Joint Optimization Scheme Based on Beam Selection and Interference Cancellation in Lens Millimeter Wave NOMA Systems

Lei Xu,Jing Cai,Jing Chang,Hongyu Fang,Xiaohui Li

School of Electronics and Information Engineering,Anhui University,Hefei 230601,China

Abstract:Non-orthogonal multiple access(NOMA)has been integrated in millimeter-wave(mmWave)Massive MIMO systems to further enhance the spectrum efficiency,but NOMA has not been fully considered in lens mmWave systems.The fusion of these two technologies requires the joint design of beam selection and interference cancellation.In addition,when users follow the spatial cluster distribution,although the user clustering schemes based on K-means algorithm have been applied,the influence of the virtual and actual cluster center users on achievable sum rate has not been differentiated and analyzed in detail.To solve the above problems,a joint optimization scheme is proposed to maximize the achievable sum rate.The optimization problem is NP-hard,which is solved by using the divide-and-conquer approach.Concretely,based on the signal power loss analysis of directional deviation,a beam selection algorithm is designed for inter-cluster interference cancellation based on the Kmeans algorithm.Further for intra-cluster interference cancellation,a power allocation algorithm based on the bisection method is designed to guarantee the fairness of users in each cluster.The simulation results show that the proposed scheme offers a significant performance improvement in terms of both achievable sum rate and energy efficiency,and it is suitable for the large-scale user scenario due to its low complexity.

Keywords:lens mmWave systems;NOMA;user clustering;beam selection;power allocation

I.INTRODUCTION

The mmWave communication is one of the main key technologies for the fifth generation(5G)wireless communication[1].The frequency range of mmWave is 30GHz-300GHz,and its abundant frequency resources can be used to support ultra-high data transmission rates.The smaller wavelength of the mmWave can integrate a large number of antennas in the same physical space,and the radiation direction of the transmitted signal can be modulated through a specific antenna configuration to provide more multiplexing gain and beamforming gain[2].The mmWave large-scale antenna system can achieve a quantity-level increase in system capacity,but the use of a large number of radio frequency chains in the system will cause higher hardware costs and energy consumption.

In order to solve this problem,there have been many studies to reduce the hardware complexity and energy consumption.A hybrid beamforming by splitting beams at baseband and radio frequency is designed to reduce the number of required radio frequency(RF)chains,thereby reducing hardware complexity and energy consumption[3,4].The concept of mmWave MIMO with the lens antenna array is proposed,which can significantly reduce the number of required RF chains[5].By using the lens antenna array,which plays the role of discrete Fourier transform,the traditional spatial channel can be converted into a beamspace channel to capture the channel sparsity at mmWave frequencies[6].In[7],a smallnumber beams are selected according to the sparse nature of beam domain channels,which greatly reduces the number of required RF chains for mmWave massive MIMO systems.Together with the sparse nature of mmWave channels,both hybrid beamforming and beamspace MIMO can implement mmWave beamforming with reduced number of RF chains.This is important to support massive connectivity because the degree of freedom available to separate the signals of different users is bounded by the number of RF chains.Power domain NOMA can support multiple users on the same time-frequency resource by realizing multiplexing in the power domain[8,9].The method is to perform overlay coding on the transmitter and use successive interference cancellation(SIC)on the receiver,which is essentially different from the traditional mmWave system that only serves one user on the same time and frequency resources.Compared with the orthogonal multiple access(OMA),the power domain NOMA can significantly improve the spectral efficiency[10].Therefore,it has been regarded as a key technology to improve spectrum efficiency and high-density connection in 5G[11].When the mmWave system employs fewer antennas,its beam width increases,which provides a necessary prerequisite for the combination of mmWave communication and NOMA technology.In[12,13],the combination of lens mmWave system and power domain NOMA technology have been studied,and the preliminary joint designs of beam selection and power allocation are carried out.However,they do not consider the influence of the cluster center user on the beam selection algorithm and system performance when the user obeys the spatial cluster distribution in a single cell.The K-means algorithm,which performs clustering through a continuous iterative calculation process,has been used for clustering in high-density communication scenarios because of its low computational complexity and fast processing speed.In the massive MIMO-NOMA scenario,[14,15]all adopt the Kmeans algorithm to cluster users,and perform a hybrid precoding design based on the user with the largest channel gain in each cluster,and optimize power distribution.However,their optimization methods cannot be applied to the lens mmWave-NOMA system directly,because these schemes are all based on the large-scale array antennas.

