapping function R by learning from the training set Q  = {( C n k ,  I k ),  k  = 1, 2, . . . ,  K }. It should be emphasized that the information encoded in non-orthogonal multiplexing channels is effectively orthogonal in the labelling of C n k . At the same time, the residual asymmetry of the optical paths plays an important role in the non-orthogonal optical multiplexing through the MMF. The residual asymmetry will be leveraged by the multiple scattering of MMF, which can facilitate the solution of multiple-to-one mapping relationship. As a result, the following equation:

is optimized, where R θ is the mapping function determined by the weight of deep learning network θ   ∈  Θ and Θ is all possible weight parameters of the network. The well trained \({R}_{{\theta }^{*}}\) can retrieve the information encoded in input amplitude and phase \(\widetilde{{C}_{n}}\) utilizing the output speckle I not belonging to Q , i.e., \(\widetilde{{C}_{n}}={R}_{{\theta }^{*}}(I)\) . This neural network builds an approximate relationship that maps the speckle intensity at the distal end of the MMF to the distributions of amplitude and phase for several input light fields at the proximal end of the MMF, where the training of the network relies on the dataset using pairs of output speckles and their corresponding input wavefronts. In other words, the multiplexed non-orthogonal input light fields can be demultiplexed by:

Neural network architecture

According to the principle analysed above, deep neural network is capable of retrieving non-orthogonal optical multiplexing signals from a single speckle output of the MMF. As shown in Fig.  2 a, multiple amplitude and phase encoded information mediated by arbitrary combinations of polarizations can be effectively retrieved by the SLRnet after propagating in the MMF. Even the typical scenario of non-orthogonal input channels with the same polarization, wavelength and input spatial region can be explicitly decoded. This is enabled by a deep neural network whose architecture is shown in Fig.  2 b, which is a variant of Unet according to the unique multiple scattering process of the MMF. It consists of a fully connected (FC) layer and a ResUnet 34 , whose main advantages over Unet are as follows: (1) a FC layer is introduced before the input of Unet to enhance the fitting and generalization ability of the network. The introduction of the FC layer can effectively undo the nonlocal dispersion of the MMF, which improves the performance of demultiplexing multidimensional encoded information using a single speckle output. The ResUnet is used for denoising and post-processing the multiplexing information towards the ground truth, which is similar to the convnet proposed recently 25 . In addition, the convolutional layer can also facilitate the manipulation of multichannel outputs in the non-orthogonal multiplexing without increasing the training burden; (2) a large number of skip connections are introduced in the encoder-decoder path to enhance the degeneration-free propagation of data in the network (See “Methods" section for details). To facilitate the experimental verification, n is chosen as 2, where the non-orthogonal inputs contain two light field channels mediated by arbitrary polarization combinations. Each light field channel is composed of spatially encoded information in both amplitude A ( x ,  y ) and phase φ ( x ,  y ) dimensions, respectively, resulting totally four multiplexing channels for transmitting independent information. Supervised learning is applied during the training process of the network. The speckle at the output of the MMF is used as the input of the SLRnet, where the network outputs predicted four matrices containing both the encoded amplitude and phase information in two light field channels. It means that the encoded information in non-orthogonal multiplexing channels is orthogonally labelled, when the network is trained. This is the key point for decoding information encoded in non-orthogonal channels.

a Non-orthogonal multiplexed information encoded in the amplitude, phase and polarization dimensions are superimposed at the proximal end of the MMF, resulting in a speckle output at the distal end of the MMF. Then the encoded multidimensional information can be unambiguously retrieved from a single-shot output speckle utilizing the SLRnet. The polarization states are outlined and the same wavelength is used. The grids superimposed on the input information indicate the information units in both amplitude and phase dimensions. b The architecture of SLRnet is composed of a fully connected (FC) block, four residual convolutional blocks with down sampling, three residual transposed convolutional blocks with up sampling, and one output convolutional layer for channel compressing. Skip connections are established among the first three down-sampling and the up-sampling modules. The sizes of feature map for each block are marked in the insets. ResConv Residual convolutional block, ResConvT Residual transposed convolutional block, Conv Convolutional layer. All images are adopted from the Fashion-MNIST dataset 41 .

Experimental results

The case when the length of MMF is 1 m is considered first. Figure  3 a presents the evolution of retrieved fidelity for two multiplexed light field channels with arbitrary combinations of polarization states during the training process of SLRnet. In total, there will be four encoded channels in the amplitude and phase dimensions, where they can be non-orthogonal depending on the polarization states. Here, the retrieved fidelity is measured by Pearson correlation coefficient (PCC). Twelve different combinations of polarization states, including linear, circular and elliptical polarizations, are considered. In these cases, their wavelengths are the same (See “Methods" section for details). As can be seen from this figure, the evolutions of the retrieved PCC utilizing the same training configuration of SLRnet are larger than 0.97 after 100 epochs, indicating the condition of Eq. ( 7 ) is approached, where \({H}^{-1}(I)\approx {R}_{{\theta }^{*}}(I)\) . At the same time, the evolutions of retrieved fidelity for twelve multiplexed scenarios are basically the same, which showcases excellent robustness of non-orthogonal multiplexing with respect to arbitrary polarization combinations. In particular, the case of 0° & 0° demonstrates the successful multiplexing using channels with the same polarization, wavelength and input spatial region, validating the promising capability of non-orthogonal optical multiplexing. Furthermore, Fig.  3 b provides the retrieved fidelity in each amplitude and phase multiplexing channel using different combinations of polarizations, respectively. The averaged retrieved fidelity in the amplitude and phase dimensions are almost the same ( ~ 0.98), which highlights the capability of SLRnet in demultiplexing information encoded in multiple non-orthogonal input channels (see Supplementary Note  1 for the results measured by structure similarity index measure (SSIM)).

a Averaged PCCs of the validation dataset during training procedures, where multiplexing scenarios of two input channels over a 1 m MMF with arbitrary polarization combinations are shown. The angles of polarizations with respect to the horizon line are indicated. Here, circle and ellipse indicate circular and elliptical polarizations, respectively. b The PCCs of retrieved information in different multiplexing channels at the final epoch. PCC Pearson correlation coefficient.

To provide a sensory evaluation of the retrieved information encoded in the wavefront, typical demultiplexing results for four polarization combinations (0° & 0°, 0° & 10°, 0° & 90°, and 0° & Ellipse) are presented in Fig.  4 . The corresponding input polarization states are outlined in the figure. And the retrieved fidelity measured by SSIM and PCC for all these cases are also provided, respectively. As can be seen from these results, four grayscale images multiplexed in the amplitude and phase of the input wavefronts using the same polarization can be effectively demultiplexed utilizing a single-shot speckle output. The retrieved fidelity of other results under different combinations of polarizations are similar, indicating the SLRnet enables the unprecedented multiplexing of non-orthogonal input channels even when the encoded wavefronts are scrambled by the MMF. To further consolidate the superiority of SLRnet in a more realistic scenario, the non-orthogonal optical multiplexing results using the same polarization state over a 50 m MMF are presented (see “Methods" section for details), as shown in Fig.  5 . As can be seen in Figs.  4 and 5 , the demultiplexing results of the 1 m MMF is better than the 50 m case. This is because the scattering properties of a longer MMF are much easier to be affected by the environment. The demultiplexing performance can be further improved by optimizing the network architecture. The high fidelity achieved for multiplexing non-orthogonal channels utilizing the same polarization, wavelength and input spatial position indicates that the SLRnet is an effective means for multiplexing non-orthogonal channels in an MMF.

