Xianling Wang,Haijun Zhang,Yitong Liu,Chen Zhu,Yue Tian
1 Fujian Key Laboratory of Communication Network and Information Processing,Xiamen University of Technology,Xiamen 361024,China
2 University of Science and Technology Beijing,Beijing 100083,China
3 Beijing University of Posts and Telecommunications,Beijing 100876,China
Abstract: In next generation networks,mobility management will be a critical issue due to dense base station (BS) deployment,for which user and control plane split architecture provides a promising solution.Jointly designing such architecture with nonorthogonal transmission brings in more flexibility to further improve system efficiency.This paper proposes a non-orthogonal transmission design for user and control plane split architecture.In this design,user equipments (UEs) will select the BS providing the strongest received signal to associate its data channel,but constantly connect its control channel to the nearest macro-cell BS (MBS).Upon non-orthogonal transmission,an MBS can multiplex data traffics and control signals on the same resource.Stochastic geometry based analysis is carried out to investigate outage probability,which extends its regular definition by jointly considering data and control channels,and then mobility-aware outage rate.Numerical results show that: 1) The proposed split architecture alleviates the increase in handover rate for ultra dense networking,compared with conventional architecture.2)Non-orthogonal transmission outperforms traditional orthogonal transmission in the split architecture,because it is capable of accommodating more control channels.3)By carefully adjusting power levels,minimum outage probabilities can be reached for macrocell UEs in the proposed design.
Keywords: heterogeneous networks; mobility management; non-orthogonal transmission; split architecture;stochastic geometry
In the fifth generation (5G) communication system and beyond,a tremendous performance improvement including enhanced capacity,massive connections,and low latency communications,is envisioned to satisfy the unprecedentedly high demands of various kinds of user equipments (UEs).To achieve these goals,network densification is considered as a major path,which is realized by densely overlaying traditional macro-cell base stations (MBSs) by small-cell base stations (SBSs)[1].The benefits of such ultra dense heterogeneous cellular network(HCN)lie in received signal power enhancement and reduced traffic load at base stations (BSs).The former is due to shortened link distance and higher possibility of lineof-sight transmission,while the latter is introduced by offloading traffics from MBSs to SBSs.However,network densification also brings in critical issues such as overburdened backhaul and frequent handover problem.For this matter,user and control plane split architecture is regarded as a promising solution[2].The split architecture is based on network function virtualization[3].Compared with conventional architecture,in which a UE always receives data traffic and control signal from the same BS,the split architecture allows associating the data and control channels of the same UE with different BSs,and thus enables a more flexible mobility management to solve the severe handover problem.
Another key technology to pave way for 5G and beyond is non-orthogonal transmission[4].As a candidate technology to boost connectivity ability,powerdomain non-orthogonal multiple access (NOMA)has exhibited a very common realization for nonorthogonal transmission,in which the signals of different users are multiplexed on the same radio resource block.This concept contradicts with traditional orthogonal utilization of resource blocks such as orthogonal multiple access in Long Term Evolution (LTE).Due to its implementation flexibility,non-orthogonal transmission has been applied in various scenarios and shown its great capability[5,6].Given the potential advantages,incorporating non-orthogonal transmission into user and control plane split architecture will be of great significance and investigations on key performance metrics are desirable.
1.1 Related Works and Motivation
Recently,in the backdrop of ultra dense networking,the user and control plane split architecture has been studied extensively.In[7],the authors modeled control overhead and handover delay cost to investigate the system performance of a split architecture based HCN.Their work demonstrated that the performance degradation caused by frequent handover can be alleviated by aggregating most control signals at the sparser MBS-tier,especially in high mobility scenario.The authors in [8]introduced aerial base stations to manage control signal transmission from the sky.Their work generalized the study in[7]into a 3D network model by taking BSs’ height into consideration.In[9],the authors proposed an analytical framework to jointly study the signal-to-interference-plusnoise ratio (SINR) of data and control channels.The coverage degradation of the split architecture based system was shown under the framework.