In summary,the introduction of power domain NOMA into the mmWave system with the lens antenna array can further improve the system achievable sum rate and energy efficiency,but a joint design of beam selection and interference cancellation is required.In particular,when users follow the spatial cluster distribution,their random distribution characteristics bring new challenges.In order to improve the achievable sum rate of the system,reducing the interference of inter-cluster and intra-cluster is an effective mean.The main contributions of this paper can be summarized as follows: 1)We study the fusion of NOMA and lens mmWave systems,and the joint design of beam selection and interference cancellation.2)The beam selection algorithm based on K-means and the digital precoding is designed to reduce intercluster interference.In addition,the influence of the virtual and actual cluster center users on achievable sum rate is differentiated and analyzed in detail.3)The power allocation algorithm with low complexity is designed to guarantee the fairness of users in each cluster and to reduce intra-cluster interference.

The remainder of this paper is organized as follows.The lens mmWave-NOMA system model is presented in Section II.Inter-cluster interference cancellation and Intra-cluster interference cancellation are investigated separately in Section III and Section IV.The system simulation results are discussed in Section V.Finally,the conclusion is presented in Section VI.

II.SYSTEM MODEL

Considering the downlink communication scenario of the lens mmWave-NOMA system,the system model of which is shown in Figure 1.The base station(BS)is equipped with a lens antenna array withNantennas andNRFRF chains,beams are used to simultaneously serveKsingle-antenna users divided intoMclusters.The variables are related as followsM=NRF ＜N≤K.

Figure 1.Lens mmWave-NOMA system model.

Figure 2.Trend of system achievable sum rate with the SNR.

Figure 3.The system achievable sum rate against SNR.

Figure 4.Energy efficiency with respect to the number of users,SNR=30dB.

2.1 System Beamspace Channel

To capture the scattering property of mmWave channels,the saleh-valenzuela(S-V)channel model has been widely used,which has been clarified in the paper and annotated with reference[16].Accordingly,the channel vector for thek-th userhkis given by:

For mmWave channels,the non-line-of-sight(NLoS)path loss is much greater than the line-ofsight(LoS)path,so when the LoS path exists in mmWave transmission,the effect of the NLoS path is negligible.Therefore,the mmWave channel model of userkcan be simplified as

2.2 System Achievable Sum Rate

Users in them-th cluster perform SIC in descending order of equivalent channel gain,and the received signal for thek-th user in them-th cluster can be expressed as

Finally,the system achievable sum rate can be ex-pressed as

In general,there are two main methods can be used to improve the lens mmWave-NOMA system performance.One is used to maximize the achievable sum rate.However,this method may cause an unbearable rate loss to weak users and make the users with low channel gains cannot work normally,because the BS tends to allocate more power to users with high channel gains.The other one is used to guarantee user fairness.But this method may lead to the system performance loss of achievable sum rate[15].In order to achieve a trade-off between achievable sum data rate and user fairness,it is considered to maximize the achievable sum rate of the system while guaranteeing the minimum rate requirement for all users.The original optimization problem can be expressed as

The optimization problem is non-convex.The clustering and power allocation are entangled with each other,which makes the optimization problem more infeasible to be solved directly.So the two-stage optimization method is proposed.In which,the beam selection algorithm based on K-means and the digital precoding vectors are firstly designed to cancel intercluster interference,and then the power allocation algorithm with low complexity is designed to cancel intra-cluster interference and guarantee user fairness.

