The Extended Hybrid Carrier-Based Multiple Access Technology for High Mobility Scenarios

Ge Song,Xiaojie Fang,Xuejun Sha

School of Electronics and Information Engineering,Harbin Institute of Technology,Harbin 150001,China

Abstract: The hybrid carrier (HC) system rooted in the carrier fusion concept is gradually garnering attention.In this paper,we study the extended hybrid carrier (EHC) multiple access scheme to ensure reliable wireless communication.By employing the EHC modulation,a power layered multiplexing framework is realized,which exhibits enhanced interference suppression capability owing to the more uniform energy distribution design.The implementation method and advantage mechanism are explicated respectively for the uplink and downlink,and the performance analysis under varying channel conditions is provided.In addition,considering the connectivity demand,we explore the non-orthogonal multiple access (NOMA) method of the EHC system and develop the EHC sparse code multiple access scheme.The proposed scheme melds the energy spread superiority of EHC with the access capacity of NOMA,facilitating superior support for massive connectivity in high mobility environments.Simulation results have verified the feasibility and advantages of the proposed scheme.Compared with existing HC multiple access schemes,the proposed scheme exhibits robust bit error rate performance and can better guarantee multiple access performance in complex scenarios of nextgeneration communications.

Keywords: extended hybrid carrier system;high mobility communications;multiple access

I.INTRODUCTION

With the commercial implementation of the 5G networks on a global scale,much attention is paid to the research of next-generation communication systems.The impending 6G,building upon the foundation of 5G,will continue to enhance the mobile Internet and is expected to support the vision of wider coverage,higher rates,more connections,lower latency,and others,which places higher demands on physical layer multiple access technologies[1–4].

Traditional multiple access technologies,with orthogonal frequency division multiple access(OFDMA) serving as a representative,have found wide applications within communication standards.Nevertheless,as the research progresses,the limitations of conventional multiple access technologies under high-mobility wireless channels render them inadequate for reliable communication requirements in complex scenarios,and an urgent necessity to explore new physical layer waveform technologies and multiple access technologies emerges [5–8].On the one hand,there is an anticipation for the continued evolution and optimization of orthogonal multiple access (OMA) schemes.Researchers have extensively explored multiple access schemes that exhibit good robustness along with universality and have investigated low-complexity detection algorithms for different models.Especially,the development of new modulation technologies aimed at 6G significantly provides support for reliable transmission in high mobility scenarios[9–12].On the other hand,considering the scarcity of spectrum resources relative to the growing number of users,non-orthogonal multiple access(NOMA)technology has been perceived as an efficient solution to the challenges of massive access.NOMA allows multiple users to use the same timefrequency resources,thereby enhancing the spectral efficiency,also known as “multi-user superposition transmission” or “layered division multiplexing”.Researchers have proposed a series of non-orthogonal multiple access schemes to serve more users through non-orthogonal designs in the power domain,code domain,and so forth.Among them,sparse code multiple access (SCMA) is a promising code domain NOMA technology and its performance is related to the design of the codebook [13–16].Moreover,research on the joint of multiple access with other communication technologies to improve system performance has also garnered attention [17–20].As investigations deepen,combined consideration of the novel waveform framework design and multiple access schemes has become a focal point.

In recent years,the hybrid carrier (HC) as a novel system based on the idea of carrier fusion has received increasing attention and study [21–23].The HC scheme provides the energy spread of the signal in the time and frequency domain by weighted fractional Fourier transform (WFRFT) to form a fused signal containing the single carrier (SC) components and multi-carrier(MC)components.Compared to traditional schemes,the HC signal has a more uniform energy distribution structure and is therefore considered to have the potential for reliable data transmission over high-mobility wireless channels.Additionally,it has the advantages of low complexity along with flexibility and can be degraded into SC or MC systems,rendering it suitable for upgrading existing communication systems.Research on HC is primarily centered around the design of symbol energy distribution,joint optimization for various scenarios,physical layer security,and others.Furthermore,compatibility is leveraged to combine with other candidate waveforms to obtain performance and flexibility enhancement[24–27].In terms of multiple access,hybrid carrier OMA schemes represented by HC-FDMA have achieved commendable application effects.The energy spread design based on carrier fusion allows them to achieve superior bit error rate (BER) performance under doubly-selective channels compared to traditional OFDMA and SC-FDMA schemes.Research on developing NOMA schemes based on hybrid carrier systems to enhance spectral efficiency and the number of user connections has also yielded certain results[28–31].However,the energy distribution design of the existing hybrid carrier multiple access technologies is highly reliant on the four-component structure of WFRFT,which constrains further enhancement of its performance.Therefore,it is valuable to extend and optimize the hybrid carrier multiple access technology to fully exploit its robustness advantages and better support for improving the performance of the HC system.

