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David Ripplinger, Aradhana Narula-Tam, Katherine Szeto
AIAA InfoTech@Aerospace 2013
August 21, 2013
Scheduling vs Random Access in Frequency Hopped Airborne Networks
This work is sponsored by the Assistant Secretary of Defense (ASD R&E) under Air Force Contract #FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the United States Government.
Scheduling vs Random Access - 2DCR 08/21/2013
Background Information
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Frequency Hopping:• Break up a packet into small pulses or hops
• Pseudo-randomly choose a new frequency for each hop
Frequency Hopping spreads the packet transmission over multiple frequencies
Scheduling vs Random Access - 3DCR 08/21/2013
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Frequency Hopping EnablesJam Resistance
If you stay on one frequency:• A jammer can concentrate his energy on a single frequency• An entire user’s packet can be lost
Scheduling vs Random Access - 4DCR 08/21/2013
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encode
Frequency Hopping EnablesJam Resistance
• With Frequency Hopping, a jammer targeting a single frequency only impacts part of a user’s packet
• With Forward Error Correction, the loss of some hops can be tolerated
10111001000011 001101110100001101100010100100 0 11011 100 01101 0101 01 0
10111001000011
10111001000011k info symbols
transmitdecode
w coded symbols(code rate = k/w)
i received symbols(doesn’t matter which ones)
i ≥ k, success
i < k, failure
Scheduling vs Random Access - 5DCR 08/21/2013
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Synchronous Frequency Hopping
• Each user transmits on a single frequency for each hop
• User hops are synchronous in time – Users move to a new frequency simultaneously
• User hopping patterns are orthogonal
• Requires user receptions to be synchronized at the hop level– Many relevant systems have hop durations in the microseconds
With synchronous hopping, there is no multi-user interference
Scheduling vs Random Access - 6DCR 08/21/2013
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Asynchronous Frequency Hopping
• Airborne networks can have up to 2-ms propagation delays– Hop receptions are no longer time aligned– A hop is only a few microseconds, so 2-ms guard times are impractical
• Large numbers of users result in many hop collisions, even if transmitted patterns are orthogonal
We have asynchronous hopping, which has multi-user hop collisions
Scheduling vs Random Access - 7DCR 08/21/2013
MAC Comparison Problem Formulation
This simple model is used to determine the throughput and delay ofrandom access and scheduled MACs
• All users within transmission range• It takes one slot to transmit a user’s packet
– Packet is transmitted over many hops– Each slot consists of many mini-slots or hops
•Multiple users transmit simultaneously • Collisions due to asynchronous frequency
hopping are modeled using synchronousfrequency hopping with random transmission patterns
• Full erasure model: If two users hop to same frequency in the same mini-slot, those hopsare erased
• A node can send on one frequency andreceive on another at the same time
System Model
Scheduling vs Random Access - 8DCR 08/21/2013
Scheduled System with FH(Illustrative Example)
1 2 3 4 5 6 7 Time Slots
User 1: RED User 2: GREEN User 3: BLUE User 4: ORANGE
2 2 2 2 2 2 2# Contending users
8 6 6 6 4 4 8
Observations:• Scheduling controls exactly how many users in a slot• Requires coordination – increased complexity
Total Successful Hops: 42
# Successful hops
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Scheduling vs Random Access - 9DCR 08/21/2013
Random Access System with FH(Illustrative Example)
1 2 3 4 5 6 7 Time Slots
User 1: RED User 2: GREEN User 3: BLUE User 4: ORANGE
3 2 2 1 2 2 2# Contending users
6 6 6 4 2 4 8
Observations:• Random access controls the average number of users in a slot• But sometimes too many or too few users contend
Total Successful Hops: 36
# Successful hops
p = 1/2p = probability of transmission 1
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Scheduling vs Random Access - 10DCR 08/21/2013
• System throughput is maximized by choosing optimal n, θ– n: optimal number of users transmitting in a slot, and– θ = k/w: forward error correction (FEC) code rate
• With scheduling, the number of users, n, can be controlled exactly
• With random access (RA), the transmission probability, p, in a slot determines average of n,
– However, n varies from slot to slot– Inability to control n exactly, results in more collisions
• Hence, compared to scheduling, RA needs either smaller averagen or a smaller code rate θ to ensure packets can be decoded
– This implies lower throughput for Random Access Systems
General Observations
Conclusion: Random Access systems need to be more robust to collisions thereby resulting in lower throughput
Scheduling vs Random Access - 11DCR 08/21/2013
1. Parameter optimization for scheduling– Determine n (# users) and θ (code rate) to maximize throughput
2. Parameter optimization for random access– Determine p (transmission probability) and θ (code rate)
to maximize throughput
