Dynamic Uplink/Downlink Resource Management in Flexible Duplex-Enabled Wireless Networks

Transcription

1 Dynamic Uplink/Downlink Reource Management in Flexible Duplex-Enabled Wirele Network Qi Liao Nokia Bell Lab, Stuttgart, Germany arxiv:7.78v [ee.sp] Sep 7 Abtract Flexible duplex i propoed to adapt to the channel and traffic aymmetry for future wirele network []. In thi paper, we propoe two novel algorithm within the flexible duplex framework for joint uplink and downlink reource allocation in multi-cell cenario, named ucceive approximation of fixed point (SAFP) and reource muting for dominant interferer (RMDI), baed on the awarene of interference coupling among wirele link. Numerical reult how ignificant performance gain over the baeline ytem with fixed uplink/downlink reource configuration, and over the dynamic time diviion duplex (TDD) cheme that independently adapt the configuration to timevarying traffic volume in each cell. The propoed algorithm achieve two-fold increae when compared with the baeline cheme, meaured by the wort-cae quality of ervice atifaction level, under a low level of traffic aymmetry. The gain i more ignificant when the traffic i highly aymmetric, a it achieve three-fold increae. I. INTRODUCTION Flexible duplex i one of the key technologie in fifth generation (5G) to optimize the reource utilization depending on traffic demand []. The main objective i to adapt to aymmetric uplink (UL) and downlink (DL) traffic with flexible reource allocation in the joint time-frequency domain, uch that the ditinction between TDD and frequency diviion duplex (FDD) i blurred, or completely removed. Depite the advantage of adaptation to the dynamic traffic aymmetry, the drawback i the newly introduced inter-cell interference (ICI) between duplexing mode DL and UL, hereinafter referred a inter-mode interference (IMI). The DL-to- UL interference play a more important role due to the large difference between DL and UL tranmiion power. Many work focu on phyical layer deign to overcome IMI. In [], pecial kind of radio frame with different ratio of UL/DL are introduced to FDD, and heuritic approach i propoed to find the mot uitable one olely baed on the traffic volume. A few tudie target the problem of dynamic UL/DL reource configuration. In [3], the author formulate a utility maximization problem to minimize the per-uer difference between UL and DL rate; while in [4] the problem i formulated a a twoided table matching game to optimize the average utility per uer. Both work conider a ingle cell ytem where IMI doe not play a role. However, in a multi-cell ytem the optimal UL/DL configuration depend not only on the traffic volume but alo the interference coupling between all tranmiion link. Although very few tudie provide olution within the flexible duplex framework, imilar problem exit in dynamic TDD. A popular olution i the cell-cluter-pecific UL/DL reconfiguration [5], but how to coordinate the cluter for intercluter IMI mitigation till remain a challenge. In thi paper, we optimize UL/DL reource configuration in multi-cell cenario, by recating max-min fairne problem into a fixed point framework. Such framework i widely ued for power control [6], [7] and load etimation [8], [9] for UL or DL ytem independently. Our previou work [] exploit the framework to tackle the joint UL/DL reource allocation and power control problem within flexible duplex, auming that ICI i imply proportional to the load. Thi aumption, however, i valid only when each reource unit ha the ame chance to be allocated to UL or DL, which may reult in high probability of generating IMI. We improved the model in thi paper. The main contribution i ummarized in below. A new interference model i defined, which allow to prioritize the poition of the reource for UL and DL tranmiion, to reduce the probability of generating IMI. We propoe a novel algorithm SAFP to find algorithmic olution to optimize UL/DL reource configuration. Unlike the model in previou work [6], [8], [9], the new interference model i nonlinear and nonmonotonic. Further we enhance SAFP to RMDI by detecting equentially the dominant interferer in the ytem, and muting the partial reource in neighboring cell to reduce ICI. We compare SAFP and RMDI numerically with two conventional cheme: a) fixed UL/DL configuration, and b) dynamic