III.INTER-CLUSTERINTERFERENCE CANCELLATION

Assuming that users in each cluster can be served by one beam.Firstly,the cluster center user is determined by the K-means algorithm.Then,the optimal beam selection is performed according to the beamspace channel coefficients of the cluster center user in one cluster.Finally,the digital precoding is designed according to the beamspace channel coefficients of the cluster center user.

3.1 Beam Selection Algorithm Based on the Kmeans

3.1.1 Analysis of Signal Power Loss in Direction Deviation

The power loss caused by the deviation between the space direction and the beam direction from the BS to the cluster center user is given by the Lemma 1.

Lemma 1.When the number of antennas is N,and the number of users in the m-th cluster is nm,the signal power loss ϖ in the intra-cluster can be expressed as

Among them,step(a)is Taylor series expansion.Step(b)is obtained by ignoring the higher order terms of Taylor series,which is reasonable because the range of the mmWave cluster is small.Becauseis much smaller than 1,so ignore it in step(c).The overall power loss in a cluster is the sum of the power loss of all users in a cluster,which is expressed by(13),so the Lemma 1 is proved.

3.1.2 Confirmation of cluster center users

3.1.3 Beam selection

3.2 Digital Precoding

Algorithm 1.Beam selection algorithm.Input: beamspace channel ˆH,cluster-center usersµ1,···,µm,set Z ={1,···,N}.1: for i=1 →M do 2: Selects desired beam of userµi in the center of the i-th cluster: nµi =arg max 1＜n≤N■｜｜｜ˆhn,µi｜｜｜■.3: Selecting beam as nµi : Φ=Z ∩{nµi}.4: Removing the selected beam form the set Z :Z =Z{nµi}.5: end for Output: Beamspace channel after selection ˜H:˜H= ˆH(n,:)n∈Φ.

Algorit hm 2.Power allocation algorithm in m-th cluster.Input: beamspace channel ˜hm,k,k ={1,···,nm},the user precoding denotes wm.1: Upper bound τ: τ =‖‖‖˜hm,1wm‖‖‖2 2 Pm/σ2.2: Define the maximum and minimum value of η :ηmin =0,ηmax =τ ,and η =(ηmin+ηmax)/2.3: while ηmax-ηmin ＜ε do 4: if f(η)＜1 then 5:Set ηmin =η 6: else 7:Set ηmax =η 8: end if 9: end while Obtain the value of η.Output: user power allocation factors ζm,k in m-th cluster,k ={1,···,nm}.

IV.INTRA-CLUSTERINTERFERENCE CANCELLATION

Through inter-cluster interference cancellation,the desired beam and the digital precoding vector of each cluster are determined.Moreover,the order of the equivalent channel gains of users in each cluster,which is the optimal decoding order to perform SIC is determined,as shown in condition(6).In order to effectively cancel the interference between users in the cluster,the power allocation needs to be optimized.Considering the case of equal power among different clusters,the original optimization problem is decomposed into independent sub-problems of power allocation inMclusters.Then the original optimization problem in equation(12)is transformed into the problem of maximizing the minimum achievable rate in the cluster:

where the constraintC1is non-linear and is still difficult to solve.Rm,k=Rminis assumed,which can satisfy the constraintC1and the constraintC2at the same time.Then we can derive the user power allocation factorζm,kaccording to the power allocation factor formula[15]of each user in them-th cluster,that is

Algorithm 2 based on bisection method always converges.Because of that,the calculation process is simple,the program is easy to implement,the traditional bisection method is very effective and the roots always can be found in a given range.In addition,if the given range is large enough,i.e.there are enough dichotomies in the interval,the error can be small enough.

V.SIMULATION RESULTS AND ANALYSIS

BS equipped withN= 32 antennas andNRF= 2 RF chains,andK= 6 users are considered.The beamspace channel,between the BS and userk,has one LoS component with path gainβk ～CN(0,1).The spatial directionsθkfollow uniform distribution withinThe clusters are randomly distributed on a circle with radiusR= 50mcentered on the BS.The transmit Signal-to-Noise-Ratio(SNR)is defined as.