On the other hand,non-orthogonal transmission has received much attention during the past few years.A substantial amount of works can be found in the context of its most important implementation as a multiple access technology,i.e.,NOMA,as well as joint design with emerging advanced network architectures.In[10]and[11],NOMA was applied in wireless powered system and ambient backscatter system,respectively,and the system performance was evaluated while taking hardware impairments into account.In [12],the authors focused on energy efficient resource management in HCN with energy harvesting technology and NOMA.A low-complexity subchannel assignment and power optimization algorithm was proposed using Lagrangian duality.Given the rapid development of applying cutting-edge machine learning approaches in advanced communication networks[13,14],much progress in solving NOMA related resource allocation problem through machine learning based algorithms can also be found in [15]and [16].In [17],the advantage of non-orthogonal transmission was inspected in an aerial base station assisted network,with nonorthogonal transmission and non-coherent joint transmission incorporated in the system.
Inspired by the great potentials of non-orthogonal transmission and split architecture,we propose a joint design incorporating these technologies in a two-tier HCN.Different from most works which focus on protocol design in such architecture,we aim to evaluate the system from the perspective of outage and transmission rate,and the performance improvement brought in by non-orthogonal transmission.Part of the work has been published in[18],and the extensions in this work are as follows: 1) The system performance of conventional architecture is also investigated as a benchmark scheme.2)Handover effect in the aspects of occurrence rate and delay cost is taken into consideration.3) Enriched results on the impacts of system parameters are provided in this paper.
1.2 Contributions
The main contributions of the paper are summarized as follows.
1) Design of the Non-Orthogonal Transmission Enabled Split Architecture:We propose a nonorthogonal transmission design for the split architecture.To be specific,under this architecture,SBSs are focused on data traffic transmissions for their associated small-cell UEs(SUEs),while MBSs transmit not only data traffics to their associated macro-cell UEs(MUEs) but also control signals to all surrounding MUEs and SUEs.The data traffics and control signals from an MBS will be superimposed on the same resource block to improve efficiency,and they are separated by different power levels.To keep consistent with general communication procedure,higher power level is assigned to the control signal so that it can be decoded prior to the data traffic.
2) Modeling and Analysis of the Non-Orthogonal Transmission Enabled Split Architecture:We develop a general analytical framework to study the system performance of the proposed non-orthogonal transmission enabled split architecture in a two-tier HCN.In particular,we build up a large-scale random network model and apply stochastic geometry approaches to capture the distributions of distances.Then,we extend the regular outage probability definition by jointly considering the data and control channels to characterize the correlation between them.Taking control overhead,handover rate and delay cost into consideration,we derive the expressions of user mobility-aware outage rate under three scenarios,i.e.,conventional architecture,split architecture with orthogonal transmission,and split architecture with non-orthogonal transmission.
3)Comparison and System Design Guidelines:We compare the proposed non-orthogonal transmission split architecture design with the baseline conventional architecture,as well as the orthogonal transmission based split architecture.We also investigate the impacts of key system parameters,including BS density,target spectral efficiency (SE),bandwidth allocation,and power allocation coefficient.Our study shows that,compared with conventional architecture,the split architecture can be beneficial in the aspect of transmission rate by reducing the handover delay cost.Moreover,for split architecture in very dense SBS deployment scenarios,normal system functioning can still be sustained by non-orthogonal transmission,but system failure will easily occur if orthogonal transmission is applied.Besides,a minimum outage probability for MUEs can be reached in non-orthogonal transmission based split architecture by carefully adjusting the power allocation coefficient.
The rest of the paper is organized as follows.In Section II,we describe the considered non-orthogonal transmission enabled split architecture and other system setup.In Section III,we provide the derivation of outage probability and introduce the metric of user mobility-aware outage rate.Section IV verifies our analytical expressions and discusses the observations in numerical results.Finally,conclusions are drawn in Section V.
2.1 Network Model
We consider a downlink two-tier single-antenna HCN including MBSs,SBSs,and UEs randomly distributed in the infinite 2D plane.The BS set is denoted by Φk={zk,i,i ∈N+},wherekequals 1 and 2 for the MBS-tier and the SBS-tier,respectively.We will frequently usekto differentiate these two tiers hereafter.The UE set is denoted by Φ0.To facilitate analysis,we arbitrarily choose a UE in Φ0as the typical UE denoted by u and set it the origin of the coordinate.We assume that MBSs,SBSs,and UEs are distributed according to three independent Poisson point processes(PPPs) and the densities areλ1,λ2andλ0,respectively.With a slight abuse of notation,we also use zk,ito represent the coordinate of a BS.The transmit power of zk,iisPk.
