10 00 11 01 Aspects on the Flow-Level Performance of Wireless Fading Channels Amr Rizk in parts joint work with K. Mahmood, Y. Jiang, N. Becker and M. Fidler Institute of Communications Technology Leibniz Universität Hannover, Germany 1/17
10 00 11 01 Outline ◮ Application of network calculus to MIMO wireless channels ◮ Ongoing work: Delays introduced on Layer 2 in a real world LTE system 2/17
10 00 11 01 Motivation h 11 1 1 h 21 h 12 Tx 2 2 Rx h 22 ◮ MIMO employed by modern wireless/cellular networks for high data rate (IEEE 802.11n, 3GPP LTE) ◮ fundamental tradeoff robustness vs. capacity ◮ MIMO studies focused mainly on capacity limits ◮ modern wireless applications are delay-sensitive Goal: ◮ Non-asymptotic delay analysis of MIMO wireless channels with memory in spatial multiplexing mode 3/17
10 00 11 01 Analytical performance evaluation of wireless networks ◮ Tools: Queueing theory, effective capacity, network calculus,.. e.g.: [Jiang’05], [Wu’06], [Fidler’06], [Li’07], [Ciucu’11].. ◮ Challenge: Time varying nature of the wireless channel Goal: ◮ Non-asymptotic probabilistic delay bound of the form P [ W > d ] ≤ ε using stochastic network calculus based on moment generating functions (MGF) 4/17
10 00 11 01 Focus: MIMO under spatial multiplexing: Example (N=2) h 11 1 1 h 21 h 12 2 Tx 2 Rx h 22 ◮ block fading characteristic for all sub-channels { h 11 , h 21 , h 12 , h 22 } ◮ CSI at transmitter such that arrivals are transmitted in FIFO manner I + ρ ◮ Capacity C = log 2 � � N HH † �� det ◮ Channel matrix describing the scattering environment � h 11 � h 12 H = , finite scatter model (NLOS, Rayleigh) h 21 h 22 5/17
10 00 11 01 A stochastic network calculus approach h 11 1 1 h 21 h 12 Tx 2 2 Rx h 22 ◮ Stochastic modeling of traffic arrivals and node service (MGF) ◮ Performance bounds, e.g., P [ W > d ] ≤ ε ◮ Multiplexing and composition results (independence) 6/17
10 00 11 01 Moment generating function MGF of a stationary process X ( t ) for θ > 0 , t ≥ 0 � e θX ( t ) � M X ( θ, t ) = E ◮ Backlog and delay bounds are known [Fidler’06], using Chernoff’s bound, Boole’s inequality: � � � � ∞ � � �� τ : 1 � W > inf inf ln M A ( θ, s − τ ) M S ( θ, s ) − ln ε ≤ 0 ≤ ε P θ θ> 0 s = τ where M S ( θ, t ) = M S ( − θ, t ) . 7/17
10 00 11 01 Discrete time block fading model On-Off Markov chain (Gilbert-Elliot) model for each sub-channel p gb 1-p gb 1-p bg g b p bg Model the N × N MIMO channel by a MC consisting of 2 N 2 states ◮ For N = 2 the MC consists of 16 permutations/states of the form { g, g, g, g } , { g, g, g, b } ... { b, b, b, b } for { h 11 , h 12 , h 21 , h 22 } ◮ Group the states according to degree of freedom (DOF): The receiver can decode two , one or no spatial streams. ◮ A receiver antenna can only decode one spatial stream at a time (i.e. { g, g, b, b } belongs to DOF 1) 8/17
10 00 11 01 Channel model cont. (Example N = 2) ◮ The state space is reduced to N + 1 DOF 2 DOF 1 DOF 0 9/17
10 00 11 01 The MGF of the service process The MGF of such a Markov chain is known [Chang’00] M S ( θ, t ) = π ( R ( − θ ) Q ) t − 1 R ( − θ ) 1 ◮ The service rates r i are ordered into a matrix e θ r 1 , ··· ,θ r N + 1 � � R ( θ ) = diag ◮ The transition probability matrix Q has the elements { p ij } denoting the transition probability from state i to state j ◮ The steady state probability vector π = π · Q 10/17
10 00 11 01 The MGF of the service process The MGF of such a Markov chain is known [Chang’00] M S ( θ, t ) = π ( R ( − θ ) Q ) t − 1 R ( − θ ) 1 ◮ The service rates r i are ordered into a matrix e θ r 1 , ··· ,θ r N + 1 � � R ( θ ) = diag ◮ The transition probability matrix Q has the elements { p ij } denoting the transition probability from state i to state j ◮ The steady state probability vector π = π · Q Nevertheless no analytical expression for M S for more than two states -> numerical evaluation. 10/17