TDD that adapt UL/DL configuration olely baed on traffic volume, and how a performance gain varying from two to three fold depending on the traffic aymmetry. The ret of the paper i organized a follow. In Section II, the ytem model i decribed together with the correpondent notation. The problem tatement i given in Section III. The propoed algorithm SAFP and RMDI are introduced in Section IV and V, repectively. Finally, in Section VI, the numerical reult are preented. II. SYSTEM MODEL In thi paper, we ue the following definition. The nonnegative and poitive orthant in k dimenion are denoted by R k + and R k ++, repectively. Let x y denote the componentwie inequality between two vector x and y. Let diag(x) denote a diagonal matrix with the element of x on the main diagonal. For a function f : R k R k, f n denote the n-fold compoition o that f n = f f n. The cardinality of et A i

2 TABLE I: NOTATION SUMMARY N K S W S (u) (S (d) ) S n n A B B (u) (B (d) ) δ t(δ f ) W t(w f ) w ν ν (u) (ν (d) ) p d H V ρ ρ et of BS with N = N et of UE with K = K et of ervice with S = S et of MRU with W = W et of UL (DL) ervice et of ervice erved by the nth BS index of BS erving the th ervice UE-to-ervice aociation matrix BS-to-ervice aociation matrix BS-to-UL (BS-to-DL) aociation matrix length of time duration (range of frequency) of an MRU number of mallet time (frequency) unit in MRU et W fraction of reource allocated to ervice cell load cell load in UL (DL) tranmit power allocated to ervice traffic demand of ervice channel gain matrix link gain coupling matrix per ervice QoS atifaction level wort-cae QoS atifaction level denoted by A. The poitive part of a real function i defined by [f(x)] + := max {, f(x)}. The notation that will be ued in thi paper i ummarized in Table I. We conider an orthogonal frequency diviion multiplexing (OFDM)-baed wirele network ytem, coniting of a et of bae tation (BS) N := {n : n =,,..., N} and a et of uer equipment (UE) K := {k : k =,,..., K}. We aume that the network enable flexible duplex, where the reource in both frequency and time domain can be dynamically aigned to UL and DL. We define minimum reource unit (MRU) a the mallet time-frequency unit, that ha a length of δ t econd in time domain and a range of δ f Hz in frequency domain. We conider a et of MRU, denoted by W, coniting of W t mallet time unit and W f mallet frequency unit, and we have W := W = W t W f. We aume that K UE generate a et of UL and DL ervice S := S (u) S (d) within the time duration of W MRU (i.e., W t δ t econd). Let the UE-to-ervice aociation matrix be denoted by A {, } K S, where a k, = mean that the th ervice i generated by the kth UE, and otherwie. Let B {, } N S denote the BS-to-ervice aociation matrix. To differentiate UL and DL ervice, we further define BS-to-UL and BS-to-DL aociation matrice, denoted by B (u) {, } N S and B (d) {, } N S, repectively. Let the et of ervice erved by BS n be denoted by S n and let the BS aociated with ervice be denoted by n. Let w := [w,..., w S ] T [, ] S be a vector collecting the fraction of reource allocated to all ervice S. The cell load, defined a the fraction of occupied reource within a cell, i denoted by ν = Bw [, ] N. The cell load in UL and DL are denoted by ν (u) = B (u) w and ν (d) = B (d) w repectively, and we have ν = ν (u) + ν (d). We collect the tranmit power (in Watt) allocated to all ervice in a vector p := [p,..., p S ] T. A. Link Gain Coupling Matrix We aume that average channel gain over W MRU from each tranmitter (TX) to each receiver (RX) are known, Fig. : Example: Interference link gain. collected in H := (h i,j ) R (N+K) (N+K) ++. Note that the TX and RX include both UE and BS. Let v l, denote the channel gain of the link between the TX of link l and the RX of link. If l =, v l, i the channel gain of link, otherwie if l, v l, i the channel gain of the interference link caued by ervice l to. We define link gain coupling matrix Ṽ a Ṽ := (ṽ l, ) R S S +, with ṽ l, := v l, /v,, () where ṽ l, i the ratio between the interference link gain from ervice l to ervice and the erving link gain of. An example i hown in Fig., where we conider a ytem enabling downlink and uplink decoupling in 5G []. The interference caued by UL ervice 3 (link l 3 ) to DL ervice (link l ) ha a link gain of v 3, = h 3,4, i.e., the link gain