PaperlayerView exact revision on arXiv

Source-linked AI summary

Saturation Throughput Analysis of IEEE 802.11 in Presence of Non Ideal Transmission Channel and Capture Effects

F. Daneshgaran, Massimiliano Laddomada, F. Mesiti, M. Mondin

arXiv:0710.5236v1cs.NI

TL;DR

The paper addresses the gap between ideal-channel IEEE 802.11 throughput analyses and fading environments where channel errors and capture affect observed throughput. It extends MAC-layer Markov models for four-way and two-way handshaking, derives saturation-throughput expressions, and compares them with simulations that confirm model validity.

  • Problem

    Ideal-channel throughput analyses do not account for channel-induced errors and capture effects that occur in Rayleigh fading environments.

  • Method

    The paper extends IEEE 802.11 Markov models with transmission states and stationary-probability analysis for channel errors, capture, handshaking variants, and system parameters.

  • Results

    Simulation results confirm the validity and effectiveness of the proposed theoretical models; under optimal operating conditions, Sm = 0.86 Mbps is close to Bianchi’s value regardless of capture threshold z0.

  • Takeaways & Limitations

    The resulting closed-form analysis incorporates channel contention, packet and header sizes, capture probability, and channel errors into saturation-throughput evaluation.

Abstract

from arXiv · show

In this paper, we provide a saturation throughput analysis of the IEEE 802.11 protocol at the data link layer by including the impact of both transmission channel and capture effects in Rayleigh fading environment. Impacts of both non-ideal channel and capture effects, specially in an environment of high interference, become important in terms of the actual observed throughput. As far as the 4-way handshaking mechanism is concerned, we extend the multi-dimensional Markovian state transition model characterizing the behavior at the MAC layer by including transmission states that account for packet transmission failures due to errors caused by propagation through the channel. This way, any channel model characterizing the physical transmission medium can be accommodated, including AWGN and fading channels. We also extend the Markov model in order to consider the behavior of the contention window when employing the basic 2-way handshaking mechanism. Under the usual assumptions regarding the traffic generated per node and independence of packet collisions, we solve for the stationary probabilities of the Markov chain and develop expressions for the saturation throughput as a function of the number of terminals, packet sizes, raw channel error rates, capture probability, and other key system parameters. The theoretical derivations are then compared to simulation results confirming the effectiveness of the proposed models.

I. INTRODUCTION

The paper addresses limitations of ideal-channel IEEE 802.11 throughput analyses by incorporating channel-induced errors and capture effects in Rayleigh fading environments. It extends Markov models for both four-way and two-way handshaking and validates the resulting throughput analysis through simulation.

  • Scope: The models use IEEE 802.11b parameters while remaining applicable to other protocol variants employing the same MAC mechanisms.The proposed mathematical models are presented as extensible beyond the reference IEEE 802.11b configuration.
  • Contribution: The paper extends prior IEEE 802.11 saturation-throughput work by treating channel-induced errors and capture effects together over Rayleigh fading channels.The extension addresses three previously outlined issues in a unified analysis.
  • Motivation: Ideal-channel analyses assume saturation traffic, no hidden terminals or capture, independent constant collision probability, and collisions as the only packet-error source.The paper identifies the ideal-channel and no-capture assumptions as invalid in real mobile fading settings.
  • Validation: Simulation results confirm the effectiveness of the proposed models across throughput conditions involving system parameters, capture probability, and SNR.The simulations use typical IEEE 802.11b MAC-layer parameters.
  • Method: The four-way-handshaking analysis modifies Bianchi’s Markov model with transmission states for errors and capture, then derives a saturation-throughput expression.The paper also extends the two-dimensional Markov chain for basic two-way handshaking.

II. DEVELOPMENT OF THE MARKOV MODEL

The paper develops a bi-dimensional Markov model for evaluating DCF throughput with finite terminals, channel errors, capture, Rayleigh fading, and four-way handshaking.

  • Model scope: The proposed model evaluates DCF throughput for a finite number of operating terminals under channel errors, capture effects, and Rayleigh fading.The analysis focuses on packet transmission using the four-way handshaking mechanism.
  • Presentation: The section limits its presentation to the ideas needed to develop the model and refers readers elsewhere for detailed DCF functionality.The cited references provide additional details on DCF operation.

A. Markovian Model Characterizing the MAC Layer: Perfect Transmission Channel

The perfect-channel baseline represents each station with a two-dimensional Markov process tracking its backoff stage and counter under constant transmission and collision probabilities.

  • State representation: Bianchi’s model uses (s(t), b(t)) to represent the contention-window stage and backoff counter for throughput computation.The model describes a WLAN using IEEE 802.11 DCF under ideal channel conditions.
  • Assumptions: The model assumes a constant transmission-attempt probability τ and a constant collision probability Pcol independent of prior collisions.These assertions support the stationary analysis of the Markov process.
  • Backoff procedure: After failed transmissions, the backoff stage increases up to m and the contention window doubles from W to CWmax = 2^mW.At stage i, the window is Wi = 2^iW.
  • Backoff procedure: The backoff counter decreases during idle slots, stops when transmission is detected, and triggers transmission when it reaches zero.A new counter value is selected from the current contention window after transmission.

