| Free Space Path Loss | FSPL | FSPL(dB) = 20·log₁₀(4π·d·f/c)
= 20·log₁₀(d) + 20·log₁₀(f) + 20·log₁₀(4π/c)
Where c=3×10⁸ m/s
Simplified: FSPL = 20·log₁₀(d_m) + 20·log₁₀(f_MHz) - 27.55 | d in metres, f in MHz
At 1m: 2.4GHz=40.1dB, 5GHz=46.4dB, 6GHz=47.8dB, 60GHz=67.9dB | FSPL Quick Calculator, Link Budget Wizard, Coverage Radius |
| Wavelength | λ | λ(m) = c/f = 3×10⁸ / f_Hz
Or: λ(m) = 300 / f_MHz | f in MHz → λ in metres
2.4GHz: λ=0.125m, 5GHz: λ=0.060m, 6GHz: λ=0.050m | FSPL, Fresnel, Two-Ray, MIMO antenna spacing |
| Fresnel Zone Radius (1st) | r1 | r1=sqrt(lambda*d1*d2/d). Min clearance=0.6*r1. At 5GHz 100m midpoint: r1=√(0.06·50·50/100)=1.22m | Metres. Obstruct >40% zone = >6dB loss | Fresnel Calculator |
| Two-Ray Breakpoint Distance | d_bp | d_bp(m) = 4·h_T·h_R / λ
Where h_T=TX antenna height, h_R=RX antenna height
Beyond d_bp: PL exponent changes from 2 to 4 | Metres. AP at 3m, client at 1.5m, 5GHz: d_bp=300m | Two-Ray Ground Reflection, AP Placement |
| Log-Distance Path Loss | PL(d) | PL(d) = PL(d₀) + 10·n·log₁₀(d/d₀) + X_σ
Where n=path loss exponent, d₀=reference distance (1m), X_σ=shadow fading (Gaussian, σ dB)
PL(d₀=1m) = FSPL at 1m for the frequency | Unitless (dB). n=2 free space, n=3.5 NLOS office
X_σ ~ N(0, σ²), σ=8-12 dB typical indoor | Path Loss Calculator, AP Density, Coverage Radius |
| Thermal Noise Floor | N | N(dBm) = -174 + 10·log₁₀(B_Hz)
= -174 + 10·log₁₀(B_MHz) + 60
Examples: 20MHz → -101dBm, 40MHz → -98dBm
80MHz → -95dBm, 160MHz → -92dBm, 320MHz → -89dBm | B in Hz. k=1.38×10⁻²³ J/K, T=290K → kT=-174dBm/Hz | Noise Floor Table, Link Budget, RSSI→MCS Advisor |
| Receiver Sensitivity | Sens | Sens(dBm) = -174 + 10·log₁₀(BW_Hz) + NF + SNR_min
= Noise_floor + NF + SNR_min
NF: AP=5-7dB typical, Client=7-10dB typical | dBm. At BW=20MHz, NF=8dB, SNR_min=5dB: Sens=-88dBm | Noise Floor Table, Link Budget Wizard, RSSI→MCS |
| Link Margin | LM | LM(dB) = RSSI - Sensitivity
LM = EIRP - Path_Loss - Sensitivity
Link margin targets: >10dB=reliable, 5-10dB=marginal, <5dB=unreliable | dB. Rule: >10dB for 99.9% link availability | Link Budget Wizard, Coverage Radius |
| EIRP | EIRP | EIRP(dBm) = P_conducted(dBm) + G_ant(dBi) - L_cable(dB)
For compliance: EIRP must not exceed regulatory limit
Max antenna gain = EIRP_limit - P_conducted + L_cable | dBm. FCC UNII-1: 30dBm EIRP. ETSI: 23dBm (200mW) | EIRP Compliance Checker, Antenna Gain Converter |
| SNR to RSSI (field conversion) | SNR | SNR(dB) = RSSI(dBm) - Noise_floor(dBm)
Noise_floor = -174 + 10·log(BW) + NF_device