The ground truths, the speckle output and the corresponding retrieved light field information by the SLRnet using a single-shot speckle output are shown, where their corresponding SSIM and PCC are given, respectively. Colorbars are also provided for the grayscale images encoded in the amplitude and phase. These images are adopted from the Fashion-MNIST dataset 41 .

The ground truths, the speckle output and the corresponding retrieved light field information by the SLRnet using a single-shot speckle output are shown, where their corresponding SSIM and PCC are given, respectively. Colorbars are also provided for the grayscale images encoded in the amplitude and phase dimensions. These images are adopted from the Fashion-MNIST dataset 41 .

In order to showcase the generality of the SLRnet for a diverse set of images, various experimental results considering more complicated grayscale encoded information from the CelebA face dataset 35 , random binary data whose digital information is uncorrelated, general natural scene images from the ImageNet database 36 , and snapshots in Muybridge recordings not belong to the same type of training dataset are presented (see Supplementary Note  2) . Typical results for general natural scene images are shown in Fig.  6 a, where the achieved averaged SSIM/PCC is 0.737/0.905. To further increase the modulation precision of the wavefront, the information is only encoded in the phase dimension of two non-orthogonal channels. The achieved averaged fidelity is 0.819/0.945 (SSIM/PCC) as shown in Fig.  6 b, which is substantially improved compared with the complex modulation case. At the same time, the achieved typical fidelity for images not belong to the ImageNet database can be up to 0.907/0.986 (SSIM/PCC), as shown in Fig.  6 c, indicating the good generalization of the SLRnet. All these results further validate that the SLRnet has an excellent ability to retrieve multiplexed information encoded in the non-orthogonal input channels.

a The ground truths, the speckle outputs, and the corresponding retrieved light field information by the SLRnet are shown, where their corresponding SSIM and PCC are given. b The corresponding results for the non-orthogonal multiplexing of phase encoded information. The images in ( a ) and ( b ) are from the ImageNet database 36 . c The results for the non-orthogonal multiplexing of phase encoded information using snapshots of Muybridge recordings from the 1870s that marked the historically important breakthrough of the first ever high-speed photography images. These images are not belong to the ImageNet database used for the training of the neural network.

We demonstrate a concept of non-orthogonal optical multiplexing over an MMF empowered by deep learning utilizing the SLRnet. Up to five optical degrees of freedom with non-orthogonal combinations of amplitude, phase, polarization and two-dimensional space ( X and Y ) are utilized for the non-orthogonal multiplexing, where the multiplexed information in the proximal end of MMF can be effectively demultiplexed using a single-shot speckle output at the distal end of MMF. The experimental results reveal that the proposed SLRnet can achieve high-fidelity ( ~ 98%) retrieval of multidimensional light field transmitted over an MMF. The performance of SLRnet is comparable to or even exceeding the reported results of orthogonal optical multiplexing in optical degrees of freedom, fidelity and spatial channel numbers (see Supplementary Note  3 for more details). At the same time, both the training and validation datasets contain the influence from the environment (see Supplementary Note  4 for more details). According to the retrieved results demonstrated above, the trained SLRnet possesses certain robustness against the perturbation from the environment. More robust demultiplexing can be achieved by using joint training of data collected at different environments 27 , 29 . If more than two input channels are involved in the non-orthogonal optical multiplexing, the total amount of data should be increased for achieving similar fidelity.

Although the proposed concept of non-orthogonal optical multiplexing over an MMF cannot be directly used in medical diagnosis at this stage, which generally requires unity fidelity, the non-orthogonal multiplexing of uncorrelated binary digital information with high accuracy indicates a step forward for realizing non-orthogonal multiplexing transmission of optical information through an MMF. It is anticipated that our results could not only pave the way for harnessing the high throughput MMFs for communication and information processing, but also might provide a paradigm shift for optical multiplexing in optics and beyond, which can substantially improve the degrees of freedom and capacity of optical systems.

Furthermore, light has many physical quantities that can be used to encode information. It is also anticipated that more optical degrees of freedom can be used for non-orthogonal optical multiplexing, such as the wavelengths and orbital angular momentum. There is room for optimizing the performance of deep neural network, where the achieved fidelity, efficiency and generalization should be further improved. Recent studies have shown that transformer structures based on self-attention mechanism may achieve higher fidelity. And the network based on the prior Fourier transform can result in superior external generalization 37 . There are still challenges to overcome in this data-driven approach. A typical one is the ability to multiplex information with higher capacity will require exponentially increasing amounts of data (see Supplementary Note  2) . Adding a physically-informed model of the MMF system in the deep neural network could be an effective solution for this challenge, which would also boosting the demultiplexing fidelity 24 , 25 . In addition, incorporating transfer learning could substantially reduce the amount of data required for training.

Experimental setup

A monochromatic laser with a power of 50 mW ( λ = 532 nm, MSL-S-532 CH80136, CNI) is used as the light source (see Supplementary Note  5 for more details regarding to the experimental setup), where it can be generalized to other wavelengths. The horizontal polarized laser beam is collimated and expanded by an objective lens (Obj 1 ) and a lens (L 1 ). Then it is divided into two beams of the same size using a dual-channel diaphragm. A phase-only spatial light modulator (SLM, PLUTO-NIR, Holoeye) is used for realizing amplitude and phase modulations simultaneously, which will be elaborated in the following. L 2 , iris and L 3 constitute a 4f filtering system, and the first-order diffracted light is selected at the focal plane to obtain the targeted amplitude and phase encoded light field. A wave plate is used to adjust the polarization state for one of the laser beams while the other beam keeps the horizontal polarization state unchanged. They are coherently superimposed with a non-polarized beam splitter cube (NPBS), forming two collinear beams with arbitrary polarization combinations. Then, two multiplexed laser beams are coupled into an MMF by an objective lens (Obj 2 ). And the outgoing light field from the MMF is collected by another objective lens (Obj 3 ), where the output speckle is recorded by a CMOS camera (MER-231-41U3C-L, Daheng Imaging). The captured speckles are translated to grayscale images. Two kinds of MMFs are tested: one is 1 m (Newport, diameter ϕ = 400 μ m, NA = 0.22) while the other one is 50 m (YOFC, diameter ϕ = 105 μ m, NA = 0.22). Both MMFs are step-index MMFs.