III. MARKOVIAN MODEL CHARACTERIZING THE MAC LAYER UNDER REAL TRANSMISSION CHANNEL AND CAPTURE EFFECTS USING THE 4-WAY HANDSHAKING MECHANISM The main aim of this section is to propose an effective modification of the bi-dimensional Markov process proposed in

The paper extends the MAC-layer Markov model to represent channel errors and capture during four-way handshaking over Rayleigh fading channels. It derives transitions and throughput-related quantities under explicit packet-error assumptions.

  • Error and collision model: Four-way handshaking confines collisions primarily to RTS packets, while channel-induced errors affect data frames after CTS reception.The data frame is protected from collision but remains vulnerable to transmission errors.
  • Capture effects: Capture is modeled as a collision subset in which the station with higher received power proceeds to transmission without detecting a collision.This captures the effect of unequal received power at the access point.
  • Markov-state extension: The extended model adds a transmit state (i, −1) absent from Bianchi’s original model to represent data transmission after successful or captured RTS exchange.A collision can lead to this state when the desired station captures the channel.
  • Assumptions: The model neglects errors in RTS, CTS, and ACK frames because their short lengths make those effects comparatively small under independent bit errors.The authors state that explicitly modeling these errors would substantially complicate the Markov chain without clear benefits.
  • Contention structure: The model uses Wi = 2^iW across m+1 backoff stages, with RTS transmissions in (i, 0) and data transmissions in (i, −1).The maximum contention window is CWmax = 2^mW.
  • State transitions: Unsuccessful RTS transmissions and data-frame errors both schedule a new backoff stage, whereas successful transmission returns the station to stage zero.The transition probabilities separately encode collision probability Pcol and packet-error probability Pe.

A. Markovian Process Analysis and Throughput Computation

The analysis extends Markovian modeling to include channel errors and capture effects, then computes stationary probabilities and normalized throughput for the 4-way mechanism. Capture is modeled as collision-associated successful reception, while channel errors affect data frames and contribute to failed transmissions.

  • Stationary analysis: The model finds the stationary distribution of the Markov chain and uses normalization to compute the transmission-attempt probability τ.τ is the probability that a station starts transmission in a randomly chosen slot.
  • Collision and capture: RTS collisions occur when at least one other station transmits simultaneously and capture does not occur.Capture is treated as a subset of collision events, occurring when the desired signal has higher received power.
  • Collision and capture: Capture probability is determined from the received useful-signal-to-interference power ratio exceeding the threshold z0g(Sf).For DSSS with spreading factor Sf = 11, the passage specifies g(Sf) = 2.
  • Throughput computation: The nonlinear system jointly determines τ, Pcol, Peq, and Pcap from the Markov relations and capture formulation.The system combines equations for the attempt, collision, equivalent failure, and capture probabilities and is solved numerically.
  • Throughput computation: Normalized throughput is defined as the fraction of time used to successfully transmit payload bits.Its computation uses transmission probability, successful-RTS probability, average busy times, payload length, and empty-slot duration.

IV. ANALYSIS OF THE MARKOV CHAIN FOR THE BASIC 2-WAY HANDSHAKING MECHANISM IN PRESENCE OF CHANNEL

For basic 2-way handshaking, the Markov model is extended to account for channel errors and capture without an RTS/CTS exchange. The resulting stationary distribution and throughput are computed by replacing the collision probability with an equivalent failed-transmission probability.

  • Protocol operation: The basic 2-way mechanism uses data transmission followed by ACK reception, with retransmission contention after an erroneous or missing ACK.No RTS/CTS exchange is used.
  • Markov model: The backoff-window Markov chain can represent the 2-way mechanism by replacing Bianchi’s collision probability p with Peq.The model treats protocol-data and information transmission without an evident distinction in this setting.
  • Failure modeling: Transmission fails either through packet collision or through channel errors affecting data transmission with probability Pe.Capture reduces the collision probability by Pcap, and the same rationale is used as for 4-way handshaking.
  • Throughput computation: The stationary distribution is evaluated using the same mathematical derivations as Bianchi’s model, with Peq substituted for p.Throughput is then evaluated after solving the nonlinear system of equations.

A. Markovian Process Analysis and Throughput Computation

The 2-way analysis derives stationary state probabilities, computes the transmission-attempt probability τ, and evaluates normalized throughput using mechanism-specific timing intervals.