For simplicity,we use zkto represent the nearest BS from thek-th tier to u.LetZk,iandRkbe the distances from zk,iand zkto u.We assume that radio signal power attenuation follows power-law path-loss in large-scale and frequency non-selective Rayleigh fading in small-scale.In specific,the received signal
power at u from zk,iis,whereαk >2 is the path-loss exponent,andis the unit-mean exponentially distributed channel power gain.For control channel and data channel,can be replaced byhk,iandgk,i,respectively.It should be noted that,if the control channel and data channel are beared on orthogonal resource blocks,hk,iandgk,iwill be independent and identically distributed whether they are describing the same communication link or not.Taking conventional architecture as an example,which will be detailed in next subsection,for the control signal and data traffic transmitted from the same BS to u,they will experience the same path-loss attenuation but independent small-scale channel power gains.The illustration of distances and small-scale fadings can be found in figure 1.
2.2 User and Control Plane Split Architecture
We describe the considered user and control plane split architecture in this subsection,as well as the baseline conventional architecture.In practical systems,data channel and control channel are two essential logical channels to maintain normal system functions,such as physical downlink shared channel (PDSCH) and physical downlink control channel (PDCCH) in LTE systems.The data traffic and control signal are delivered on the two channels parallelly,where the former is of the service subscribers’interest and the latter includes modulation and coding scheme for data channel,handover command,and resource allocation indicator.Evidently,a successful control signal delivery is of great importance and should be prior to decoding data traffics.
As depicted in figure 2,in conventional architecture,the data and control channels of a UE are always associated with the same BS.Whereas,in user and control plane split architecture,a UE is enabled to receive data traffic and control signal from different BSs.For both architectures,we divide the UE set into the MUE subsetU1and the SUE subsetU2according to their data channel association,which implies that any u∈Ukwill choose zkto receive data traffics.We assume maximum received signal strength indicator (RSSI)based association strategy for the data channel,which can be mathematically presented as
As for the control signal,a UE will associate its control channel with the same BS as its data channel in conventional architecture.On the contrary,in split architecture,a UE will always receive control signals from z1without taking RSSI into account,which reduces the handover occurrence probability since MBSs are much sparser than SBSs.To sum up,we list all association cases in Table 1.
Table 1.Association under different architectures,where x1 and x2 in(x1,x2)respectively manage data and control channel.
2.3 Non-Orthogonal Transmission Design
In this subsection,we detail the proposed nonorthogonal transmission based split architecture,as well as two baseline schemes,i.e.,orthogonal transmission based conventional architecture and split architecture.For notational brevity,we formally term these three schemes orthogonal conventional architecture(CO),orthogonal split architecture(SO),and nonorthogonal split architecture(SN)hereafter.
As shown in figure 2,the total bandwidthWis divided into two non-overlapping subbands,i.e.,W1-band for the MBS-tier andW2-band for the SBS-tier withW1+W2=W.To avoid cross-tier interference,ak-th tier BS only transmits radio signals inWkband.For simplicity,we consider round robin scheduling,under which a BS will sequentially serve one of its associated UEs with all of its allocated resources.Now we describe the subband usage for above three schemes.We will useto represent further division of theWk-band,where subscriptxcan be replaced by“c”and“d”to differentiate the control channel and data channel,andy ∈{CO,SO,SN}is used to distinguish schemes.
1) Orthogonal Conventional Architecture:In CO,theWk-band will be further divided into-band and-band,using which thek-th tier BS will deliver data traffic and control signal to its associated UEs inUk,respectively.Assume that the control channel bandwidth is proportional to the data channel bandwidth,such as the LTE systems,and the ratio isµ(0< µ <1)for both MUEs and SUEs in CO.To deliver a sufficient quantity of control overhead,the control channel should maintain a target SE denoted byτ,which implies that given a-band for data traffic transmission,the control channel should support a target transmission rate of=.We can find the expressions ofandas functions ofW2presented in(2)that
Under round robin scheduling,the whole-band and-band will be assigned to the selected UE during its service period.
