Cooperative Transmissions in Ultra-Dense Networks under a Bounded Dual-Slope Path Loss Model
Yanpeng Yang, Ki Won Sung, Jihong Park, Seong-Lyun Kim, Kwang Soon Kim
CCooperative Transmissions in Ultra-Dense Networksunder a Bounded Dual-Slope Path Loss Model
Yanpeng Yang and Ki Won Sung
Wireless@KTHKTH Royal Institute of Technology, SwedenEmail: { yanpeng, sungkw } @kth.se Jihong Park
Dept. of Electronic SystemsAalborg University, DenmarkEmail: [email protected]
Seong-Lyun Kim and Kwang Soon Kim
School of Electrical & Electronic EnginerringYonsei University, Seoul, KoreaEmail: { slkim, ks.kim } @yonsei.ac.kr Abstract —In an ultra-dense network (UDN) where there aremore base stations (BSs) than active users, it is possible thatmany BSs are instantaneously left idle. Thus, how to utilizethese dormant BSs by means of cooperative transmission is aninteresting question. In this paper, we investigate the performanceof a UDN with two types of cooperation schemes: non-coherentjoint transmission (JT) without channel state information (CSI)and coherent JT with full CSI knowledge. We consider a boundeddual-slope path loss model to describe UDN environments wherea user has several BSs in the near-field and the rest in thefar-field. Numerical results show that non-coherent JT cannotimprove the user spectral efficiency (SE) due to the simultaneousincrement in signal and interference powers. For coherent JT, theachievable SE gain depends on the range of near-field, the relativedensities of BSs and users, and the CSI accuracy. Finally, weassess the energy efficiency (EE) of cooperation in UDN. Despitecosting extra energy consumption, cooperation can still improveEE under certain conditions.
Index Terms —Ultra-dense networks, cooperative transmis-sions, bounded path loss model, multi-slope path loss model
I. I
NTRODUCTION
Mobile communication technologies are rapidly promptedby the tremendous growth of traffic demand. Deploying mas-sive number of cheap small base stations (BSs), so called anultra-dense network (UDN), represents a paradigm shift fromconventional deployment strategies [1] [2]. Compared with thetraditional networks designed for fully loaded operation, UDNis partially loaded in its inherent design because the BS densityexceeds that of users [2] [3].
A. Motivation and Related Work
The existing studies of UDN mainly focus on the single BSassociation [3], [4]. The BSs without user in their coverageareas are considered in sleep mode to save energy and reduceinterference. In extreme cases, a large number of BSs willtemporarily stay idle in the network. Thus, it raises a researchquestion if we can exploit such temporary infrastructure ’re-dundancies’ in UDN to improve the system performance.Joint transmission (JT) is a potential solution which allowsmultiple BSs to jointly serve one user. In traditional fullyloaded cellular networks, JT could turn dominant interferersinto useful signals as shown in Fig. 1(a) while the otherinterferers remain the same. Thus, the desired signal strengthincreases and the interference decreases simultaneously, at the near-field
Active UEInactive UEActive BSCooperating BSInactive BS critical distancebounded region radius R b R c (a) Traditional joint transmission near-field Active UEInactive UEActive BSCooperating BSInactive BS critical distance R c bounded region radius R b (b) UDN joint transmissionFig. 1: An illustration of joint transmission in (a) traditional fully-loaded network and (b) partially-loaded UDN. cost of reduced scheduling probability. It is known that JTenhances the performance of cell-edge users in macro cellu-lar networks [5]. However, interference nature is completelydifferent in a UDN because turning on dormant BSs is like a r X i v : . [ c s . N I] M a y double-edged sword, i.e., improving the desired receivedsignal strength, but generating extra interference and energyconsumption. In Fig. 1(b), if all the users get assistance fromnearby sleeping BSs, the interference will grow rapidly aswell as the desired signal power. Therefore, how to designcooperation schemes in UDN to overcome the concurrentinterference becomes a big challenge. A cooperative UDNarchitecture is proposed in [6], but without further discussionson cooperation schemes and performance evaluation.To examine the impact of JT on UDN, it is important toincorporate the propagation characteristics of UDN properly.In a UDN environment where the cell sizes are getting muchsmaller, a widely accepted unbounded single-slope path lossmodel, i.e., G ( d ) = d − α , becomes dubious. The radio signalsin the near-field may experience much less absorption anddiffraction losses than those in the far-field, resulting indissimilar path loss exponents. Besides, the probability of alink within a reference distance, d ∈ (0 , , becomes high,and thus this phenomenon cannot be neglected in the analysis.Hence, a path loss model with multiple slopes and boundbecomes necessary in modeling the UDN scenario. The impactof bounded and multi-slope path loss models in fully loadednetworks are separately studied in [7] and [8] [9]. However,the combination of the two effects remains to be explored.Moreover, the full load assumption becomes implausible inthe UDN environment since the BS density exceeds the userdensity [10] [11]. B. Contributions