10 00 11 01 Example: Flow level delay bounds for IEEE 802.11n ◮ periodic arrival source with known M A ( θ, t ) ◮ parametrize arrivals according to MCS ◮ parametrize MC: normalized Doppler frequency to block transmission rate [Zorzi’98] -> p bg , p gb 50 N = 2 60 ε = 10 −2 45 N = 3 ε = 10 −4 N = 4 50 delay bound [time slots] 40 delay bound [time slots] ε = 10 −6 35 40 30 30 25 20 20 10 15 10 0 −7 −6 −5 −4 −3 −2 100 150 200 250 300 10 10 10 10 10 10 Arrival Rate v [Mbps] violation probability ε Stochastic delay bounds for N = 2 . Exponential decay due to Chernoff’s bound. Arrival rate v = 240 Mbps. 11/17
10 00 11 01 Fading speed and end-to-end delay bounds 500 140 N=2 N=2 N=3 120 400 delay bound [time slots] delay bound [time slots] 100 300 80 N=3 200 60 N=4 100 40 0 20 −2 −1 0 10 10 10 2 4 6 8 10 12 14 16 fading speed p bg Number of hops η End-to-end bounds for statistically ◮ Impact of statistical independent wireless links. multiplexing vs. memory ◮ Bound scales at most linearly ◮ Slope changes with the number of antennas N (increase in capacity) 12/17
10 00 11 01 Outline ◮ Application of network calculus to MIMO wireless channels ◮ Ongoing work: Delays introduced on Layer 2 in a real world LTE system 13/17
10 00 11 01 Measurement study in a major commercial LTE network ◮ Measurements from user equipment (UE) perspective ◮ Layer 2 mechanism: Discontinuous Reception Mode (DRX) 1. UE turns off circuitry to save power 2. UE monitors control channel in intervals seeking paging messages 3. If UE idles for too long -> logical connection tear down 14/17
10 00 11 01 Discontinuous reception mode (DRX) ◮ UE is in one of the radio resource control (RRC) states: 1. RRC_CONNECTED state 1.1 Continuous Reception 1.2 Short DRX Mode 1.3 Long DRX Mode 2. RRC_IDLE state RRC CONNECTED RRC IDLE Continuous Short DRX Mode Long DRX Mode Reception T ON T IN T SC T LC time N SC End of transmission T BS = active UE 15/17
10 00 11 01 Discontinuous reception mode (DRX) ◮ we measure packet 0 10 round-trip times (RTT) for Continuous 0ms − 200ms Reception 200ms − 2.5s periodic ping packets 2.5s − 10.5s Short DRX Cycle >10.5s RRC_IDLE ◮ we vary the period length, Long DRX Cycle CCDF −1 10 i.e., the inter-packet gap and measure for each gap 5 × 10 3 RTTs ◮ delay increase due to “wake −2 10 0 0.05 0.1 0.15 0.2 0.25 up time” RTT [s] 16/17
10 00 11 01 Summary ◮ Delay analysis of MIMO wireless channels in spatial multiplexing using MGF network calculus 1. impact of channel memory (fading speed) 2. impact of the number of antennas ◮ Real world measurements: Layer 2 mechanism that contributes substantially to packet delay. 17/17
10 00 11 01 Backup 17/17
10 00 11 01 Web Servers B D 100 Mbps (down) 50 Mbps (up) DOCSIS Client Internet Cellular Gateway 30 Mbps (down) Provider 2 Mbps (up) 100 Mbps (up & down) 1 Gbps (up & down) . . . A A T NTP + control local . . . local . . . Test Server NTP + control NTP + control 17/17
10 00 11 01 HARQ-retransmissions Block retransmission after error detection. Combination of multiple copies of the data block to increase decoding likelihood. Out-of-order blocks wait in the receive buffer. ◮ we measure packet 0.16 server 1 round-trip times (RTT) in HARQ retransmission server 2 0.14 continuous reception 0.12 mode. 0.1 ◮ LTE specifies pmf 0.08 HARQ-retransmissions in 0.06 rigid 8 ms intervals. 0.04 ◮ substantial delay increase 0.02 0 for short RTT connections. 0.015 0.02 0.025 0.03 0.035 RTT [s] 17/17
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