Energy-Efficient Resource Allocation for Ultra-reliable and Low-latency Communications

Enery-Efficient Resource Allocation for Ultra-reliable and Low-latency Communications Chenjian Sun, Chanyan She and Chenyan Yan School of Electronics and Information Enineerin, Beihan University, Beijin, China Email: sunchenjian,cyshe,cyyan}@buaa.edu.cn arxiv:77.972v [cs.it] 3 Jul 27 Abstract Ultra-reliable and low-latency communications URLLC is expected to be supported wiout compromisin e resource usae efficiency. In is paper, we study how to maximize enery efficiency EE for URLLC under e strinent quality of service QoS requirement imposed on e end-to-end E2E delay and overall pacet loss, e E2E delay includes queuein delay and transmission delay, and e overall pacet loss consists of queuein delay violation, transmission error wi finite bloclen channel codes, and proactive pacet droppin in deep fadin. Transmit power, bandwid and number of active antennas are jointly optimized to maximize e system EE under e QoS constraints. Since e achievable rate wi finite bloclen channel codes is not convex in radio resources, it is challenin to optimize resource allocation. By analyzin e properties of e optimization problem, e lobal optimal solution is obtained. Simulation and numerical results validate e analysis and show at e proposed policy can improve EE sinificantly compared wi existin policy. I. INTRODUCTION Ultra-reliable and low-latency communications URLLC is crucial to enable mission critical applications such as autonomous vehicle communications, factory automation and haptic communications [, 2]. To ensure e low end-to-end E2E delay includin uplin UL and downlin DL transmission delay, codin and processin delay, queuein delay, and routin delay in bachaul and core networs, short frame structure becomes necessary [3], queuein delay should be controlled [4], and networ architecture needs to be updated. To ensure e hih reliability characterized by e overall pacet loss probability, includin transmission errors in UL and DL transmissions, pacet loss due to queuein delay violation and proactive pacet droppin in deep fadin [5], toeer wi e short delay uarantee, channel codin wi finite bloclen ouht to be used [6], and various diversity techniques are critical [7]. While supportin e strinent quality of service QoS of URLLC is not an easy tas for radio access networs, e resource usae efficiency should not be compromised. Enery efficiency EE is a ey performance metric of e fif eneration 5G mobile communications, which has been extensively studied please see [8, 9] and references erein. However, e meods in literatures can hardly be extended to URLLC mainly due to e followin reasons. First, bo e EE and QoS depend on e achievable rate. The Shannon s capacity used in existin studies cannot characterize e maximal achievable rate wi iven transmission error, and hence can no loner be applied to URLLC. Second, owin to e very short delay bound, existin tools of analyzin queuein delay may not be applicable to URLLC. An early attempt to desin enery efficient URLLC in [] showed at effective bandwid [] can be used to characterize queuein delay for Poisson process. More recently, e study in [5] validated at effective bandwid can be applied for arrival processes at are more bursty an Poisson process. By furer introducin a simple approximation to e achievable rate wi finite bloclen channel codes, e transmit power and bandwid allocation policy was optimized wi closed-form solution to maximize system EE under constraints on transmission and queuein delays and correspondin pacet loss components []. However, such an approximation is not always accurate, since e sinalto-noise ratio SNR and e bloclen of different users chane in a wide rane. In practice, circuit power consumption hihly depends on e number of active antennas, which was not optimized in []. How to jointly allocate transmit power and confiure bandwid and antenna to maximize e EE for URLLC wi accurate achievable rate approximation deserves furer study. In is paper, we optimize EE of URLLC. Since around 8% enery consumption in cellular networs comes from BSs [8], we only consider e enery consumed at e BSs. We jointly