1. Announcements Deadline extensions –HW 1 dues May 17 (next Wed) –Progress report due May 24 HW 1 clarifications: –On problem 3 users can lower their power –On problem 4 the “optimal” power allocation between Rock and Roll is for each state. Their average powers are fixed and equal. Can find true optimal allocation for extra credit. –References for 3G standards will be posted shortly, but idea is to debate technology, not specifics

2. Power Control Motivation Maintain link SIR (QOS) Increase battery life Efficient channel allocation Better handoff control Reduced delays Increased throughput/capacity

3. Power Control Centralized Power Control Distributed Power Control Active Link Protection Admission Control Channel Probing Power Control with Channel Assignment Minimum Power Routing Throughput vs. Delay vs. Power

4. Centralized Power Control Link QOS maintenance SIR of ith link above threshold: Alternate form: where G ij is gain from Xmtr i to Recvr j, P i is power of transmittter I, and  i is noise

5. Optimal Power Solution Need to solve (I-F)P>u –The matrix F has nonnegative elements and is irreducible. –Maximum modulus eigenvalue  F of F is real, positive, and simple. –Corresponding eigenvector is positive component-wise Soln exists if and only if Pareto optimal soln (min power)

6. Power Solutions P1P1 P2P2 P*P*

7. Recursive Calculation When  F <1, Follows from recursive substitution Comments: –Recursive algorithm minimizes the transmit power reqd to meet QOS –Update eqn requires knowledge of path gains for all users (via F ).

8. Distributed Power Control Can rewrite recursion as For user i, this recursion only depends on –His target SIR  i –His local SIR measurement R i (k) –His previous power P i (k) Fully distributed algorithm. –Same calculation as centralized algorithm. –Converges to Pareto optimal when it exists.

9. Convergence Step size  used to tradeoff speed versus stability. –Stability not included previously (  =1). For 6 users, algorithm converges within 5-10 iterations for  =1, 10-20 iterations for  =.5. Small  reduces SIR fluctuations during convergence or due to new users.

10. Dynamics Algorithm must reiterate every time the channel changes –Existing users may not be feasible under new channel –How to “kick out” users (channel deallocation) –Algorithm convergence must be faster than the channel dynamics Algorithm must reiterate when new users enter the system

11. Effect of New Users New users cause a new iteration of algorithm –Existing users may drop below SIR threshold, even if new user can be eventually accommodated –May cause call dropping If new user cannot be accepted: –All SIRs will degrade –Power will escalate uncontrollably Need mechanism to block new users that cannot be accepted –Admission and power control

12. Active Link Protection Maintain active user SIRS while suppressing infeasible new users. Basic idea: –Increase active user SIR (in A k ) threshold to ,,  >1. –Increase new user SIR (in B k ) slowly

13. Algorithm Properties For at most 1 new user per iteration, for active links: This implies that –Active links stay active –New links that become active stay active. Bounded power overshoot New links improve with time

14. Additional Dynamics Let A 0 denote initally active users and B 0 denote new users If no new link ever becomes active –Active users will converge to desired SIR threshold  i –Powers will explode exponentially If set A 0 U B 0 is feasible then all new users become active in finite time. –Powers explode to infinity if enhanced SIR thresholds (  i ) infeasible –Can dynamically relax  to 1.

15. Voluntary Dropout (VDO) New links voluntarily drop out if target SIR seems infeasible –Reduces power of active links. –Facilitates admission of feasible new users. –Don’t want to drop out too early. Channel dynamics and user departures may make infeasible user feasible. Timeout-Based VDO –New link sets timeout horizon T –At time T, computes dropout time D as decreasing function of  - R(T) –New link drops out if it has not reached  by time T+D. –Retries after random wait time

16. SIR-Saturation Based VDO –Each new user retains previous M SIRs values of iteration. M wide enough to allow channel and user dynamics to improve link, but narrow enough to limit persistance. –At each new iteration, user checks if SIR has significantly increased over last M steps. –If so, continues power iteration –If not, drops out with probability p that is an increasing function of (  - R(k) ) –Retries after random wait time Forced dropout –New users may cause active users to violate max power constraint –Force new users to drop out as active users approach max power

17. Channel Probing New users cause interference without being active New users can probe channel to predict if they are feasible –Use 1-2 interations, low power. –Drops out if predicts infeasible. –Does not significantly impact active users –When multiple users trying to gain admission, probing becomes more complicated.

18. Channel Allocation When multiple channels are available –New link can probe multiple channels simultaneously –Choose channel with lowest power requirements –Active users can intermittently probe other channels to minimize power requirements. –55% delay reduction and 45% power savings for two channels versus single channel (Bambos) –Modeling time dynamics essential. Dynamics of using, probing, and switching channels causes large increase in call dropping (Foschini)

19. Ad-Hoc Issues Minimum Power Routing –Route in multihop network based on minimum power. –Uses a Viterbi-like trellis search to find best route Throughput vs. Delay vs. Power –A user can increase chances of successful transmission by increasing his power Entails tradeoff of delay vs. power –May raise power as buffer size increases to prevent overflow –Optimizing power relative to channel can increase throughput.