2) Orthogonal Split Architecture:The subband usage for SO is different from CO,because an SUE receives control signals from its nearest MBS instead of any SBS.To be specific,theW1-band is similarly divided into-band and-band.An MBS will use the-band to transmit data traffics to its associated MUEs,whereas the-band is reserved for control signal transmission for all MUEs and SUEs whose control channels are associated with this MBS.The-band should contain sufficient resources for an MBS to deliver the control signals for: a) its scheduling MUE in this service period; b)the SUEs whose data channels are associated with the SBSs anchoring in this MBS.For simplicity,we consider fixed anchoring relationship between MBSs and SBSs,which means that each MBS accommodates a deterministic amount of SBSs and the number isλ2/λ1.Therefore,each MBS should provides control signals for 1 MUE andλ2/λ1SUEs in total at the same time.As for theW2-band,it will be used only for the purpose of data traffic transmission for SUEs.Assume that the control overhead bandwidth ratio is the sameµfor MUEs as in CO,andκµfor SUEs,whereκis a control overhead reduction factor for SUEs under split architecture[7].Then we can haveand find in(3)that
It should be noted that,if1,system failure will occur.
3) Non-Orthogonal Split Architecture:The SN is the proposed scheme and it takes the advantage of higher efficiency in exploiting the frequency spectrum.By enabling non-orthogonal transmisison,further division inW1-band andW2-band is not necessary.An MBS will multiplex the control signal and data traffic transmission on the wholeW1-band.Similar to the SO scheme,each MBS will accommodate the control signal transmission for 1 MUE andλ2/λ1SUEs at the same time.It should be noted that,if control channels are accommodated on the same resource block,the allocated power for each channel will decrease and hence the received SINR will severely deteriorate.So we assume that these UEs share the control signal stream in an orthogonal manner to maintain reliable control signal reception.Hence,the system can be regarded as a two-user downlink NOMA system,in which the first user is the MUE receiving data traffics and the second user is also that MUE or one of the SUEs receiving control signals.It can also be interpreted that,only two streams,i.e.,one data traffic stream and one control signal stream,are simultaneously transmitted on each resource.The MBS will split its transmit power intoβcP1for the control channel andβdP1for the data channel,whereβc+βd=1.At the receiver side,successive interference cancellation(SIC)is adopted to separate the two data streams.To keep consistent with the higher decoding priority of the control signal in most practical systems,we setβc> βd.So the optimal SIC decoding order is to decode control signals before data traffics,and is naturally in line with practical systems.
The advantage of SN scheme over SO scheme lies in its higher efficiency in utilizing the spectrum resource.This can be seen by comparing the bandwidth allocation in SO and SN schemes that1and1,which is due to the non-orthogonal utilization of the resource block.
2.4 Performance Metrics
We take outage probability and outage rate as the key performance metrics.
The regular outage probability definition is extended to jointly take data and control channels into consideration.Formally,we define that an outage occurs if the data channel signal-to-interference ratio (SIR) is too low to guarantee the SE targetι,or the control channel is unable to sustain the target transmission rate.Although the three schemes manage control channel in different manners,their control channel target transmission rates originate from the same target SEτintroduced in CO.More precisely,the control channel in SO and SN should be able to support the same transmission rate as if CO is applied given the same data bandwidth.Hence,the control channel target transmission rates are calculated byin CO,in SO,andµW1τ+2τin SN,which can be transformed into control channel target SEcalculated by
with subscriptsk,x,and superscriptyfollowing the same usage as previously stated.Letbe the SE and Oykbe the outage probability.So we have
where P(·)measures the occurrence probability of an event,and=ιis to unify the target SE presentation of data channel with control channel.
Besides outage probability,we will also investigate mobility-aware outage rate performance,which takes handover effect into consideration.Handover is the process that occurs when a moving UE crosses the border between different cells.When handover happens,the system changes cell association for this UE,which consumes a period of time termed handover delay.During this period,data traffic transmission will temporarily stop until stable connection is reestablished,and hence reduces effective transmission rate.Formal definition will be given in the last part of Section III after the derivations of association probability and outage probability.
3.1 Preliminary Results for Association Probability and Distance Distribution
We start the analysis from association probabilities and relevant distance distributions.
As previously mentioned,association probability is defined from the respect of data channel,which is treated in the same way by all three schemes.So the association probability for all schemes can be identically represented by Ak=P(u∈Uk).Previous work in [19]has established solid results in this regard,so we directly introduce the expressions in (6) as a preliminary result.
Then we provide the probability density functions(PDFs) for relevant distances,which are the PDF ofRkdenoted byfRk(r),the conditional PDF ofRkgiven the data channel associated with thek-th tier denoted byfRk|k(r),the conditional PDF ofR1for an SUE denoted byfR1|2(r),and the conditional PDF ofR2for an SUE givenR1=r1denoted byfR2|2,r1(r).The unconditional distribution forRkhas also been well studied in stochastic geometry literature thatfRk(r)=2πλkrexp(−πλkr2).So we focus on the expressions for the conditional PDFs,which are given in following Lemma 1.