optimize transmit power, bandwid and e number of active antennas to maximize EE under e QoS constraints. To capture e basic idea, we focus on DL resource allocation. Different from [], an accurate approximation of e achievable rate wi finite bloclen channel codes in [6] will be applied, which however leads to very complicated QoS constraints. By furer introducin an approximation and an upper bound, e QoS constraints are expressed in closedform, but are still non-convex in bo transmit power and bandwid. By analyzin e properties of e optimization problem, e lobal optimal resource allocation policy is obtained. Simulation and numerical results show at e proposed policy can satisfy e QoS requirement and provide remarable EE ain over existin policy. A. System and Traffic Models II. SYSTEM MODEL Consider a cellular system, each BS wi N t antennas serves K + M sinle-antenna nodes. The nodes are

divided into two types. The first type of nodes are K users, which upload and download pacets to and from e BS. The second type of nodes are M sensors, which only upload pacets. We consider e local communication scenario each user only needs e pacets from e nodes located in a few adjacent cells. All e nodes upload eir own messaes in short pacets to eir accessed BSs in UL. If a BS receives e messaes from e nodes e.., node K+ in Fi. a at are required by e users accessed to an adjacent BS e.., node 2, e BS forwards e required messaes to e adjacent BS via bachaul, and en e adjacent BS transmits e relevant messaes to e taret users. Such a scenario can be found in autonomous vehicle communications, smart factory and some aumented reality applications [2], e propaation delay is neliible, and e fiber bachaul latency is very short around. ms [2]. For lon distance communication scenarios, e E2E delay ranes from ms to ms, dependin on e use cases [3]. Nevereless, accordin to [4], e latency in radio access networ should not exceed ms. We reserve e delay for bachaul transmission for simplicity, and focus on e latency in radio access networs. Time is discretized into frames. Each frame has duration T f, which includes UL and DL transmissions. We consider frequency reuse and frequency division multiple access to avoid interference. node K+M user sensor Bachaul node node K+ a b node 2 UL DL Bachaul Queuein Frame B. Channel Model Fi.. System model and E2E delay.... UL DL node K node K+2 Concerned area of node 2 UL DL Frame We consider typical use cases in URLLC, e E2E delay requirement D max and hence channel codin bloclen and e queuein delay is shorter an e channel coherence time. Since e data rate for URLLC is not hih, it is reasonable to assume at e bandwid for each user is less an e channel coherence bandwid, and en e channel is flat fadin. Denote e averae channel ain and e normalized channel coefficient for e user as α and h C Nt, respectively, e elements of h are independent and identically complex Gaussian distributed wi zero mean and unit variance. When bo α and h are nown at e BS, for a iven transmission error probability ε c, e achievable pacet rate wi finite bloclen can be accurately approximated by [6] s φw [ ln + α P t ] } V Q G u ln 2 N W φw εc, P t and W is e transmit power and bandwid allocated to e user, respectively, u is e number of bits contained in each pacet, φ, T f is e time at can be used for DL transmission in one frame, = h H h, [ ] H denotes conjuate transpose, N is e sinle-side noise spectral density, Q G x is e inverse of e Gaussian Q- function, and V is e channel dispersion iven in [6] C. QoS Requirement V = [ ] + α P t 2. 