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Information about Fairness of the WiMAX System

Published on December 17, 2008

Author: gverticale

Source: slideshare.net

Presentation of paper "Impact of Multipath Fading on the Fairness of the WiMAX System" ICLAN 2008

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Outline Introduction A Markovian Model for the WiMAX Radio Channel Scheduling Disciplines for WiMAX The Simulation Scenario Performance Evaluation Conclusions G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 2 / 19

Introduction Objective of this work In WiMAX, the Base Station (BS) can select, for each subchannel, the user that can achieve the maximum throughput. This is at the expense of fairness. By using a WiMAX channel model based on Markov Chains, we show which schedulers strike a balance between throughput and fairness. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 3 / 19

The WiMAX Radio Frame The WiMAX OFDMA frame is divided in slots spanning a subchannel and one or more OFDM symbols. Frame-by-frame the Base Station (BS) assigns each slot to a Subscriber Station (SS), selects the most appropriate Modulation and Coding Scheme (MCS) to guarantee a target BER. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 4 / 19

The WiMAX Radio Channel Assumptions Several techniques (aka permutations) to match OFDMA subcarriers and subchannels are available. We assume the BandAMC permutation in which subchannels: use adjiacent subcarriers; are frequency ﬂat and change frame-by-frame; propagation channel follows the Hata channel model; have independend fading. We assume slowly moving users, so only multipath (aka fast) fading is present. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 5 / 19

The WiMAX Radio Channel Multipath Fading On each channel the istantaneous SINR at the receiver can be described by a Negative Exponential Random Variable with mean γ. Due to fading, SINR evolves over time. Given a SINR threshold γ, the level-crossing rate is: 3 √ γ γ 2 fd exp − N= 2π γ γ where fd is the Doppler spread. For each value of the SINR, the BS uses the most eﬃcient Modulation and Coding Schemes (MCS) to achieve target BER. We model the channel as having W + 1 states, corresponding to the available W MCSes plus the too-low SINR state. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 6 / 19

Makovian Model States and Stationary Probabilities The SINR range is partitioned in (W + 1) regions with boundary points γn . The BS uses MCSn if γn ≤ γ < γn+1 . We model the channel as an (W + 1)-states Markov Chain. The stationary probabilities of the state n is pn = Pr{γn ≤ γ < γn+1 }. pdf , fγ (γ) γ1 γ2 γn ... p0 p1 pn SINR, γ G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 7 / 19

Makovian Model Transition Probabilities Transitions are and frame-by-frame and only between adjacent states. Tf is the frame duration. Nn the level crossing rate for threshold γn . (Nn +Nn+1 )Tf Nn+1 Tf 1− pn pn n n−1 n+1 Nn Tf pn The Markovian Model is usable when the SS moves slowly (e.g. pedestrian). G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 8 / 19

Modulation and Coding Schemes in WiMAX Table: Modulation and Coding Schemes State MCS slot rate (kbit/s) γn (dB) 0 Bad Channel 0 – 1 QPSK 1/2 (2x rep.) 4.8 -0.06 2 QPSK 1/2 9.6 3.22 3 QPSK 3/4 14.4 5.64 4 16QAM 1/2 19.2 8.42 5 16QAM 3/4 28.8 11.91 6 64QAM 1/2 28.8 12.37 7 64QAM 2/3 38.4 15.25 8 64QAM 3/4 43.2 17.11 G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 9 / 19

Scheduling The BS assigns users to subchannels so as to maximize the sum of the users’ utilities User j having throughput rj has utility: rj1−β Uβ (rj ) = if β = 1 1−β Uβ (rj ) = log(rj ) if β = 1 where β is a system parameter that controls the system fairness. The total utility is maximized when the current slot is assigned to the user j ∗ that has: max U (rj )cj j where cj is the number of bits/slot for the MCS associated to user j for the particular subchannel. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 10 / 19

Scheduling Notable Schedulers Some choices for β result in notable schedulers β Objective function Scheduler Name 0 maxj cj Max-SINR cj 1 maxj rj Proportional Fair (PF) cj 2 maxj r 2 Weighted Potential Delay (WPD) j ∞ max{minj rj } Max-min Fair G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 11 / 19

System Model A 3-sector WiMAX cell with 2 tiers of interfering cells All sectors and cells reuse the same 10-MHz channel Frame duration Tf = 5 ms: 448 downlink slots/frame Fixed transmit power Pt = 43 dBm. Received power as in the Hata model: −3.76 Pr = 1.55 · 10−13 Pt dkm 10ζ/10 where d is the SS-BS distance (in km) and ζ is the lognormal shadowing (σ = 8 dB) SS arrive as in a Poisson process and stay in the system for 120 s. During this time SS receive as much data as possible. SS with average SINR < 0 dB are not admitted (about 1%). . . . please see the paper for more details G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 12 / 19

Performance Parameters Total cell throughput and per-SS throughput Jain’s Fairness Index among SS: 2 K rj j=1 f= K rj2 K j=1 where rj is the throughput of the j-th SS and K is the number of SSes. Per-SS maximum latency, deﬁned as the maximum time between two consecutive slots for the same SS. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 13 / 19

Cell-wide Performance results Throughput Fairness Scheduler β (Mbit/s) Index 58 0.35 Max-SINR 0 48 0.89 Proportional Fair 1 45 0.95 Weighted Potential Delay 2 ∞ 15 1.00 Max-min Fair Eﬀect of fd not shown (has minimal eﬀect on throughput). Diﬀerent values of β strike a diﬀerent balance between eﬃciency and fairness. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 14 / 19

Per-mobile throughput 2500 Max−SINR PF 2000 WPD Throughput (kbit/s) Max−min Fair 1500 1000 500 0 0 10 20 30 40 50 Average SINR (dB) Extreme scheduling disciplines should be avoided. Max-SINR → starvation. Max-min Fair → waste of resources. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 15 / 19

Latency Maximum per-mobile latency with fd = 1Hz 2 10 Max−SINR PF WPD Max−min Fair 1 10 Maximum Latency (s) 0 10 −1 10 −2 10 0 5 10 15 20 25 30 35 40 45 50 Average SINR (dB) As β decreases the SSes with better SINR are scheduled more often. With PF and WPD the diﬀerence between high-SINR and low-SINR SSes can be of two magnitudes (100 ms vs 5 s). G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 16 / 19

Latency Maximum per-mobile latency with Proportional Fair scheduler 2 10 fd = 1 Hz fd = 5 Hz uncorrelated fading 1 10 Maximum Latency (s) 0 10 −1 10 −2 10 0 5 10 15 20 25 30 35 40 45 50 Average SINR (dB) Lower fd results in higher latencies and higher diﬀerences between high-SINR and low-SINR SSes. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 17 / 19

Conclusions The balance between throughput and fairness can be controlled with the single parameter β. The PF and WPD schedulers (β = {1, 2}) provide a good trade-oﬀ. Latency is a critical performance metric especially when the Doppler frequency is very low (e.g. SS are stationary). G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 18 / 19

Thank you. G. Verticale (Politecnico di Milano) Fairness of the WiMAX System ICLAN 2008 19 / 19

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