Lemma 1.The conditional PDF of Rk given the data channel associated with the k-th tier is provided in(7),while the conditional PDFs of R1for an SUE and R2for an SUE given R1=r1are presented in(8)and(9),respectively.
Proof.The expression offRk|k(r)is readily obtained in[19].
To obtainfR1|2(r),we resort to its cumulative distribution function(CDF)that
After taking the derivative of (10),we can reach the PDF in(8).As forfR2|2,r1(r),it is also calculated by firstly studying its CDF given by
Again,by taking the derivative of (11),we can reach the PDF in(9),and the proof ends here.
3.2 Outage Probability Analysis
As shown in (5),the outage probability is defined by SE,which can be changed into SIR form in interference limited scenario according to Shannon capacity.The SIR expressionsunder different schemes are listed in following(12),(13),and(14)that
It can be observed that,for MUEs in SN,the data and control channels are on the sameW1-band.Hence the small-scale channel power gains for the desired and interfering signals inare the same as those inpresented byh1andh1,i.
After obtaining the distance distributions and SIR expressions,we now give the outage probabilities in Theorem 1 and Theorem 2.
Theorem 1.The outage probabilitiesdefined by(5)for MUEs and SUEs under conventional architecture are expressed as(15)given by
where1are equivalent SIR thresholds.(sc,sd,r)is the Laplace transform (LT) of the aggregate interference on data and control channels from the k-tier with r being the distance to the nearest interfering BS given byProof.The SIRs of MUEs and SUEs in CO hold identical expressions as given in (12).Therefore,by definition,the outage probability in CO can be derived in(17)that
In (17),E[·]is the expectation,(a) is due to interchanging SE thresholds into SIR thresholds.Then,(b)and (c) are obtained by calculating the complementary cumulative distribution function(CCDF)and the moment generating function (MGF) of exponentially distributed variables.Finally,the expectation over Φkin(17)can be obtained in(16)by using the probability generating functional(PGFL)of PPPs[20],and the proof ends here.
It is revealed that the outage probabilities for MUEs and SUEs in CO can be unified by (15).But for SO and SN,their expressions will be diversified due to fixed control channel association with MBSs.We provide the expressions in Theorem 2.
Theorem 2.The outage probabilitiesOSkOandOSkNunder orthogonal and non-orthogonal split architectures are expressed as(18),(19),and(20)given by
where G(a,b,c)=2F1(a,b;b+1;c)is the Gauss hypergeometric function[21].
Proof.By reviewing the composition of the desired and interference signals,we can see that the calculation of OS1Ois the same as that in Theorem 1 with the same SIR thresholds.Hence OS1Oin(18)follows a unified expression as(15).
Secondly,we turn to the outage probability for MUE in SN and the derivation can be found in(22)that
In (23),(g) is due to the independence betweenh1andg2.Finally,by applying the PGFL of PPPs and averaging overR1|2andR2|2,we can reach (20).It should be noted thatR1|2andR2|2are correlated,owing to the SUE condition.
As for the outage probability OS2Nfor SUE in SN,we omit the procedure because it shares similar desired and interference signals circumstance as those in SO case.The difference only lies in transitioning the control channel equivalent SIR thresholds,i.e.,and.The proof ends here.
Theorem 2 implies another advantage of the SN scheme over the CO and SO schemes.By carefully tuning the power allocation coefficients,i.e.,βcandβd,the outage probabilities of MUE and SUE in SN can be further adjusted,which is summarized in following Corollary 1.
Corollary 1.Tuning the power allocation coefficient βcin SN has different effect over the outage proba-bility of MUE and SUE,i.e.,OS1NandOS2N.To bespecific,increasing βcalways leads to the decrease inOS2N,while an optimal βc∗ given in(24)exists to reachthe lowestOSN1.
3.3 Outage Rate Performance Analysis
After the derivation of outage probability,we evaluate the rate performance,which is measured by the achievable user rate defined by
whereis the transmission rate of data traffic,+1 is the amount of UEs in the BS providing data traffics to the typical UE.This definition captures the user rate by averaging the outage rates of MUEs and SUEs,under fixed data channel target SE.