between TX 3 (tranmitter of l 3 ) and RX 4 (receiver of l ). Given that the channel gain of l i h,4, the interference coupling ratio i given by ṽ 3, = h 3,4 /h,4. Remark (Incorporating different interference condition). Without lo of generality, we can modify Ṽ to take into account different interference condition. For example, to allow elf-interference cancellation we can define ṽ, := for every S, while to allow zero intra-cell interference we have ṽ l, := if l and are aociated with the ame BS. B. Quality of Service Metric In [] we aume that the probability that l caue ICI to aociated with a different BS i approximated by the fraction of it allocated reource w l, which lead to Pr {l interfere n l n } w l for l, S. () The average ignal-to-interference-plu-noie ratio (SINR) of S i approximated by p p SINR = ], (3) ṽ l, p l w l + σ [ṼT diag(w)p + σ v, l S where σ := [ σ /v,, σ /v,,..., σ S /v S,S] T, σ denote the noie power in the receiver of. Note that in (3) w l erve a a probability. The interference condition i taken into account in ṽ l, a illutrated in Remark. Note that ṽ l, i computed with average channel gain over W MRU. Thu, (3) i the ratio between average received ignal trength and average received interference, rather than the actual average SINR. Since we do not aume to know the ditribution of the channel gain, here we ue (3) to approximate the average SINR.

3 However, the approximation () and (3) are only valid under the aumption that each MRU i conidered to be equal for all the ervice to be allocated, namely, the poition of reource i not pecified for UL or DL. Unfortunately, uch aumption reult in a high probability of IMI. In the following we introduce an improved SINR model baed on a imple UL/DL reource poitioning trategy to reduce IMI. Recall that conventional TDD or FDD pecifie a et of reource for UL and DL repectively to prevent IMI. With flexible duplex, the challenge i to allow different reource partitioning between UL and DL in each cell, while limiting the probability of generating IMI. Let u take an example, cell m with UL load ν m (u) and cell n with DL load ν n (d) hare ame et of available reource. It i obviou that the minimum overlapping area between UL reource in cell m [ and DL reource in cell n i ν m (u) be eaily achieved by allocating the et of reource to UL traffic in cell m in ome priority order while allocating the ame et of reource to DL traffic in cell n in revere order. Given the aforementioned trategy, to derive the interference coupling matrix that incorporate the probability that a link caue ICI to another, we introduce a reue factor coupling matrix C(w) depending on w. Let x {u, d} denote the UL or DL traffic type of ervice S, and recall that n denote the erving BS of, C(w) i defined a + ν (d) n ] +, which can C(w) := C := (c l, ) R S S +, (4) [( ) ] + ν (x l) n l + ν n (x) /ν n (x) if x l x c l, := { } min, ν (x l) n l /ν n (x) if x l = x, where the load of cell [ n occupied ] by traffic type x i computed by ν n (x) := B (x) w. In general, c l, i defined n a the ratio of the overlapping area on the reource plane between the load of cell n l erving traffic type x l and the load of cell n erving traffic type x to the load of cell n erving traffic type x l. With C(w) in hand, given the power vector p, we can modify (3) and derive the SINR of ervice S a p SINR (w) [ ( Ṽ) ] T, (5) C(w) diag(p)w + σ where with a light abue of notation, X Y denote the Hadamard (entrywie) product of matrice X and Y. Note that the firt term in the denominator i the interference power received by ervice divided by the channel gain of, and it i equivalent to l c l,w l v l, p l /v,, where c l, w l approximate the probability that ervice l caue interference to ervice. The maximum achievable number of bit for ervice S within the time pan of reource et W i η (w) = δ t δ f W w log ( + SINR (w)), (6) where the unit of δ t δ f i Hz /MRU, while W w i the number of MRU allocated to. Auming that the nonzero traffic demand d := (d,..., d S ) T R S ++ i known, where d i defined a number of required bit of during the time pan of W, we introduce per ervice quality of ervice (QoS) atifaction level, written a ρ (w) = η (w)/d, S. (7) III. PROBLEM FORMULATION The objective i to partition the reource et W in each cell n N into three ubet: reource for UL, reource for DL, and