arXiv:1512.03149v1 [cs.NI] 10 Dec 2015 7593 mi:qli Email: 87557943, the it with Therefore, enlarged [4]–[6]. radius is coverage networks cell of cell the impact of the small hand, decrease 5G other wireless on the On mobility 5G networks. user cell i small network in of cellular type 5G distance a Hence, [3]. transmission [2] furth systems wireless communication technologies the transmission technologies, reduce wireless key wave 5G antenna of millimeter (MIMO) thus multi-output two cells, multiple-input Moreover, massive of i.e., [1]. bas radius (BSs) and coverage users stations effectiv between the distances the communication reduce the of reducing to one networks, is cellular approaches (5G) generation fifth coy iDW(rn o 192 n rjc coy CROWN acronym (grant project and S2EuNet 318992) acronym no. Minis (grant project WiNDOW research the acronym FP7-PEOPLE-IRSES, This EU and 2014DFE10160. the 61461136003, grant by and under (MOST) 61231009 Scie Technolgoy grants Natural National under the (NSFC) 15511103200, grant Commissi Technology under and (STCSM) Science 2013014212 F the grant by Research under supported 20 Special (SRFDP) partially Centr grants Education the Higher the 2014QN155, the of for and Program under 2015XJGH011 Funds China grant grant 614 Research of the the and Fundamental (MOST) under the 61301128 Technology 2014DFA11640, Project and grants Research Science the of Joint under International (NSFC) Major China of Foundation N XX, VOL. 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(grant 5D150and 15FDG12580 1304 NFSC 61136004, aluat- rrival and l san is man ility rks, and cell ors ate .Y OT 2016 MONTH Y, O. nt ce nt er ll e e s l 1 agYang Yang , r motn.B esrn h nrp fec individuals each of entropy Song the trajectory, measuring mobility By of important. locations are relative the which in investigations eeoe ocnev h nryb euigtert of rate the reducing by energy w the algorithm conserve target-tracking to a networks, developed wireless sensor wireless mod for mobility in Gauss-Markov th management the from [17].Adopting model mobility trajectory networks target of service the cost communication for personal the Accounting proposed evaluate was [16]. framework user to analytical mobile an of model, location Gauss-Markov Gauss- depends last user the networks mobile the in of cellular on location considered next is in the user where user model, mobile Markov mobile of memory residenc the The area cell for [15]. location cellular analyzed a a the model, was as that flow time such fluid probability area, the the Utilizing closed calculating [14]. a accesses for flow node used fluid mobile The mobile widely [13]. the is model where waypoint model networks random hoc the ad follows in incurr user recovery opportunist latency route the position-based local reduce A to by for developed [12]. evaluated was protocol solution was routing networks centric networks wireless user performance wireless of the a in model, benefits waypoint and user random pre- bounds the mobility was the on the model into Based [11]. waypoint simulate time random pause to the the sented model, communications adding walk personal By to random in [10]. proposed users networks was mobile services capturing approach of models new movement walk A the random independent two-dimensional [9]. and velocity the status stochastic simplify and past fully are the direction physics model with mobility in walk The random mobility of atom topics. is the chemistry model describing walk and for random used and The model originally flow [8]–[18]. model, fluid walk model the random model, Gauss-Markov (RWP) the waypoint i.e., random types, model the four such mobility classified been convention user networks, have In investigations, wireless networks. communication vehicular for mobile and used mo- networks been cellular After human as have [7]. some attentions base models and more user bility attracted researchers whole have telecommunication models the from mobility across human mobility this, user in ity n5 ml elntok osdrn ua ciiyhabits activity human considering mobilit networks user cell the small of impact 5G the on evaluate to problem important nweg fhmnmblt eairi seta o all for essential is behavior mobility human of Knowledge 2 , 3 in Li Qiang , tal. et ,Hbi .R China. R. P. Hubei, 4, g (SIMIT), ogy on 3 oeta predictabil- potential 93% a found 1 users ed as el ic al y e e s 1 . IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 2 sensing in temporal management [18].Except of above four sidering the group cell scheme, the number of available mobility models, some user mobility models measured from small cell BSs is derived for the static user in 5G small real data have been adopted for wireless networks [19], [20]. cell networks. By mining the extensive trace datasets of vehicles in an 3) Furthermore, the coverage probability of macro cell BSs urban environment through conditional entropy analysis, a is derived for the mobile user in 5G small cell networks. packet delivery probability was derived for vehicular networks Numerical simulations validate the proposed coverage [19]. Based on measured results from cellular networks, e.g., probabilities for 5G small cell networks. handoff rates and call arrival rates, a solution was proposed to The rest of this paper is organized as follows. Section II predict how people spread from one location to another after describes the system model of 5G small cell networks within a period of time [20]. However, the tendency and clustering a community area and the IMM. In Section III, the user arrival, habits in human activities have not been considered for above departure and pause probabilities are derived to evaluate the human mobility models. In real scenarios, people habitually user mobility performance for 5G small cell networks with stay at some locations for a long time compared with other community area. Furthermore, in Section IV the coverage locations. To describe the user clustering habit, the concept probabilities inside and outside the community are derived for of community was introduced to evaluate the user mobility 5G small cell networks. Considering the group cell scheme, the in wireless networks [21]. Based on the human mobility number of available small cell BSs is derived for the static user trajectory measured from real data, the individual mobility in 5G small cell networks. Moreover, the coverage probability model considering the human mobility tendency habit was of macro cell BSs is derived for