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

In Pictures

T_DROP T_ADD Active Since >T_DROP: 0 Current

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

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

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

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

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

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

Active Set Estimates, Steady State

Active Set Estimates, General

Conclusions

• Simulation of motion not needed for rough estimates
• More analysis of AR
• Apply to more complicated algorithms?
• Thanks!