This paper investigates the extended hybrid carrier system multiple access scheme.Leveraging the energy distribution design capability of EHC modulation,we design matched orthogonal multiple access schemes for the uplink and downlink respectively.The system architecture and principles are illustrated,and the performance of the proposed scheme is analyzed under different channel conditions.Moreover,we introduce a novel extended hybrid carrier sparse code multiple access(EHC-SCMA)scheme,elucidating its implementation flow,describing the transform domain input-output relation,and explaining the signal detection algorithm.Finally,simulations are provided to demonstrate the feasibility and advantages of the proposed scheme.The main aim of this paper is to confirm that the extended hybrid carrier multiple access scheme can better ensure reliability in complex scenarios,and is a promising alternative solution for the next generation communication systems.

The rest of this paper is organized as follows: Section II presents the basics of the HC system.Section III proposes the EHC-OMA scheme and analyzes its performance.Section IV investigates the nonorthogonal multiple access for the EHC system and describes the proposed EHC-SCMA scheme.Section V gives the simulation and discussion.Finally,conclusions are illustrated in Section VI.

II.PRELIMINARY

2.1 Hybrid Carrier System Based on WFRFT

The hybrid carrier system is proposed based on the carrier fusion concept,which can be regarded as the integration of the SC system and MC system.The classical HC system is generally implemented by WFRFT which can be expressed as

whereFis the normalized Fourier transform matrix,satisfying [F]m,n=,m,n=0,1,...,N−1 and [·]m,ndenotes themth row andnth column elements.Fix,i=0,1,2,3 denote the 0-3 times normalized DFT ofxrespectively.,l=0,1,2,3 are the weighting coefficients,which can be generated by

whereαdenotes the transform order.Due to the periodicity,FsatisfiesF0=I,F1=F,F2=Π,F3=FΠ,F4=I,where[Π]m,n=δ(〈m+n〉N),and the result of WFRFT can be considered as a weighted sum of the time domain characterizations and frequency domain characterizations of the input sequence.In particular,HC is equivalent to SC whenα=0,and to MC whenα=1.According to the hybrid carrier fusion mechanism,the single carrier component and the multi-carrier component of the HC signal can be expressed as

For anyα,there is=WSC(α)+WMC(α)=1.By choosing the transform order,the HC system obtains more freedom in the design of the energy distribution and therefore exhibits better interference suppression performance.

2.2 Sparse Code Multiple Access

SCMA is a promising non-orthogonal multiple access scheme for mobile communication systems.Consider an SCMA system containingVindependent users,and the overloading factor is denoted asζ=V/K＞1,whereKis the number of the resource.The role of the SCMA encoder is to map log2M bits databvof uservinto M′dimension constellation and theKdimension codewordcvby mapping matrixΥv∈.The codebook C is shared by the transmitter and the receiver,and M is the number of codewords.Then,for thevth user,the SCMA encoding is defined as the following mapping rule

wherebv∈is the information vector from thevth user,Cv=∈CK×1denotes the SCMA codeword selected from the codebook,and M=0,1,...,M−1.Define the indicator matrixsatisfying

SCMA can be determined directly by the indicator matrix.The user nodek′is connected to the resource nodekwhen and only when.For the downlink,it can be obtained that

wherec∈CK×1is called the superimposed codeword.At the receiver,based on the indicator matrix,the SCMA codeword can be decoded using the message passing algorithm decoder with the computational complexity,wheredcis the number of non-zero entries in each row of indicator matrix,andt′is the number of MPA iterations.