Data acquisition and preprocession

The parameters of all used datasets and their corresponding averaged fidelity are summarized in Supplementary Note  6 . Each dataset is divided into a training set (90%) and a validation set (10%). The data in the validation set is uniformly sampled in its corresponding dataset. The resolution of the speckle output fed to the network is 200 × 200. All the images encoded in the amplitude dimension are scaled from 0-1 to 0.2-1.

Amplitude and phase modulation scheme

To achieve simultaneous phase and amplitude modulations of the light field by a phase-only SLM, a complex amplitude modulation algorithm based on phase-only hologram coding is used 38 . The amplitude information is encoded into the phase information by modifying the spatial diffraction efficiency, where the target light field information is obtained by filtering.

Network structures

The proposed SLRnet consists of a FC layer and a ResUnet. In the FC block, a linear layer and an adaptive average pooling layer are used to control the size of the layer’s output. The linear layer can increase fitting and generalization abilities of the network. At the same time, the ResUnet introduces abundant skip connections to the Unet structure and accelerates the training process of network 34 . In this case, the ResUnet consists of four parts, including residual convolutional blocks (ResConv), residual transposed convolutional blocks (ResConvT), an output convolutional layer (Conv), and skip connections, as shown in Fig.  2 b. The ResConv achieves downsampling feature extraction by using a convolutional layer with a stride of 2, while ResConvT achieves upsampling reconstruction by using a transposed convolutional layer with a stride of 2. And there are skip connections between every two symmetrically arranged ResConv and ResConvT for concatenating channels. Finally, the channel matching output is carried out through the Conv with the convolution kernel size of 1 × 1. After adding batch normalization to the convolution layer of ResConv and ResConvT, the convergence of network training is faster. At the same time, adding a Rectified Linear Unit (ReLU) activation function introduces nonlinear factors to enhance the fitting ability of the network (see Supplementary Note  7 for detailed structure).

Training configuration

The SLRnet is implemented using python 3.9.13 in PyTorch 1.13.0. It is trained with the AdamW optimizer 39 , an improved version of the Adam optimizer with better generalization performance. The initial learning rate is set at 2 × 10 −4 , rising to 1 × 10 −3 after five epochs of warm-up, and subsequently dropping to 0 at the last epoch according to the cosine annealing schedule (see Supplementary Note  8 for the learning rate curve). This is an advanced learning rate adjustment strategy 40 , where its loss function value during the training process does not fluctuate significantly. The total training epoch is set to 200 to ensure that the training is converged. Mean absolute error is selected as the loss function to train the network.

Reporting summary

Further information on research design is available in the  Nature Portfolio Reporting Summary linked to this article.

Data availability

The example dataset for the non-orthogonal multiplexing of phase encoded information is available at: https://doi.org/10.5281/zenodo.10391031 . Any additional data are available from Yi Xu ([email protected]) upon request.  Source data are provided with this paper.

Code availability

The Python codes used in this paper are available at https://doi.org/10.5281/zenodo.10391031 .

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Acknowledgements

The authors would like to thank Cheng-Wei Qiu, Songnian Fu, Jianping Li and Meng Xiang for their inspired suggestions and comments. This work was supported by National Key R&D Program of China under grant no. 2018YFB1801001 (Y.Q.), National Natural Science Foundation of China under grant nos. 62222505 (Y.X.) and 62335005 (Y.X.) and Guangdong Introducing Innovative, Entrepreneurial Teams of “The Pearl River Talent Recruitment Program" under grant nos. 2019ZT08X340 (Y.Q.) and 2021ZT09X044 (Y.X.).

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Tuqiang Pan, Jianwei Ye, Haotian Liu, Fan Zhang, Pengbai Xu, Ou Xu, Yi Xu & Yuwen Qin

Guangdong Provincial Key Laboratory of Information Photonics Technology, Institute of Advanced Photonic Technology, School of Information Engineering, Guangdong University of Technology, Guangzhou, 510006, China

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Y.X. conceived the idea. T.P., J.Y. and H.L. conducted the experiments with the assistance of F.Z., P.X. and O.X. T.P. designed and trained the deep learning network. Y.X. and T.P. analysed the results. Y.X. and T.P. wrote the manuscript with inputs from all authors. All authors reviewed the manuscript. Y.X. and Y.Q. supervised this project.

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Pan, T., Ye, J., Liu, H. et al. Non-orthogonal optical multiplexing empowered by deep learning. Nat Commun 15 , 1580 (2024). https://doi.org/10.1038/s41467-024-45845-4

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Home > Books > Multiplexing - Recent Advances and Novel Applications

Multiplexing Techniques for Applications Based-on 5G Systems

Submitted: 23 October 2021 Reviewed: 26 November 2021 Published: 06 January 2022

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Multiplexing is an important technique in modern communication systems that allows simultaneous transmission of multiple channels of information on the same transmission media. Fifth-generation (5G) mobile communication systems allow Enhanced Mobile Broadband (eMBB), Ultra Reliable Low Latency Communications (URLLC), and Massive Machine Type Communications (mMTC). 5G has carrier frequency bands from sub-1 GHz to mid-bands and millimetre waves. The sub-1 GHz frequency band is for mobile broadband, broadcast and massive IoT applications. The mid-bands (between 1–6 GHz) offer wider bandwidths, focusing on mobile broadband and mission-critical applications. The frequency bands above 24 GHz (mmWaves) support super wide bandwidth applications over short, line-of-sight coverage. For each application on a corresponding frequency band, 5G allows defining of an optimized waveform from a family of waveforms. 5G uses massive MIMO, NOMA and network slicing techniques which allows spatial multiplexing and multibeam multiplexing. Multiplexing techniques play a major role in 5G systems in terms of data rate and bandwidth efficiency. This chapter presents multiplexing techniques for applications based-on 5G systems.

• duplexing schemes
• spatial multiplexing
• MIMO schemes
• CSI framework
• service-based multiplexing

Author Information

Nguyen huu trung *.

• Hanoi University of Science and Technology, Hanoi, Vietnam

*Address all correspondence to: [email protected]

1. Introduction

From the first generation (1G) that were introduced in 1979 by Nippon Telegraph and Telephone (NTT) to today’s fifth generation (5G), mobile communication networks are constantly improving the speed and efficiency of bandwidth usage to support various applications with diverse requirements such as latency, high data rates and real-time support for random traffic demands [ 1 ].

The increasing number of not only smart phones, tablets and laptops but also the huge number of other devices such as IoT (Internet of Things) nodes, wearable devices for healthcare will demand significant challenges in 5G systems to manage a huge amount of devices and connections [ 2 ]. Besides, the exponential growth of mobile video services (e.g., live video streaming, online video gaming, mobile TV) requires wider bandwidth and higher spectral efficiency than that of 4G systems [ 3 ].