blanked reource, repectively, to maximize the wortcae QoS atifaction level, defined a ρ(w) := min S ρ (w). (8) All demand of the ervice are feaible, when ρ(w). We formulate the problem in Problem, where (9a) and (9b) imply the objective of maximizing the wort-cae QoS atifaction level ρ, and (9c) i the per-cell load contraint. Problem max. ρ (9a) w R S +,ρ R+.t. w ρf(w), g(w) := Bw, where the vector-valued function f i defined by f : R S + R S ++ :w [f (w),..., f S (w)] T, where f (w) := δ t δ f W log ( + SINR (w)). d (9b) (9c) (a) (b) In [], we how that with conventional model of SINR (3), Problem i equivalent to olve a nonlinear ytem of equation uch that w = ρf(w), g(w) = and that ρ i maximized. It i worth mentioning that, with the modified model of interference coupling (4) and SINR (5), Problem i a multi-variate nonconvex optimization problem. Moreover, the contraint (9b) i neither convex nor continuouly differentiable, and Problem i not necearily equivalent to the nonlinear ytem of equation. In Section IV we provide algorithmic olution to Problem, denoted by w. The per-cell fraction of reource to allocated to UL and DL are then obtained a ν (u), = B (u) w and ν (d), = B (d) w, repectively. If ρ := ρ(w ), all demand are feaible. However, if ρ <, the olution to Problem i not a good operating point, ince the demand of all ervice are infeaible. In other word, all uer are unatified. Therefore, a further quetion arie: how can we tranform the deired demand in Problem from infeaible to feaible? One of the factor cauing infeaible demand i the bottleneck ervice. In Section V we modify Problem by dedicating partial reource for bottleneck ervice, while muting them for other, and develop an algorithm with heuritic trategie. Under certain condition, enhanced interference mitigation can be achieved by muting partial reource in ome cell. However, it i alo poible that the optimal olution return an empty et of the blanked reource.

4 Remark (New challenge due to complex interference coupling). Problem i formulated along imilar line to our previou work [, Problem a]. However, in [], the received interference in SINR (3) i an affine function of w, which further lead to ome nice propertie of f (a hown in Lemma ). In thi paper, becaue we introduce more complex interference coupling (4) and the reulting modified SINR model (5), the deired propertie of f do not exit, which bring new challenge with developing efficient algorithmic olution. IV. SUCCESSIVE APPROXIMATION OF FIXED POINT In thi ection, we firt provide background information about the mathematical tool to olve the problem. Then, we propoe a novel efficient algorithm SAFP to find a feaible point of w with good, if not optimal, objective value of ρ. A. Background Information and Previou Reult With the conventional SINR model in (3), f defined in () ha the following property. Lemma ([, Lemma ]). With SINR defined in (3), f : R S + R S ++ i a tandard interference function (SIF) (ee Appendix A for definition). Knowing that f i SIF, and that g : R S ++ R ++ in (9c) i a monotonic norm, we encounter the ame type of problem a [, Problem a]. The following propoition i provided baed on the previou reult [, Theorem ], which give rie to an algorithmic olution to Problem with conventional SINR model baed on the fixed point iteration cheme. Propoition. Suppoe SINR i modeled with (3), and f : R S + R S ++ i SIF, g : R S ++ R ++ i monotonic, and homogeneou with degree (i.e., g(αx) = αg(x) for all α > ) There exit a unique olution to Problem, denoted by {w, ρ }, where w can be obtained by performing the following fixed point iteration: w (t+) = f ( w (t)) g f ( w (t)), t N, () where with a light abue of notation, g f denote the compoition of function g and f. The iteration in () converge to w, and we have ρ = /g f(w ) and g(w ) =. Proof. The proof i omitted here ince it ue our previou reult [, Theorem ] and i along the ame line a [, Propoition ]. B. Succeive Approximation of Fixed Point Propoition provide an algorithmic olution to Problem with SINR (3), by utilizing the propertie of SIF. Unfortunately, with the modified SINR in (5), f i not SIF becaue the coupling matrix C(w) depend on w in a non-monotonic and non-differentiable manner. However, it i eay to how that by replacing C(w) in (5) with ome approximation C := C(w ) computed