1. 1 OUTLINE Motivation Distributed Measurements Importance Sampling Results Conclusions

2. 2 MOTIVATION Provide a detailed picture of spatial and temporal signal coverage and interference Improve radio resource management Improve network planning and deployment Support for MIMO or beamforming

3. 3 DISTRIBUTED MEASUREMENT APPROACHES Combining of site data with drive testing Deploying a dedicated network of sensors Renting service from an existing multi-purpose sensor network Using a set of subscriber mobiles, equipped with GPS, to periodically measure and report power measurements

4. 4 EXAMPLE FROM CELLULAR ENGINEERING: SIGNAL COVERAGE ESTIMATION A Cellular System with Distributed Measurements  Red dots: measurement locations Outage Locations ('holes') in a Circular Cell  Black dots: outage areas  Yellow dots: good areas

5. 5 PATH LOSS MODEL A generic model for most environments of interest DB Path Loss [1] A and : Model Parameters (environment-specific) d 0 : Reference Distance (100 m outdoors, 1 m indoors) s : Shadow Fading Shadow Fading [2, 3] s: A zero-mean Gaussian random variable at any location, : Standard deviation (ranges from ~ 4-12 dB) For two measurement locations i and j separated by distance d ij, the shadow fadings to each from a given point are correlated via X c : Correlation distance (ranges from ~10-100 m) This model is used to test the techniques proposed here

6. 6 SNR-BASED OUTAGE PROBABILITY SNR= P t -PL- P N (Signal-to-Noise Ratio in dB) P t : Transmit Power (dBm) PL : Path Loss (dB) P N : Receiver Noise Power (dBm) For required SNR of SNR o or more, PL must obey Outage Probability, P o, is the fraction of locations where PL> PL o. Distributed-measurement (e.g., sensor) network measures received power at N sensors, converts each to path loss, and estimates P o as the fraction for which PL< PL o. Can be done for P o in both directions (uplink and downlink), provided correct assumptions are made for P t, P N and SNR o.

7. 7 SIR-BASED OUTAGE PROBABILITY Calculations made for the downlink of a CDMA system, where co-channel interference dominates noise and comes from the 6 base stations surrounding the user’s base station. Each sensor measures power in the pilot of each base, then computes Outage Probability, P o, is the fraction of N sensors for which SIR< SNR o (minimum acceptable SIR). Extension to estimated uplink P o is possible, provided that the sensor network can combine measurements from sensors in different cells. <- Pilot Power Received from User Base <- Pilot Power Received from j-th Interfering Base

8. 8 OPTIMAL SENSOR PLACEMENT VIA IMPORTANCE SAMPLING [4] If is the pdf of the radial distance x of a given sensor, the optimal pdf in terms of estimating outage probability is where This solution is: Parametric (Requires knowledge of channel parameters) Degenerate (Requires knowledge of P o )

9. 9 NON-PARAMETRIC STRATEGIES Full-cell Placement  N sensors placed with uniform randomness over the entire cell Partial-cell Placement (Importance Sampling)  N'<N sensors placed with uniform randomness between R min and R  Example shown: R min =0.5 R

10. 10 RESULTS: SNR-BASED P o ESTIMATION (OUTDOOR CELL)  R = 1 km  P o =0.05 & 0.10  Average of Estimate Standard Deviation of Estimate

11. 11 RESULTS: SNR-BASED P o ESTIMATION (INDOOR CELL)  R = 100 m  P o =0.10  Three cases for Average of Estimate Standard Deviation of Estimate

12. 12 RESULTS: SIR-BASED P o ESTIMATION (OUTDOOR CELL, CDMA SYSTEM [5])  R = 1 km  CDMA system [5] with K users per sector or cell  Average of Estimate Standard Deviation of Estimate

13. 13 RESULTS: AN 'OUTAGE' MAP [6] Diamonds: sensor locations Stars: outage locations All stars inside the circles: outage locations detected

14. 14 RESULTS: PERCENTAGE OF HOLES DETECTED  R = 1 km  R min =0.5 R  dB  Various combination of N and X c

15. 15 CONCLUSION Partial-cell placement is a generic approach and does not rely on the specific channel model. Improved measurement efficiency (33% fewer measurements needed) by applying the principle of importance sampling. A cell outage probability of ~ P o can be accurately estimated using ~ 10/ P o power measurements distributed in a random uniform way over base-mobile distances from 50% to 100% of the cell radius. Applies to a wide range of channel model parameter sets. Applies to both SNR and SIR-based outage probabilities, in both indoor and outdoor environments. Applications to mobile positioning and 'hole' mapping.

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