Such a huge volume of data traffic and connections will lead to 5G systems to use new and higher frequency bands [ 4 ]. Some other factors such as ultra-low latency (less than one millisecond), fast-tracking will also be considered in the design of 5G system architecture. 5G systems support radio connections and end-to-end network connectivity at ultra-high speed, lower latency, higher reliability and massive connectivity [ 5 ].

1.1 Scope and contributions

First, this book chapter provides a brief introduction of 5G system architecture for the readers to understand the components of 5G systems.

Second, provides an overview of basic multiplexing techniques as a foundation for 5G systems to implement FDD, TDD modes.

Finally, it describes MIMO service and data multiplexing operations from a mathematical background, physical antenna configurations, channels and signals, procedures for downlink and uplink MIMO schemes.

1.2 5G system architecture

Today we see the evolution of Industry 4.0 manifested in smart factories, where collaborative robots are instantly connected. The entertainment industry advances dramatically with AR/VR technologies. People are using Zero Search with intelligent personal digital assistants. The Intelligent Transportation Systems (ITS) require all cars connected via C-V2X protocol. The Industrial Internet of Things (IIoT) is used in smart cities and smart agriculture. This is the business ecosystem of 5G systems [ 6 ]. 5G systems enable people for living in an intelligently connected world. The 5G system architecture is illustrated in Figure 1 . At the highest level, the 5G system consists of 5G NR RAN (gNB), 5G Core Network (5GCN)/EPC and different kinds of UEs for three kinds of service including Enhanced Mobile Broadband (eMBB), Ultra-reliable and Low-latency Communications (uRLLC), and Massive Machine Type Communications (mMTC) in a business ecosystem [ 7 ].

5G system architecture (vRAN approach).

1.2.1 5G NR RAN (gNB)

5G NR (New Radio) is the global standard for the air interface of 5G networks developed by 3GPP with operation from below 1 GHz up to more than 40 GHz and massive MIMO beamforming capability [ 8 ].

RAN stands for Radio Access Network. RAN provides radio access and coordinates network resources across User Equipment (UE). For more general, the RAN is divided into two parts. The first part is the lower layer RAN split including the antenna integrated Radio Unit (RU) and the Distributed Unit (DU). The second part is the higher layer RAN split, a 3GPP standard F1 interface between the DU and the Centralized Unit (CU). DU and CU constitute Baseband Unit (BBU) [ 9 ].

Legacy LTE uses Evolved Node B (eNodeB or eNB) like Base Station (BTS) in GSM networks. Similarly, gNodeB (gNB – next generation Node B) is 5G Base Station. gNB features Software Defined Radio (SDR) with various MIMO options described in session 3 of this chapter [ 10 ].

In 5G NR, RU handles digital front end (DFE), part of the physical layer (low physical) and multiple beamforming operation. RU consists of a Remote Radio Head (RRH) and Active Antenna System (AAS) [ 11 ]. Antennas in AAS for 5G NR make use of the shorter element sizes at high frequencies to incorporate a larger count of radiating elements. These antenna arrays are essential for MIMO beamforming operations that play a vital role in 5G systems [ 12 ]. The RRH performs all RF functions like ADC/DAC, digital up/down-conversion, filtering and transmitting and receiving signals to the BBU including beamforming. RRH can also provide monitoring and control functions to optimize system performance.

In LTE systems, RRH is connected to the antenna by RF coaxial cable and is usually mounted near the antenna to reduce transmission line losses. In 5G NR, RRH and AAS are integrated in a small and compact form factor [ 6 ].

Common Public Radio Interface (CPRI) is the standardized interface that sends data from the RRHs to the Base Band Unit (BBU). CPRI is a very high-speed connection on fiber optic cable. eCPRI is enhanced CPRI which is used to reduce the burden on the fiber. The connection between the RUs and the DU is called fronthaul and it is fiber optic cable.

DU stands for Distributed Unit. DU is placed close to RU and runs RLC, MAC, parts of the Physical layer. This function consists of signal processing, network access. DU is controlled by CU (Centralized Unit). DU also supports FFT/IFFT functions [ 13 ].

CU provides support for the higher layers of the protocol stack such as SDAP, PDCP and RRC. Practically, there is a single CU for each gNB. A CU can control multiple DUs (can be more than 100 DUs). Each RU corresponds to one cell. Each DU can support one or more RUs, so in 5G systems, one gNB can control hundreds of cells. 5G NR cell can be femtocell, smallcell or macrocell [ 14 ]. 5G Small Cell Radio Nodes can be installed on walls or ceilings with network connectivity and power are provided over Ethernet. Midhaul connects the CU with the DU via F1 interface. Backhaul connects the 5G core to the CU. The 5G core may be up to 200 km away from the CU.

RIC is RAN Intelligent Controller which is responsible for all RAN operation and optimization procedures such as radio and resource connection management, mobility management, QoS management to support the best effective network operation.

There are three different approaches to design a RAN as abstracted in Table 1 [ 15 ].

RAN classification.

COTS: commercial-off-the-shelf.

1.2.2 5G Core network

According to the definition of 3GPP, 5G has two networking modes: SA (Standalone) and NSA (Non-Standalone). 5G system Service-based architecture is illustrated in Figure 2 and corresponding functions are described in Table 2 [ 16 ].

5G system service-based architecture with core network functions.

Core network functions.

The EPC (Evolved Packet Core) network consists of MME (Mobility Management Entity), S-GW (Service Gateway) and PDN gateway. EPC performs functions such as mobility management, IP connection, QoS management, and billing management.

1.3 Chapter structure and organization

The structure and organization of this book chapter are illustrated in Figure 3 .

Structure and organization of the book chapter.

2. Basic multiplexing techniques

The term “multiplexing” refers to the sharing of a system resource (SR) to a set of users. There is a subtle distinction between multiplexing and multiple access, while multiplexing means the SR sharing is “fixed” ( static multiplexing) or adaptive change ( dynamic multiplexing), multiple access techniques are those techniques that enable multiple users to share limited SRs remotely.

Multiplexing allows multiple channels/users to share the same SR. Multiplexing helps to increase the efficiency of using the SR and the transmission capacity of the system. Dynamic multiplexing makes the allocation of the SR more efficient.

5G NR systems also use “duplexing schemes” for Uplink (UL) and Downlink (DL) data transmission.

Frequency Division Multiplexing (FDM): Specified subbands of frequency are allocated. Suitable for analog signal transmission, widely used in analog broadcast radio and television.

Time Division Multiplexing (TDM): User data are assigned in periodically recurring timeslots. Suitable for digital signal transmission, commonly used in digital telephone systems.

Code Division Multiplexing (CDM): Specified orthogonal spread spectrum codes are allocated.

Wavelength Division Multiplexing (WDM): WDM is used in fiber-optic communications. In WDM, several optical carrier signals are multiplexed onto a single optical fiber by using different wavelengths.

Space Division Multiplexing (SDM): Transmitting separate data streams in parallel using the same time/frequency resources. The receiver side also requires multiple antennas to the same level (degrees of freedom) as the number of streams or layers to spatially decorrelate, demodulate and decode.