III.EXTENDED HYBRID CARRIER ORTHOGONAL MULTIPLE ACCESS

3.1 Extended Hybrid Carrier Frequency Division Multiple Access

In this section,we propose a novel extended hybrid carrier multiple access scheme for the uplink.The proposed scheme combines the energy spread concept of hybrid carrier with the model of frequency division multiple access and is referred to as the extended hybrid carrier frequency division multiple access(EHCFDMA).Since the enhanced capability of energy distribution design,the proposed scheme provides superior interference suppression performance compared to the HC-FDMA scheme.Simultaneously,the compatible framework renders it suitable for the smooth evolution of the hybrid carrier multiple access system.The block diagram of the proposed scheme is depicted in Figure 1.

Consider a multiple access system withVusers.At the transmitter,as shown in Figure 1(a),assuming thatNvsubcarriers can be assigned to thevth user.Then,for each data block,the sequencesvof lengthNvobtained by baseband mapping can be regarded as a signal in the transform domain.Transform it to the frequency domain by EWFRFT as

whereTl[·]=（Tl）[·]is the base operator of the transform,which can be chosen as a cyclic shift operator,andΩ=denotes the weighting coefficient vector,which can be generated by the following method.

The frequency domain sequence of lengthNvis mapped to the subcarrier assigned to the userv,and the subcarriers occupied by other users are filled with zeros.The signal is transformed to the time domain expressed as

whereEvis the extended weighted fractional Fourier transform matrix.Let,0≤k′≤Nv−1 denote the subcarrier index allocated to userv,then the subcarrier mapping matrixΘvmeets

The sequence is processed by cyclic prefix insertion and sent through a single antenna.Assume that the signals fromVuser terminals are transmitted through separate channels to reach the base station.After removing the cyclic prefix and other operations,the baseband signal can be expressed as

whereHvdenotes the time domain channel matrix of the uservandzis additive white Gaussian noise.By transforming the received signal into the frequency domain and performing subcarrier demapping along with the corresponding inverse EWFRFT,the transform domain signal of thevth user can be expressed as

Due to the channel time-frequency dispersion,the orthogonality between signals of different users is destroyed at the base station,causing multi-user interference.Jointly considering the received signals of multiuser,lets=h（s0,s1,...,sV−1）denote the equivalent transmitted signal,whereh(a0,a1,...,ak)=,then we have

where the second and third rows of the equation denote subcarrier interference and multi-user interference for thetsymbol of thevth user,respectively.τn,mdenotes thenth row andmth column element of matrixQ=where=DΛRH,andρε,ι=+ι.Then the theoretical BER underJ-QAM modulation can be expressed as

In particular,for the frequency-selective channels,the equivalent channel matrix satisfies

Therefore,the equivalent signal-to-noise ratio can be expressed as

It can be found that

At this point,according to the property ofQfunction,the following Jensen inequality holds and satisfies the condition of taking the minimum value.

That is,the BER of the proposed scheme can be expressed as

According to the hybrid carrier fusion mechanism,the equivalent signal-to-noise ratio of the conventional HC-FDMA scheme is the weighted superposition of SC components and MC components,with the power allocation scheme controlled by the transform order.However,due to the constraints of the four-component structure,it is challenging to satisfy the condition shown in Eq.(25),thereby revealing defects in its BER performance.In contrast,the proposed scheme exhibits superior time-frequency energy distribution design capability,enabling improved compensation for channel interference and multiple access interference,and thus displaying superior performance.