the mobile user in 5G small proposed to describe the human mobility in real world [22]. cell networks. In Section V, Numerical results validate the The impact of the user mobility on small cell networks has proposed coverage probabilities for 5G small cell networks. been studied in [23]–[27]. By modeling positions of mobile Finally, Section VI concludes this paper. users as an independent Poisson point process in each time slot, the backhaul delay of heterogeneous networks including II. SYSTEM MODEL small cell networks and macro cell networks was analyzed in [23]. A new small cell discovery mechanism based on the A. Network Model user mobility state was investigated to improve the energy effi- Assume that both users and BSs are located in a finite plane R2 R2 ciency and access efficiency of LTE-Advanced heterogeneous t whose area is St. Moreover, a rectangle c is located in the R2 wireless networks [24]. Considering mobile user scenarios, finite plane t and the area of rectangle is Sc. The complement R2 R2 an energy efficient and backhaul aware small cell activation region of rectangle c is denoted as s whose area is Ss. mechanism with the use of dual connectivity was evaluated for In this paper, the concept of community is introduced to 5G small cell networks [25]. To reduce the signal overhead, represents a specified region where a large number of users are R2 a new scheme was proposed by having the mobile users assembled [21]. Without loss of generality, the rectangle c R2 autonomously decide small cell addition, remove, and change is configured as a community in the finite plane t . Macro without any explicit signaling of measurement events to small cell BSs and small cell BSs are located in the finite plane R2 cell networks or any signaling of handoff commends from t . Macro cell BSs are assumed to be governed by a Poisson small cell networks [26]. Based on 5G wireless network point process distribution with the density λm,BS.The macro scenarios, the downlink and uplink of power consumption was cell boundary, which can be obtained through the Delaunay evaluated for small cell networks where static and low mobility Triangulation method by connecting the perpendicular bisector users are associated with macro cell BSs and high mobility lines between each pair of macro cell BSs, splits the plane R2 user are associated with small cell BSs [27]. t . into irregular polygons that correspond to different cell However, the user mobility performance of small cell net- coverage areas. This stochastic and irregular topology forms a works in all aforementioned research considers only simple so-called Poisson-Voronoi tessellation (PVT) [28], [29]. Small mobility models, such as the random walk model or the ran- cell BSs inside and outside the community are assumed to dom waypoint model. Besides, the impact of human tendency follow uniform distributions with densities λc,BS and λs,BS, and clustering behaviors on small cell networks has not been respectively. Macro cells and small cells are overlapped in the R2 investigated. Moreover, detailed investigation of IMM used for infinite plane t . Macro cell BSs and small cell BSs transmit small cell networks is surprisingly rare in the open literature. wireless signal in different frequencies. Hence, there does not Motived by above gaps, we first analyze the user mobility exist the interference between macro cell networks and small performance and derive coverage probabilities for 5G small cell networks. Users inside and outside the community are cell networks based on IMM. The contributions and novelties assumed to follow uniform distributions with densities λs and of this paper are summarized as follows. λc, respectively. Based on the community concept, the follow- 1) Based on IMM, the user arrival, departure and pause ing constraints are configured: λc > λs and λc,BS > λs,BS. probabilities are derived to evaluate the user mobility An illustration of users and BSs deployment is depicted in performance for 5G small cell networks with the com- Fig. 1. munity area. When the orthogonal frequency division multiplexing 2) Based on the proposed arrival and departure probabil- (OFDM) scheme is adopted by BSs to support multi-user ities, the coverage probabilities inside and outside the transmission in this paper, the co-channel interference gener- community are derived for 5G small cell networks. Con- ated from the intra-cell is ignored. Only downlink transmission IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 3
2) The user will returned an old location where has been 13 visited in the past. The probability visiting an old 12 location is expressed as
11 γ Pret (n)=1 ρS(n)− . (2) − 10 The user will pause at a location for a waiting time after 9 the user complete a jump. The probability of waiting time 1 β 8 is expressed by P (∆t) ∆t − − , where 0 <β 6 1 is a fixed parameter which is∼ measured | | by empirical data. 7 Based on the user mobility regulation in IMM, the user 6 visits more locations, i.e., the value of S (n) becomes larger, the probability of the user returning an old location becomes 5 larger. 4
3 III. USER MOBILITY PERFORMANCE 3 4 5 6 7 8 9 10 11 12 13 Based on the IMM, the user mobility performance is ana- Fig. 1. System model. The community is limited in rectangle plotted lyzed for 5G small cell networks in this section. Considering by the green line, blue nodes are macro cell BSs and blue lines are the community configuration in Fig. 1, a Lemma is proposed the coverage boundaries of macro cells, the red nodes are the small as follows. cell BSs. Lemma1: When the user mobility follows the IMM, the probability that the user jumps into the community of 5G small is studied in this paper. Moreover, the static user is assumed cell networks is equal to Sc/St, which is independent on the to be associated with small cell BSs and the mobile user is jump number n. assumed to be associated with macro cell BSs [30]. To realize Proof: Considering that the user mobility follows the IMM, the result that the user jumps into the community in the n th the high transmission rate, the group cell scheme is proposed − for the static user in small cell networks. In the group cell jump can be composed of two cases, which are depicted as scheme, the static user can be associated with multiply small follows. Case 1: The user explores a new location in the n th cell BSs if signal-to-interference-plus-noise ratios (SINRs) − over wireless links are larger than or equal to a given threshold jump and the