  • Stationary analysis: The stationary distribution describes the probability of occupying each backoff state at a discrete time.The states span stages i ∈ [0, m] and backoff counters k ∈ [0, Wi − 1].
  • Stationary analysis: Normalization of the stationary probabilities yields the equation used to compute b0,0.The resulting state relations support the normalization calculation.
  • Transmission probability: The computed state result is used to obtain τ, the probability that a station starts a transmission in a randomly chosen time slot.A data packet transmission occurs when the backoff counter reaches zero.
  • Throughput computation: The nonlinear system computes τ, Pcol, Pcap, and Peq using the same definitions as the 4-way mechanism.The resulting probabilities are used in the normalized system-throughput computation.
  • Timing model: For 2-way handshaking, collision and error intervals are H + PL + ACKtimeout, while successful transmission additionally includes SIFS, propagation, ACK, and DIFS durations.These timing definitions replace the corresponding 4-way intervals.

V. SIMULATION RESULTS AND MODEL VALIDATIONS

The simulation section validates the theoretical models and derivations using a C++ simulator of IEEE 802.11b DCF and station backoff behavior. The simulator includes physical propagation delays and other station operations.

  • Validation setup: The simulations are used to validate the theoretical models and derivations presented in the preceding sections.The section explicitly frames the experiments as model validation.
  • Simulator: The C++ simulator models IEEE 802.11b DCF details and backoff procedures for a specified number of independent transmitting stations.It represents multiple independent transmitters contending for the channel.
  • Simulator: The simulator includes physical propagation delays and other real operations of each transmitting station.These operations extend beyond abstract backoff behavior.

A. Simulation Setup

The simulation models saturated IEEE 802.11b infrastructure networks with nonideal channels, Rayleigh fading, capture effects, and standard MAC behavior. It evaluates throughput across station placements, data rates, FER conditions, and access modes using both analytical channel models and randomized simulation scenarios.

  • Network and MAC configuration: The simulator represents an infrastructure BSS with an AP and mobile stations transmitting under saturated conditions.The MAC follows standard waiting times and supports post-backoff, backoff, basic, and RTS/CTS access modes.
  • Topology and capture modeling: Stations are uniformly distributed within a 50 m-radius circular area, with the AP at the center, to model capture effects.Throughput is averaged over 100 randomly generated station-placement scenarios.
  • Channel and capture modeling: Rayleigh fading models received power as an exponential random variable around a path-loss mean A · r^-np, using np = 3.5 in simulations.Capture occurs when a colliding station's signal ratio γj exceeds the threshold z0 · g(Sf).
  • PHY configuration: 802.11b simulations use DSSS with four supported data rates: 1, 2, 5.5, and 11 Mbps.The PHY includes DBPSK, DQPSK, CCK5.5, and CCK11 modulation-dependent error-rate models.

B. Simulation Results

The simulations examine how SNR, capture effects, payload size, station count, and handshaking affect IEEE 802.11 saturation throughput. Theoretical curves generally match simulations and show convergence to ideal-channel or Bianchi-model behavior under appropriate conditions.

  • Channel quality and probabilities: Transmission probability τ increases with SNR until saturating around 40dB, and increases with higher capture probability.The curves use N = 20 stations and 1024-byte payloads, parameterized by capture threshold z0.
  • Channel quality and probabilities: Equivalent transmission failure probability decreases with SNR, approaching collision probability at high SNR but nearly equaling 1 at very low SNR.As SNR tends to infinity, Peq approaches the collision probability when channel errors and capture effects vanish.
  • 2-way handshaking: 2-way throughput improves with SNR up to 35 dB, while capture can make throughput nearly independent of station count.With low capture probability at z0 = 24dB, increasing the number of contending stations reduces throughput.
  • Payload size: Shorter packets can be preferable at low SNR, whereas longer packets increase throughput when channel quality improves.The comparison varies payload size as a function of SNR.
  • 2-way and 4-way comparison: The 4-way mechanism is less sensitive to capture effects and achieves throughput close to Bianchi’s Sm = 0.86 Mbps across capture thresholds.Channel errors reduce throughput below Sm, especially below 45dB, while throughput can exceed Sm for N ≤20 and low capture thresholds.

VI. CONCLUSIONS

The paper extends IEEE 802.11 DCF Markov modeling to include channel-induced errors and capture effects in fading environments, then derives saturation-throughput expressions validated by simulation.

  • The Markov model accounts for channel-induced errors and capture effects characteristic of fading environments.
  • The modeling incorporates channel contention into throughput analysis rather than treating contention through a static mean period.
  • Stationary Markov-chain probabilities are used to obtain saturation throughput under the paper’s assumptions.
  • Closed-form expressions derive throughput as a function of packet and header sizes and other system-level parameters.
  • Simulation results confirm the validity of the proposed theoretical models.

TYPICAL NETWORK PARAMETERS

The section presents a scenario for examining throughput dependence on per-station FER with nine contending stations, using the 2-way mechanism without capture and 1024-byte packets.

  • The analysis considers throughput dependence on per-station FER with N = 9 contending stations.
  • The scenario uses the 2-way mechanism without capture.
  • The packet size is E[P_L] = 1024 bytes.
Loading 0710.5236v1…