3.2 Extended Hybrid Carrier Orthogonal Power Layered Multiple Access

In this subsection,we design a novel orthogonal multiple access scheme for the downlink,aimed at the enhancement of HC-OMA system performance.Unlike existing multiple access schemes,each user can occupy the entire time-frequency resources in the proposed scheme.The symbols of different users superimpose on the time-frequency plane in the form of power layered multiplexing and maintain transform domain orthogonality.Hence,we call it the extended hybrid carrier orthogonal power layered multiplex access(EHC-OPLMA)scheme.Due to the uniform signal distribution,the proposed scheme exhibits superior anti-fading performance,further improving the reliability of the multiple access scheme.Figure 2.illustrates the basic structure of the proposed scheme.At the base station,the extended hybrid carrier modulation is performed on the transform domain signal after symbol mapping,which can be expressed as

Figure 2. The model of the EHC-OPLMA scheme.

whereEdenotes the extended hybrid carrier modulation matrix of sizeL×L.In this system,each user can utilize all the available time-frequency resources,thus gaining better channel diversity.At the receiver,since multiplexed power layers are orthogonal in the transform domain,the signal of different users can be separated and extracted.For thevth user,we can obtain

whereHvis the channel matrix of uservands=.Due to the even energy spread,different symbol mapping methods have little effect on the EHC-OPLMA downlink,so we assume that a continuous symbol mapping scheme is adopted.The extended hybrid carrier demodulation is conducted as

The third and fourth terms of the equation represent the multipath interference and multi-user interference after compensation,respectively.We defineas the residual interference of thetth symbol of userv.Then,for the proposed scheme,the total residual interference can be expressed as

The overall residual interference in the system is related to the channel conditions each user experiences,independent of the signal processing method.Consequently,the EHC-OPLMA scheme alters only the distribution of residual interference,without introducing additional multipath or multiple access interference.The proposed scheme implements uniform energy spread through extended hybrid carrier modulation.And the residual interference of each symbol can be shared by the entire time-frequency resource,thereby exhibiting stronger residual interference suppression capability,a prominent advantage of the proposed scheme.For thevth user,the equivalent signalto-noise ratio can be expressed as

Owing to the energy distribution design,the proposed scheme achieves more uniform residual interference.Consequently,for each user,the equivalent signal-to-noise ratio of different symbols is identical over the single-selective channels,meeting the optimal BER condition under Jensen inequality,and the results are close in the case of the doubly-selective channels.Specifically,in the frequency-selective channels,we have

Therefore,the BER satisfies

The proposed scheme constructs a power layered multiplexing model through extended hybrid carrier modulation and achieves higher gain as each user fully utilizes the available time-frequency resources.Compared to the HC-OMA system,the proposed scheme exhibits a notable performance improvement over both single-selective channels and doubly-selective channels.

IV.EXTENDED HYBRID CARRIER NONORTHOGONAL MULTIPLE ACCESS

In this section,we investigate the non-orthogonal multiple access technology of the extended hybrid carrier system,proposing an EHC-SCMA scheme based on transform domain signal processing.The proposed scheme combines the carrier fusion advantage of the extended hybrid carrier signal with the massive connectivity capability of non-orthogonal multiple access,which can better meet the requirements of the nextgeneration communication systems.

4.1 In Downlink

Consider a downlink scenario withVusers.At the base station,the signal of different users is processed in the transform domain with coding and superposition,which can be expressed as

wherevec(·) denotes the vectorization operator,and ⊗ denotes the Kronecker product.Lets=vec(S)=,then we havex=PM,N(IM⊗E)sand the permutation matrix can be expressed as

After EHC modulation,the CP is inserted and RF processing is conducted.Figure 3.depicts the model of the proposed scheme,whereMandNare generally chosen as an integer multiple ofK.In the EHC-SCMA scheme,the energy spread is feasible both between codewords and within codewords.WhenM=1,the energy of each codeword is extended equally over the entire data block containingMN/Kcodewords,achieving a uniform distribution of symbol energy.In the following analysis,we will use this case,and the results will be easily extended to other conditions.

Figure 3. The model of EHC-SCMA in downlink.