new location is located in the community, the corresponding probability is derived by γ0. To simplify derivation, the static user is only associated with small cell BSs inside the community when the static user in Sc γ Sc is located inside the community. Similarly, the static user is Pnew (n)=Pnew (n) = ρS(n)− . (3) S S only associated with small cell BSs outside the community t t when the static user is located outside the community. Case 2: The user returns an old location in the n th jump and the old location is located in the community,− the B. Individual Mobility Model corresponding probability is derived by In this paper the IMM is first introduced to evaluate the user S(n) in NcSc ki (n) mobility performance in 5G small cell networks. Differing Pret (n)=Pret (n) , (4) St n 1 with traditional user mobility models, the human tendency i=1 X − and clustering behaviors has been considered for IMM [22].In where ki (n) is the visiting number at the i th location in practical human society, the user visiting frequencies at differ- S(n) − the n th jump. Accounting for ki (n)= n 1, (4) can ent locations present obviously difference [31], [32], i.e., the − − user trends to visit some locations where he/she usually visits i=1 be further derived by P in the past. In this case, the user does not move with a fully random model in the real scenarios. S(n) One mobility of user is called as one jump in IMM and the in Sc ki (n) γ Sc Pnew (n)=Pret (n) = 1 ρS(n)− . detail user mobility regulation is explained as follows [33]: St n 1 − St i=1 − The user has two potential active modes before the next X (5) jump: When (3) and (5) are summed, the probability that the user 1) The user will visit a new location where has never jumps into the community in the n th jump is Pc,in = Sc/St. − been visited. The probability visiting a new location is In the end, the proof of Lemma 1 is completed. expressed as Let t (n) is the total time spending for the number of n γ jumps. tc,in (n) is the time spending in the community for Pnew (n)= ρS(n)− , (1) tc,in(n) the number of n jumps. Let ψ (n) = t(n) is the ratio where 0 <ρ 6 1 and γ > 0 are fixed parameters which between the time spending in the community and the total are related with user mobility habits, S (n) is the number time spending for the number of n jumps. tc,m (n) is the of visited locations before the jump, is the jump number. moving time spending in the community for the number of n IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 4
jumps. tc,p (n) is the pause time spending in the community points in the community and are governed by two independent for the number of n jumps. Therefore, the time spending in uniform distributions. Locations of uK and uM are denoted as the community for the number of n jumps is extended as uK (xK ,yK ) and uM (xM ,yM ), respectively. Moreover, x1 6 xK 6 x and x 6 xM 6 x , lc = x x . y 6 yK 6 y , 2 1 2 | 2 − 1| 1 2 y1 6 yM 6 y2 and wc = y2 y1 , where x1, y1, x2, y2 tc,in (n)= tc,m (n)+ tc,p (n)= tc,m (n)+ nc,in∆tc, (6) | − | R2 are the coordinates of the boundaries of community area c. where nc,in is the jump number falling into the community Therefore, the distance between two points inside the commu- 2 2 in the jump number n, ∆tc is the waiting time a user spent nity is denoted as di,i = (xK xM ) + (yK yM ) . The at one location in the community. Based on the result in − − probability density functionq (PDF) of di,i is expressed as [33], the distribution of waiting time ∆tc is governed by 1 βc P (∆tc) ∆tc − − , 0 < βc 6 1. Let the user arrival and ∼ | | 2 2 departure probabilities of the community are πc,in and πc,out dP (xK xM ) + (yK yM ) < x respectively, which are expressed as − − fdi,i [x]= q dx t (n) 2 2 2 c,in dP (xK xM ) + (yK yM ) < x πc,in = lim E [ψ (n)] = lim E , (7) n n t (n) = − − . (13) →∞ →∞ h dx i x2 tc,in (n) d f 2 2 [X] dX πc,out =1 πc,in =1 lim E , (8) 0 (xK xM ) +(yK yM ) − − n t (n) = − − →∞ dx R 2 E 2 2 where [ ] is the expectation operation. =2xf(xK xM ) +(yK yM ) x · − − Let ni,o is the moving number departing from the commu- Let ΦX [t] is the characteristic function of the random nity, no,i is the moving number arriving at the community, 2 variable X , the term of f 2 2 x in (13) is n is the moving number inside the community, n is the (xK −xM ) +(yK −yM ) i,i o,o further derived by (14a) with (14b) and (14c). Based on (13) moving number outside the community. Therefore, total jump and (14), the expectation of the distance d is given by (15). number is expressed by n = n + n + n + n and i,i o,i i,i i,o o,o Without loss of generality, the length and width of finite the jump number falling into the community is expressed by plane R2 are configured as l and w , respectively. The center n = n + n . The time spending in the community t t t c,in o,i i,i point of finite plane R2 is also configured at (0, 0). The for the number of t (n) jumps is derived by (9) where t c,in location of a point u is denoted as u (x ,y ), where L (I) is the location where the user moves at the I th jump, H H H H x 6 x 6 x and y 6 y 6 y , l = x x and is the distance function between two locations,− v is the 3 H 4 3 H 4 t 4 3 w = y y . To simplify the derivation, two| formulations− | averagek·k user moving velocity, 1 ( ) is the indicator function, t 4 3 are configured| − | as (16) and (17). which equals to 1 when the event inside· the bracket is occurred Based on the derivation method for (15), E [d ] and E [d ] and 0 otherwise. A is the event that the user explores a new o,i o,o are derived as (18) and (19). location at the I th jump and B is the event that the user Substitute (15), (18) and (19) into (11) and (12), the user returns an old location− at the I th jump. Similarly, the total arrival and pause probabilities, i.e., π and π can be time spending for the number− of n jumps t (n) is derived c,in pause obtained in the end. by (10) Based on the result in Appendix A, πc,in is derived by (11) where di,i is the distance between two points inside IV. COVERAGE MODEL the community, do,i is the distance between one point located inside the community and another point located outside the Based on the group cell scheme, a static user UE can community, do,o is the distance between two points outside the associate with multiply small cell BSs if SINRs over wireless community, ∆ts is the waiting time a user spent at one location links are larger than or equal to a given threshold γ0. Assume outside the community, the distribution of ∆ts is governed by that SINRs