with fixed w, the SINR in (5) fall into the ame cla a (3), and the approximated problem can be olved by Propoition with f(w) replaced by f C (w) := f(w, C(w )). Therefore, our eential, natural idea i to efficiently compute a uboptimal olution of Problem by olving a equence of (impler) max-min fairne ubproblem whereby the noncontractive mapping f i replaced by uitable contraction approximation f C. Thee ubproblem can be olved with Propoition. More pecifically, the propoed SAFP algorithm conit in olving a equence of approximation of Problem in the form max. ρ;.t. w ρf C (w) ; g(w), () w R S +,ρ R+ where f C (w) repreent approximation of f(w) at the current iterate w. The unique olution to () can be obtained by the fixed point iteration (), with C(w) replaced by C(w ). Unfortunately, due to the complexity of C(w), the convergence of SAFP to a limit point cannot be guaranteed, ince multiple fixed point can exit in the ytem where the inequality ign in (9b) i replaced by the equality ign. Different initial value of ŵ may lead to different fixed point. Moreover, the olution to the ytem of nonlinear equation may not be the optimal olution to the original problem of maximizing the minimum, due to the nonmonotonicity of the mapping f when including C into the interference model. Thu, we deign the earching algorithm to guarantee the utility increae with initial value of {ρ, w }, maximum number of random initiation N max, and algorithm topping criterion depending on the maximum number of iteration N iter and the ditance threhold ɛ, illutrated a below. The algorithm run for N max time, each with a different random initialization of ŵ and the correponding C(ŵ). For each initialization ŵ n, n =,,..., N max, we iteratively perform the fixed point iteration in () with f(w) replaced by f Ĉn (w) where Ĉn := C(ŵ n ). The iteration top if the number of iteration exceed N iter or the ditance yield w w ɛ and return the olution {w, ρ } with repect to the nth random initialization. The olution i updated with w w, ρ ρ if ρ > ρ. The propoed SAFP algorithm i ummarized in Algorithm. Although the convergence of SAFP to a global optimum cannot be guaranteed and heuritic are introduced, numerical reult in Section VI (e.g., Fig. b) how that each random initialization converge to a fixed point, and with limited number of initialization, the algorithm find a uboptimal, if not optimal, olution among multiple fixed point. V. RESOURCE MUTING FOR DOMINANT INTERFERER The propoed SAFP find a feaible point of w with uboptimal, if not optimal, objective value of ρ. If ρ, the obtained w provide fairne on the ervice, and the demand of all ervice are feaible. However, if ρ <, w i not a good operating point ince the traffic demand of all ervice are infeaible. Therefore, in thi ection we focu the following quetion: how can we tranform the deired demand in Problem from infeaible to feaible?

5 Algorithm : SAFP algorithm for reource partitioning input : i, N max >, N iter >, ɛ >, ρ, w output: {w, ρ } while i N max do random initialization of w ; C C(w ); j, w ; (j) w w ; w (j) w ; while j N iter or (j) ɛ do % olving approximated ubproblem with C ; while w w ɛ do w w ; w f C (w)/g f C (w) ; % Update C with optimized w ; w (j+) w ; C (j+) = C C(w ) ; (j+) w (j+) w (j) ; j j + ; ρ = ρ (w ) min S w /f C,(w ); % update the olution if ρ exceed the tored value; if ρ > ρ then ρ ρ ; w w ; i i + ; In [], the author propoe a removal election criterion for an infeaible DL power control problem, that remove equentially the bottleneck ervice until the demand for all the remaining ervice are feaible. However, i there a method of further increaing ρ without removal of ervice? Motivated by coordinated muting uing almot blank ubframe (ABS) for time domain intercell interference coordination introduced in [3], we are intereted in exploring the tradeoff between reource utilization and interference reduction by introducing the reource muting in flexible duplex. A. Modified Load Contraint Incorporating Reource Muting The key concept i to equentially reerve ome reource in a cell for the dominant interferer, while muting them in the cell trongly impacted by the interferer. To thi end, we rank the ervice baed on the interference level that they generate to other, given by ( ) I (w) := c ṽ T p w, for S, (3) where c := row C(w) denote