Skip to content

WiFi Model

The WiFi model derives link rates from propagation, SNR-based MCS selection, and 802.11 MAC contention. Explicit link bandwidths specify clean PHY rates; Solo and Full modes apply MAC overhead to those rates too. See wireless modes for the canonical API and optional treatment.

The implementation lives in two modules:

  • ncsim/models/wifi.py -- RF propagation, MCS tables, conflict graph construction, Bianchi MAC efficiency
  • ncsim/models/interference.py -- CsmaCliqueInterference and CsmaBianchiInterference classes

Path Loss and Received Power

ncsim uses the log-distance path loss model with a Friis free-space reference at distance d0 = 1 m.

Friis Reference Loss

The free-space path loss at the reference distance d0:

PL(d0) = 20 * log10(4 * pi * d0 * f / c)

At 5 GHz with d0 = 1 m, this evaluates to approximately 46.4 dB. At 2.4 GHz with d0 = 1 m, approximately 40.0 dB.

Log-Distance Path Loss

For distance d >= d0:

PL(d) = PL(d0) + 10 * n * log10(d / d0)

Where n is the path loss exponent:

Environment Typical n
Free space 2.0
Indoor (open office) 2.5 - 3.0
Indoor (with walls) 3.0 - 4.0
Dense indoor 4.0 - 5.0

Received Power

Prx(d) = Ptx - PL(d) - X_SF

Where X_SF is the shadow fading component (0 by default, see Shadow Fading below).

SNR

Signal-to-noise ratio in dB:

SNR = Prx - N0

Where N0 is the noise floor (default -95 dBm).

MCS Rate Adaptation

The received SNR selects the highest MCS (Modulation and Coding Scheme) whose minimum SNR threshold is met. If the SNR falls below 5 dB (the lowest threshold), the link is considered not viable and the rate is 0.

MCS Tables (1 Spatial Stream, 20 MHz Base)

802.11n (HT)

MCS Modulation Min SNR (dB) Rate (Mbps)
0 BPSK 1/2 5 6.5
1 QPSK 1/2 8 13.0
2 QPSK 3/4 11 19.5
3 16-QAM 1/2 14 26.0
4 16-QAM 3/4 18 39.0
5 64-QAM 2/3 22 52.0
6 64-QAM 3/4 25 58.5
7 64-QAM 5/6 29 65.0

802.11ac (VHT)

MCS Modulation Min SNR (dB) Rate (Mbps)
0 BPSK 1/2 5 6.5
1 QPSK 1/2 8 13.0
2 QPSK 3/4 11 19.5
3 16-QAM 1/2 14 26.0
4 16-QAM 3/4 18 39.0
5 64-QAM 2/3 22 52.0
6 64-QAM 3/4 25 58.5
7 64-QAM 5/6 29 65.0
8 256-QAM 3/4 32 78.0
9 256-QAM 5/6 35 86.7

802.11ax (HE)

MCS Modulation Min SNR (dB) Rate (Mbps)
0 BPSK 1/2 5 8.6
1 QPSK 1/2 8 17.2
2 QPSK 3/4 11 25.8
3 16-QAM 1/2 14 34.4
4 16-QAM 3/4 18 51.6
5 64-QAM 2/3 22 68.8
6 64-QAM 3/4 25 77.4
7 64-QAM 5/6 29 86.0
8 256-QAM 3/4 32 103.2
9 256-QAM 5/6 35 114.7
10 1024-QAM 3/4 38 129.0
11 1024-QAM 5/6 41 143.4

Summary by Standard

Standard MCS Range Peak Rate (20 MHz) Modulation Range
802.11n 0--7 65.0 Mbps BPSK -- 64-QAM
802.11ac 0--9 86.7 Mbps BPSK -- 256-QAM
802.11ax 0--11 143.4 Mbps BPSK -- 1024-QAM

Channel Width Scaling

Rates scale linearly with channel width. The table values are for 20 MHz; multiply by the channel width factor:

Channel Width Factor
20 MHz 1x
40 MHz 2x
80 MHz 4x
160 MHz 8x

For example, 802.11ax MCS 11 at 80 MHz: 143.4 * 4 = 573.6 Mbps.

Unit Conversion

ncsim uses MB/s internally for bandwidth. PHY rates are converted:

rate_MBps = rate_Mbps / 8

Conflict Graph

The conflict graph determines which links cannot transmit simultaneously under the 802.11 CSMA/CA protocol model.