over wireless links are independent each other, the 1 βs P (∆ts) ∆ts − − , 0 < βs 6 1. Substitute (11) into (8), selection process of small cell BSs associated with a static user ∼ | | the user departure probability πc,out can be obtained. can be denoted as Nb independent Bernoulli experiments, i.e., Based on the derivation method in (11), the user pause R2 probability , i.e., the probability that a user pauses at a location, λc,BSSc, UE c Nb = ∈ 2. (20) is derived by (12) where tp (n) is the total pausing time for the λs,BS Ss, UE R ( ∈ s number of n jumps. E [di,i], E [do,i] and E [do,o] in (11) and (12) are derived as follows. Considering the derivation method In this case, the number of small cell BSs associating with a static user inside and outside the community is denoted is same for E [di,i] , E [do,i] and E [do,o] , we only depict the as nc,s and ns,s , respectively. Moreover, nc,s and ns,s are detail derivation process for E [di,i] and then directly list the independent each other and are governed by binomial distribu- final derivation result for E [do,i] and E [do,o]. Considering that the community is a rectangle, the length tions. Let coverage probabilities of a small cell BS inside and outside the community are Pc cover and Ps cover , respectively. and width of the community are denoted as lc and wc , respectively. Without loss of generality, the center point of Probabilities of nc,s and ns,s inside and outside the community rectangle R2 is configured as the original point of Euclid are expressed as (21) and (22). where is the bottom c M ⌊·⌋ integral function, is the binomial coefficients meaning coordinate (0, 0). uK and uM are two independent random N IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 5
n i,i L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) t (n)= k − ∈ − k1 (A)+ k − ∈ − k1 (B) c,in v v i=1 n X o,i L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) + k − ∈ − k1 (A)+ k − ∈ − k1 (B) v v . (9) i=1 Xn i,o L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) + k − ∈ − k1 (A)+ k − ∈ − k1 (B) v v i=1 X +nc,in∆tc
n i,i L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) t (n)= k − ∈ − k1 (A)+ k − ∈ − k1 (B) v v i=1 Xn o,i L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) + k − ∈ − k1 (A)+ k − ∈ − k1 (B) v v i=1 Xn i,o L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) . (10) + k − ∈ − k1 (A)+ k − ∈ − k1 (B) v v i=1 Xn o,o L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) + k − ∈ − k1 (A)+ k − ∈ − k1 (B) v v i=1 X +n∆t
(ni,i + no,i + ni,o) kL (I) − L (k,k ∈ [0,I − 1])k +(ni,i + no,i)∆tc πc,in = lim E n→∞ vt (n) 2 1 Sc Sc Sc Sc n E [di,i]+ 1 − E [do,i] + nE [∆tc] v St St St St = lim n→∞ 2 2 1 Sc E Sc Sc E Sc E Sc E Sc E n v S [di,i] + 2 1 − S S [do,i]+ 1 − S [do,o] + n S [∆tc]+ n 1 − S [∆ts] . (11) t t t t t t 2 1 Sc Sc Sc Sc E [di,i]+ 1 − E [do,i] + E [∆tc] v St St St St = 2 2 1 Sc E Sc Sc E Sc E Sc E Sc E v S [di,i] + 2 1 − S S [do,i]+ 1 − S [do,o] + S [∆tc]+ 1 − S [∆ts] t t t t t t
tp (n) πpause = lim E n→∞ t (n)
Sc Sc E [∆tc]+ 1 − E [∆ts] , (12) St St = 2 2 1 Sc E Sc Sc E Sc E Sc E Sc E v S [di,i] + 2 1 − S S [do,i]+ 1 − S [do,o] + S [∆tc]+ 1 − S [∆ts] t t t t t t
2 1 ∞ jtx2 2 2 2 2 f(xK xM ) +(yK yM ) x = Φ(xK xM ) [t]Φ(yK yM ) [t]e− dt, (14a) − − 2π − − Z−∞ the number of ways of picking N unordered outcomes from is assumed to be the Rayleigh fading channel [34]. Therefore, M possibilities. Considering the OFDM scheme is adopted (23) is further derived by at small cell BSs, the interference received at the static user is only generated from adjacent small cell BSs with the co- channel. The coverage probability of a small cell BS inside α the community is expressed by (23), where γ0 is the SINR Ptshsds− 2 Pc cover =P >γ0 , threshold over wireless links, σ is the Gaussian noise power, λc,BS Sc Ncover ⌊ − ⌋ α Prs and Pri are the desired signal power and the interference σ2 + P h d − tin in in power at the static user, and N denotes the total number k=0 cover (24) of available small cell BSs. In this paper the wireless channel P where Pts and Pti are the transmission power from the desired IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 6
2 dP (xK xM ) < x ∞ jtx 2 − Φ(xK xM ) [t]= e dx − 0 h dx i Z x d √ f (X) dX ∞ √x xK xM jtx = − − e dx dx Z0 R √x d 1 ∞ Φc (t)Φc (t) e jtX dt dX , (14b) ∞ √x 2π xK xM − = − −∞ − ejtxdx h h dx i i Z0 R R − − √x (ejtx2 ejtx1 )(e jtx1 e jtx2 ) 1 ∞ − − jtX d √x 2π t2(x x )2 e− dt dX ∞ − −∞ 2 1 = − ejtxdx R R dx Z0
√y 1 c c jtY d ∞ Φy (t)Φ y (t) e− dt dY ∞ √y 2π K M jty 2 − −∞ − Φ(yK yM ) [t]= e dy − h h dy i i Z0 R R jty jty −jty −jty √y (e 2 e 1 )(e 1 e 2 ) . (14c) 1 ∞ − − jtY d √y 2π t2(y y )2 e− dt dY ∞ − −∞ 2 1 = − ejtydy R R dy Z0
E ∞ [di,i]= xfdi,i [x]dx 0 Z − √x (ejtx2 e jtx1 )(ejtx2 ejtx1 ) ∞ − − jtX ∞ 2 ∞ ∞ d √x t2(x x )2 e− dt dX x − −∞ 2 1 = − ejtxdx 4π3 R R dx Z Z Z . (15) 0 0 0 jty −jty jty jty √y e 2 e 1 e 2 e 1 ( − )( − ) jtY d ∞ 2 2 e− dt dY √y t (y2 y1) ∞ − −∞ − jty jtx2 e dy e− dtdx R R dy Z0
− − √x (ejtb ejta )(e jtc e jtd) ∞ − − jtX ∞ d √x t2(b a)(d c) e− dt dX − −∞ − − jtx fΦ (a,b,c,d)= e dx, (16) R R dx Z 0
ya,b (xn xm) (yb ya) ςx = | − − | . (17) m,n (y y ) (x x ) (y y ) (x x ) 4 − 3 4 − 2 − 2 − 1 2 − 1
∞ ∞ 2 E x y3,4 y2,3 [do,i]= ςx2,4 fΦ (x2,x4,x1,x2) fΦ (y3,y4,y1,y2)+ ςx2,3 fΦ (x2,x3,x1,x2) fΦ (y2,y3,y1,y2) Z 4π3 Z , (18) 0 0 2 y1,4 y2,4 −jtx + ςx1,3 fΦ (x1,x3,x1,x2) fΦ (y1,y4,y1,y2)+ ςx1,2 fΦ (x1,x2,x1,x2) fΦ (y2,y4,y1,y2) e dtdx small cell BS and the interfering small cell BSs, respectively. is the distance between the static user and the interfering hs and hin are the small scale fading over the desired wireless small cell BS. Considering that locations of the static user and channel and the interfering wireless channels. Moreover, hs the small cell BSs are governed by two independent uniform and hin are independent each other and governed by an distributions, ds and di are assumed to be independent and exponential distribution with the mean λh . ds is the distance identically distributed (i.i.d.) random variables. Assume that between the static user and the desired small cell BS. din small cell BSs have the equal transmission power Pt, i.e., IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 7