At the receiver,as shown in Figure 4,after removing CP and other operations,the signal is first processed by the extended hybrid carrier demodulation,followed by a two-stage detector combining transform domain signal detection and SCMA decoding to obtain the estimated signal.For thevth user,the transform domain equivalent baseband signal can be expressed as

Figure 4. The block diagram of the receiver.

Since the extended hybrid carrier modulation matrix is a circulant matrix,it can be decomposed intoE=FHΣFby the Fourier transform matrix of sizeL×L,whereΣ=diag[ϖ0,ϖ1,...,ϖN−1] andωk=.Thenith path of the equivalent channel matrix can be expressed as

In this way,we obtain the transform domain inputoutput relation of the signal.It can be found that the equivalent channel matrix has good sparsity and is suitable for low-complexity detection algorithms.Finally,the estimated signal is obtained by the SCMA detector separately.The proposed scheme achieves the symbol extension and superposition of multi-user through extended hybrid carrier modulation.The available time-frequency resources can be occupied by the symbol of each user,thereby obtaining higher diversity.At the receiver,the user processes and detects the received signals in the transform domain to cope with the delay and Doppler spread of the doublyselective channels.Compared to the existing SCMA scheme,due to the uniform energy distribution design of the proposed scheme,the channel interference of each codeword is shared by all codewords,which effectively reduces the impact of residual interference on detection,thereby enhancing the reliability of the multiple access scheme.

4.2 In Uplink

In this subsection,we introduce the uplink of the proposed EHC-SCMA scheme,as shown in Figure 5.For thevth user,the SCMA is conducted and the signal is converted to the time domain by codeword mapping and extended hybrid carrier modulation.The add/remove CP and RF processing modules are omitted from the block diagram for simplicity.The transmit signal for thevth user can be expressed as

Figure 5. Block diagram of the EHC-SCMA in uplink.

Figure 6. The model of EHC-SCMA in uplink.

At the receiver,the signal after transform domain signal processing can be expressed as

whereΓv=eV(v)⊗IL,andHvcan be expressed as

After iteration,the final probability of each symbol is calculated,and the symbol for which the posterior probability value takes the maximum value is selected as the estimation result expressed as

The proposed EHC-SCMA scheme can be viewed as a fusion of the extended hybrid carrier power layered multiplexing and the concept of multi-user superposition transmission.Through the transform domain signal processing,the symbol energy superimposition is extended to multiple codewords,hence exhibiting a stronger ability to suppress residual interference.The proposed scheme shows the advantages of the superior energy distribution design and the high spectral efficiency,which can achieve robust BER performance under multi-user scenarios.

V.SIMULATION RESULTS

In this section,simulation results are presented to illustrate the advantages of the proposed scheme.In the simulation,a carrier frequency of 5.9 GHz,subcarrier spacing of 15 kHZ,and the assumption of perfect channel state information at the receiver are used.Performance for both uplink and downlink will be verified.

We first evaluated the EHC-OMA system.In the simulation,it is assumed that there are 4 users with equally allocated resources in the system.The signal of each user experiences independent channels and the MMSE detector is employed at the receiver.Figure 7.presents the theoretical and simulation results of the bit error rate of the EHC-OMA uplink over the frequency-selective channels.The QPSK signal is adopted without considering the coding gain.ITU Pedestrian-B channel mode is used to generate the frequency-selective channels,and the relative delay and the average power are [0,200,800,1200,2300,3700]ns and[0,-0.9,-4.9,-8.0,-7.8,-23.9]dB respectively.It can be seen that the theoretical curves overlap with the simulation results,and the proposed scheme can achieve optimal bit error rate performance under the same subcarrier mapping scheme,which is consistent with the results of the theoretical analysis.

Figure 7. BER performance of EHC-OMA system in uplink over the frequency-selective channels.