Polarization Division Multiplexing (PDM) or dual polarization frequency reuse: Orthogonal polarizations are used to transfer signals, allowing for reuse of the same frequency band.

We are now considering basic multiplexing techniques.

2.1 Frequency division multiplexing

Frequency division multiplexing (FDM) is the division of total channel bandwidth into multiple, non-overlapping subbands. Each of these subbands is assigned to a user or a signal by modulating with the appropriate carrier frequency.

The multiplexer from the transmit side is responsible for multiplexing the modulated signals with different carrier frequencies into a total signal for transmission. The demultiplexer at the receiver is responsible for separating the total signal into signals of different users by different frequencies.

Example 1. Primary FDM system ( Figure 4 ) with total frequency bandwidth from 60 kHz to108 kHz is divided into 12 subbands, each subband has a bandwidth of 4 kHz. At the transmitter, the signal of a user is transmitted through a low pass filter (LPF) which is then a single side band (SSB) modulated with an appropriate carrier frequency. At the receiver, the total signal passes through a band pass filter (BPF) and a single side band demodulator to obtain a signal for the corresponding user.

Frequency division multiplexing.

Analog system: noise accumulates in each hop if we use repeaters.

Difficult to fabricate high-Q bandpass filters.

Low multiplexing factor.

2.2 Time division multiplexing

Time Division Multiplexing (TDM) is a technique for the serial transmission of user data over a common medium such as a coaxial cable.

At a time, only one user’s data are transmitted serially in a time slot. TDM allows each user to use the entire system bandwidth.

In addition to user data, signaling and frame alignment word (FAW) are inserted into the frame. At the receiver, there is clock recovery and frame synchronization to recover data for each channel ( Figure 5 ).

Time division multiplexing.

2.3 Optical space-division multiplexing for MIMO systems

Space-Division Multiplexing (SDM) is a multiplexing technique for optical data transmission where multiple spatial channels are utilized. Figure 6 shows a generic optical MIMO-SDM system. At the transmitter, the user data signals are encoded, modulated, E/O converted and then multiplexed onto different wavelengths (λ 1 , λ 2 … λ N ) in a WDM multiplexer [ 17 ].

Space-division multiplexing for optical communications and application to 5G systems.

At the receiver, the transmitted signals are recovered using MIMO digital signal processing consisting of an N × N array of equalizers by DSP (digital signal processor). First, the N channels signal is demultiplexed by an SDM demultiplexer. Then the separate signals r 1 … r N are fed into the N × N MIMO DSP block that is capable of eliminating all linear impairments of the transmission system and giving the reconstructed signals as output. Optical fibers are utilized at fronthaul, midhauld and backhaul of 5G systems. Data from RUs (at smallcells, for example) are multiplexed and transmitted to DU via fronthaul by optical fiber [ 18 ]. At present, a dense optical wavelength-multiplexing system has a transmission capacity of more than 1 Tera bit/s (1000 Gbit/s) per wavelength [ 19 ].

2.4 Code division multiplexing or code division multiple access

Code Division Multiple Access (CDMA) is a multiple access method that allows multiple users to share the same time and frequency resources.

In a CDMA system, each user is assigned with specific spreading code, and all users can send information simultaneously over a single communication channel. Since CDMA is based on the spread spectrum principle, each transmitter will use a pseudo-random code to modulate the data, and the receiver decodes the modulated signal using its own pseudo-random code. The principle of CDMA is illustrated in Figure 7 .

Code division multiple access.

2.5 Duplexing schemes in 5G NR

5G NR supports both Frequency Division Duplex (FDD) and Time Division Duplex (TDD) schemes. TDD is the main duplexing mode for higher frequencies while FDD is used for lower frequencies as the interference problems with large cells is reduced by having different frequencies in UL and DL. FDD is similar to FDM, UL and DL use separate carrier frequencies. Data are transmitted in both directions simultaneously. TDD is similar to TDM, only one carrier frequency is used. Transmission/Reception in UL and DL is assigned by different time slots.

2.5.1 5G NR frame structure

Since TDD is the main duplexing mode of a 5G NR, we will discuss more detail about TDD. We start with 5G NR frame structure. Just like the TDM system, 5G NR is frame structured. A frame has a fixed duration of 10 ms which consists of 10 subframes of 1 ms duration. Each subframe can have 2 μ slots.

Figure 8 shows the 5G NR frame structure. The number of slots per subframe (i.e., 2 μ ), hence the slot duration depends on subcarrier spacing (SCS). 5G NR supports two frequency ranges FR1 (Sub 6GHz) and FR2 (millimeter wave range, 24.25 to 52.6 GHz). 5G NR uses flexible SCS derived from basic 15 KHz used in LTE to values of 30, 60, 120 Khz. For SCS of 15 KHz, a subframe has 1 slot of 1 ms duration. For SCS of 30 KHz, a subframe has 2 slots of 500 μs duration as shown in Table 3 and Figure 9 [ 20 ].

5G NR frame structure.

Number of slots per subframe, slot duration, number of slots in a frame and guard period for reference SCS.

5G NR scalable slot duration.

Each slot is comprised of either 14 OFDM symbols or 12 OFDM symbols based on normal Guard Period (GP) and extended GP respectively. However, mini slots (2, 4, or 7 symbols) can be allocated for shorter transmissions. Slots can also be aggregated for longer transmissions.

2.5.2 5G NR UL-DL pattern

Now we know the frame structure. When operating in TDD mode, we have to specify the exact timing for the uplink and downlink transmission. So, how do we define the time slots for uplink and downlink transmission?

Timeslots for uplink and downlink transmission are organized into DL-UL patterns. In LTE TDD, there are 7 predefined patterns for UL and DL allocation in a radio frame. There is no predefined pattern for 5G NR, but we can define a flexible pattern thanks to parameters in TDD UL/DL Common Configuration ( tdd-UL-DL-configurationCommon ) as shown in Table 4 below.

5G NR TDD DL/UL common configuration parameters.

You may ask yourself what is the difference between the DL-UL pattern and radio frame? The dl-UL-TransmissionPeriodicity parameter, for example 5 ms, defines the periodicity of the DL-UL pattern. So, a radio frame of 10 ms contains 2 DL-UL patterns.

From the above parameters, we can define TDD DL/UL configuration, aka. DL-UL pattern for 5G NR radio transmission as shown in Figure 10 . In 5G NR, the slot configuration is flexible and can be changed from time to time while maintaining the focus on inter-cell interference aspects [ 21 ].

5G NR TDD UL/DL common configuration frame structure.

Then, the next question is how to design a transmission pattern? We know that time slots allocation for UL and DL depends on UL and DL traffic. We call that UL/DL traffic load ratio. To adapt with actual traffic, 5G NR supports 3 different TDD configurations as follows:

Static TDD configuration: For static TDD, the UL/DL traffic ratio is usually decided by the statistical UL/DL traffic load ratio among multiple operators in a specific country or region. The slots and symbols are defined over a period of time that are dedicated to either the UL or DL based on the UL/DL traffic ratio.