This paper intends to give a first look at applying BScooperation in a partially loaded UDN scenario. We employa bounded dual-slope path loss model in order to capture thecharacteristics of UDN. Furthermore, two cooperation schemesare investigated: non-coherent JT without the assistance ofinstantaneous channel state information (CSI) and coherentJT with full CSI knowledge. Our key findings on UDNcooperation are summarized as follows: • Exploiting CSI is necessary for cooperative transmissionsin UDN (Remark 1). • Cooperation gain in spectral efficiency (SE) increaseswith the range of near-field, i.e critical distance (Remark2), as well as both near/far-field path loss exponents(Remark 3). • Cooperation gain also grows with active user density(Remark 4 and Fig. 5), but is convex-shaped over BSdensity (Remark 5). • With imperfect CSI, cooperation is more preferable underlower operating frequency. • Cooperation can also increase network energy efficiency(EE) within a limited number of cooperating BSs.II. N
ETWORK AND C HANNEL M ODELS
A. Network Setup
We consider the downlink of a UDN with BS density λ b and user density λ u that follow independent Poisson PointProcesses (PPPs) Φ b and Φ u , respectively. According to the Active UEActive BSCooperating BSInactive BS
Fig. 2: User-centric Voronoi cells for a modeling of cooperativetransmissions in a UDN. definition of UDN, we set λ b (cid:29) λ u as in [3] [10]. This canbe interpreted as off-peak hours under extremely dense BSdeployment. It is also supported by real traffic measurement[12] where only up to 20% BSs are active to make trafficqueues stable.Both BSs and users are equipped with single antenna andBS transmits with unit power. Each user is associated withits closest BS when no cooperation occurs. Each BS becomesdormant when its coverage is empty of users. Dormant BSsdo not transmit signals, i.e. not interfering with others, butconsume energy to be specified in Section II-C. We assumeRayleigh fading in this work with the fading coefficients h to be i.i.d. complex normal distributed random variables withzero mean and unit variance.In previous studies [8] [10], the network topology is com-posed by BS-centric Voronoi cells which represent the BScoverage areas as shown in Fig. 1(a). However, for the caseof UDN, massive empty cells result in an ineffective mappartition. Concerning this, we propose to reverse the roles ofBS and user in the topology and define user-centric Voronoicells for modeling the cooperation in UDN, as shown in Fig.2. In cooperation model, up to N BSs in the Voronoi cell willjointly serve one user. Since the system can be approximatedas interference-limited in dense networks [13], we will neglectthe noise power and examine signal-to-interference-ratio (SIR)throughout the paper.
B. Path Loss Model
We apply a bounded dual slope path loss model in this work.The model divides the entire region into three parts: boundedregion, near-field area, and far-field area (Fig. 1(a)). Boundedregion is a closed circle centered at the user, inside which thepath loss is assumed constant. It is to avoid received powerlarger than transmitted power in a short distance. Outsidethe bounded region, the signal experiences different path lossxponents in near-field and far-field areas, divided by thecritical distance. The model can be expressed as in [4], [8]: (cid:96) ( α , α , x ) = , ≤ (cid:107) x (cid:107) ≤ R b ; (cid:107) x (cid:107) − α , R b < (cid:107) x (cid:107) ≤ R c ; τ (cid:107) x (cid:107) − α , (cid:107) x (cid:107) > R c (1)where we set R b = 1 as the radius of bounded path lossregion for simplicity,; τ (cid:44) R α − α c to keep the continuity ofthe function; R c ≥ R b denotes the critical distance; α and α are the near- and far-field path loss exponents respectively,assuming ≤ α ≤ α . C. Power Consumption Model
We assume transmitting BSs and dormant BSs are in anactive-mode and a sleeping-mode. The power consumptionsfor active- and sleeping-mode are P t and P s , respectively. Wedefine θ < as the ratio between two power consumptions,i.e., θ = P s P t . By applying N cooperating BSs as proposed inSection III-A, the densities of active BSs and sleeping BSs ina unit area are N λ u and λ b − N λ u . Thus, the area averagepower consumption can be expressed as: P A = P t ( N λ u + θ ( λ b − N λ u )) . (2)III. C OOPERATIVE T RANSMISSION M ODELS