∞ ∞ 2 x y3,4 y3,4 y2,3 y2,3 E [do,o]= ςx ςx fΦ (x2,x4,x2,x4) fΦ (y3,y4,y3,y4)+ ςx ςx fΦ (x2,x3,x2,x3) fΦ (y2,y3,y2,y3) Z 4π3 Z 2,4 2,4 2,3 2,3 0 0 y y y y +ς 3,4 ς 1,4 f (x ,x ,x ,x ) f (y ,y ,y ,y )+ ς 3,4 ς 2,3 f (x ,x ,x ,x ) f (y ,y ,y ,y ) x2,4 x1,3 Φ 2 4 1 3 Φ 3 4 1 4 x2,4 x2,3 Φ 2 4 2 3 Φ 3 4 2 3 . (19) y3,4 y2,4 y2,3 y1,4 +ςx2,4 ςx1,2 fΦ (x2,x4,x1,x2) fΦ (y3,y4,y2,y4)+ ςx2,3 ςx1,3 fΦ (x2,x3,x1,x3) fΦ (y2,y3,y1,y4) y2,3 y2,4 y2,4 y1,4 +ςx2,3 ςx1,2 fΦ (x2,x3,x1,x2) fΦ (y2,y3,y2,y4)+ ςx1,2 ςx1,3 fΦ (x1,x2,x1,x3) fΦ (y2,y4,y1,y4) 2 y1,4 y1,4 y2,4 y2,4 −jtx + ςx1,3 ςx1,3 fΦ (x1,x3,x1,x2) fΦ (y1,y4,y1,y2)+ ςx1,2 ςx1,2 fΦ (x1,x2,x1,x2) fΦ (y2,y4,y1,y2) e dtdx
λc,BSSc nc,s λc,BS Sc nc,s P (nc,s)= ⌊ ⌋ (Pc cover) (1 Pc cover)⌊ ⌋− , (21) nc,s ! −
λs,BS Ss ns,s λs,BS Ss ns,s P (ns,s)= ⌊ ⌋ (Ps cover) (1 Ps cover)⌊ ⌋− , (22) ns,s ! −
Prs Pc cover = P [Recieved SINR > γ0]=P > 0 , (23) λc,BS Sc Ncover σ2 + ⌊ − ⌋ P ri k=0 P
λc,BS Sc Ncover ⌊ − ⌋ α 2 α Pc cover =P Pthsds− γ σ γ Pthindin− > 0 . (25) − 0 − 0 k X=0
Pt = Pts = Ptin (24) can be rewritten by (25). α 2 Considering that three terms in (25), i.e., Pthsds− , γ0σ ∞ 1 x jtx λc,BS Sc Ncover ΦP h d −α [t]= fh f −α (x) e dx ⌊ − ⌋ α t s s P P · ds · and γ0 Pthindin− are independent random Z0 t t . k=0 λ ∞ λh h x α 1 α jtx variables, (25)P can be calculated by the joint probability of = e− Pt αx − fD (x ) e dx 0 Pt · · three independent random variables. Z (30) Considering that hs and hin are governed by an exponential Based on the same derivation method used for (30), the distribution with the mean λh , the PDF of hs and hinis α PDF of γ0Pthindin− is derived by (31). Furthermore, the expressed by − α characteristic function of γ0Pthindin− is derived by (32). Assume that the noise over− wireless channels is governed λhx 2 fh (x)= λhe− . (26) by the standard normal distribution. The PDF of γ0σ is derived by (33). Furthermore, the characteristic functi− on Furthermore, the PDF of the variable Pths is expressed by 2 of γ0σ is derived by (34). Based on (30), (32) and − −α 2 (34), the characteristic function of ξ = PthsDs − σ γ0 − x ⌊λc,BSSc−Ncover ⌋ dP hs < −α dP [Pths < x] Pt γ0 Pthindin is derived by (35). Base on the fPths (x)= = k=0 dx h dx i Fourier inversionP transform, the PDF of ξ is derived by x . Pt λhX d λhe− dX 1 x λ λh 0 h P x = = fh = e− t 1 ∞ jtx dx P P P fξ [x]= Φξ [t] e− dt , (36) R t t t 2π · (27) Z−∞ Based on the result of (13), the PDF of ds and din is Based on (25) and (36), the coverage probability of a small α expressed by (28). Furthermore, the PDF of the variable ds− cell BS for a static user inside the community is derived by is expressed by 0 1 ∞ jtx xα Pc cover =1 Φξ [t] e− dt dx , (37) d 0 fD (X) dX α 1 α − 2π · −α −∞ −∞ fds (x)= = αx − fD (x ) . (29) Z Z R dx Based on the derivation method used for (37), the coverage Based on (27) and (29), the characteristic function of probability of a small cell BS for a static user outside the α Pthsds− is derived by community is derived by (38a) with (38b) IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 8
R2 fdi,i (x) , xK , xM ,yK,yM c fD (x)= f 2 2 (x)= ∈ . (28) √(xK xM ) +(yK yM ) 2 fd (x) , xK , xM ,yK,yM R − − ( o,o ∈ s
α x α dP Pthindin− > dP γ0Pthindin− < x γ0 f −α [x]= − = − γ0Pthindin h i − dx dx α x α x d 1 P P h d − < dP P h d − < t in in γ0 t in in γ0 = − − = − h h dx ii − h dx i x . (31) λh − γ0 λh X α 1 α d e− P αX − fd [X ]dX = 0 Pt · i,i − dx R α 1 α 1 λ λhx x − x h P γ = e t 0 α fd , x ( , 0] γ P · −γ i,i −γ ∈ −∞ 0 t 0 0
0 α 1 α 1 λ λhx x − x h P γ jtx −α t 0 Φ γ0Pthindin [t]= e α fdi,i e dx . (32) − γ0 Pt · −γ0 −γ0 · Z−∞
x x 2 dP σ2 > d 1 P σ2 < dP σ γ0 < x γ0 γ0 f 2 [x]= − = − = − − σ γ0 h i h h ii − dx dx dx dP σ2 < x dP x <σ< x − γ0 − − γ0 − γ0 = = . (33) − h dx i − h q dx q i x X2 √ γ0 1 d − e− 2σ2 dX x √2πσ x √ γ0 1 2 = − − = e 2γ0σ , x ( , 0] − R dx 2πx ∈ −∞ γ0σ − γ0 q
2 0 x 0 1+2jtγ0 σ 1 2 jtx 1 2 x 2 2γ0σ 2γ0σ Φ σ γ0 [t]= e e dx = e dx . (34) − 2πx · 2πx γ0σ γ0σ Z−∞ − γ0 Z−∞ − γ0 q q
λc,BS Sc Ncover −α 2 −α ⌊ − ⌋ Φξ [t]=ΦPthsds [t] Φ σ γ0 [t] Φ γ0Pthidi [t] · − · − λ ∞ λh h x α 1 α jtx = e− Pt αx − fd [x ] e dx P · i,i · Z0 t 0 2 1 1+2jtγ0σ x 2γ σ2 (35) e 0 dx . · 2πx γ0σ Z−∞ − γ0 λc,BS Sc Ncover 0 q α 1 α ⌊ − ⌋ 1 λh λhx x − x Ptγ0 jtx e α fdi,i e dx · γ0 Pt · −γ0 −γ0 · "Z−∞ #
0 1 ∞ jtx Ps cover =1 Φ′ [t] e− dt dx , (38a) − 2π ξ · Z−∞ Z−∞
0 1+2jtγ σ2 λh 0 ∞ λh x α α jtx 1 2 x Pt 1 2γ0σ Φξ′ [t]= e− αx − fdo,o (x ) e dx e dx 0 Pt · · · γ σ 2πx Z Z−∞ 0 γ0 − . (38b) λs,BS Sc Ncover 0 α 1 α q ⌊ − ⌋ 1 λh λhx x − x Ptγ0 jtx e α fdo,o e dx · γ0 Pt · −γ0 −γ0 · "Z−∞ # IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 9
Based on (11), (12), (37) and (38), the number of available small cell BSs for a static user is derived by (39a) 0.95
0.945 Ncover = (πc,inE [nc,s]+(1 πc,in) E [ns.s]) πpause , − (39a) 0.94 with 0.935 E [nc,s]= λc,BSScPc cover , (39b) pause IMM, average user velocity 3m/s p 0.93 IMM, average user velocity 4m/s IMM, average user velocity 5m/s E [ns.s]= λs,BSSsPs cover . (39c) RWP, average user velocity 3m/s 0.925 RWP, average user velocity 4m/s RWP, average user velocity 5m/s Considering that Pc cover and Ps cover both are functions 0.92 of Ncover, The computation of Ncover in (39) has to be performed by iteration calculations. 0.915 Differing with the coverage probability for the static user, 1 2 4 6 8 10 12 14 16 18 20 S /S (%) the coverage probability of the moving user is defined as: c t when the user moves with the average velocity v for a period ∆tm , the moving user is covered by macro cell BSs only Fig. 2. User pause probability with respect to the average user if the moving user SINR is always larger than or equal to velocity and the area ratio of the community and the finite plane Sc/St . a given threshold γ0 in the period ∆tm . Assume that the distance between the initial location of moving user and the associated macro cell BS is rp = −→rp , where −→rp is the distance | | R2 2 R2 vector from the moving user to the associated macro cell BS. plane t is St = 10km , the area of the community c is 2 The user moving distance is denoted as ∆rm = v ∆tm . Sc = 1km , densities of small cell BSs inside and outside · The included angle between the user moving direction and the community are λc,BS = 20 per square kilometers and the distance vector −→rp is dented as θm . Hence, the distance λs,BS =5 per square kilometers, respectively; the parameters between the location of moving user and the associated macro of IMM are ρ =1 , βc =0.5 and βs =1.5 ; the transmission 2 2 power of small cell BS is Pt = 0.1W , the parameter of cell BS is rm = rp + ∆rm 2rp∆rm cos(θm) after the − Rayleigh fading channel is , the path loss exponent user moves a distance ∆r .Let the event C is that the moving λh = 1 q m and the velocity of user is m/s , the user moving user is associated with the macro