the th row of C(w), and ṽ := row Ṽ denote the th row of Ṽ. Moreover, to prevent the wate of reource, we elect the trongly affected cell to mute their reource. The et of cell to mute the reource reerved for i elected by M := {m N \ {n } : J,m (w) α}, (4) where α i a threhold and J,m (w) i the interference generated from ervice to a cell m n, defined a [ J,m (w) := B ( c ṽ ) ] T p w. (5) m If a et of dominant interferer S i choen, and for each S a ubet of the cell M i elected to mute reource w, then, in each cell we have the load contraint g m(w) := {m M}w + w l, for m N, (6) S l S m where { } i the indication function, the firt term i the total amount of reource to be muted in cell m, and the econd term i the amount of available reource for ervice in m. Since g m(w) need to be held for every m N, the load contraint can be rewritten a g (w) := max m N g m(w). (7) Note that without the muting cheme, i.e., if S =, the firt term in (6) i zero and (7) i equivalent to the per-cell load contraint in (9c). B. Deign of Heuritic Algorithm It i obviou that the modified g i alo monotonic and homogeneou with degree, which enable leverage of Propoition to olve the modified Problem, with g(w) replaced by g (w) to incorporate the reource reervation and muting trategy. Compared to the olution to the original Problem, reource muting may not necearily improve the deired utility ρ, becaue muting of w in cell m M may lead to wate of reource. Therefore, we develop a heuritic algorithm RMDI to guarantee a utility that i no le than the ρ derived in Algorithm. The Algorithm i decribed briefly in the following tep.. Derive w () = w to Problem with Algorithm and compute the correponding ρ () = ρ.. Compute I (w ) and rank the ervice baed on I. Let q denote the rank of, e.g., the maximum interferer ŝ := arg max I ha a rank of qŝ =. Set k =. 3. Add the ervice with highet rank into S (k), e. g., S (k) = { : q k}. 4. Solve modified Problem with S (k) uing Algorithm (with g replaced by g ), derive w (k) and ρ (k). 5. If ρ (k) ρ (k ), increment k and go back to Step 3; otherwie top the algorithm. 6. Obtain olution w = w (k ). VI. NUMERICAL RESULTS In thi ection, we analyze the performance of the propoed algorithm SAFP and RMDI, by conidering the aymmetry of UL and DL traffic in two-cell cenario. The ditance between the two BS i km. The tranmit power of BS and UE are 43 and dbm repectively and all the other imulation parameter mainly related to channel gain can be found in [4, Tab. A..-]. We define the minimum time unit δ t a.5 m and the minimum frequency unit δ f a 5 khz. Further we have W t = and W f = 3, i. e., a reource plane that pan a time duration of. econd and frequency of 5 MHz (including the guard band).

6 We defined a fixed total traffic demand Λ = d = 5 kbit within W t δ t =. econd, which implie a total erving data rate of 5 Mbit/. The total traffic can be aymmetrically ditributed between the two cell with different ratio among T inter := {/9, /8, 3/7,..., 9/, /}. Within each cell, the traffic can be aymmetrically ditributed between UL and DL traffic with ratio among T intra := {/9, /8, 3/7,..., 9/}. UE with either UL or DL traffic are generated with uniform ditribution within the interection of two ball with radiu km, and with BS and a their center repectively, to analyze the cenario of high inter-cell interference. Without lo of generality, we can place one UL and one DL ervice in each cell with the traffic demand computed by the traffic ratio mentioned above. ) Algorithm convergence of SAFP. Let u firt examine the convergence of Algorithm, and compare it with Algorithm FP that i ummarized in Propoition with conventional SINR model (3). The parameter are et a N max = 3, N iter =, ɛ = 4. In Fig. a we how the convergence of the SAFP with one particular initialization of w and C (w ) and compare it with FP. The magenta circle indicate the tarting point with an updated C ( w (j)), and the green dahed line how that with each fixed C ( w (j)), by performing fixed point iteration, ρ monotonically increae and converge to the fixed point with repect to C ( w (j)). Note that the green dahed line i not the actual utility ρ, ince it i computed with updated w (i) and the approximation C ( w (j )). Therefore, we plot the red line to how the convergence of the actual utility at each tep of updating