PHY LayerL1-L2

Modulation & dB Math

PHY Math RF Reference

MODULATION LADDER - constellation → bits/symbol → SNR - the foundation of every MCS table11 rows#

Modulation	Bits/Symbol	Scheme	Min SNR (dB, approx)	First Used	MCS Position	Notes
DBPSK	1	DSSS (11 Mchip Barker)	~2-4	802.11 (1 Mbps)	-	Differential - no carrier phase reference needed.
DQPSK	2	DSSS	~5-7	802.11 (2 Mbps)	-	-
CCK	4/8 chips	HR-DSSS	~8-10	802.11b (5.5/11 Mbps)	-	Complementary Code Keying - 8-chip codewords, not classic QAM.
BPSK	1	OFDM	~2-5	802.11a → all	MCS 0	2 constellation points on I axis. Most robust; used for SIG fields and MCS 0.
QPSK	2	OFDM	~5-9	802.11a → all	MCS 1-2	4 points. 3 dB less noise margin per bit vs BPSK at same power.
16-QAM	4	OFDM	~11-16	802.11a → all	MCS 3-4	16 points, 4×4 grid.
64-QAM	6	OFDM	~18-22	802.11a → all	MCS 5-7	64 points. Legacy max (54 Mbps era).
256-QAM	8	OFDM	~25-31	802.11ac →	MCS 8-9	Needs clean channel + good EVM. Typically only at short range.
1024-QAM	10	OFDM(A)	~31-35	802.11ax →	MCS 10-11	Requires EVM ≤ -35 dB; practical only <~10 m LoS-ish.
4096-QAM	12	OFDM(A)	~36-39	802.11be →	MCS 12-13	Requires EVM ≤ -38 dB. +20% rate over 1024-QAM. Very short range.
BPSK-DCM	0.5 eff	HE OFDMA	< 0	802.11ax	MCS 0 + DCM	Dual Carrier Modulation: same data on 2 subcarriers → 3-4 dB robustness gain, half rate. Range/IoT tool.

DECIBEL MATH - rules every wireless engineer must be able to do mentally9 rows#

Rule / Anchor	Statement	Notes
dB definition	dB = 10·log₁₀(P2/P1) for power; 20·log₁₀(V2/V1) for voltage/field.	Ratios only - dimensionless.
dBm definition	dBm = 10·log₁₀(P / 1 mW). Absolute power.	0 dBm = 1 mW.
+3 dB / -3 dB	×2 / ÷2 power.	Memorize with 10s below - covers everything.
+10 dB / -10 dB	×10 / ÷10 power.	E.g. 26 dBm = 20+3+3 → 100 mW×2×2 = 400 mW.
+1 dB	×1.26 (≈ +26%).	1 dB rule of thumb: ~25%.
dB + dBm math	dBm + dB = dBm (gain applied). dBm - dBm = dB (a ratio). dBm + dBm = INVALID.	Most common link-budget mistake.
dBi / dBd	Antenna gain vs isotropic / vs dipole. dBi = dBd + 2.15.	Datasheets mix them - check the suffix.
mW→dBm anchors	1 mW=0 · 10 mW=10 · 100 mW=20 · 1 W=30 · 4 W=36 dBm.	FCC 2.4 GHz max EIRP = 36 dBm point-to-multipoint.
RX-side anchors	-30 dBm ≈ 1 µW (very hot) · -50 excellent · -67 voice-grade edge · -72 data edge · -85 marginal · -95 noise-floor region (20 MHz ≈ -101 dBm thermal).	Design targets: -65 to -67 dBm for VoWiFi cells.

OFDM NUMEROLOGY MASTER TABLE - per generation11 rows#

Rule / Anchor	Statement	Notes
Parameter	802.11a/g	802.11n
Subcarrier spacing	312.5 kHz	312.5 kHz
FFT size @20/40/80/160/320 MHz	64 / - / - / - / -	64 / 128 / - / - / -
Useful symbol time	3.2 µs	3.2 µs
Guard intervals	0.8	0.8 / 0.4 (SGI)
Symbol total (best case)	4.0 µs	3.6 µs (SGI)
Data+pilot tones @20 MHz	48+4 = 52	52+4 = 56
@40 MHz	-	108+6 = 114
@80 MHz	-	-
@160 MHz	-	-
@320 MHz	-	-

Calculating the Wi-Fi Physical Layer (PHY) data rate1 rows#

Rule / Anchor	Statement	Notes
Rate formula	PHY rate = N_data_tones × bits/symbol × coding_rate × N_SS ÷ symbol_time. Example 11ax MCS11 80 MHz 2SS 0.8 GI: 980 × 10 × 5/6 × 2 ÷ 13.6 µs = 1201 Mbps.