cell BS MBS and the event α =4 v =5 D is that the distance between the location of moving user time is ∆tm = 10s . Fig. 2 shows the user pause probability with respect to the and the associated macro cell BS MBS is rm after the user average user velocity and the area ratio of the community and moves a distance ∆rm . Therefore, the coverage probability of a macro cell BS for the moving user is expressed by the finite plane Sc/St based on IMM and RWP (random way- point model) [37]–[39]. When the area ratio of the community Pm cover = P (C D) . (40) and the finite plane S /S is fixed, the user pause probability | c t increases with the increase of the average user velocity. Based on the result in [35], (40) can be extended as (41) πpause Considering IMM and the average user velocity is fixed, the where ( ) is the Laplace transform of the interference at Ir user pause probability first decreases with the increase of the movingL user,· ( )is the Laplace transform of the desired h until the value of reaches at , and then the user signal at the movingL user.· Sc/St Sc/St 5% pause probability increases with the increase of . Hence, Considering that the location of macro cell BS is governed Sc/St the user pause probability achieves a minimum when the area by a Poisson point process distribution and the initial location ratio of the community and the finite plane is configured of moving user is governed by a uniform distribution, the PDF Sc/St as 5%. This result provides a basic guideline to evaluate the of the distance r is expressed as [36] p user pause probability in a region with different ratio of hot 2 πλm,BS x sports. Furthermore, the deployment of small cell BSs can frp (x)=2πλm,BSxe− . (42) be considered for the user pause probability, especial in the Assume that θm is uniformly distributed in [0, π] and ∆rm is urban region with different ratio of hot sports. Considering fixed, the PDF of rm is derived by (43a) with (43b) RWP and the average user velocity is fixed, the user pause Substitute (43a) into (41a), the coverage probability of the probability is a constant without respect to the area ratio of moving user is derived by (44). the community and the finite plane Sc/St . Therefore, the user pause probability based on IMM considers the human V. NUMERICAL RESULTS AND DISCUSSIONS clustering behavior, e.g. people would like to stay at the Based on proposed user mobility probabilities and coverage community, in 5G small cell networks. probabilities in Section III and section IV, the effect of various Fig. 3 illustrates the user arrival probability πc,in with system parameters on the user mobility probabilities and respect to the average user velocity and the area ratio of coverage probabilities have been analyzed and compared by the community and the finite plane Sc/St . When the IMM numerical simulation in this section. In what follows, some is considered in Fig. 3, numerical results are explained as default parameters are configured as: the area of the finite follows. When the area ratio Sc/St is fixed, the user arrival IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 10
2πσ2sj 1 ∞ e− Ir (2πsj) h 2π(γ0x)− sj 1 P = f (x) L L − − dsdx , (41a) m cover rm h2πsj i x>Z0 Z −∞ ∞ λh 2πx 1 −α vdv − − λh+2πsv j I (2πsj)= e Rx , (41b) L r 1 λh − h 2π(γ0x) sj = 1 , (41c) L − λh 2π(γ0x)− sj −
2 2 dP rp + ∆rm 2rp∆rm cos(θm) < x f (x)= − rm q dx 2 2 2 π ∆rm cos θm+√x +(∆rm cos(θm)) ∆rm 1 − d π dθm frp (y) dy 0 0 = R R dx 2 2 2 , (43a) π ∆rm cos θm+√x +(∆rm cos(θm)) ∆rm − 2 1 πλmy d π dθm 2πλmye− dy 0 0 = R R dx π 2 πλm(ωm(x,θm)) 1 2πxλmωm (x, θm) e− = dθm π ωm (x, θm) ∆rm cos θm Z0 −
2 2 2 ωm (x, θm) = ∆rm cos θm + x + (∆rm cos(θm)) ∆rm . (43b) − q
π 2 πλm,BS(ωm(x,θm)) 1 2πxλm,BSωm (x, θm) e− Pm cov er = dθm π ωm (x, θm) ∆rm cos θm x>Z0 Z0 − ∞ λ . (44) 2πx 1 h vdv 2 λ +2πsv−αj 2πσ sj − x − h λh ∞ e− e R −1 1 λ 2π(γ0x) sj h− − dsdx · 2πsj Z −∞
probability πc,in decreases with the increase of the average user velocity. When the average user velocity is fixed, the user 0.35 IMM, average user velocity 3m/s arrival probability πc,in increases with the increase of the area IMM, average user velocity 4m/s 0.3 ratio Sc/St . When the RWP is considered in Fig. 3, the user IMM, average user velocity 5m/s RWP arrival probability πc,in is independent with the average user 0.25 velocity and increases with the increase of the area ratio Sc/St . Compared with curves in Fig. 3, the user arrival probability 0.2 based on IMM is larger than the user arrival probability based c,in p on RWP. This result implies that people would like to stay 0.15 at the community in 5G small cell networks considering the human tendency behavior. 0.1
In Fig. 4, the impact of the SINR threshold γ0 and the density of small cell BSs inside and outside the community 0.05 on the number of available small cell BSs Ncover for a static 0 user is evaluated. When the density of small cell BSs outside 1 2 4 6 8 10 12 14 16 18 20 S /S (%) the community is fixed as λs,BS =5 , the number of available c t small cell BSs Ncover for a static user with respect to the SINR Fig. 3. User arrival probability πc,in with respect to the average user threshold γ0 and the density of small cell BSs λc,BS inside velocity and the area ratio of the community and the finite plane the community is depicted in Fig. 4(a). When the density of Sc/St . small cell BSs λc,BS is fixed, the number of available small IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 11
7 10 IMM, l =10 IMM, l =5 0.25 c,BS 9 s,BS IMM, =20 IMM, =8 6 lc,BS ls,BS IMM, =30 8 IMM, l =10 l =10 lc,BS s,BS c,BS cover 5 RWP, l =10 cover RWP, l =5 c,BS 7 s,BS l =20 RWP, l =20 RWP, l =8 c,BS c,BS s,BS 0.2 6 RWP, l =10 4 RWP, l =30 s,BS l =30 c,BS c,BS 5 3 4
c_cover 2 3 0.15 2 Number of SBSavailable Number N 1 of SBSavailable Number N 1
0 0 1 10 20 30 40 50 1 10 20 30 40 50 0.1 SINR threshold SINR threshold g0 g0 (a) (b)
Coverage probability P Coverage Fig. 4. Number of available small cell BSs Ncover with respect to 0.05 the SINR threshold γ0 and the density of small cell BSs inside and outside the community. 0 1 5 10 15 20 25 30 35 40 45 50 SINR threshold g0 cell BSs for a static user decreases with the increase of the Fig. 5. Coverage probability of a small cell with respect to the SINR SINR threshold. When the SINR threshold is fixed, the number threshold and the density of small cell BSs inside the community. of available small cell BSs for a static user increases with the increase of the density of small cell BSs inside the community.