2 N W As shown in Fi. b, e E2E delay D max consists of UL transmission delay, bachaul latency, queuein delay and DL transmission delay. Since e pacet size is very small e.., 2 bytes [4], we assume at bo UL and DL transmission for a pacet can be finished wi iven error probability in one frame wiout retransmission, i.e., e transmission delay can be ensured by e properly desined frame duration. For simplicity, assume at e bachaul delay is wiin one frame. Then, to ensure e E2E delay, e queuein delay should be Dmax q =D max 2T f. If e queuein delay of a pacet is loner an e delay bound Dmax, q en it has to be dropped reactively. Denote e queuein delay violation probability as ε q. Since e queuein delay is shorter an channel coherence time in typical scenarios, e optimal transmit power allocated to ensure Dmax, q ε q is channel inverse and could become unbounded [5]. To uarantee e overall pacet loss wi finite transmit power, we can discard some pacets proactively [5], i.e., drop some pacets durin deep channel fadin even when eir queuein delay is less an Dmax. q Denote proactive pacet droppin probability as ε h. Then, e ree pacet loss components should satisfy ε c +εq +εh ε D to ensure e overall reliability, ε c is e DL transmission error probability and e UL transmission error probability has been subtracted from ε D. D. Enery Efficiency and Power Model EE is defined as e ratio of e averae data rate to e averae total power consumed at e BSs. By settin e frequency reuse factor as /3, ere is no stron interference and resource allocation policy of one BS does not depend on at of e oer BSs. Therefore, maximizin e networ EE is equivalent to maximizin e EE of each cell, which is η = ε D K = E i A a i n }, 3 E P tot } A is e set of indices of nodes at lie in e concerned area of user, a i n is e number of pacets uploaded by node i in e n frame, and E P tot } is e

averae total power consumed by e BS, which can be simplified as [5], E P tot } = ρ E P} t + P ca N t + P c, 4 = ρ, ] is e power amplifier efficiency, P t is e transmit power allocated to user, P ca is e circuit power consumed by each antenna for transmission pacets in DL and receivin pacets from UL, and P c is e fixed circuit power independent of e number of antennas. III. RESOURCE ALLOCATION OPTIMIZATION In is section, we optimize e resource allocation at maximizes e EE meanwhile satisfies e QoS requirement. Since e nominator in 3 approximately does not depend on e resource allocation because ε D, maximizin EE is equivalent to minimizin e averae total power consumption. A. Problem Formulation Denote e maximal transmit power of e BS as Pmax. t Then, e transmit power allocated to e users should satisfy K = P t P max. t Wi is constraint, e power allocated to each user depends on e channels of oer users. As a result, it is hard to obtain e averae transmit power of each user in closed-form. In order to find a closed-form expression of E P tot } to facilitate optimization, we introduce a maximal transmit power constraint for each user as P t P, K = P P max. t The minimal constant service rate required to ensure e queuein delay requirement Dmax, q ε q is e effective bandwid of e arrival process []. For a Poisson process wi arrival pacet rate λ, e effective bandwid is [5], E B T f ln/ε q = [ ]. 5 Dmax q ln + T f ln/ε q λ Dmax q Then, e queuein delay requirement can be satisfied if [] s E B. 6 For oer arrival processes, e expressions of E B will differ, but e proposed meod to optimize resource allocation is still applicable. By substitutin e achievable pacet rate i.e., service rate in and effective bandwid in 5 into 6, e required SNR to uarantee bo ε c and Dq max, ε q should satisfy γ exp l ε q = T f u ln 2 ln /ε q [ l ε q W + v ε c W /V }, 7 φd q max ln + T f ln /ε q D q max λ ], and v ε c = Q G εc / φ. Accordin to 2, we have V. Since e riht hand side of 7 increases wi V, e QoS requirement can still be satisfied wi V =. By substitutin V = into 7, e riht hand side does not depend on γ, and en we obtain a conservative QoS constraint in closed-form. To satisfy 7 wi V = and e maximal transmit power constraint, P t, depends on accordin to P t = NW γ α P P, if <, N W γ α, if, 8 is a reshold. When e channel ain is lower an, e required SNR to ensure QoS cannot be achieved. In is scenario, we can proactively discard several pacets wiout transmission, and en control e overall pacet loss/droppin probability. The achievable pacet rate wi transmit power P can be obtained by substitutin P t = P into, and is denoted as s. Then, e number of pacets at are discarded when < is [5], d n = mint f E B s, Qn, if Qn >, 9 Qn is e number of pacets waitin in e queue at e beinnin of e n frame. From e derivation in [5], e pacet droppin probability can be approximated as B Nt ε h E[d n] λ B Nt, ln + γ f Nt d. ln + γ Accordin to 8, e averae transmit power for e user can be expressed as E P t } = P f Nt d+ N W γ α f Nt d, 2 f Nt = N t N t! e is e probability density function of. By substitutin f Nt into 2, we obtain E P t } N W γ [ ] = FNt α N t, 3 F Nt =Nt f Nt d = f Nt d 4 = N t e N t 2 n= n +e n! Nt 2 N t 2!. We can prove at F Nt is an upper bound of BNt. The proof is omitted due to lac of space. Since e upper bound is in closed-form, we apply it as e QoS constraint imposed on e pacet droppin probability. While e optimal combination of ε c, εq and εh will