Example: RSSI=-65dBm, BW=20MHz, NF=8dB → SNR=-65-(-101+8)=28dB | dB. Used to map RSSI to achievable MCS | RSSI→MCS Advisor, Link Budget |
| CP Efficiency | η | η = T_data / (T_data + T_CP)
802.11a/n/ac LGI: 3.2/(3.2+0.8)=80.0%
802.11n/ac SGI: 3.2/(3.2+0.4)=88.9%
802.11ax 0.8µs GI: 12.8/(12.8+0.8)=94.1%
802.11ax 1.6µs GI: 12.8/(12.8+1.6)=88.9%
802.11ax 3.2µs GI: 12.8/(12.8+3.2)=80.0% | Unitless (0-1). Higher GI → lower efficiency but better multipath robustness | OFDM Symbol Timing, Throughput Calculator |
| TCP Goodput Efficiency | TCP_eff | TCP_goodput ≈ 0.65 × PHY_rate (rule of thumb)
More precisely: TCP_goodput = PHY_rate × (1 - overhead)
Overhead factors: MAC headers(34B), IP(20B), TCP(20B), ACKs, CSMA backoff, SIFS/DIFS, retransmissions
Typical efficiency: 60-75% depending on frame size and channel conditions | Unitless (0-1). Short packets (VoIP 200B): ~50% efficiency
Large packets (1500B): ~70-75% efficiency
A-MPDU adds ~15% efficiency over non-aggregated | Throughput Calculator, Shannon Capacity |
| Shannon Capacity | C | C(bps) = B · log₂(1 + SNR_linear)
SNR_linear = 10^(SNR_dB/10)
Spectral efficiency SE = C/B = log₂(1+SNR) (b/s/Hz)
At SNR=20dB (linear=100): SE=6.66 b/s/Hz
At SNR=30dB: SE=9.97 b/s/Hz
At SNR=35dB: SE=11.83 b/s/Hz | bps, B in Hz. 802.11be MCS13 reaches ~78% of Shannon at 35dB SNR | Shannon Capacity vs PHY Rate |
| Eb/N0 to SNR | Eb/N0 | SNR(dB) = Eb/N0(dB) + 10·log₁₀(R_b/B)
Where R_b=bit rate (bps), B=noise bandwidth (Hz)
For BPSK: R_b/B=1 → SNR=Eb/N0
For QPSK: R_b/B=2 → SNR=Eb/N0+3dB
Spectral efficiency SE = R_b/B (b/s/Hz) | dB. Required Eb/N0: BPSK=9.6dB@BER=10⁻⁵, QPSK same, 16-QAM=13.1dB | Eb/N0 Converter, BER vs SNR Calculator |
| PAPR (theoretical) | PAPR | PAPR(dB) = 10·log₁₀(N_subcarriers)
N=256 (802.11ax 20MHz): 24.1dB theoretical
Practical after CCDF clipping: 8-13dB
Required PA Input Back-Off (IBO): ≈ PAPR - DPD_gain
DPD gain: 3-6dB reduction in required back-off
Effective TX power = P_rated - IBO_required | dBc. High PAPR limits effective output power
320MHz 802.11be: N=4096 → 36.1dB theoretical | PAPR + Amplifier Backoff, EVM Budget |
| Coherence Bandwidth | Bc | Bc(Hz) ≈ 1/(5·σ_τ) [90% coherence threshold]
Bc(Hz) ≈ 1/(2π·σ_τ) [50% coherence threshold]
Where σ_τ = RMS delay spread
Rule: OFDM subcarrier spacing << Bc to avoid frequency-selective fading per subcarrier
802.11ax: 78.125kHz << Bc_min (indoor office ~4MHz) ✓ | Hz. Indoor office σ_τ=30-50ns → Bc≈4-6MHz
Warehouse σ_τ=100ns → Bc≈2MHz | Delay Spread Advisor, Channel Simulator |
| Coherence Time | Tc | Tc(s) = 0.423 / f_D_max
Where f_D_max = v·f_c/c (max Doppler)
