WiFi Model¶

The WiFi model replaces manually specified link bandwidths with physically grounded data rates derived from RF propagation, SNR-based MCS selection, and 802.11 MAC contention. It is used by the csma_clique and csma_bianchi interference models.

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 via fixed-point iteration:

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

Where:

W = 16 (CWmin, minimum contention window for 802.11)
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:

n (stations)	eta(n)	Per-station share eta(n)/n
1	1.000	1.000
2	~0.88	~0.44
5	~0.72	~0.14
10	~0.59	~0.059
20	~0.47	~0.024

Properties:

eta(1) = 1.0 -- a single station has no contention overhead.
eta(n) is monotonically decreasing but always positive.
The per-station share eta(n)/n decreases faster than 1/n due to collision overhead.

ncsim precomputes a lookup table for n = 1 to 100 at startup.

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 conservative worst-case bound: the bandwidth assumes all links in the largest clique are always active, even if only a subset actually transmits at any given time.

CSMA Bianchi Model¶

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

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) / n

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 = sinr_factor * contention_factor
       = (R_SINR / R_base) * (eta(n) / n)

The factor is clamped to the range [0.01, 1.0].

Recalculation¶

When any transfer starts or completes, all other active links have their factors recalculated. This ensures both contention domain changes and hidden terminal changes are captured symmetrically.

flowchart TD
    A["Transfer starts/completes on link L"] --> B["Identify active links"]
    B --> C["For each active link K != L"]
    C --> D["Classify neighbors:<br/>contending vs. hidden"]
    D --> E["Compute contention_factor = eta(n)/n"]
    D --> F["Compute SINR from hidden terminals"]
    F --> G["Select MCS from SINR -> R_SINR"]
    E --> H["factor = (R_SINR / R_base) * (eta(n) / n)"]
    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 will be kept as-is (not overwritten by the WiFi model), which is useful for mixing wired and wireless links in the same topology.

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