The change trend of system achievable sum rate with the SNR is shown in Figure 2.The radiusrof the cluster is set to 5m,3mand 1mrespectively.It can be seen from Figure 2 that,as the radius of the cluster decreases,the system achievable sum rate curves of the proposed NOMA-virtual user scheme and the proposed NOMA-actual user scheme are closer to coincidence.This is because of that,the virtual user at the cluster center is directly obtained when the K-means algorithm converges,while the actual user is the user closest to the virtual user at the cluster center.The smaller the radius size is,the closer they are together.When the determination of the cluster center user is analyzed,the relationship of the signal power loss isϖvirtual ≥ϖactual,so the performance of the actual cluster center user is better.

In the following simulation,the following two comparison schemes are considered,(1)K-means: OMA.The beam selection scheme is based on K-means,and users in the same cluster are allocated with orthogonal frequency resources.(2)Cluster-Head: NOMA[18].It selectsMusers with the largest channel gains as the cluster-head of each cluster,which can be used for the optimal beam selection.

Whenr= 5m,the achievable sum rate changes with the SNR as shown in Figure 3.It can be seen from Figure 3 that the proposed optimization scheme can significantly improve the achievable sum rate.In the NOMA-virtual scheme,the selected beam direction may slightly deviate from the actual direction of the cluster center.In the cluster-head beam selection scheme[18],the cluster heads are determined based on the user’s channel gain.However,the influence of the correlation between user channels on the beam selection is ignored,so inter-cluster interference cannot be effectively suppressed.In addition,the proposed scheme also outperforms MIMO-OMA since NOMA can achieve higher spectrum efficiency than that of OMA.The proposed NOMA-actual user scheme analyzes the signal power loss of the beam direction deviation,and selects the desired beam.The simulation verifies that the proposed scheme can improve the achievable sum rate,when the users obey the spatial cluster distribution.Particularly,the system achievable sum rate can be 10 bps/Hz and 3 bps/Hz higher than the Cluster-Head:NOMA and the NOMA-virtual user scheme,respectively.

When SNR=30dB,the performance comparison in terms of energy efficiency against the number of users is shown in Figure 4.The energy efficiencyEEis defined as the ratio between the system achievable sum rateRsumand the total power consumption[19],i.e.,wherePtotalis the maximum transmitted power,PRFis the power consumed by each RF chain,PSWis the power consumption of switch,andPBBis the baseband power consumption.Particularly,we adopt the the typical valuesPRF= 300mW,PSW= 5mW,PBB= 200mW[20].It can be seen from Figure 4 that as the number of users increases,the energy efficiency of the proposed scheme is higher than that of the other two comparative schemes.The energy efficiency of the proposed NOMA-actual user scheme is also significantly better than that of the proposed NOMA-virtual user scheme,mainly because of its advantages in system achievable sum rate.When multiple users in the NOMA service cluster are applied to the lens mmWave system,the proposed scheme can effectively reduce the power consumption required by the system.

VI.CONCLUSION

A joint optimization scheme including beam selection and interference cancellation is proposed in this paper.By analyzing the random characteristics of users obeying the cluster distribution,the scheme is derived,which is divided into two stages: inter-cluster interference cancellation and intra-cluster interference cancellation.In the inter-cluster interference cancellation stage,a beam selection algorithm based on Kmeans is designed,considering the signal power loss analysis for directional deviation.In the intra-cluster interference cancellation stage,based on the results of the beam selection algorithm,a power allocation method is designed,which can guarantee the fairness of users in the cluster and the optimal decoding order.The simulation results verify that the proposed scheme achieves better performance in terms of the system achievable sum rate and energy efficiency,compared with the existing schemes.

ACKNOWLEDGEMENT

This work was supported by the National Natural Science Foundation of China(62001001).