v=walking speed 1.5m/s, f_c=5GHz: f_D=25Hz → Tc=17ms
v=vehicle 30m/s, f_c=5GHz: f_D=500Hz → Tc=0.85ms
Rule: T_symbol << Tc for time-flat fading per symbol | Seconds. 802.11ax symbol=16µs << Tc at walking speed ✓
At vehicle speed: Tc≈0.85ms = 53 symbols - ICI risk | Doppler & Coherence, Channel Simulator |
| Outage Probability | P_out | Rayleigh fading (K=0): P_out(γ) = 1 - exp(-γ_thresh/γ_avg)
With N-branch MRC diversity: P_out(N) ≈ (γ_thresh/γ_avg)^N for low SNR
Rician (K>0): P_out = Q₁(√(2K), √(2(K+1)·γ_thresh/γ_avg))
Diversity gain G_d = N (slope of log-log P_out curve)
MRC gain vs SISO: 10·log₁₀(N) dB at P_out=10⁻³ | Unitless. N=2 branches: P_out improves by factor ~(1/γ_avg)² vs SISO
N=4: factor ~(1/γ_avg)⁴ | Outage Probability Calculator |
| MRC Combining Gain | G_MRC | SNR_MRC = Σᵢ SNRᵢ (linear sum of branch SNRs)
In dB for equal branches: G_MRC(dB) = 10·log₁₀(N)
N=1: 0dB, N=2: 3dB, N=4: 6dB, N=8: 9dB
EGC: ~0.5dB worse than MRC
Selection Combining: G_SC = 10·log₁₀(Σₖ₌₁ᴺ 1/k)
N=2: 1.76dB, N=4: 3.18dB | dB. STBC Alamouti (2×1): 3dB TX diversity gain
2×2 STBC: 6dB combined TX+RX | Diversity Gain Calculator |
| MIMO Capacity | C_MIMO | C = Σᵢ₌₁ʳ log₂(1 + λᵢ·SNR/Nₜ) [b/s/Hz]
λᵢ = eigenvalues of HH† (SVD of channel matrix H)
r = rank(H) = min(Nr,Nt) for full-rank channel
Equal power (no waterfilling): Pᵢ = SNR/Nₜ for all i
Correlated channel (ρ): C ≈ r·log₂(1+SNR·(1-ρ²)/r) approximately
2×2 at SNR=20dB: C=6.9 b/s/Hz (independent), 5.2 b/s/Hz (ρ=0.9) | b/s/Hz. Rank collapse in LOS: dominant eigenvalue, others ≈0
Antenna correlation ρ<0.3 recommended for MIMO gain | MIMO Capacity Estimator |
| A-MPDU Efficiency | η_AMPDU | η = (N_success × L_data) / (N_total × (L_data + L_overhead))
Where N_success=MPDUs decoded OK, N_total=MPDUs in A-MPDU
At PER=p: N_success = N_total·(1-p)
With Block ACK: single BA covers all N MPDUs
Efficiency vs non-aggregated: scales with N
802.11ax: max 256 subframes vs 802.11n: max 64 | Unitless. At PER=5%: N=64 → efficiency drops from ~93% to ~88%
High PER kills aggregation benefit | A-MPDU Efficiency Calculator |
| Airtime per Frame | T_air | T_air = T_preamble + T_header + T_data + T_ACK + SIFS + DIFS
T_data = ceil(8·L / N_dbps) × T_symbol
N_dbps = N_data_tones × bits_per_tone × coding_rate
At 802.11ax MCS11 80MHz 1SS: N_dbps=980×10×5/6=8167 bits/sym
At 802.11b 1Mbps: T_data(1500B)=12ms vs ax 1Gbps: T_data≈12µs | µs. Legacy 802.11b 1Mbps: 1500B frame = ~12.5ms airtime
802.11ax MCS11: 1500B ≈ 20µs airtime - 625× efficiency gain | Airtime Fairness Analyzer, Throughput Calculator |