A. Cooperation Scheme
Any user i in the network is jointly served by the set of N closest BSs in its own Voronoi cell, denoted by C i = (cid:83) Nj =1 BS j . Within the cooperation set, all BSs jointly transmitthe same message to the user using the same frequency band.We denote Φ C as the set of active BSs in the whole network.Thus, the signal received by user i is: y i = (cid:88) x ∈C i (cid:96) ( d x,i ) h x,i w x,i X i + (cid:88) x ∈ Φ C \C i (cid:96) ( d x,i ) h x,i w x,i X x (3)where d x,i and h x,i denote the distance and channel betweenBS x and user i , h x,i ∼ CN (0 , ; w x,i is the precoder appliedby BS x . X i and X x are the transmitted symbols sent bycooperating BSs and interfering BSs respectively.In non-coherent JT, the receivers apply open-loop jointprocessing CoMP scheme as in [14], where signals fromdifferent transmitters are added by power summation. Theprecoder w x is set to be 1 for non-coherent JT. The desiredsignal power for non-coherent JT is given by S NJ i = (cid:88) x ∈C i | h x,i | (cid:96) ( d x,i ) . (4)In coherent JT, we assume the CSI is available at the BSside. In this case, BSs can design precoder to adjust the phaseshift of the channel and amplify the corresponding channelgain. We employ maximal ratio transmission (MRT) precodersuch that w x = h ∗ x | h x | . The desired signal power for coherentJT is thus S CJ i = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:88) x ∈C i h x,i w x,i (cid:113) (cid:96) ( d x,i ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) . (5) Therefore, the SIR of user i with two cooperation schemes, γ NJ i and γ CJ i are shown as follows: γ NJ i = S NJ i (cid:88) x ∈ Φ C \C i | h x,i | (cid:96) ( d x,i ) (6) γ CJ i = S CJ i (cid:88) x ∈ Φ C \C i | h x,i | (cid:96) ( d x,i ) . (7) B. Imperfect CSI
We focus on the delayed CSI feedback caused by the move-ments of users. The standard Gaussian Markov process (GMP)is used to model the temporal variation of the channel state. Weassume a block fading model [15] where h remains constantover a time separation and evolves thereafter according to anergodic stationary autoregressive (AR) GMP of order 1. Thechannel evolves in time as: h [ t ] = ρ h [ t − T s ] + e [ t ] (8)where h [ t ] denotes the channel realization at time t , < ρ < is the channel correlation coefficient, and e [ t ] ∼ CN (0 , − ρ ) represents the error vector. For the coefficient ρ , we useClarke’s model [16] and set ρ = J (2 πf d T s ) , where J ( · ) isthe zero-th order Bessel function of the first kind, f d is theDoppler frequency shift, and T s is the time separation. Since f d = f c vc , the accuracy of the feedback will highly dependson operating frequency f c and the moving speed v of the user. C. Cooperation Gains
In this study, the user SE R and the average network EE η are chosen as the performance metrics. The SE derived bythe Shannon formula is given by R = log (1 + γ ) . (9)We set the user SE under the single association R o as ourbaseline to measure the gain of cooperation. The SE gain G c is defined as the ratio between SE difference ∆ R and R o asfollows: G c = ∆ R R o = R J − R o R o (10)where R J and R o are the SE with and without cooperation,respectively.The average network EE η is defined as the area SE dividedby the average power consumption. Considering the powerconsumption model described in Section II-C, we can expressthe average network EE as: η = λ u R P A = λ u R P t ( N λ u + θ ( λ b − N λ u )) . (11)At last, EE gain is the ratio between the average network EEwith cooperation η J and that EE without cooperation η o , givenby G η = η J η o . (12)
10 20 30 40 50 60 70 80 90 100 110 120 130 140 1502345678 Critical distance Rc (m) U s e r SE ( bp s / H z ) Co−JT, N=2Co−JT, N=5No cooperationNon−JT, N=2Non−JT, N=5No gain for nonJT Higher gain for larger RcLittle gain for small Rc,more cooperation BSsmay be even worse
Fig. 3: User performance with different critical distances when [ α , α ] = [2,4], λ b = 4000 / km , λ u = 200 / km . IV. N
UMERICAL R ESULTS AND D ESIGN G UIDELINES FOR C OOPERATIVE T RANSMISSION
In this section, we present results for cooperation in UDNby Monte Carlo simulations. Since the potential cooperationregion is the Voronoi cell of a certain user, each BS can serveat most one user. If the number of BSs in the Voronoi cell M is less than the cooperation number N , we pick min( M , N ) asthe cooperation number. In the following, we investigate theimpacts of near/far-field channel characteristics and BS/userdensity on UDN cooperation, followed by the the effect ofimperfect CSI and EE behaviors. A. Critical Distance
The effect of critical distance is illustrated in Fig. 3. As thecritical distance gets longer, all the performances decline dueto more interference generated from the near-field.