C, computed with w (j) and C ( w (j)). By comparing the red curve and the blue curve (convergence of FP algorithm), we oberve a ignificant increae of utility ρ by uing SAFP. Thi i becaue, comparing with FP that randomly place the UL and DL reource, SAFP i baed on an improved interference model, where ICI only appear in the interection of the et of allocated MRU between different cell. Fig. b illutrate that with each random initialization of w, the propoed SAFP converge to a fixed point. The example how that 3 initialization converge to two different fixed point with utilitie 4.35 and.9 repectively. w correponding to higher utility i choen a the final olution. ) Performance comparion. We compare the performance of SAFP and RMDI to the performance of the other three protocol, decribed in below. FIX: Fixed ratio and ame poition of the UL and DL reource in different cell. IMI doe not exit due to the orthogonal frequency band for UL and DL. The amount of the UL and DL reource are fixed to be the ame. dtdd: Adaptive UL and DL reource proportional to the traffic volume in each cell independently. FP: Propoed algorithm in [] (ummarized in Propoition ) that olve Problem with old SINR model (3). To compare the performance of protocol FIX, dtdd, FP, SAFP, and RMDI under different traffic aymmetry, we define a meaure inter-cell traffic ditance, given by D m,n := ϑ n ϑ m, where ϑ n := [ ϑ (u) n ] T, ϑ (d) n characterize the UL and [ ] DL traffic ditribution in cell n, and ϑ n (x) := B (x) d /Λ, n n =,, x {u, d} denote the fraction of the total traffic Λ that traffic of type x in cell n account for, uch that n N x {u,d} ϑ(x) n =. For example, if ϑ = ϑ = [.5,.5] T, we have D, =. Fig. 3a and 3b how the cumulative ditribution function (CDF) of utility ρ derived by applying the five protocol under low and high inter-cell traffic ditance, repectively. The CDF i derived from imulation run time, each with different uer location and channel propagation, for every combination of the inter-cell traffic ditribution ratio in et T inter and intracell traffic ditribution ratio in et T intra. All cae with D,.5 are conidered a low inter-cell traffic ditance, while with D, >.5 a high inter-cell traffic ditance. Both Fig. 3a and 3b how that CDF F (dtdd) d () >.95 for dtdd, implying that ervice outage probability, i.e., the probability that at leat one ervice cannot be erved with atified QoS requirement, i above 95%. The performance i wore than protocol FIX with F (FIX) d () >.45. Thi i becaue although UL/DL reource plitting i adapted to the traffic volume, the full occupation of the reource may caue evere IMI to ome ervice. Such obervation encourage the application of our propoed algorithm, which are able to reduce the interference coupling among ervice. By comparing FP, SAFP and RMDI, we how that FP further decreae the outage probability to below %, and SAFP and RMDI ignificantly outperform FP, with the outage probability for low traffic ditance below %. Among the three, RMDI provide the bet performance of the utility ditribution. By comparing Fig. 3a and 3b, we oberve that SAFP and RMDI provide even higher performance gain under high traffic aymmetry. 3) Performance gain depending on traffic aymmetry. To analyze the performance gain depending on the traffic aymmetry, we average the utility obtained from imulation run time for D, falling into the interval [,.6), [.6,.3), [.3,.48), [.48,.64), [.64,.8), [.8, ], repectively. Let u conider FIX a the baeline. Fig. 3c how that the performance of FIX decreae with the traffic aymmetry, and the average utility i below (infeaible QoS target) when traffic ditance D, >.6. Although dtdd adaptively plit the UL/DL reource, the full occupation of the reource caue evere IMI, leading to the wort performance. On the other hand, FP reduce interference coupling among ervice, and provide 5% gain when traffic aymmetry i low, and almot -fold gain when the aymmetry i ultra high. The propoed SAFP incorporate interference coupling with UL/DL reource localization, which improve the gain to -fold when the traffic aymmetry i low while.7-fold when aymmetry i high. The enhanced verion RMDI further improve the gain by muting partial reource for interference cancellation. The gain i more ignificant when the traffic i highly aymmetric, achieving 3.-fold increae when D,.64.