Carrier Sensing Range

The maximum distance at which a transmission triggers Clear Channel Assessment (CCA):

d_CS = d0 * 10^((Ptx - theta_CCA - PL(d0)) / (10 * n))

Where theta_CCA is the CCA threshold (default -82 dBm).

Conflict Rules

Two links A and B conflict if carrier sensing prevents them from transmitting at the same time.

Without RTS/CTS (default): links A and B conflict if:

  • Transmitter of A can sense any node of link B, OR
  • Transmitter of B can sense any node of link A

"Can sense" means the distance between the two nodes is within the carrier sensing range.

With RTS/CTS (rts_cts: true): links A and B conflict if:

  • Any node of link A can sense any node of link B

RTS/CTS extends the conflict zone to protect receivers, which reduces hidden terminal problems but increases contention.

graph TB
    subgraph "Without RTS/CTS"
        direction LR
        txA1["TX(A)"] -->|"sense?"| txB1["TX(B)"]
        txA1 -->|"sense?"| rxB1["RX(B)"]
        txB1 -->|"sense?"| txA1b["TX(A)"]
        txB1 -->|"sense?"| rxA1["RX(A)"]
    end

    subgraph "With RTS/CTS"
        direction LR
        txA2["TX(A)"] -->|"sense?"| txB2["TX(B)"]
        txA2 -->|"sense?"| rxB2["RX(B)"]
        rxA2["RX(A)"] -->|"sense?"| txB2b["TX(B)"]
        rxA2 -->|"sense?"| rxB2b["RX(B)"]
    end

Max Clique Computation

For each link, ncsim computes the maximum clique size -- the largest set of mutually conflicting links that includes the given link.

  • Exact (Bron-Kerbosch with pivoting): used when the network has 50 or fewer links. Finds all maximal cliques and records the largest one containing each link.
  • Greedy approximation: used for larger networks. Builds a clique greedily starting from each link by adding the most-connected candidate that is adjacent to all current clique members.

Bianchi MAC Efficiency

Bianchi's saturation throughput model computes the MAC-layer efficiency eta(n) for n contending stations sharing the channel under 802.11 DCF.

Coupled Equations

The model solves for the transmission probability tau and collision probability p using a bracketed scalar solve, evaluating the removable singularity at p = 0.5 through a finite geometric sum:

tau = 2(1 - 2p) / [(1 - 2p)(W + 1) + pW(1 - (2p)^m)]
p   = 1 - (1 - tau)^(n - 1)

Where:

  • W = 16 (CWmin + 1, the initial contention-window size)
  • m = 6 (maximum backoff stage; CWmax = W * 2^m = 1024)

Efficiency Values

From the converged tau and p, the model computes idle, success, and collision probabilities per slot, then derives the fraction of channel time carrying successful payload:

Efficiency depends on the PHY rate and RTS/CTS setting as well as station count: eta(n, R). Even one station incurs interframe, backoff, preamble, and acknowledgment overhead, so eta(1, R) is below one. Values are cached on demand; there is no 100-station lookup-table cap. Per-link saturated goodput is R * eta(n, R) / n for homogeneous contenders.

CSMA Clique Model

The static WiFi interference model. Contention is computed once at setup and baked into each link's bandwidth.

Bandwidth Assignment

link.bandwidth = PHY_rate / omega(l)

Where omega(l) is the maximum clique size containing link l.

Interference Factor

Always 1.0. Since contention is already reflected in the bandwidth, the interference model does not apply any additional reduction during simulation.

When To Use

csma_clique is appropriate when you want WiFi-aware bandwidth estimation without the computational cost of dynamic recalculation. It provides a static approximation: the bandwidth assumes all links in the largest clique are always active, even if only a subset actually transmits at any given time. It is not a physical throughput bound.

CSMA Bianchi Model

The dynamic WiFi interference model. It correctly separates two interference mechanisms and recalculates the factor whenever transfers start or complete.

Mechanism 1: Contention Domain Time-Sharing

Links that are neighbors in the conflict graph operate under CSMA/CA and cannot transmit simultaneously. Each of n contending links gets:

contention_factor = eta(n, R) / (n * eta(1, R))

No SINR degradation occurs from these links because CSMA prevents concurrent transmission.