3. Throughput comparison for scheduling vs random access
4. Delay comparison for scheduling vs random access
Analysis Objectives
Scheduling vs Random Access - 12DCR 08/21/2013
• Hop success probability with n active users:
• Probability of i out of w hop successes:
• Probability packet is successfully decoded:
Throughput Analysis:Packet Success Probability
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Scheduling vs Random Access - 13DCR 08/21/2013
• Normalized throughput for scheduling system:
• Under RA, n is a random variable
• With transmit probability p, RA normalized throughput:
Throughput Analysis
)()( nPqn
wknEsched
)()(ˆ
)( ˆˆ
nEppnN
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1
Scheduling vs Random Access - 14DCR 08/21/2013
Parameter Sweep Results
Scheduling Random Access
• For scheduling, the optimal operating point in all cases was near n ≈ q and θ ≈ 1/e = 0.368• For random access, optimal θ was slightly smaller and optimal p ensured average n ≈ q • Note: Can get close to optimal throughput with n or θ “in the neighborhood” of the optimal solution
q = number of frequencies; here, q = 50
Thro
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w = 4000.5
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20 40 60 80 1000
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w = 4000.5
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Scheduling vs Random Access - 15DCR 08/21/2013
• Assume code rate, θ = 0.368
• For each q, find optimal n
• Packet length w = 1000
• In most cases:– Scheduling: choose n = 0.9q– RA: want n = 0.8q
• N is number of backlogged users• Choose p = 0.8q/N
• Alternatively, could have fixed n and optimized θ
Optimizing n Given Fixed Code Rate
0Frequencies
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Scheduling vs Random Access - 16DCR 08/21/2013
Throughput Comparison for θ = 1/e
• RA: throughput increases with increasing q, getting closer to scheduling throughput– n has lower variance
•At q = 50, scheduling is 16% better in this example
N = 100, w = 1000, θ = 1/e
For large w, as the number of channels q becomes large,the throughput difference between RA and scheduling decreases
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Scheduling vs Random Access - 17DCR 08/21/2013
• Each node has i.i.d. Poisson packet arrivals
• Deterministic departures – Assume all packets are received
• 500 users
• Static scheduling (TDMA)– Schedule n users in each time slot
• RA knows how many backlogged users each slot– Back-off strategy: p = q/N, where N = # of backlogged users
Delay Analysis and Simulation: Assumptions
Scheduling vs Random Access - 18DCR 08/21/2013
Delay Performance: Analysis and Simulation with Poisson Arrivals
TDMA SimulationRandom Access SimulationTDMA AnalysisRandom Access Analysis
RandomAccess
Scheduling
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Arrival Rate (packets per slot per frequency)
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Poisson Arrivals
)λ/E(zT *
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• Static time slot allocationresults in unused time slots
• Result is extra delay
Scheduling
• Very low delay, even formoderate loads
• Slightly less maximum throughput
Random Access
Scheduling vs Random Access - 19DCR 08/21/2013
Delay Performance: Simulation Results for Bursty Arrivals
Scheduling(Bursty Arrivals)
Random Access (Bursty Arrivals)
Delay Performance: Bursty vs Poisson Arrivals
Scheduling(Poisson Arrivals)
Random Access(Poisson Arrivals)
Bursty Arrival Model:• Geometrically
distributed bursts of average length 5
Static scheduling handles bursty traffic poorly, but RAmeasures the traffic and adapts
TDMA BurstyRandom Access BurstyTDMA (Poisson Model)Random Access (Poisson)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Arrival Rate (packets per slot per frequency)
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Scheduling vs Random Access - 20DCR 08/21/2013
• Optimal users in a slot is n ≈ q (num frequencies)
• The optimal code rate is θ ≈ 1/e = 0.368– Assumes no jamming or noise
• Random access can’t control n exactly, just average n– Needs to be more robust than scheduling to packet loss
• RA needs smaller n or θ
• Scheduling achieves higher throughput– RA throughput improves with more hopping frequencies q– At q = 50, scheduling gets 10% to 20% more throughput, depending on
codeword length w– As the number of frequencies gets large, scheduling and random
access achieve similar throughputs
• RA gets lower delay especially with bursty traffic
Conclusions
Scheduling vs Random Access - 21DCR 08/21/2013
• Dynamic scheduling– Significant reduction in delay possible– Delay may be comparable to RA for
both Poisson and Bursty traffic– Potentially higher throughput than RA
• Requires significant overhead for coordination thereby lowering effective throughput
• Incorporate transmit while receive constraints– Many systems do not enable receiving
while transmitting– This will result in more collisions for
random access• Possible solution is time hopping
– Scheduling can reduce transmit while receive issues
Future Model Improvements and Research
Time (and Frequency) Hopping