improve EE, e optimization leads to an intractable resource allocation problem but wi marinal ain [5]. In e sequel, we consider ε c = εq = εh = ε D/3. Then, e optimization problem can be formulated as minimize P,W,N t ρ s.t. E P} t + P ca N t + P c 5 = γ exp F Nt εd /3, = = N W γ α P P l ε D /3 W + v ε D /3 W }, 5a P t max, 5b, 5c W W max, = P >, W >, N t 2, =, 2,..., K, 5d 5a is e constraint on ε c and Dq max, ε q obtained by substitutin V = and ε c = εq = ε D/3 into 7, 5b is e constraint on ε h since F N t is an upper bound of B Nt, 5c reflects e relation of P in 8, and W max is e total bandwid. After substitutin γ in 5c into 5a, we can see at e feasible reion of e problem is non-convex. This is because e achievable rate wi finite bloclen in is non-convex. As a consequence, it is very challenin to find e lobal optimal solution. B. Optimal Resource Allocation Policy and In is subsection, we propose a meod to find e lobal optimal solution of problem 5. It is not hard to prove at E P tot } increases wi P iven W and N t. Moreover, accordin to e definition of, P decreases wi. Hence, minimizin E P tot } is equivalent to maximizin. Furermore, we can prove at F Nt increases wi e proof is omitted due to e lac of space. Therefore, e maximal can be obtained from F N t = ε D/3, and e minimal P wi iven W and N t can be expressed as P = N W γ α, if P Pmax, t 6 = γ is e minimal value at satisfies constraint 5a. If K = P > Pmax, t we need to increase N t until e power constraint satisfies. By substitutin e optimal W and N t into 6, optimal P can be obtained, and hence we optimize W and N t in e sequel. Substitutin F Nt =ε D/3 into 3, we have E P t } N W γ ε D /3 =. 7 α N t Substitutin 7 into 4, we can obtain at E P tot } = N K W γ = α ε D /3 + P ca N t + P c. ρ N t 8 The optimal value of W at minimizes E P tot } is e same as at minimizes K W γ = α, which does not depend on N t. However, e optimal value of N t at minimizes E P tot } depends on W. Therefore, we first find e optimal bandwid allocation W, and en optimize N t iven W in e sequel. Since 8 increases wi γ, e minimal E P tot } is obtained when e equality of 5a holds. Denote l ε D /3 W + y W = W γ = W e v ε D /3 W. 9 Then, e optimal bandwid allocation at minimizes E P tot } under e QoS constraints can be found from e followin problem, minimize W,=,2,...,K s.t. = y W α, 2 W W max and W >. = y W is non-convex in W. Essentially, is results from e non-convex achievable rate in. Fortunately, we can exploit e followin properties to find e lobal optimal solution. Property. y W first strictly decreases and en strictly increases wi W. See proof in Appendix A. Property indicates at a unique solution W at minimizes y W can be obtained via binary search alorim. Property 2. y W is strictly convex in W when W, W. See proof in Appendix A. Wi ese properties, we consider two complementary cases to find e lobal optimal solution of problem 2. Case : In e case e bandwid is sufficiently lare such at K = W W max, W,..., WK } is a feasible solution of problem 2. Accordin to Property, y W is minimized at W, and hence e objective function 2 is minimized at W,..., WK }. Therefore, W,..., WK } is e lobal optimal solution, i.e., W = W. 2 Case 2: In e case K = W > W max, W,..., WK } is not a feasible solution of problem 2. However, wi Property, it is not hard to see at e lobal optimal bandwid allocation satisfies W W. Then, problem 2 is equivalent to e followin problem, minimize W,=,2,...,K s.t. = = y W α 2 W = W max, < W W, which is convex accordin to Property 2. Then, e lobal optimal bandwid allocation W can be obtained wi interior point meod. By substitutin W into 8, e lobal optimal number of active transmit antennas at minimizes E P tot } under e