Mechanism 2: Hidden Terminal SINR Degradation

Active links that are not in the conflict graph may transmit simultaneously, causing interference at the receiver. The SINR is computed in the linear domain:

SINR = P_signal / (P_noise + sum(P_interferers))

Where P_interferers includes only hidden terminal transmitter powers as received at the evaluated link's receiver node. The SINR determines a (potentially lower) MCS rate R_SINR.

sinr_factor = R_SINR / R_base

Combined Factor

factor = R_effective * eta(n, R_effective)
         / (n * R_base * eta(1, R_base))

Here R_effective is the SINR-selected PHY rate capped at the clean base rate. The installed link bandwidth already includes eta(1, R_base), so this normalization avoids counting single-link overhead twice. Outages give zero service; no positive floor is applied unless explicitly requested for diagnosis.

Recalculation

When a transfer starts or completes, affected links are found through directed interference dependencies. Bytes served before the event are credited at the old rates before new completion times are scheduled.

flowchart TD
    A["Transfer starts/completes on link L"] --> B["Identify active links"]
    B --> C["For each affected active link K"]
    C --> D["Classify neighbors:<br/>contending vs. hidden"]
    D --> E["Count contenders n"]
    D --> F["Compute SINR from hidden terminals"]
    F --> G["Select MCS from SINR -> R_SINR"]
    E --> H["Normalize rate-aware goodput by clean solo goodput"]
    G --> H
    H --> I["Recalculate transfer completion time"]

Key design decision

Contending links affect throughput via time-sharing (Bianchi), not via SINR. Only hidden terminals cause SINR degradation. Conflating the two (e.g., including contending links in the SINR calculation) would double-count their impact and produce unrealistically low throughput.

Shadow Fading

Optional log-normal shadow fading adds randomness to path loss. In the dB domain, fading values are drawn from a Gaussian distribution N(0, sigma).

  • Per-node-pair: each pair of nodes gets its own fading value.
  • Symmetric: fading(A, B) = fading(B, A).
  • Deterministic from seed: the same seed always produces the same fading map, ensuring reproducibility.
  • Configured via shadow_fading_sigma (default 0.0, meaning no fading).
config:
  rf:
    shadow_fading_sigma: 4.0   # dB standard deviation

The fading value is subtracted from received power:

Prx(d) = Ptx - PL(d) - X_SF

Where X_SF ~ N(0, sigma) for the specific node pair.

RF Configuration Parameters

All RF parameters are specified in the rf: section of the scenario YAML. Several can also be overridden via CLI flags.

YAML Key CLI Flag Unit Default Description
tx_power_dBm --tx-power dBm 20.0 Transmit power (typical AP: 15--23 dBm)
freq_ghz --freq GHz 5.0 Carrier frequency (2.4 or 5.0)
path_loss_exponent --path-loss-exponent -- 3.0 Path loss exponent n (2.0 = free space, 3--4 = indoor)
noise_floor_dBm -- dBm -95.0 Effective noise floor including receiver noise figure
cca_threshold_dBm -- dBm -82.0 CCA signal detect threshold
channel_width_mhz -- MHz 20 Channel width (20, 40, 80, 160)
wifi_standard --wifi-standard -- ax MCS table selection (n, ac, ax)
shadow_fading_sigma -- dB 0.0 Std dev of log-normal shadow fading (0 = none)
rts_cts --rts-cts -- false Enable RTS/CTS (extends conflict zone)

Full YAML Example

config:
  interference: csma_bianchi
  rf:
    tx_power_dBm: 20
    freq_ghz: 5.0
    path_loss_exponent: 3.0
    noise_floor_dBm: -95
    cca_threshold_dBm: -82
    channel_width_mhz: 20
    wifi_standard: "ax"
    shadow_fading_sigma: 0.0
    rts_cts: false

Omitting link bandwidth

When using csma_clique or csma_bianchi, link bandwidth is derived from RF parameters and node positions. You can omit the bandwidth key from link definitions -- ncsim will compute it automatically. If you do specify a bandwidth, it supplies the clean PHY rate. Solo and Full modes still apply MAC overhead; specifying it does not exempt a link from WiFi.

CLI Override Example

ncsim --scenario wifi_topology.yaml --output results/ \
      --interference csma_bianchi \
      --tx-power 23 \
      --freq 2.4 \
      --path-loss-exponent 3.5 \
      --wifi-standard ac \
      --rts-cts