Semi-Static TDD configuration: This configuration is more flexible than the static TDD. We have a certain number of UL and DL slots within a transmission periodicity (defined by dl-UL-TransmissionPeriodicity ). The remaining slots, which are neither UL nor DL, can be considered ‘Flexible’ with the help of another IE TDD-UL-DL-ConfigDedicated .

Dynamic TDD configuration: This is the most flexible configuration for UL/DL transmission for dynamic assignment and reassignment of time-domain resources between the UL and DL transmission. Dynamic TDD is used to adapt to actual traffic but requires coordination to avoid interference between cells, so that there is no fixed UL/DL allocation. With the popularity of video streaming increasing, it is forecast that the proportion of DL content will grow even further in the future, hence it is natural that more resources should be allocated to the DL.

Example 2. The DL-UL pattern design. Assuming SCS = 30 kHz and the carrier is FR1 with 100 MHz bandwidth.

Since slot duration for reference SCS of 30 kHz is 0.5 ms, the number of slots in DL-UL periodicity would be

NumberOfGuardSymbols = TotalSymbolsInPattern ‐ TotalSymbolsWithTypeSpecified = 14 ∗ NumSlotsDLULPeriodicity numDLSlots ∗ 14 + numDLSyms + numULSyms + numULSlots ∗ 14 = 2 symbols .

This DL-UL pattern is illustrated in Figure 11 . This pattern repeats itself in the timeline.

Example on design a TDD downlink frame structure.

3. 5G NR MIMO multiplexing operation

Perhaps the most challenging part of the 5G NR system is the MIMO operation modes. Let us start with SU-MIMO and MU-MIMO. SU-MIMO stands for Single-User MIMO. In Single User MIMO, both the base station and UE have multiple antennas, and the base station can transmit multiple data streams simultaneously to the UE using the same time/frequency resources. By doing so, it doubles (2 × 2 MIMO), or quadruples (4 × 4 MIMO) the peak throughput of a single user.

MU-MIMO stands for Multi User MIMO. The base station serves more than 2 UEs simultaneously. Since in MU-MIMO, the base station sends multiple data streams, one per UE, using the same time-frequency resources, MU-MIMO mode increases the total cell throughput, i.e., cell capacity. MU-MIMO is not a new concept. We have MU-MIMO in LTE (Transmission Mode 5 - TM5) and WLAN (802.11ad). However, in 5G NR the scale of MU-MIMO will be much larger and deployment will also be more common. 5G NR uses massive MIMO.

Massive MIMO employs a large number of transmit and receive antennas, improves spectral efficiency and increases the transmission data rate through spatial multiplexing to deliver multiple streams of data within the same resource block (time and frequency). Massive MIMO is also called Large Scale MIMO.

By now, you may ask a question: Why massive MIMO, and how many antenna elements are needed to be called massive MIMO ? In conventional 4G LTE using a normal MIMO, the maximum number of the antenna is 2x2 or 4x4 and even 8x8 is mentioned. We know that the larger the number of antennas, the narrower the beam width. It means the coverage of a specific beam would be smaller. We need a more precise beam control algorithm, but in return, the achievable data rate will be higher. The number of antennas in massive MIMO should be ≫ 8 [ 22 ].

3.1 Mathematical background

Figure 12 shows a typical MIMO system equipped with N T transmit antennas and N R receive antennas. The data are encoded in both space and time domains and then transmitted by N T transmit antennas through a MIMO propagation channel.

System and channel model for spatial multiplexing.

The relationship between the input and output of a MIMO system can be written as follows

x = x 1 x 2 … x N T T is transmitted signal,

y = y 1 y 2 … y N R T is received signal,

n = n 1 n 2 … n N R T is AWGN,

H = h 11 h 21 ⋮ h N R 1 h 12 h 22 ⋮ h N R 2 ⋯ ⋯ ⋱ ⋯ h 1 N T h 2 N T ⋮ h N R N T is channel matrix,

where h i , j is an element of the i th row and the j th column in the matrix H , denotes a channel from the j th TX antenna to the i th RX antenna.

If the channel matrix H is known at both base station (gNB) and UE (i.e., Channel state information - CSI) then we could take singular value decomposition (SVD) on channel matrix H as

where U ∈ C N R × N R and W ∈ C N T × N T are orthogonal unitary matrices and D ∈ ℜ N R × N T is diagonal matrix, whose diagonal elements are non-negative real numbers and whose off-diagonal elements are zero. The diagonal elements of matrix D λ 1 ≥ λ 2 ≥ … ≥ λ r are the ordered singular values of channel matrix H , where r = min N T N R is rank of H .

Assume the receiver knows the U matrix and the transmitter knows the W matrix. The transmitted data x is precoded by W matrix and the received data y is equalized by U matrix, we have

where n ˜ ∈ CN 0 N 0 I N R has the same distribution as n . Thus, we have an equivalent representation as a parallel Gaussian channel

W = w 1 w 2 … w N T is a precoding matrix. Each symbol x i is precoded by precoding vector w i .

From the Eq. (4) , we can see that the base station can transmit simultaneously maximum of r data streams to the target UE, increasing the channel throughput. This is called spatial multiplexing (SM). MIMO spatial multiplexing takes advantage of multipath effects, where a transmitted signal arrives at the receiver through several different paths. Each path can have a different time delay, and the result is that multiple instances of a single transmitted symbol arrive at the receiver at different times [ 23 ].

If SNR is high, the number of data streams and data rate for each stream is chosen by the waterfilling algorithm [ 24 ]. In the opposite case, with low SNR, the best thing to do is to simply choose one subchannel with the highest singular value. This is called beamforming [ 25 , 26 ]. We can rewrite the Eq. (3) as

Instead of transmitting a vector of symbols, we just transmit a single symbol at a time. The w 1 vector defines the beamforming weights and u 1 here defines the receive beam.

Now we know how to transmit multiple data streams to a UE. We consider the way 5G NR implement MIMO modes.

Clearly, to implement SM, the network (gNB and UEs) should know the channel matrix H then calculate the 3 matrixes U , D , W out of H . The transmitter applies W as a precoder and the receiver apply U for processing of the received signal. For downlink transmission, gNB is a transmitter and UE is receiver and vice versa for uplink transmission.

3.2 Basic terminologies

The first thing we have to know is the codebook. The codebook is a set of predefined precoders (precoding matrices). Why codebook? Consider DL transmission, gNB has to calculate a precoder from a reference signal or selects a predefined precoder with a requested index from UE before transmitting data. The first case is called non-codebook and the second is called codebook-based precoding.