Remark 1 (Non-coherent JT):
Non-coherent JT has worseperformance than single BS association.In a UDN scenario, the interferer coordinates can be approx-imated as the corresponding user coordinates [3]. Therefore,interference can be considered as almost linearly increasingwith the number of cooperating BSs due to longer interferingdistance. In non-coherent JT, the desired power summationgrows diminishingly as the cooperation number increasesbecause the transmitting distance gets longer. As a result, theincrement in the desired signal is less than interference whichleads to no gain. Therefore, we will not consider non-coherentJT in further discussions. All the rest of remarks are regardingcoherent JT.
Remark 2 (Effect of critical distance):
The cooperation gaingrows with increasing critical distance. For a short criticaldistance, more cooperating BSs make SE even worse. For alarge critical distance, the cooperation gain is higher with moreBSs. To show the cooperation gain, we can make the followingapproximations: ∆ R = log (1 + γ J ) − log (1 + γ o ) (13) ( a ) ≈ log (cid:18) γ J γ o (cid:19) (14) ( b ) ≈ log (cid:18) S J N S o (cid:19) (15)where (a) is because SIR (cid:29) in UDN [17] and (b) followsfrom the linear relation approximation of the interference.When R c is small, using (1) and (5) in (15) we can get : ∆ R = log (cid:32) | (cid:80) Kj =1 | h j || d j | − α + (cid:80) Nj = K | h j | τ | d j | − α | N | h | | d | − α (cid:33) (16)where K cooperating BSs are inside near-field and N − K fallinto the far-field area. The N − K ’far-field’ BSs can hardlymake a contribution with a larger path loss exponent. Thus,incorporating more BSs into JT even decreases the gain.When R c is large, all the cooperating BSs will fall into thenear-field, then (13) can be written as: ∆ R = log (cid:32) | (cid:80) Nj =1 | h j || d j | − α | N | h | | d | − α (cid:33) (17)which is independent of R c because both the numerator anddenominator are inside near-field. However, a larger R c leadsto a lower baseline R o which results in a higher cooperationgain. In our simulation, a . gain is obtained by 5 coherentcooperating BSs with R c = 70 m while it increases to when R c = 150 m. B. Path Loss ExponentRemark 3 (Effect of path loss exponent):
The cooperationgain decreases with both near-field and far-field path lossexponents.Fig. 4 depicts the user SE in different dual-slope path lossenvironments. We choose a large enough R c so that all thecooperating BSs are in the near-field. The cooperation gain G c can be expressed as: G c = log (cid:18) | (cid:80) Nj =1 | h j || d j | − α | N | h | | d | − α (cid:19) R o . (18)It is easy to prove that the numerator is a decreasing functionof α . Meanwhile, R o is an increasing function of both α and α [8]. Combining the two aspects, a higher path lossexponent returns a lower cooperation gain.As stated above and shown in the Fig. 4, the case with α =2 and α = 4 is the most suitable situation for cooperationamong the three exemplary cases. In large near-field path lossexponent scenarios where R o is already superb, cooperationis not preferable. The bounded region will not affect the conclusion. It is not considered in(16) because BS density is not large enough. U s e r SE ( bp s / H z ) No cooperationCo−JT α =4 α =3 α =2 Fig. 4: User performance with different near-field exponents α when α = 4 , λ b = 4000 / km , λ u = 200 / km , R c = 70m. C. User and BS Densities
In this part, we discuss the impact of active user and BSdensities on cooperation, shown in Fig. 5 and Fig. 6.