Note that,although Tyreflects the impact of outage,handover is not yet taken into consideration.As previously mentioned,handover consumes a period of time termed handover delay,during which no data transmission is available.Hence,by reducing the average handover delay Dyin a unit time period,we can incorporate handover into the transmission rate metric and define the user mobility-aware outage rate as
Now we focus on Dy.Under different schemes,the required delay in each handover event varies and is related to the channel involved[7].LetDcandDdbe the handover delays for control channel and data control,respectively.We haveDc>Ddsince higher layer signal exchange is required for control channel.Denote by Hk1,k2the two-tier HCN handover rate,measuring the occurrence probability of data channel handover in a unit length.The subscriptsk1andk2identify that,during this type of handover,u changes its data channel association from ak1-th tier BS to ak2-th tier BS.It can be inferred that whenk1=k2=k,Hk1,k2calculates the occurrence probability that u crosses the border between two BSs within thek-th tier.
In CO,control channel handover accompanies data channel handover because they are always associated to the same BS.But in SO and SN,it is incorrect to use H1,1to represent the handover rate of the control channel.This is because,in split architecture,the control channel only connects to the MBS-tier,and the SBStier is ignored as if transparent.Hence,the control channel handover rate for SO and SN should be measured by H1,which calculates the occurrence probability that u crosses the border between two MBSs in a single tier network.Letvbe the speed of a moving UE.So Dycan be calculated by(27)and(28)that
According to[22],whenα1=α2=α,Hk1,k2and H1can be calculated by
whereF(x)=andBy plugging (29) and (30) into(27)and(28),we can evaluate the user mobility-aware outage rate in(26).
In this section,we firstly compare the analytical results with the Monte Carlo simulation-based results to validate our expressions,including handover rates,i.e.,Hk1,k2and H1,and outage probability,i.e.,Oyk.Then we study the impacts of main system parameters and optimize the power allocation coefficient for the nonorthogonal transmission.
We consider a two-tier HCN in dense urban environment.The transmit powers areP1=40 dBm andP2=37 dBm,while the total bandwidth isW=10 MHz.The path-loss exponent isα1=α2=3.2 and the control overhead isµ=0.3.The density of UEs isλ0=50 UEs per square kilometer.The values ofλ1andλ2will be varying in different scenarios.So we will detail their values when presenting the results.The handover delays for control and data channels areDc=0.6 s andDd=0.1 s.Other specific setup can be found in the description below each figure.
4.1 Validation of Results
We firstly validate our analytical expressions in figure 3a and figure 3b.Both analytical and simulation results are obtained through Matlab based platforms.
Figure 3a verifies the derived outage probabilities Oyk.Simulation results are averaged over 1000000 independent runs in a large circular area with a radius of 100 km.The figure shows that the derived outage probabilities perfectly match simulated ones for all schemes.This confirms that our following investigations on outage probabilities are valid.
Figure 3b plots the handover rate Hk1,k2with varying SBS densityλ2under fixed MBS denstiyλ1=1 BS/km2,as well as H1with varying MBS densityλ1.We focus on a large circular area with a radius of 50 km,and randomly generate 4 consecutive segments starting from the origin within the center 20×20 km2square.The test UE will move along the segments and the whole trajectory will be partitioned with a 2000-point resolution to record the association status at each point.In total,1000 runs are performed to average the handover rate.Figure 3b also shows a perfect match between the analytical expression and the simulation result,which validates the accuracy of the following average handover delay cost modeling.
4.2 Comparison and Impacts of System Parameters
We firstly compare the outage performance of different schemes in figure 3a.Degradation can be found for MUEs in SN,which is the price of dividing transmit power to realize non-orthogonal transmission.As for SUEs,both SO and SN will increase the outage probability for SUEs because their control channel associations neglect all SBSs in split architecture.Meanwhile,the SUE in SN has slightly better outage performance than that in SO.This is because the wholeW1-band is utilized to transmit control signals in SN,and hence the equivalent SIR target fot the control channel is lower.
Secondly,we plot user mobility-aware outage rates in figure 4a,figure 4b,and figure 5a,and study the impacts of moving speed,SBS density,SBS bandwidth,target control SE,and control overhead reduction factor.
