Investigating a Physically-Based Signal Power Model for Robust Low Power

Wireless Link Simulation

Tal Rusak, Philip LevisMSWIM 2008

Goal

• Presents an improvement to the TOSSIM simulator by suggesting a way to model reception power of wireless links

Outline

– TOSSIM– Signal power generating algorithm• Constant• Log normal shadowing power model• CPM

– Fill in the trace– Comparison Metrics• PRR• MK Distance

TOSSIM Signal Model• Assume signal power |S| to be constant– RSSI = |S+N|, |N| is the noise+interference value– Assumption is a simplification to reality.

Log normal shadowing power model

• assumes that the received RF power between two nodes shows logarithmic pattern in the function of distance as follow:–

Desired signal power

Transmit power

Path loss exponent

Reference distance

Gaussian random variable

CPM Algorithm• CPM(Closest-fit Pattern Matching)

– CPM algorithm uses an experimental trace to create a conditional model of observed values.

– CPM scan the trace and computes a probability distribution of the expected value v given k prior values.

Collecting Signal Power Traces• Packet lost!

– (1) filling in missing signal power values into the experimental trace• EVP (Expected Value PMF) Algorithm• Average Signal Power Value (AV) Algorithm

– (2) correcting for the phase differences between noise and signal traces•

•

In phase -> addition: actual power < RSSI …………………. p= -1Out of phase -> subtraction: actual power > RSSI ……… p = 1Phase differences cancel each other out ……………………. P = 0

• SNR(Signal-to-Noise Ratio):– , =>

• |S| magnitude of the signal power of a received packet• |N| magnitude of any environmental noise or disruption

• PRR(Packet Reception Rate)• SNR can be mapped to a

PRR using the function -> (TI/Chipcon CC2420 SNR/PRR Curve)

SNR -> PRR

Expected Value PMF (EVP)

Expected Value PMF (EVP)

Average Signal Power Value (AV) Algorithm

Average Signal Power Value (AV) Algorithm

Experimental Work

Evaluation

• Comparing simulation and experiment PRRs• KW Distance of Fixed-PRR simulations

Comparing simulation and experiment PRRs

CPDF• CPDF(Conditional packet delivery functions)

– a conditional packet delivery function describes the probability that a packet will be received successfully given n previous failures or successes.

– CPDF investigate trends in packet reception burstiness.• If packet losses are independent, then the CPDF is for the most

part uniform.• If packet losses are bursty, then the CPDF is non-uniform.

CPDF

CPDF

KW Distance of Fixed-PRR simulation

• KW (Kantorovich-Wasserstein) Distance– Quantify how much elements of two distributions would have to be

shifted to make the two distributions equal.

Conclusion

• Improve on the prediction of PRR for the following reasons:– Considers the variations in signal power which may

account for some PRR variation– There are two algorithms proposed for filling-in

experimentally determined signal power traces.