Remark 4 (Effect of active user density):
As active userdensity increases, cooperation gain keeps growing while theuser SE drops.Equation (17) can be reused since λ u does not affect ∆ R same as R c . Besides, R o gets smaller as λ u increases dueto more interference. Therefore, cooperation performs betterwith a larger λ u . This is similar with the effect of criticaldistance aforementioned because increasing critical distanceis equivalent with increasing user density in the near-field. Remark 5 (Effect of BS density):
As BS density increases,cooperation gain is convex-shaped: first decreases logarithmi-cally, then decreases in a lower speed, and finally starts toincrease after the BS density reaches a threshold.We can write the cooperation gain G c as: G c = log (cid:16) S J N S o (cid:17) R o = log (cid:18) | (cid:80) Nj =1 | h j || d j | − α | N | h | | d | − α (cid:19) log (cid:16) | h | | d | − α I (cid:17) (19)where d j will increase in the order of λ b leading to a fixednumerator. Thus in region 1, the cooperation gain will decreaselogarithmically since R o will increase logarithmically with λ b [13]. In region 2, the decreasing speed of the gain slowsdown because users start to enter the bounded region where S o and R o no longer increase with λ b . Finally in region 3,the probability of d < R b is quite high and R o tends to be aconstant. Therefore, the cooperation gain increases via furtherdensification. D. Operating Frequency under Imperfect CSI
We set T s = 10ms, v = 3km/h and control the operatingfrequency to identify the effect of imperfect CSI. From Fig. 7,cooperation is sensitive to frequency bands. Operating in
50 100 150 200 250 300 350 400 450 5002345678 UE density λ u (active users/km ) U s e r SE ( bp s / H z )
50 100 150 200 250 300 350 400 450 5000.10.150.20.250.3 C oope r a t i on ga i n CoJTNo cooperationCooperation gain
Fig. 5: Cooperation gain with different user densities when [ α , α ] = [2,4], λ b = 4000 / km , R c = 70m, N = 5. λ b (BSs/km ) U s e r SE ( bp s / H z ) C oope r a t i on ga i n No cooperationCoJTCooperation gainRegion 1 Region 2 Region 3
Fig. 6: Cooperation gain with different BS densities when [ α , α ] = [2,4], λ u = 200 / km , R c = 70m, N = 5. higher frequency bands leads to a strong Doppler effect andinaccurate channel feedback for moving users. Therefore, theprecoders mismatch the instantaneous channel and cannotprovide the full cooperation gain. E. Network Energy Efficiency
The network EE assessment is present in Fig. 8. There existsa tradeoff between SE and EE by waking up the dormantBSs in UDN. Depending on the power consumption modeland environmental parameters, EE can even improve whenincreasing the cooperation number.When θ is large, cooperation can improve EE becauseturning on sleeping BSs will enhance the user SE with littleextra energy consumption. On the contrary, a small θ will costmuch more energy consumption resulting in a declining EE.Furthermore, we evaluate EE under favorable environments U s e r SE ( bp s / H z ) Perfect CSIImperfect CSINo cooperation
Fig. 7: Effect of imperfect CSI when [ α , α ] = [2,4], λ b =4000 / km , λ u = 200 / km , R c = 70m, N = 5. EE ga i n θ =0.2 θ =0.8 θ =0.5 θ =0.5, Imperfect CSI θ =0.5,Rc=120m θ =0.5, α = α =2 Fig. 8: Network energy efficiency gain when [ α , α ] = [2,4], λ b =4000 / km , λ u = 200 / km , R c = 70m if not specified in the figure. of cooperation: larger critical distance and small path lossexponents. Both of them can improve EE within certaincooperation number range when θ =0.5. When imperfect CSIis considered, we can hardly achieve an EE improvement dueto the SE performance.V. C ONCLUSION AND F UTURE W ORK
In this paper, we have studied cooperative transmissionsin a UDN. Two cooperation schemes, non-coherent JT andcoherent JT, are evaluated under a realistic path loss model.We conclude that cooperation is not beneficial without CSI ina UDN. Regarding coherent JT, an environment with longercritical distance and smaller near-field path loss exponent isfavorable. Moreover, employing cooperation when user densityis higher will be more effective. On the contrary, lower BSdensity is more helpful except when BS density becomesextremely high, thereby triggering the effect of bounded region. Meanwhile, cooperation is favorable to static users andlower frequency bands operation which allows accurate CSIfeedback. Finally, EE can also be improved by cooperationwithin limited cooperation numbers as long as the extra powerconsumption is small. Future work can extend to investigationon more advanced BSs with multi-antenna and/or beamform-ing and seeking the optimal cooperation number.A
CKNOWLEDGMENT
This research has been partly supported by the H2020project METIS-II co-funded by the EU. The views expressedare those of the authors and do not necessarily represent theproject. It was also supported by Basic Science ResearchProgram through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science andTechnology (NRF-2015K2A3A1000189).R
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