QoS-Guaranteed User Association in Sokun, Gohary, HetNets via - PowerPoint PPT Presentation

User Association for QoS- Guaranteed Load Balancing in HetNet via Semidefinite Relaxation 1 / 22 QoS-Guaranteed User Association in Sokun, Gohary, HetNets via Semidefinite Relaxation Yanikomeroglu Introduction Related work Hamza Sokun, Ramy Gohary and Halim Yanikomeroglu Problem formulation Carleton University, Ottawa, ON, Canada Solution via semidefinite relaxation September 2015 Simulations Conclusion

User Association Introduction for QoS- Guaranteed Load • The fundamental limitations of existing cellular Balancing in networks, e.g., HetNet via Semidefinite • higher data rates, Relaxation 2 / 22 • user-coverage in hot-spots and crowded areas, Sokun, • energy consumption. Gohary, Yanikomeroglu • To mitigate these limitations, cellular networks have evolved to include low-power base stations (BSs), Introduction so-called heterogeneous networks (HetNets). Related work • HetNet: Problem formulation • improving network capacity, Solution via • eliminating coverage holes in the macro-only system, semidefinite • reducing energy consumption. relaxation Simulations Conclusion Figure: An example of HetNet

User Association Introduction (cont’d) for QoS- Guaranteed Load Balancing in HetNet via Semidefinite • Disparate transmit powers and BS capabilities of Relaxation 3 / 22 HetNets render user-to-BS association a challenge. Sokun, • The problem of user-to-BS association is inherently Gohary, Yanikomeroglu combinatorial NP-hard and hence difficult to solve. Introduction • Two considerations must be taken into account in Related work selecting of the serving BS of each user: Problem • Channel conditions, and formulation • Load condition of BSs. Solution via semidefinite • Problem statement : Find the user-to-BS association relaxation which ensures that (1) the number of accommodated Simulations Conclusion users is maximized but also that (2) the network resources are efficiently utilized and (3) the users’ quality of service (QoS) demands are met.

User Association Introduction (cont’d) for QoS- Guaranteed Load • For example, Balancing in HetNet via Semidefinite Relaxation 4 / 22 Sokun, Gohary, Yanikomeroglu Introduction Related work Problem formulation Solution via semidefinite relaxation Simulations Conclusion Figure: Load Balancing in HetNet • Max-SINR: (1, 2, 4) at macro and (3) at pico. • (4) cannot be accepted (call blocking). • Load Balancing: (2, 4) at macro and (1, 3) at pico.

User Association Related work for QoS- Guaranteed Load Balancing in HetNet via Semidefinite Relaxation 5 / 22 • Cell range expansion [Guvenc et al., VTC Fall 2011]. Sokun, • Similarities: Gohary, Yanikomeroglu • User association problem in HetNet considered. • Differences: Introduction Related work • Solution method re-adjusting cell boundaries by adding Problem a constant bias terms to SINR values. formulation • Comment: Solution via semidefinite • It is a heuristic method. There is no theoretical guidance relaxation on the optimal biasing factors in the sense of load Simulations balancing or achieving a particular optimization criteria. Conclusion • QoS requirements not considered.

User Association Related work (cont’d) for QoS- Guaranteed Load Balancing in • Lagrange dual decomposition [Ye et al., IEEE Trans. HetNet via Semidefinite Wireless Commun. 2013, Shen and Yu, IEEE J. Sel. Relaxation 6 / 22 Areas Commun. 2014]. Sokun, • Similarities: Gohary, Yanikomeroglu • User association in HetNet. Introduction • Differences: Related work • Different objective functions presented. Problem • Each BS equally shares the total bandwidth among formulation users. Solution via semidefinite • Load definition the number of associated users to a BS. relaxation • Relaxing the binary BS association variables to Simulations continuous variables in [0, 1] allows a user to be served Conclusion by multiple BSs, which may require more overhead to implement. • Comment: • QoS requirements not considered.

User Association Related work (cont’d) for QoS- Guaranteed Load Balancing in HetNet via Semidefinite Relaxation 7 / 22 • Game theory [Aryafar et al., IEEE Infocom 2013]. Sokun, • Similarities: Gohary, Yanikomeroglu • User association in HetNet. • Differences: Introduction Related work • Assignment problem thought of as a game among BSs. Problem • The Nash equilibrium of the game is found. formulation • Comment: Solution via semidefinite • QoS requirements not considered. relaxation • Convergence of the algorithms not guaranteed. Even if Simulations the algorithms converge, the solution may be far from Conclusion optimal.