For the doubly-selective channels,we consider the EVA model with the multipath delay[0,30,150,310,370,710,1090,1730,2510]ns and the average power[0,-1.5,-1.4,-3.6,-0.6,-9.1,-7.0,-12.0,-16.9]dB.The normalized Doppler shift FDT is used to describe the time-varying properties.Figure 8.presents the BER performance of the uplink when FDT is 0.001.The HC-OMA schemes with different parameters are provided for comparison.Simulation results show that the proposed scheme achieves significant performance advantages.Compared to the optimal parameter HC scheme,SC-FDMA,or OFDMA scheme,it has a performance gain of no less than 1.5dB,2dB,and 4dB at the BER of 10−3respectively.Figure 9.gives the BER comparison of the EHC-OMA downlink,where FDT=0.002.Compared to the HC scheme,due to the implementation of a completely uniform symbol energy distribution design,the performance advantage of the proposed scheme is more pronounced.

Figure 8. BER performance of EHC-OMA system in uplink over the doubly-selective channels.

Figure 9. BER performance of EHC-OMA system in downlink over the doubly-selective channels.

Figure 10.to Figure 12.evaluate the EHC-NOMA scheme.We consider an EHC-SCMA system containing 6 users with the overloading factorλ=150%.The SCMA codebook proposed in [32] is chosen for the simulation.The factor matrix is shown in Eq.(58),and the mapping matrix can be obtained from.

Figure 10. BER performance of EHC-SCMA system in uplink over different FDT.

Figure 10 examines the performance of the uplink EHC-SCMA system under different FDT,using a transform domain message passing algorithm for detection,demonstrating that the proposed scheme outperforms the SCMA scheme in terms of bit error rate under various Doppler conditions.Figure 11 presents the simulation results for the downlink and offers a comparison with the HC-SCMA scheme.A two-stage detector with MMSE and MPA in the transform domain is adopted.Notably,HC-SCMA degrades to the SCMA scheme whenα=0 and to the MCSCMA scheme whenα=1.Compared to the existing scheme,our proposed scheme,due to exhibit stronger channel distortion compensation capability,showcases superior BER performance and reliability benefits,making it well-suited for supporting massive connectivity in high-mobility scenarios.Lastly,we present the relationship between the bit error rate and the number of iterations.As illustrated in Figure 12,the BER decreases with each iteration,stabilizing gradually.We observed that typically,five iterations are sufficient to achieve stable BER performance.The proposed scheme achieves significant performance gains at the cost of a minor increase in complexity.

Figure 11. BER performance of EHC-SCMA system in downlink over the doubly-selective channels.

Figure 12. BER performance of EHC-SCMA system in downlink versus the iterations.

Simulation results show that compared with the hybrid carrier multiple access scheme,the proposed scheme effectively improves the bit error rate performance of the system,which is an advantage brought about by its unique energy distribution design and power layered multiplexing structure.In addition,unlike the hybrid carrier multiple access scheme,which relies on parameter selection to obtain performance advantages,the proposed scheme has better channel adaptability.It can achieve robust bit error rate performance without acquiring channel state information at the transmitter,demonstrating its feasibility and advantage in achieving multiple access and reliable communication under complex channel conditions.

VI.CONCLUSION

This paper concerns the multiple access issue and studies a novel multiple access scheme for the extended hybrid carrier system,proposing corresponding OMA schemes for uplink and downlink respectively.The proposed scheme fully utilizes the timefrequency energy distribution design capability of the EHC system to average out residual interference and improves the BER performance compared to the HC scheme at the cost of a slight increase in computational complexity.On this basis,regarding the demand for massive connectivity,the EHC-SCMA scheme is proposed.The distribution of the codewords in the transform domain is studied,and a message passing algorithm detector is designed for the uplink.The proposed scheme combines EHC modulation and SCMA,possessing both excellent bit error rate performance and superior capability of multiple access,which can better meet the complex scenarios and requirements of the next-generation communication system.Future research will focus on low-complexity channel estimation algorithms,and extending the proposed scheme to the multi-antenna scenario is considered.

ACKNOWLEDGEMENT

This work was supported in part by the National Natural Science Foundation of China under Grant U23A20278,in part by the National Natural Science Foundation of China under Grant 62171151,in part by the Fundamental Research Funds for the Central Universities under Grant HIT.OCEF.2021012.