When the density of small cell BSs inside the community is 0.14 =5 fixed as λc,BS = 20 , the number of available small cell BSs ls,BS =8 Ncover for a static user with respect to the SINR threshold γ0 0.12 ls,BS l =10 and the density of small cell BSs λs,BS outside the community s,BS is described in Fig. 4(b). When the SINR threshold is fixed, the 0.1 number of available small cell BSs for a static user increases s_cover with the increase of the density of small cell BSs outside the 0.08 community. Compared with curves in Fig. 4(a) and Fig. 4(b), the number of available small cell BSs based on IMM is less 0.06 than the number of available small cell BSs based on RWP. 0.04 This result implies that the number of small cell BSs used probability P Coverage for cooperative communications is overestimate for small cell 0.02 networks when RWP is used for the user mobility model. 0 In Fig. 5, the effect of the SINR threshold γ0 and the density 1 5 10 15 20 25 30 35 40 45 50 SINR threshold g of small cell BSs λs,BS on the coverage probability of a small 0 cell BS Pc cover is investigated inside the community. When Fig. 6. Coverage probability of a small cell BS with respect to the density of small cell BSs λc,BS is fixed, the coverage probability of a small cell BS P decreases with the the SINR threshold and the density of small cell BSs outside the c cover community. increase of the SINR threshold. When the SINR threshold γ0 is fixed, the coverage probability of a small cell BS Pc cover decreases with the increase of the density of small cell BSs inside the community. 0.2
In Fig. 6, the impact of the SINR threshold γ0 and the 0.19 density of small cell BSs λs,BS on the coverage probability 0.18 of a small cell BS Ps cover is analyzed outside the community. 0.17 g =10 When the density of small cell BSs λs,BS is fixed, the 0 0.16 g =20 coverage probability of a small cell BS Ps cover decreases with 0 g =30 0.15 0 the increase of the SINR threshold. When the SINR threshold m_cover P γ0 is fixed, the coverage probability of a small cell BS Ps cover 0.14 decreases with the increase of the density of small cell BSs 0.13 outside the community. 0.12 Finally, Fig. 7 evaluates the coverage probability of a macro 0.11 cell BS Pm cover with respect to the SINR threshold and the 0.1 average user velocity. When the SINR threshold is fixed, the 2 4 6 8 10 12 14 16 18 20 coverage probability of a macro cell BS decreases with the Average user velocity [m/s] increase of the average user velocity. When the average user velocity is fixed, the coverage probability of a macro cell BS Fig. 7. Coverage probability of a macro cell BS Pm cover with respect to the SINR threshold and the average user velocity. decreases with the increase of the SINR threshold. IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 12
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n i,i L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) B = k − ∈ − k1 (A)+ k − ∈ − k1 (B) 1 v v i=1 X no,i L (I) L (k, k [0, I 1]) 1 A L (I) L (k, k [0, I 1]) 1 B B2 = k − ∈ − k ( )+ k − ∈ − k ( ) v v . (45) i=1 Xni,o L (I) L (k, k [0, I 1]) L (I) L (k, k [0, I 1]) B3 = k − ∈ − k1 (A)+ k − ∈ − k1 (B) v v i=1 X B4 = nc,in∆tc B1 + B2 + B3 + B4 πc,in = lim E n vt (n) →∞ B B B B = lim E 1 + E 2 + E 3 + E 4 . (46) n vt (n) vt (n) vt (n) vt (n) →∞ B B B B = lim E 1 + lim E 2 + lim E 3 + lim E 4 n vt¯ (n) n vt¯ (n) n vt¯ (n) n vt¯ (n) →∞ →∞ →∞ →∞
n n γ γ ρS(k)− 1 (F) ρS(k)− 1 (F) me k=1 k=1 lim E = lim E = E lim . (47) n t (n) n P t (n) n P t (n) →∞ →∞ →∞ n γ ρS(k)− 1 (F) me k=1 δ lim E = E lim = E lim =0 . (48) n t (n) n P t (n) n t (n) →∞ →∞ →∞
ni,i B1 kL (I) − L (k,k ∈ [0,I − 1])k kL (I) − L (k,k ∈ [0,I − 1])k lim E = lim E 1 (A)+ 1 (B) /t (n) n→∞ t (n) n→∞ " v v # Xi=1 kL(I)−L(k,k∈[0,I−1])k kL(I)−L(k,k∈[0,I−1])k me v + mr v = lim E n→∞ h t (n) i
kL(I)−L(k,k∈[0,I−1])k kL(I)−L(k,k∈[0,I−1])k me mr = lim E v + v n→∞ " t (n) t (n) # kL(I)−L(k,k∈[0,I−1])k . (49) mr = lim E v n→∞ " t (n) # (ni,i − δ) kL (I) − L (k,k ∈ [0,I − 1])k = lim E n→∞ vt (n) ni,i kL (I) − L (k,k ∈ [0,I − 1])k δ kL (I) − L (k,k ∈ [0,I − 1])k = lim E − n→∞ vt (n) vt (n) ni,i kL (I) − L (k,k ∈ [0,I − 1])k = lim E n→∞ vt (n)
B no,i L (I) L (k, k [0, I 1]) lim E 2 = lim E k − ∈ − k n t (n) n vt (n) →∞ →∞ B3 ni,o L (I) L (k, k [0, I 1]) lim E = lim E k − ∈ − k , (50) n t (n) n vt (n) →∞ →∞ B (n + n ) ∆t lim E 4 = lim E o,i i,i c n t (n) n vt (n) →∞ →∞
[25] A. Prasad and A. Maeder, “Backhaul-aware energy efficient heteroge- 1, pp.25–41, Jun. 2015. neous networks with dual connectivity,” Telecommun. Syst., vol. 59, no. [26] K. I. Pedersen, P. H. Michaelsen, C. Rosa, and S. Barbera, “Mobility IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 14
enhancement for LTE-advanced multilayer networks with inter-site carrier Xiaohu Ge (M’09-SM’11) is currently a Profes- aggregation,” IEEE Commun. Mag., vol. 51, no. 5, pp. 64–71, May 2013. sor with the School of Electronic Information and [27] L. Sanguinetti, A. L. Moustakas and M. Debbah, “Interference manage- Communications at Huazhong University of Science ment in 5G reverse TDD hetnets with wireless backhaul: a large system and Technology (HUST), China. He received his analysis,” IEEE J. Sel. Areas Commun., vol. 15, no. 6, pp. 1187–1200, PhD degree in Communication and Information En- Sep. 2015. gineering from HUST in 2003. He has worked at [28] F. Baccelli, M. Klein, M. Lebourges and S. Zuyev, “Stochastic geometry HUST since Nov. 2005. Prior to that, he worked and architecture of communication networks,” Telecommun. Syst., vol.7, as a researcher at Ajou University (Korea) and no. 1, pp. 209–227, Jun. 1997. Politecnico Di Torino (Italy) from Jan. 2004 to Oct. [29] X. H. Ge, B. Yang, J. L. Ye , G. Q. Mao, C. X. Wang and T. Han, 2005. He was a visiting researcher at Heriot-Watt “Spatial Spectrum and Energy Efficiency of Random Cellular Networks,” University, Edinburgh, UK from June to August IEEE Trans. Commun., vol. 63, no. 3, pp. 1019–1030, Mar. 2015. 