Jang Won Lee, Ravi Mazumdar and Ness B. Shroff VTC2003 Presented by: Shuang Li

1. Joint Power Allocation and Base-Station Assignment Based on Pricing for the Downlink in Multi-class CDMA Networks Jang Won Lee, Ravi Mazumdar and Ness B. Shroff VTC2003 Presented by: Shuang Li

2. Introduction • Base station assignment is important to maintain good QoS for mobiles • Link status between the mobile and the base-station • The amount of available resource to the mobile • We study joint power allocation and base-station assignment problem for the downlink in CDMA networks • A utility and dynamic pricing based power allocation algorithm and a pricing based base-station assignment algorithm proposed in this paper

3. Motivation • This joint problem has been studied, especially for the uplink. • The min transmission power satisfying the SINR threshold of each mobile is obtained. • Saraydar et. al. model it as an N-person non-cooperative power allocation game • Each mobile selects the optimal power level and the BS to max its net utility in a selfish way • Performance depends on the choice of price • No strategy to decide the optimal price • We consider a downlink case (bottleneck) • BS assignment takes into account the link status and the congestion level

4. System model • B base-stations and M mobiles • The system is assumed to be time-slotted • Each BS has a max power limit PT • Assumptions of Ui (utility function for each mobile i) • Ui is an increasing function of γi, the SIR of mobile i • Uiis twice continuously differentiable • Ui (0) = 0 • Uiis bounded above • has at most one solution for γi>0, Ni is processing gain. • If has one solution at , for and for • So, Ui can be: a sigmoidal-like function, a concave function or a convex function

5. Mobilei communicates with BS b, the SIR: • M(b): set of mobiles communicating with b • Pi: allocated power for mobile i • : power allocation vector for mobiles communicating with b • Ni: processing gain for i • Gi(b): path gain from b to i • Ii(b): background noise and intercell interference to i • Ai(b): Ii(b)/Gi(b)

6. Power allocation (for one cell) • Problem formulation subject to i = 1, 2, …, M. • The objective function is not concave in • It is a non-convex problem which requires a complex alg. to obtain a global optimal solution • Developed a distributed alg. that provides Pareto-optimum as well as asymptotically optimum

7. Dynamic pricing based algorithm • BS broadcasts λ • Each mobile i requests a Pi(λ) that maximizes its net utility • To maximize the system utility, BS must transmit at PT • Mobiles are non-cooperative, so BS has to find an equilibrium price λ* such that (1) • Difficulties: • Utility function is non-concave → Pi(λ) may not be continuous → BS may not find λ* satisfying (1)

8. A two-stage algorithm • Mobile selection stage: • Order mobiles in decreasing order by λimax(unique for each i), the max willingness to pay per unit power of mobile i • Main idea: select mobiles from 1 to K satisfying:

9. Power allocation stage: • Power allocated to selected mobiles • Reduce to a convex problem • We can always find λ*satisfying

10. Base-station assignment (multi-cell system) • Two open problems • Total transmission power allocation problem for each BS • BS assignment problem for each mobile • Information we need: • Status of each cell • Channel state of each mobile • Strategy we adopt: each BS tries to maximize its total system utility in a non-cooperative way • Problem: Nash equilibrium operating point might be inefficient, especially when the load of each cell is unbalanced • Solution: reassigning some mobiles in heavily loaded cells to lightly loaded ones

11. Pricing based base-station assignment • Sc(b): Set of mobiles that are not selected for transmission by BS b among those communicating with b • λimax(b): max willingness to pay per unit power of mobile i if connected to b • λ*(b): equilibrium price per unit power for b • if 0 otherwise

12. If mobile i is connected to BS b at the current time slot, it keeps being connected to b at the next time slot • Otherwise, it selects and is connected to BS d that satisfies where B is the set of BSs.

13. Interpretation 1: is the profit per unit power that mobile i can obtain if it is selected by BS b • Interpretation 2: mobile i selects the BS that has relatively best transmission environment (link status + congestion level). • λimax(b) interpreted as “goodness” of the transmission environment of mobile i when it is connected to BS b • λ*(b) interpreted as the congestion level at BS b

14. Two propositions for the two interpretations • Proposition 1: If λimax(n) < λimax(m), then Ai(n) > Ai(m) • Proposition 2: Suppose that mobile i is selected by base-station n and mobile j is selected by base-station m. Further suppose that Ui=Uj, Ni=Nj, and Ai(n) = Aj(m). Then, if λi*(n) < λi* (m), Pi(λ*(n))≥Pj(λ*(m))

15. Do we need less information to solve the problem now? • Information that mobile i needs to perform this alg. • PT, λ*(b) and w(b) for (base-station specific information) • Can be broadcasted by BS b • Do not need to know mobile-specific information

16. Numerical results • We compare the performance of the algorithm proposed with that of the SIR based BS assignment alg. • The latter: mobile i is assigned to BS d s.t. • 9 square cells to model the cellular network • Base station in the center of each cell

17. Ui(γ): a sigmoid function • Set and for the normalization • Mobiles use the same utility function (single-class) • Mu mobiles in each cell with uniform distribution, then Mh mobiles are located one by one in the center cell with uniform distribution (hot spot mobiles)

18. Compare the increment of the system utility during the hop-spot period • Pricing based alg. Performs better than SIR based alg.

19. Mh small → performance gain increases with smaller Mu • Hot spot cell with smaller Mu less congested → smaller performance gain • Hot spot cell sufficiently congested → performance depends on the congestion level of adjacent cells instead of only itself

20. Conclusion • Study a BS assignment problem for the downlink in multi-class CDMA networks • Propose a pricing-based BS assignment alg. that uses info. from the power allocation alg. based on utility and dynamic pricing • Congestion level and link status are both important factors taken into account which make the alg. outperforms SIR based alg.

21. Thank you