Figure 4a shows that deterioration can be expected in user mobility-aware outage rates for all three schemes when UEs move with higher speed,which is due to more frequent handover in high speed scenarios.Better rate performance of SO and SN can be observed when SBSs are slightly denser than MBSs,proving the superiority of split architecture over conventional architecture.For explanation,the split architecture benefits from not only the lower handover delay cost,but also the more spared spectrum for data traffic transmission inW2-band.However,when the SBSs are very densely deployed,this superiority of SN will gradually diminish and the outage rate in SO will dramatically decrease to zero.This is because,with the increase of SBS density,each MBS in split architecture needs to bear higher control overhead burden within its limitedW1-band and the benefit is neutralized.More details in this aspect are left to discuss with the help of figure 4b.
Figure 4b plots user mobility-aware outage rate with varying SBS bandwidth under different target control SEs.The results show that user outage rate in CO will increase almost linearly with SBS bandwidthW2,because SBSs are much more densely deployed than MBSs and most UEs are receiving data traffics from the SBSs.On the contrary,the user outage rate in SO will firstly increase withW2,but decline rapidly to zero beyond feasible region.This is because the bandwidth consumed to deliver control signals inW1-band is proportional toW2.Hence,a very largeW2will easily exhaustW1-band and system failure will occur ifW1is too scarce to provide a sufficient-band.Likewise,similar feasible region in SBS density can also be observed in figure 4a,beyond which,ultra densely deployed SBSs will require so much reserved-band.The trend is similar in the SN scheme,although the rate performance degrades in a much more gentle manner.This can be explained by the fact that allW1-band is non-orthogonally utilized by each MUE to manage the control signal transmission,illustrating the more flexible implementation of split architecture under non-orthogonal transmission.
It is also shown in figure 4b that target control SEτplays an important role in determining user outage rate.For SO scheme,the feasible region remains the same for varyingτ,but higher outage rate can be achieved when control channel has lower QoS requirement.Meanwhile,the impact of target control SE is more obvious in SN scheme.For example,when target control SE is not so rigorous,both achievable user outage rate and the corresponding optimal value ofW2will increase.
Figure 5a investigates the impact of control overhead reduction factorκon user mobility-aware outage rate.As previously discussed,owing to the limit ofW1-band,a feasible region exists for the SN scheme.This feasible region is much more rigorous in the SO scheme,as control signal transmission directly consumes additional spectrum resources at the MBS.Figure 5a shows that,the superiority of the split architecture over conventional architecture severely relies onκ.If control overhead can be compressed,i.e.,κ<1,the split architecture can be better implemented and higher user outage rate can be reached,since more bandwidth can be spared to realize data traffic transmission.
At last,we study the impact of power allocation coefficientβcon outage probability OSN1in figure 5b.As discussed in Corollary 1,the SN scheme admits further adjustment for OS1Nof MUE through tuningβc.Figure 5b illustrates minimum outage probabilities,for which the optimalβccan be calculated according to (24).It can be observed that,for different target data SE,i.e.,ι=0.3 bps/Hz andι=0.5 bps/Hz,the outage probability OS1Nremains the same beforeβcincreases to its optimal valueβ∗c.This is because,OSN1is determined by the control channel asholds for thoseβcsmaller thanβ∗c.It should be noted that,whenλ2=5 BS/km2andι=5 bps/Hz,the derivedβ∗cis smaller than 0.5.So OSN1will monotonically increase withβcin this setting.
This paper proposes a non-orthogonal transmission based user and control plane split architecture.The proposed system manages cell association in a more flexible manner,in which data and control channels can be separately connected to BSs of different tiers.Higher system efficiency can be envisioned by applying non-orthogonal transmission for the MBS to simultaneously deliver data traffic and control signal on the same resource block.Stochastic geometry based approach is leveraged to investigate key performance.Regular outage probability is extended by jointly taking SIRs of data and control channels into consideration.Handover delay cost is also modeled to incorporate handover effect in outage rate.Simulation results validate our analytical expressions,based on which extensive investigation is carried out.We show that split architecture can lower average handover delay cost by reducing the handover rate of control channel.Introducing non-orthogonal transmission into the split architecture helps accommodate more control channels than traditional orthogonal transmission.Besides,non-orthogonal transmission also enables a new dimension to reach the minimum outage probability by adjusting power allocation coefficient.
ACKNOWLEDGEMENT
This work is supported by the Youth Innovation Foundation of Xiamen (3502Z20206067),the Natural Science Foundation of Fujian Province,China(2021J011219,2022J011276),the National Natural Science Foundation of China (61801412,62201482),the National Key Research and Development Program of China (2021YFB2900801),Beijing Natural Science Foundation (L212004),and China University Industry-University-Research Collaborative Innovation Fund(2021FNA05001).