Report

Scheduling vs Random Access in Frequency Hopped Airborne Networks David Ripplinger, Aradhana Narula-Tam, Katherine Szeto AIAA [email protected] 2013 August 21, 2013 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. Background Information Frequencies 1 2 3 4 5 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 - 2 DCR 08/21/2013 Frequency Hopping Enables Jam Resistance Frequencies 1 2 3 4 5 If you stay on one frequency: Scheduling vs Random Access - 3 DCR 08/21/2013 • A jammer can concentrate his energy on a single frequency • An entire user’s packet can be lost Frequency Hopping Enables Jam Resistance Frequencies 1 2 3 4 5 • 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 i ≥ k, success 10111001000011 10111001000011 encode k info symbols Scheduling vs Random Access - 4 DCR 08/21/2013 001101110100001101100010100100 transmit 0 11011 100 01101 0101 01 0 w coded symbols i received symbols (code rate = k/w) (doesn’t matter which ones) decode 10111001000011 i < k, failure Synchronous Frequency Hopping Frequencies 1 2 3 4 5 • 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 - 5 DCR 08/21/2013 Asynchronous Frequency Hopping Frequencies 1 2 3 4 5 • 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 - 6 DCR 08/21/2013 MAC Comparison Problem Formulation System Model • 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 synchronous frequency hopping with random transmission patterns • Full erasure model: If two users hop to same frequency in the same mini-slot, those hops are erased • A node can send on one frequency and receive on another at the same time This simple model is used to determine the throughput and delay of random access and scheduled MACs Scheduling vs Random Access - 7 DCR 08/21/2013 Scheduled System with FH (Illustrative Example) User 1: RED User 2: GREEN User 3: BLUE User 4: ORANGE 1 2 3 4 5 6 7 # Contending users 2 2 2 2 2 2 2 # Successful hops 8 6 6 6 4 4 8 Frequencies 1 2 3 4 5 Total Successful Hops: 42 Observations: • Scheduling controls exactly how many users in a slot • Requires coordination – increased complexity Scheduling vs Random Access - 8 DCR 08/21/2013 Time Slots Random Access System with FH (Illustrative Example) User 1: RED User 2: GREEN User 3: BLUE User 4: ORANGE 1 2 3 4 5 6 7 # Contending users 3 2 2 1 2 2 2 # Successful hops 6 6 6 4 2 4 8 p = 1/2 Frequencies p = probability of transmission Time Slots 1 2 3 4 5 Total Successful Hops: 36 Observations: • Random access controls the average number of users in a slot • But sometimes too many or too few users contend Scheduling vs Random Access - 9 DCR 08/21/2013 General Observations • 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 average n or a smaller code rate θ to ensure packets can be decoded – This implies lower throughput for Random Access Systems Conclusion: Random Access systems need to be more robust to collisions thereby resulting in lower throughput Scheduling vs Random Access - 10 DCR 08/21/2013 Analysis Objectives 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 Scheduling vs Random Access - 11 DCR 08/21/2013 Throughput Analysis: Packet Success Probability • Hop success probability with n active users: ps (1 1/ q)n1 • Probability of i out of w hop successes: • Probability packet is successfully decoded: w P(n) i k w ps (n)i (1 ps (n))wi i k 1 i 0 Scheduling vs Random Access - 12 DCR 08/21/2013 w ps (n)i (1 ps (n))wi i Throughput Analysis • Normalized throughput for scheduling system: k n Esched (n) P ( n) wq • Under RA, n is a random variable • With transmit probability p, RA normalized throughput: Nˆ n Nˆ n Erand ( p ) p (1 p ) Esched ( n ) n 1 n Nˆ Scheduling vs Random Access - 13 DCR 08/21/2013 Parameter Sweep Results Scheduling Random Access w = 400 0.5 0.4 Throughput Throughput 0.4 0.3 0.2 0.1 0 w = 400 0.5 0.3 0.2 0.1 20 40 n 60 80 100 0 20 40 n 60 80 100 q = number of frequencies; here, q = 50 • 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 Scheduling vs Random Access - 14 DCR 08/21/2013 Optimizing n Given Fixed Code Rate • Assume code rate, θ = 0.368 • 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 Average Number of Active Users • For each q, find optimal n 50 Scheduling Random Access 40 30 20 10 0 0 10 20 30 Frequencies Scheduling vs Random Access - 15 DCR 08/21/2013 40 50 Throughput Comparison for θ = 1/e 100% Scheduling Scheduling Throughput Gain Agg Throughput (per frequency) N = 100, w = 1000, θ = 1/e 0.5 Random Access 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 Frequencies 80% 60% 40% 20% 0 10 20 30 40 Frequencies • 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 For large w, as the number of channels q becomes large, the throughput difference between RA and scheduling decreases Scheduling vs Random Access - 16 DCR 08/21/2013 50 Delay Analysis and Simulation: Assumptions • 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 Scheduling vs Random Access - 17 DCR 08/21/2013 Delay Performance: Analysis and Simulation with Poisson Arrivals Poisson Arrivals Scheduling 200 180 Delay (slots) 160 TDMA Simulation Random Access Simulation TDMA Analysis Random Access Analysis • Static time slot allocation results in unused time slots 140 • Result is extra delay 120 100 80 Random Access 60 40 Scheduling 20 Random Access 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 • Very low delay, even for moderate loads • Slightly less maximum throughput Arrival Rate (packets per slot per frequency) TTDMA Scheduling vs Random Access - 18 DCR 08/21/2013 z 1 * 2( 1 λ /Esched ) Trand 1 1 * 2( 1 λ /Erand ) Delay Performance: Simulation Results for Bursty Arrivals Delay Performance: Bursty vs Poisson Arrivals 200 TDMA Bursty 180 Random Access Bursty TDMA (Poisson Model) 160 • Geometrically distributed bursts of average length 5 140 Delay (slots) Bursty Arrival Model: Random Access (Poisson) Scheduling (Bursty Arrivals) 120 100 80 Random Access (Poisson Arrivals) 60 40 Scheduling (Poisson Arrivals) 20 Random Access (Bursty Arrivals) 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Arrival Rate (packets per slot per frequency) Static scheduling handles bursty traffic poorly, but RA measures the traffic and adapts Scheduling vs Random Access - 19 DCR 08/21/2013 0.35 Conclusions • 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 Scheduling vs Random Access - 20 DCR 08/21/2013 Future Model Improvements and Research • 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 Scheduling vs Random Access - 21 DCR 08/21/2013 Time (and Frequency) Hopping