Averae total power dbm QoS constraints can be derived as Nt 4N ε D /3 K = + + 2 ρp ca = y W α x denotes e minimal inteer no less an x. IV. SIMULATION AND NUMERICAL RESULTS, In is section, we validate e approximation and upper bound introduced to ensure e QoS, illustrate properties and and evaluate e EE achieved by e proposed policy. We set ε c =εq =εh =ε D/3= 7. The users are uniformly distributed in e rane of 5 m 25 m away from e BS. There are 2 nodes lie in e concerned area of each user, which may be sensors or oer users around e taret user. The averae pacet arrival rate from each node is pacets per second, which is e typical value in vehicle networs as well as some oer use cases [3]. Oer parameters are listed in Table I. TABLE I SIMULATION PARAMETERS E2E delay requirement D max Duration of each frame T f Duration of DL transmission φ ms. ms.5 ms Bachaul latency. ms [2] Queuein delay requirement Dmax q.8 ms Sinle-sided noise spectral density N 73 dbm/hz Available bandwid W max 2 MHz Pacet size u 6 bits [4] Pa loss model lα 35.3 + 37.6 ld Maximal transmit power of BS Pmax t 4 dbm Circuit power consumed per antenna P ca 5 mw [5] Fixed circuit power P c 5 mw [5] power amplifier efficiency ρ.5 [5] TABLE II VALIDATION OF THE APPROXIMATION AND BOUND Required ε h 8 7 6 5 Achieved ε h.9 9 9.2 9.8 7 3.9 6 The impact of usin e approximated ε h in and e upper bound of B Nt i.e., FNt in e optimization is shown in Table II, K =, M = 2 and e user-bs distance is 25 m. The achieved ε h is obtained by computin e averae number of discarded pacets from 9 wi e optimal policy over Rayleih fadin channel realizations and en substitutin it into. We can see at e achieved ε h are lower an e required ε h, which means at e QoS requirement can be uaranteed wi e approximation and upper bound used in constraint 5b. Similar results have been obtained for K 2 at ive rise to e same conclusion, which are omitted for conciseness. By substitutin F Nt = into 3, we can see at e averae transmit power is ε h insensitive to proactive pacet droppin probability, i.e., e approximation and e bound have minor impact on EE. TABLE III VALUES OF W THAT MINIMIZE y W ε c 8 7 6 5 W MHz 7.35 7.42 7.53 7.7 Values of W wi different transmission error probability requirements are shown in Table III, E B =. It can be seen at W is much larer an e coherence bandwid e..,.5 MHz. Furermore, we can be prove at W increases wi E B and u, and does not chane wi e channel ain. The proof is omitted due to lac of space. Thus, 9 strictly decreases wi W and is convex in W if W is smaller an coherence bandwid. 45 4 35 3 25 K=4 K=2 K=6 K=8 K= minimal power consumption and Nt * power consumption wi fixed K 4 8 6 32 64 28 256 Number of active antennas Fi. 2. Averae total power consumption v.s. active number of antennas. The averae total power consumption obtained wi different numbers of active transmit antennas is shown in Fi. 2. The dash curves are obtained wi different number of users, which reflect e traffic load. It shows at e averae total power consumption first decreases and en increases wi N t for iven user density. This is because ere is a tradeoff between transmit power and circuit power. Transmit power is hih when N t is small, and circuit power is hih when N t is lare. The solid curve shows e relation between e minimal averae total power consumption and e correspondin optimal number of active transmit antennas. It shows at bo e minimum averae total power and N t increase wi K. The maximized EE versus number of users is demonstrated in Fi. 3. The dash curves are e maximal EE achieved by optimizin transmit power and bandwid allocation wi iven number of antennas which can be rearded as a modified policy of [] by considerin a more accurate approximation of achievable rate, e circle in each curve indicates e maximal number of users at can be supported wi e iven resources. The solid curve is e maximal EE achieved by e proposed optimal resource allocation, e number of antennas is jointly optimized wi transmit power and bandwid. As is shown, e EE increases wi K under liht traffic load, but decreases wi K under heavy traffic load.