7 Utility ρ Utility ρ 4 3 FP: updated ρ at each FP iteration SAFP: updated ρ at each FP iteration SAFP: optimized ρ for each SA SAFP: actual ρ at each iteration of SA Number of iteration (a) Comparion between FIX and SAFP Number of iteration (b) Examination of the random initialization. An example: With 3 randomly initialized ŵ, SAFP converge to two local optima with ρ () = 4.35 and ρ () =.9. Fig. : Examination of SAFP. APPENDIX A Definition. A vector function f : R k + R k ++ i a tandard interference function (SIF) if the following axiom hold:. (Monotonicity) x y implie f(x) f(y). (Scalability) for each α >, αf(x) > f(αx) In Definition we drop poitivity from it original definition [6] becaue it i a conequence of the other two propertie [5]. REFERENCES [] NGMN, NGMN 5G white paper, Next generation mobile network (NGMN), A deliverable by the NGMN Alliance, Feb. 5. [] H. Liu, Y. Jiao, Y. Gao, L. Sang, and D. Yang, Performance evaluation of flexible duplex implement baed on radio frame election in LTE heterogeneou network, in ICT. IEEE, 5, pp [3] A. M. El-Hajj and Z. Dawy, On optimized joint uplink/downlink reource allocation in OFDMA network, in ISCC. IEEE,, pp [4] A. M. El-Hajj, Z. Dawy, and W. Saad, A table matching game for joint uplink/downlink reource allocation in ofdma wirele network, in ICC. IEEE,, pp [5] Z. Shen, A. Khoryaev, E. Erikon, and X. Pan, Dynamic uplinkdownlink configuration and interference management in TD-LTE, IEEE Communication Magazine, vol. 5, no., pp. 5 59,. [6] R. D. Yate, A framework for uplink power control in cellular radio ytem, IEEE Journal on elected area in commun., vol. 3, no. 7, pp , 995. [7] C. J. Nuzman, Contraction approach to power control, with nonmonotonic application, in GLOBECOM. IEEE, 7, pp [8] I. Siomina and D. Yuan, Analyi of cell load coupling for LTE network planning and optimization, IEEE Tran. on Wirele Commun., vol., no. 6, pp ,. CDF CDF FIX dtdd FP. SAFP RMDI Utility ρ (a) Utility CDF under low inter-cell traffic ditance FIX dtdd FP SAFP RMDI Utility ρ (b) Utility CDF under high inter-cell traffic ditance. Average Utility FIX dtdd FP SAFP RMDI Inter-cell traffic ditance (c) Average utility under different inter-cell traffic ditance. Fig. 3: Performance comparion among protocol. [9] R. L. Cavalcante, Y. Shen, and S. Stańczak, Elementary propertie of poitive concave mapping with application to network planning and optimization, IEEE Tran. on Signal Proceing, vol. 64, no. 7, pp , 6. [] Q. Liao, D. Aziz, and S. Stanczak, Dynamic joint uplink and downlink optimization for uplink and downlink decoupling-enabled 5G heterogeneou network, arxiv preprint, 6. [Online]. Available: [] H. Elhaer, F. Boccardi, M. Dohler, and R. Irmer, Downlink and uplink decoupling: A diruptive architectural deign for 5G network, in GLOBECOM, 4. IEEE, 4, pp [] N. Takahahi, M. Yukawa, and I. Yamada, An efficient ditributed power control for infeaible downlink cenario global-local fixed-pointapproximation technique, IEICE Tran. on fundamental of electronic, commun. and computer cience, vol. 89, no. 8, pp. 7 8, 6. [3] 3GPP, TR 36.33, Requirement for upport of radio reource management, Rel-4, Oct. 6. [4], TR 36.84, Further advancement for E-UTRA phyical layer apect, Rel-9, Mar.. [5] K. K. Leung, C. W. Sung, W. S. Wong, Lok, and Tat-Ming, Convergence theorem for a general cla of power-control algorithm, IEEE Tran. on Commun., vol. 5, no. 9, pp , 4.