User Association Related work (cont’d) for QoS- Guaranteed Load Balancing in HetNet via Semidefinite • Semidefinite Relaxation and Randomization [Corroy Relaxation 8 / 22 and Mathar, IEEE Globecom Wkshp. 2012]. Sokun, • Similarities: Gohary, Yanikomeroglu • User association in HetNet. • Solution approach towards solving the problem. Introduction • Differences: Related work Problem • The objective to maximize the sum rate. formulation • Each BS equally shares the total bandwidth among Solution via users. semidefinite relaxation • Load definition the number of associated to a BS. Simulations • Comment: Conclusion • QoS requirements not considered. • A simple HetNet with one macro and one pico is considered.

User Association Problem formulation for QoS- Guaranteed Load Balancing in HetNet via Semidefinite Relaxation 9 / 22 • P i : the transmit power of BS i , Sokun, Gohary, Yanikomeroglu • g ij : the average channel gain, • The average SINR between BS i and the user j : Introduction Related work P i g ij Problem SINR ij = , formulation � P k g kj + σ N Solution via k ∈ B , k � = i semidefinite relaxation • The bandwidth efficiency to a user j from BS i : Simulations η ij = log 2 ( 1 + SINR ij ) [bps/Hz], Conclusion

User Association Problem formulation (cont’d) for QoS- Guaranteed Load Balancing in HetNet via Semidefinite Relaxation 10 / 22 • t i : total available resources of BS i and Sokun, t i = t M for macro BSs and t i = t P for pico BSs Gohary, Yanikomeroglu • Q j : demanded data rate of user j Introduction • W : bandwidth of an RB Related work � � �� • The amount of resource allocated: b ij = Q j / W η ij Problem and ˆ formulation b ij = b ij / t i ( given input ) Solution via • x ij ∈ { 0 , 1 } : assignment indicator variable semidefinite relaxation ( optimization variable ) Simulations ˆ • The load of BS i : ℓ i = � b ij x ij Conclusion j ∈ U i

User Association Problem formulation (cont’d) for QoS- Guaranteed Load Balancing in Find the optimal user-to-BS association that ensures HetNet via Semidefinite maximizing the number of accommodated users and Relaxation 11 / 22 simultaneously minimizing the number of expended Sokun, resources: Gohary, Yanikomeroglu � � � � max ρ x ij − ( 1 − ρ ) b ij x ij , x ij Introduction i ∈ B j ∈ U i ∈ B j ∈ U Related work Problem formulation • Total resource limit for the i -th BS: � b ij x ij ≤ t i , i ∈ B , Solution via j ∈ U i semidefinite relaxation • User-to-BS association: � x ij ≤ 1 , j ∈ U , Simulations i ∈ B j Conclusion • Binary association variable: x ij ∈ { 0 , 1 } , i ∈ B , j ∈ U i , • ρ ∈ [ 0 , 1 ] parametrizes a family of objectives, � � i ∈ B t i � • The optimal choice of the value of ρ ∈ i ∈ B t i , 1 . 1 + �

User Association Semidefinite relaxation for QoS- Guaranteed � � Load φ β , where φ = ββ T and β = 2 x − 1 . • Ψ = Balancing in β T 1 HetNet via Semidefinite Relaxation 2 Tr ( A 1 Ψ ) − 1 − ρ ρ 12 / 22 max Tr ( A b Ψ ) , ( a linear function in Ψ ) 2 Ψ Sokun, (1a) Gohary, Yanikomeroglu 1 2 Tr ( A d i Ψ ) ≤ t i , i ∈ B , ( a linear inequality in Ψ ) subject to Introduction (1b) Related work 1 2 Tr ( A e j Ψ ) ≤ 1 , j ∈ U , ( a linear inequality in Ψ ) Problem formulation (1c) Solution via diag ( Ψ ) = 1 , ( a linear inequality in Ψ ) (1d) semidefinite relaxation Ψ � 0 , ( positive semidefinite constraint ) (1e) Simulations rank ( Ψ ) = 1 . ( non-linear constraint ) (1f) Conclusion • Semidefinite programming is an extension of linear programming to the space of symmetric matrices. • Non-convex rank-1 constraint is removed based on the premise of solving strategy.

User Association Randomization Method for QoS- Guaranteed Load Approach: Balancing in HetNet via • Phase-1 : The semidefinite relaxation generates a Semidefinite Relaxation positive semidefinite covariance matrix together with an 13 / 22 upper bound on the objective. Sokun, Gohary, Yanikomeroglu • Phase-2 : Using Randomization, we exploit output of Phase-1 to compute good approximate solutions with Introduction provable approximation accuracies. Related work Problem Steps: formulation • For j = 1 , ..., J Solution via semidefinite • Generate a random vector sample: relaxation δ j ∼ N ( z ∗ , Z ∗ − z ∗ z ∗ T ) . Simulations • Find the candidate solution: ˜ β = sgn ( δ j ) . Conclusion x j = 0 . 5 (˜ • Find the candidate binary solution: ˜ β + 1 ) . • Determine the feasibility of the candidate solution: • Select the best among the feasible solutions, which has the highest objective function value and assign it to x ∗ .