Enery efficiency Mbit/J 5 4 3 K=53 maximal EE. Hence, we can find W in W, +, which is e solution of xw =. Then, we have > if < W < W, y W = if W = W, A.3 < if W > W. 2 Nt=8 Nt=6 K=78 Nt=32 K=95 K=8 Nt=64 Nt=28 2 3 4 5 6 7 8 9 2 Number of users Fi. 3. Maximal EE v.s. e number of users. The aps between e solid curve and e dash curves indicate at adjustin e number of active antennas accordin to e number of users is critical to maximizin e EE. V. CONCLUSION In is paper, we studied how to optimize enery efficient resource allocation for URLLC. We formulated a problem to optimize transmit power, bandwid, and number of active antennas at maximizes e EE under e ultra-low E2E latency and ultra-hih overall reliability requirements. Alouh e optimization problem is non-convex owin to e nonconvex achievable rate wi finite bloclen channel codes, e lobal optimal solution was obtained. Simulation and numerical results validated our analysis and showed at by jointly optimizin e number of active antennas toeer wi e transmit power and bandwid, e EE of e system can be improved sinificantly. APPENDIX A PROOF OF THE PROPERTIES OF 9 Proof. The index is omitted in is appendix for notational simplicity. The first order and second order derivatives of yw are respectively y W = l W v 2 e l W + v W, A. W y W = vw 3 /2 +v 2 W +4lv W +4l 2 e l W + v W 4W 3. A.2 Denote xw = vw 3 /2 + v 2 W + 4lv W + 4l 2. Notice at y W = if and only if xw =. We can also obtain at x W >, W [, W and x W <, W W, +, W is e solution of x W =. Since x = 4l 2 > and xw increases wi W when W [, W, xw >, W [, W. Moreover, xw decreases wi W when W W, +, and xw when W By analyzin A.2, we can find W, W at satisfies y W = e details are omitted due to e lac of space. Then, from A.3 and lim W y W = we have < if < W < W, y W = if W = W, A.4 > if W < W. Therefore, ere exists a unique point W, + at minimizes yw. Since y W < and y W > when W, W, yw is a strict decreasin and convex function of W when W, W. REFERENCES [] O. N. C. Yilmaz, Y.-P. E. Wan, N. A. Johansson, et al., Analysis of ultra-reliable and low-latency 5G communication for a factory automation use case, in IEEE ICC Worshops, 25. [2] M. Simse, A. Aijaz, M. Dohler, et al., 5G-enabled tactile internet, IEEE J. Select. Areas Commun., vol. 34, no. 3, pp. 46 473, Mar. 26. [3] P. Kela, J. Tura, et al., A novel radio frame structure for 5G dense outdoor radio access networs, in Proc. IEEE VTC Sprin, 25. [4] A. Aijaz, Towards 5G-enabled tactile internet: Radio resource allocation for haptic communications, in Proc. IEEE WCNC, 26. [5] C. She, C. Yan, and T. Q. Que, Cross-layer optimization for ultrareliable and low-latency radio access networs, IEEE Trans. Wireless Commun., revised, https://arxiv.or/pdf/73.9575.pdf. [6] W. Yan, G. Durisi, T. Koch, et al., Quasi-static multiple-antenna fadin channels at finite bloclen, IEEE Trans. Inf. Theory, vol. 6, no. 7, pp. 4232 4264, Jul. 24. [7] G. Pocovi, B. Soret, M. Lauridsen, et al., Sinal quality outae analysis for ultra-reliable communications in cellular networs, in IEEE Globecom Worshops, 25. [8] G. Wu, C. Yan, S. Li, and G. Li, Recent advance in enery-efficient networs and its application in 5G systems, IEEE Wireless Commun. Ma., vol. 22, no. 2, pp. 45 5, Apr. 25. [9] W. Yu, L. Musavian, and Q. Ni, Tradeoff analysis and joint optimization of lin-layer enery efficiency and effective capacity toward reen communications, IEEE Trans. on Wireless Commun., vol. 5, no. 5, pp. 3339 3353, May 26. [] C. She and C. Yan, Enery efficient desin for tactile internet, in Proc. IEEE/CIC ICCC, 26. [] C. Chan and J. A. Thomas, Effective bandwid in hih-speed diital networs, IEEE J. Sel. Areas Commun., vol. 3, no. 6, pp. 9, Au. 995. [2] G. Zhan, T. Q. S. Que, A. Huan, et. al., Delay modelin for heteroeneous bachaul technoloies, in Proc. IEEE VTC Fall, 25. [3] P. Schulz, M. Maté, H. Klessi, et al., Latency critical IoT applications in 5G: Perspective on e desin of radio interface and networ architecture, IEEE Commun. Ma., vol. 55, no. 2, pp. 7 78, Feb. 27. [4] 3GPP, Study on Scenarios and Requirements for Next Generation Access Technoloies. Technical Specification Group Radio Access Networ, Technical Report 38.93, Release 4, Oct. 26. [5] B. Debaillie, C. Desset, and F. Louaie, A flexible and future-proof power model for cellular base stations, in Proc. IEEE VTC Sprin, 25.