Announcements

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 Gij is gain from Xmtr i to Recvr j, Pi is power of transmittter I, and hi 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 rF 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 P2 P* P1

7. Recursive Calculation • When rF<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 gi • His local SIR measurement Ri(k) • His previous power Pi(k) • Fully distributed algorithm. • Same calculation as centralized algorithm. • Converges to Pareto optimal when it exists.

9. Convergence • Step size b used to tradeoff speed versus stability. • Stability not included previously (b=1). • For 6 users, algorithm converges within 5-10 iterations for b=1, 10-20 iterations for b=.5. • Small b 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 Ak) threshold to dg,, d>1. • Increase new user SIR (in Bk) 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 A0 denote initally active users and B0 denote new users • If no new link ever becomes active • Active users will converge to desired SIR threshold gi • Powers will explode exponentially • If set A0 UB0 is feasible then all new users become active in finite time. • Powers explode to infinity if enhanced SIR thresholds (dgi) infeasible • Can dynamically relax d 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 g-R(T) • New link drops out if it has not reached g 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 (g-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.