Codebook type in 5G NR: There are two types of codebooks specified in 5G NR. Type I is designed for SU-MIMO and selected by UE report and RRC Configuration. Type II is designed mainly for MU-MIMO and is based on a more detailed CSI report. Type I codebook has predefined matrices based on the number of layers and CSI-RS ports. Type II codebooks contain mathematical formula for selecting a set of beams and then specifying relative amplitudes and phases to generate a weighted combination of beams for each layer of transmission.

The requested index into a set of predefined matrices, a so-called codebook is a precoding matrix indicator (PMI). PMI is used for DL transmission, conditioned on the number of layers indicated by the RI. In the uplink direction, the PMI is denoted by Transmit Precoder Matrix Indicator (TPMI) to differentiate it from the downlink PMI.

Together with the codebook, the number of layers is the number of simultaneous data streams. The number of layers is less than or equal to the rank of the channel matrix that we mentioned before. The number of layers depends upon the channel condition between receiver and transmitter antennas. Low correlation propagation paths increase rank and the number of layers and vice versa. Rank indicator (RI) defines the number of possible transmission layers for the downlink and uplink transmission under specific channel conditions. However, gNG does not need to transmit RI as requested by the UE.

Channel state information (CSI) are parameters related to the state of a channel including the channel quality indicator (CQI), precoding matrix indicator (PMI) and rank indicator (RI). UE reports CSI parameters to gNB as feedback in CSI-RS mode.

Channel quality indicator (CQI) is an indicator of channel quality. The CQI index is a scalar value from 0 to 15 representing the highest modulation-and-coding scheme (MCS) to achieve the required block error rate (BLER) for given channel conditions.

CSI-RS resource indicator (CRI), used in conjunction with beamformed CSI reference signals. The CRI indicates the beam the device prefers in case the device is configured to monitor multiple beams.

SRI is an SRS resource indicator.

3.3 Physical antenna configuration versus antenna ports

It is very important to understand the physical antenna configurations, the antenna port and the relationship between them. The antenna system in 5G NR is an Active Antenna System (AAS). Typical active antennas are made up of a matrix of subarrays. Each subarray consists of individual dual-polarized elements. Each polarization is controlled by a beamforming (BF) coefficient. Therefore, the number of columns is doubled.

For example, Figure 13a shows 8T8R configuration with 4 columns, 1 row (4x1) consisting of 4 (1x8) subarrays. Figure 13b shows 64T64R configuration which is made up of 8 columns, 4 rows of (1x2) subarrays.

Physical antenna configuration.

Figure 14a shows single panel antenna. 5G NR supports both single panel and uniform (b) and non-uniform multi-panel (c). In 5G NR, logical antenna configuration is described by 3 parameters: N g is the number of panels, N 1 is number of columns and N 2 is the number of rows in a panel.

Single panel and multi panel antenna configurations.

In association with N 1 and N 2 , 3GPP defines DFT oversampling factors O 1 and O 2 to determine the sweeping steps of a beam during the beam management (beam tracking). O 1 determines the sweeping step in the horizontal direction and O 2 determines the sweeping step in the vertical direction.

Number of polarizations = 2,

Number of CSI-RS antenna ports = (2* N 1 )* N 2 ,

Number of beams in a column =  N 1 * O 1 ,

Number of beams in a row =  N 2 * O 2 ,

Number of beams = ( N 1 * O 1 )*( N 2 * O 2 ) = from 8 to maximum 256 beams.

Antenna port: This is a logical concept and different from the physical one that you see on the antenna tower. You can find the definition of antenna port from the 3GPP specification as “ an antenna port is defined such that the channel over which a symbol on the antenna port is conveyed can be inferred from the channel over which another symbol on the same antenna port is conveyed ” [ 27 ]. We can understand the antenna port like socket and port concept which is used on Internet. For example, port 80 is used for the HTTP protocol, port 20 for FTP, port 22 is for SSH, port 25 is for SMTP. We use “antenna ports” to transmit and receive data. Why the definition of antenna port of 3GPP is related to the channel because we have to estimate the channel model before decoding transmitted data. The channel model has estimated thanks to reference signals. Each antenna port is assigned by a dedicated reference signal. Each antenna port represents a specific and unique channel model. The receiver can use a reference signal transmitted on an antenna port to estimate the channel model for this antenna port and this channel model can subsequently be used for decoding data transmitted on the same antenna port.

Each antenna port carries its own resource grid. One resource grid is transmitted on a given antenna port, subcarrier spacing configuration and transmission direction (downlink or uplink). The resource grid consists of a number of RBs (Resource Blocks) for one subframe.

3.4 Physical channels and signals

Physical Channels and Signals for DL, UL and corresponding antenna port addresses are as follows ( Table 5 ):

Physical channels and signals and corresponding antenna port addresses.

3.5 Mapping antenna ports to physical antennas

There is no strict mapping of antenna ports to physical antenna ports. Figure 15 indicates the mapping between antenna ports and physical antennas. One antenna port can be mapped to single or multiple physical antenna(s). Due to each antenna port representing a specific and unique channel model, the number of layers in the physical layer may reach the number of antenna ports. The number of layers may range from a minimum of one layer up to a maximum number of layers equal to the number of antenna ports. The layers are then mapped to the antenna ports.

Mapping antenna ports to physical antennas.

3.6 Downlink MIMO schemes

Legacy LTE supports 9 transmission modes (TM). To avoid sophisticated transmission mode handover for different scenarios, 5G NR uses the term unified transmission mode [ 28 ]. However, according to the channel state information (CSI) acquisition method, downlink MIMO schemes are categorized into ( Figure 16 ):

Downlink MIMO schemes.

SRS-based (sounding reference signal)

CSI-RS-based (CSI - reference signal, codebook type I, Single / Multi panel)

CSI-RS without Beamforming (codebook type II Single Panel)

CSI-RS Beamformed (codebook type II Port Selection)

DL and UL channels are considered reciprocal. From a channel calculation perspective, in SRS-based Single User MIMO scheme, channel calculation obligation belongs to gNB, the remaining schemes rely on UE’s CSI report from its channel calculation. The device’s capability and channel condition decide the best MIMO mode among the above schemes.

3.7 Single user MIMO schemes

3.7.1 procedure for srs-based single user mimo.

UE transmits sounding reference signals through each of its antenna ports.

gNB estimates the channel (e.g., downlink precoding weights) based on received sounding reference signals

gNB transmits PDSCH using a calculated precoder.

This scheme is illustrated in Figure 17a , and very simple but due to size and power at the UE are limited, the number of the antenna of UE is smaller than that of gNB and adding more RF chains to UE is difficult, SRS resources are transmitted on antenna ports one by one by transmit antenna switching (TAS).

Downlink single user MIMO operation.

3.7.2 CSI-RS based single user MIMO

Figure 18 shows a typical downlink transmission CSI-RS based SU/MU-MIMO scheme. First of all, UE needs to know the H matrix. The gNB is obligated to transmit CSI-RS ports so that UE can observe the full MIMO channel matrix. UE calculates the channel matrix and reports PMI, RI and CQI to gNB.

CSI reporting and equivalent channel for SU-MIMO.

