A Model of Soft Handoff under Dynamic Shadow Fading
Kenneth L. Clarkson
John D. Hobby
Bell Labs
Lucent Technologies
Simplified IS95a Model of Soft Handoff
Antenna
becomes
active (in soft handoff) when:
Signal > T_ADD
Antenna
stays
active when:
Signal > T_DROP recently
Within T_TDROP seconds
Reduces variability of active set
Reduces chance that temporary reduction in signal takes antenna out
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In Pictures
T_DROP
T_ADD
Active
Since >T_DROP: 0
Current
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Challenges for Performance Modeling
For a given mobile, want to estimate the active set numerically.
Needed for analyzing capacity, for example
Set is quasi-random, because fading is;
Will assume fading is lognormal [G]
Generally, rough approximation is good enough
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Modeling Approaches
"Snapshot" models fail to capture effects over time
(Models of conditions at a given instant)
Could use `P_d\equiv`prob of being above T_DROP
Or `P_a`, or `(P_a+P_d)/2`
Dynamic simulations:
Too slow for some applications
Need data (speed, direction, history) we don't have
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An Easy Case: Steady State
Consider vehicle moving at constant speed, and no change in mean signal
Active-set probability can be readily found:
Initially assume discrete time steps
Simple function of probabilities `P_a` and `P_d`:
`1/(1+(1/Q-1)\frac{P_d}{P_a})`
where
`Q`
=`1 - (1-P_d)^{k+1}`
`k`
=time steps in T_TDROP
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Our Steady-State Approximation
We can also find a linear recurrence for the probability (as in [LM]), but that's still expensive.
Instead:
Pretend conditions at each location are steady-state
Hope that average over time of steady-state equals average of time for real situation
Close to accurate for some situations
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Experiments
We consider straight-line "trips" for a moving mobile, with basic conditions:
Constant speed
T_TDROP = 4s
Initially: assume fades 20m apart are independent
Start of trip at 400m from antenna
Equal traffic in both directions
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Experiments, more about
We compare our approximation to the recurrence, and to just using `P_d`, for all combinations of:
Speeds from 1 to 30 m/s
Trips of 12, 18, and 24s duration
`P_d` at start of 0.05, 0.15,0.25,...0.95
`P_d` at end of 0.95
T_ADD - T_DROP of 2, 4, 6 dB
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Active Set Estimates, Steady State
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Active Set Estimates, General
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Conclusions
Simulation of motion not needed for rough estimates
More analysis of AR
Apply to more complicated algorithms?
Thanks!
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