From Outage Probability to ALOHA MAC Layer Performance Analysis in Distributed Wireless Sensor Networks MEA. Seddik 1 , 2 , V. Toldov 2 , 3 , L. Clavier 1 , 3 , N. Mitton 2 1 IMT Lille-Douai, 2 Inria, 3 IRCICA USR CNRS 3380 WCNC’18, 16 Apr, Barcelona, Spain 1/27
Outline Introduction: Wireless Sensor Networks (WSNs) Problem Statement & Outage Probability Slotted-ALOHA with Channel Reservation and Without Interferences Slotted-ALOHA with Channel Reservation and Interferences Experimental Analysis and Main Result 2/27
Introduction: Wireless Sensor Networks (WSNs) 3/27
Nowadays, WSNs are everywhere! ◮ Environmental applications. ◮ Home applications. ◮ Medical applications, etc. 4/27
LIRIMA PREDNET Project ◮ Even Rhinos need smartphones! 5/27
Challenges behind WSNs ◮ Keep the network up for several years (5-10 years). ◮ Generally the deployed architectures are distributed ⇒ Interferences! (partially responsible for the loss of energy). 6/27
To face these challenges Two directions are natural: ◮ Use different sources of energy (solar for example). ◮ Optimizing the hardware and the software . The software concerns essentially: ◮ The physical layers. ◮ The Medium Access Control (MAC) Layer. In this work, we study: ◮ The influence of the MAC layer on the network performance. ◮ In particular, we address the following question: How many channels do we need to achieve high performance distributed wireless sensor network? 7/27
Problem Statement & Outage Probability 8/27
MAC Protocol: Slotted-ALOHA ◮ Multiple nodes and a unique BTS. ◮ Distributed access policy ⇒ the nodes make the decision (randomly) to transmit on their own (e.g. Slotted-ALOHA MAC protocol). Multiple nodes could choose the same channel ⇒ Interferences! 9/27
Interferences quantification: Outage Probability The probability that the signal-to-interference-plus-noise-ratio (SINR) is less than a given threshold τ > 0 , Op = P { SINR < τ } , where, SINR ( o , r ) = S ( o , r ) / ( I ( o ) + N 0 ). 10/27
Assumptions ◮ Π λ ⊂ R 2 Homogeneous Poisson Point Process (HPPP) spacial distribution of the nodes with density λ . ◮ The wireless channel consists of path loss attenuation with no fading: ∀ X i ∈ Π λ , P i = P e � X i � − α , where α, P e > 0. ◮ The Medium Access Control strategy is a Slotted-ALOHA , the communicating nodes have a density λ ∗ s.t. λ ∗ = 2 T s 1 λ. T N c 11/27
Expression of Op Proposition The Outage probability for Slotted-ALOHA MAC protocol is given by the following expression: N 1 ξ Op SA ≡ � I � Σ j lim α > ( λ ∗ π ) α/ 2 � (1) N N → + ∞ j =1 where I � . � is the indicator function, ξ = r − α − N 0 P e and τ � − α/ 2 � 1 Σ j α = log 1 − U j 0 − α/ 2 � � (1 − U j + ∞ log k ) k ! − 1 � + − kW 0 k exp . k k =1 12/27
Slotted-ALOHA with Channel Reservation and Without Interferences 13/27
MAC Protocol Description: Slotted-ALOHA with Channel Reservation (SACR) N n Assuming N ∼ Poiss ( µ = N ts N fc ), the reservation probability is Rp = P { N = 0 } = e − µ 14/27
SACR Strategy Illustration 15/27
Communicating Node States Modeling: Markov Chain 16/27
Communicating Node States Modeling: Markov Chain Given its transition matrix Γ, the distribution over states is given by a stochastic row vector π s.t. π ( k +1) = π ( k ) Γ and so π ( k ) = π (0) Γ k , thus π ∞ = π (0) lim k →∞ Γ k . In particular the success transmission likelihood is given by � � k →∞ Γ k Tx i = lim (1 , 4 i ) 17/27
Communicating Node States Modeling: Markov Chain 1 Tx 1 0 . 8 Tx 2 Tx 3 0 . 6 Tx 4 Tx i ’s Fail 0 . 4 0 . 2 0 0 5 10 15 20 25 30 35 40 Number of nodes Figure 1: Curves of Tx i ’s. 18/27
Slotted-ALOHA with Channel Reservation and Interferences 19/27
When interfering nodes in the out range of the BTS � � � ξ Op � X 0 � > R = P � Σ α > � � X 0 � > R , � ( λ ∗ π ) α/ 2 where R denotes the range of the BTS. 20/27
When interfering nodes in the out range of the BTS 1 With interference 0 . 8 Without interference 0 . 6 Tx 1 0 . 4 0 . 2 0 0 10 20 30 40 Number of nodes Figure 2: Comparison of the transmission success likelihood after one trial with no interfering nodes (in blue) and with interference (in black). 21/27
Experimental Analysis and Main Result 22/27
Experiment using Fit-IoT-Lab platform 23/27
Experiment details λ = 1 . 7 · 10 − 6 Density of nodes Attenuation coeff. α = 2 . 2 Noise power N 0 = − 100 dBm Trans. power P e = 25 dBm SINR thresh. τ = − 10 dB Dist. node r = 50 m Numb. nodes N n = 40 Numb. channels N c = 5 Numb. time-slots N ts = 4 24/27
Theory vs Experiments 1 0 . 8 0 . 6 Tx 1 0 . 4 Experimental Tx 1 (5 experiments) 0 . 2 Mean of Experimental Tx 1 Theoretical Tx 1 0 0 5 10 15 20 25 30 35 40 Number of nodes Figure 3: Comparison between the theoretical transmission likelihood and its practical estimation for 20 channels. Best view in color. 25/27
Main result: How many channels do we need to a achieve high performance distributed wireless sensor network? 150 Number of channels 100 N fc N ts = 80 Tx 1 = 0 . 93 50 Tx 1 = 0 . 97 Tx 1 = 0 . 98 Tx 1 = 0 . 99 N n = 60 0 0 20 40 60 80 100 Number of nodes Figure 4: Transmission success likelihood in terms of number of nodes in the network and number of channels assuming the presence of interfering nodes in the out range of the BTS. 26/27
Thank you for your attention! 27/27
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