In the equivalent MIMO channel, we have N L data streams, corresponding to N L layers. Each i -th diagonal element of D , λ i , represents the i -th layer’s channel magnitude; w i , the i-th column vector of W , is the beamforming weights for the i -th layer.

UE reports gNB is its preferred PMI but gNB is not obligated to apply the precoding indicated by the PMI, and the gNB does not provide the UE with explicit information regarding the precoding procedure. The UE relies upon using the Demodulation Reference Signal (DMRS) when decoding the PDSCH.

CSI-RS single user MIMO scheme uses type I codebook which is based upon a specific set of assumed antenna configurations. The antenna configurations are Single Panel and Multi Panel as described in Tables 6 and 7 .

Single panel antenna configuration.

Multi panel antenna configuration.

For codebook type I single panel: MIMO ranks: 1 to 8; CSI RS Ports: 2, 4, 8, 12, 16, 24, 32.

For codebook type I multi panel: MIMO ranks: 1 to 4; CSI RS Ports: 8, 16, 32.

3.7.3 Procedure for CSI-RS based single user MIMO

gNB transmits 32 CSI-RS ports to UE ( Figure 17b ). If DL antenna ports for CSI measurement is limited to ≤8, for example = 8, gNB has to transmit 4 CSI-RS sets of resources of 8 ports ( Figure 17c )

UE estimates the channel based on the received CSI-RS resources, selects the best PMI.

UE reports PMI, RI, CQI to gNB.

gNB decides a precoder to transmit PDSCH.

3.8 Multi-user MIMO schemes

In Multi User MIMO schemes, gNB tries to communicate simultaneously with a set of UE through the same time/frequency resources. MU-MIMO schemes uses Type II codebook to provide more details about Channel State Information. MU-MIMO schemes support to a maximum of 2 layers per UE. This is smaller than that of SU-MIMO (up to 8 layers for type I single panel) but the maximum number of layers per cell is higher to allow multiple UE to use 2 × 2 MIMO simultaneously.

DL MU-MO Type II codebook allocates a set of beams to each UE. Each set of the beam is the weighted combination of beams with relative amplitudes and co-phasing phase shifts.

Beamformed CSI-RS relies upon the gNB having some advanced information to allow beamforming of the CSI Reference Signal transmissions.

Procedure for beamformed CSI-RS as follows: gNB transmits one or more CSI-RS, each in different “directions”. UE computes and reports CRI/PMI/CQI to gNB.

3.9 Uplink transmission modes

5G NR supports uplink PUSCH precoding up to 4 layers. However, in the case of DFT-based transform precoding, only single-layer transmission is supported. The transmitted symbols are layer mapped and then precoded at the UEs.

If gNB instructs UE on PDCCH regarding the choice of precoding matrix selected from a codebook: codebook based ( Figure 19a ). Otherwise, UE measure DL CS-RS signal to determine precoding weights (not constrained to a codebook): Non-codebook based ( Figure 19b ).

Uplink MIMO operation.

3.9.1 Procedure for non-codebook-based transmission mode

UE measures DL SCI-RS signal to design suitable precoders for the SRS transmission.

UE transmits up to four SRS resources where each resource has one antenna port.

gNB determines one or multiple SRIs based on the received SRSs, number of layers for PUSCH. In this example, SRS1 and SRS3 are selected. TRI is equal to the number of SRIs.

UE uses selected resources to transmit PUSCH.

3.9.2 Procedure for codebook-based transmission mode

UE transmits SRS from each of its antenna ports.

gNB estimates UL channel based on the received SRSs to select the best SRS for antenna port, appropriate rank and precoding matrix. gNB transmits SRI (SRS resource indicator), RI and TPMI to UE.

UE uses selected resources to transmit PUSCH from the indicated antenna port, the number of layers and precoding matrix.

4. Service-based multiplexing

4.1 principle.

5G networks are designed for a wide variety of use cases including urban mobile broadband, massive machine-type communications, ultra-reliable low latency communications, applications such as remote surgery, autonomous driving, a massive number of sensors communicating with the network, 3D video streaming.

The problem is that the physical infrastructure resources are limited. The need for data, services and operators working on the same network increase. The solution is network slicing (NS). NS will create virtual network segments for the different services within the same 5G network. NS will divide the physical network into independent logical subnets for different kinds of services, each of which has a size and structure suitable for dedicated service [ 29 ].

NS is one of the key features of 5G NR. NS allows operators to support efficiently different use cases and enterprise customers on a dedicated 5G network. NS leverages the running of multiple logical subnets on top of physical network, multiplexes data services over physical infrastructure.

The concept of network slicing is illustrated in Figure 20 showing two slices. One slice supports smartphones with 3D streaming, virtual reality (VR) connections with guaranteed throughput slice, the other supports automotive connectivity, IIoT for smart factory with low latency slice on the same network infrastructure [ 30 ].

Service multiplexing by network slicing.

4.2 5G network slicing implementation

Create slice profile:

The customer will provide their service requirements they want to run on a network slice including bandwidth, capacity, and latency. The operator creates a service level agreement, and allocates the necessary capacity and bandwidth for the slice by NSSAI (Network Slice Selection Assistance Information). NSSAI consists of up to 8 S-NSSAI (Single –NSSAI). The S-NSSAI contains two components: the SST (Slice/Service Type) and an optional SD (Slice Differentiator).

UE gathers information for slices when registering for the network:

The UE gathers information for the available slices when registering for the network via NAS signaling. A single UE may be assigned up to eight difference slices [ 31 ].

Determines the candidate AMF(s) or AMF Set to be used to serve the UE:

Once a PDU session is set up, the UE is then signaled to the NSSAI, assuming this has been provided earlier to the UE.

Selects which slices the UE can connect:

Based on required NSSAI and registered information, the network will select the appropriate slice instance and related resources, with the AMF coordinating the actions in the 5G core network. There is one AMF that is common for all the slices a single UE has.

5. Conclusion

This chapter presented multiplexing techniques utilized in 5G systems. Duplexing is one of the key factors affecting the performance of 5G NR in terms of their wide-area coverage. The Frequency Division Duplex (FDD) and Time Division Duplex (TDD) schemes utilized in 5G NR are inherited from FDM and TDM, providing flexibility for designing UL/DL patterns.

Spatial multiplexing supports multi layer transmission. Multiple beamforming will transmit data through targeted beams and advanced signal processing that could speed up data rates and boost bandwidth and reduce interference for nearby users. 5G NR permits to use different waveforms on subbands with scalable subcarrier spacing and transmission time interval operating on one frequency band. Network slicing creates independent logical subnets for different kinds of services.

With these multiplexing techniques, 5G systems could provide data rate up to 20 Gbps and capacity increase by 1000 times and flexible platform for the services like massive Industrial Internet of Things (IIoT), connected society, smart factories. It is expected that 5G combined with artificial intelligence can improve social life, make life better, more productivity, and safety.

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