2010. His research interests are in the area of mobile communications, [30] S. Sadr and R. S. Adve, “Handoff rate and coverage analysis in multi- traffic modeling in wireless networks, green communications, and interference tier heterogeneous networks,” IEEE Trans. Wireless Commun., vol. 14, modeling in wireless communications. He has published about 90 papers in no. 5, pp. 2626–2638, May 2011. refereed journals and conference proceedings and has been granted about 15 [31] Halepovic, Emir and C. Williamson, “Characterizing and Modeling User patents in China. He received the Best Paper Awards from IEEE Globecom Mobility in a Cellular Data Network,” in Proceedings of the 2nd ACM 2010. He is leading several projects funded by NSFC, China MOST, and international workshop on Performance evaluation of wireless ad hoc, industries. He is taking part in several international joint projects, such as sensor, and ubiquitous networks, pp. 71–78, 2005. the EU FP7-PEOPLE-IRSES: project acronym S2EuNet (grant no. 247083), [32] Bayir, M. Ali, M. Demirbas and N. Eagle, “Characterizing and Modeling project acronym WiNDOW (grant no. 318992) and project acronym CROWN User Mobility in a Cellular Data Network,” in Proceedings of World of (grant no. 610524). Wireless, Mobile and Multimedia Networks and Workshops 2009, pp. 1–9, Dr. Ge is a Senior Member of the China Institute of Communications 2009. and a member of the National Natural Science Foundation of China and the [33] D. Brockmann, L. Hufnagel and T. Geisel, “The scaling laws of human Chinese Ministry of Science and Technology Peer Review College. He has travel,” Nature Letters, vol. 439, pp. 462–465, Jan. 2006. been actively involved in organizing more the ten international conferences [34] J. M. Park and G. U. Hwang, “Mathematical modeling of rayleigh fading since 2005. He served as the general Chair for the 2015 IEEE International channels based on finite state Markov chains,” IEEE Commun. Letters, Conference on Green Computing and Communications (IEEE GreenCom). He vol. 13 , no. 10, pp. 764–766, Oct. 2009. serves as an Associate Editor for the IEEE ACCESS, Wireless Communications [35] J. G. Andrews, F. Baccelli and R. K. Ganti, “A tractable approach to and Mobile Computing Journal (Wiley) and the International Journal of coverage and rate in cellular networks,” IEEE Trans. Commun., vol. 59, Communication Systems (Wiley), etc. Moreover, he served as the guest no. 11, pp.3122–3134, Nov. 2011. editor for IEEE Communications Magazine Special Issue on 5G Wireless [36] M. Haenggi, “On distances in uniformly random networks,” IEEE Trans. Communication Systems. Inform. Theory, vol. 51, no. 10, pp. 3584–3586, Oct. 2005. [37] J. Y. Le Boudec and M. Vojnovic, “The Random Trip Model: Stability, Stationary Regime, and Perfect Simulation,” IEEE/ACM Trans. Network- ing, vol. 14, no. 6, pp. 1153–1166, Dec. 2006. [38] J. Yoon, M. Liu and B. Noble, “A general framework to construct Junliang Ye recieved the B.Sc. Degree in com- stationary mobility models for the simulation of mobile networks,” IEEE munication engineering from China University of Trans. Mobile Computing, vol. 5, no. 7, pp. 860–871, July 2006. Geosciences, Wuhan, P.R China, in 2011, and he [39] C. A. V. Campos, R. J. Brazil and L. F. M. de Moraes, “Realistic is currently a Ph.D student in communication and Individual Mobility Markovian Models for Mobile Ad hoc Networks,” information system in Huazhong University of Sci- Wireless Communications and Networking Conference 2004, vol. 4, pp. ence and Technology, Wuhan, P.R China. 1980–1985, 2004. His research interests include heterogeneous net- [40] J. Stewart, Calculus: Early Transcendentals, 7th edition, Cengage Learn- works, stochastic geometry, mobility based access ing, 2011. models of cellular networks and next generation wireless communication.
Yang Yang (SM’10) received the BEng and MEng degrees in Radio Engineering from Southeast Uni- versity, Nanjing, P. R. China, in 1996 and 1999, respectively; and the PhD degree in Information Engineering from The Chinese University of Hong Kong in 2002. Dr. Yang Yang is currently a Professor with the School of Information Science and Technology, ShanghaiTech University, and the Director of Shang- hai Research Center for Wireless Communications (WiCO). Prior to that, he has served Shanghai Insti- tute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences, as a Professor; the Department of Electronic and Electrical Engineering at University College London (UCL), United Kingdom, as a Senior Lecturer; the Department of Electronic and Computer Engineering at Brunel University, United Kingdom, as a Lecturer; and the Department of Information Engineering at The Chinese University of Hong Kong as an Assistant Professor. His research interests include wireless ad hoc and sensor networks, wireless mesh networks, next generation mobile cellular systems, intelligent transport systems, and wireless testbed development and practical experiments. Dr. Yang Yang has co-edited a book on heterogeneous celluar networks (2013, Cambridge University Press) and co-authored more than 100 technical papers. He has been serving in the organization teams of about 50 international conferences, e.g. a co-chair of Ad-hoc and Sensor Networking Symposium at IEEE ICC15, a co-chair of Communication and Information System Security Symposium at IEEE Globecom15. IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. Y, MONTH 2016 15
Qiang Li Qiang Li received the B.Eng. degree in communication engineering from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2007 and the Ph.D. degree in electrical and electronic engineering from Nanyang Technological University (NTU), Singa- pore, in 2011. From 2011 to 2013, he was a Re- search Fellow with Nanyang Technological Univer- sity. Since 2013, he has been an Associate Pro- fessor with Huazhong University of Science and Technology (HUST), Wuhan, China. His current research interests include future broadband wireless networks, cooperative communications, wireless power transfer, cognitive radio networks.