PHY LayerL3

BER vs SNR Reference

BER vs Eb/N0 Reference - AWGN Channel Theory | Proakis 'Digital Communications' + IEEE 802.11 PHY Specs10 rows#

Modulation	Bits/Symbol	Theoretical BER Formula	Eb/N0 @ BER=10⁻²	Eb/N0 @ BER=10⁻³	Eb/N0 @ BER=10⁻⁴	Eb/N0 @ BER=10⁻⁵	IEEE 802.11 MCS Index	Engineering Notes
BPSK	1	BER = Q(√(2·Eb/N0))	4.3 dB	6.8 dB	8.4 dB	9.6 dB	MCS 0 (all gen)	Best BER performance. Used for most robust/control frames. Q(x)=erfc(x/√2)/2.
QPSK (coherent)	2	BER = Q(√(2·Eb/N0))	4.3 dB	6.8 dB	8.4 dB	9.6 dB	MCS 1-2	Same BER as BPSK per bit. 2× spectral efficiency. Used for range-efficient data.
16-QAM	4	BER ≈ (3/8)·erfc(√(Eb/N0·4/5))	8.8 dB	10.6 dB	12.0 dB	13.1 dB	MCS 3-4	4 dB penalty vs BPSK at BER=10⁻³. First step in capacity vs range tradeoff.
64-QAM	6	BER ≈ (7/24)·erfc(√(Eb/N0·2/7))	14.4 dB	16.0 dB	17.3 dB	18.3 dB	MCS 5-7	Standard high-throughput mode. ~5 dB penalty vs 16-QAM.
256-QAM	8	BER ≈ (15/64)·erfc(√(Eb/N0·1/10))	20.0 dB	21.6 dB	22.8 dB	23.8 dB	MCS 8-9 (802.11ac/ax)	Introduced in 802.11ac. Requires very low noise floor and good RF design.
1024-QAM	10	BER ≈ (31/160)·erfc(√(Eb/N0·1/17.5))	26.0 dB	27.5 dB	28.7 dB	29.6 dB	MCS 10-11 (802.11ax)	New in 802.11ax. Requires EVM ≤ -35 dB. Only viable very close to AP.
4096-QAM	12	BER ≈ (63/384)·erfc(√(Eb/N0·1/30))	32.0 dB	33.5 dB	34.6 dB	35.5 dB	MCS 12-13 (802.11be)	New in 802.11be. EVM ≤ -38 dB. Phase noise and IQ imbalance critical.
DBPSK	1	BER = 0.5·exp(-Eb/N0)	4.7 dB	7.3 dB	9.0 dB	10.2 dB	802.11b/g legacy	Differential BPSK: no coherent phase reference needed. ~1 dB penalty vs BPSK.
DQPSK	2	BER ≈ erfc(√(Eb/N0·sin(π/4)))	5.3 dB	8.0 dB	9.7 dB	11.0 dB	802.11b HR-DSSS	~1 dB penalty vs QPSK. Used in 802.11b 2 Mbps.
CCK (11 Mbps)	-	Chip-level: effectively ≈ QPSK	~10 dB	~12 dB	~14 dB	~15 dB	802.11b 11 Mbps	Complementary Code Keying. Complex spreading codes. BER approximation only.

SNR to Sensitivity Conversion - IEEE 802.11-2020 §17.3.10.7 | Formula: Sens(dBm) = -174 + NF + 10·log₁₀(BW) + SNRmin8 rows#

Channel BW	Thermal Noise @ BW	+ NF (8 dB client)	Noise Floor (kTB)	+ SNR MCS0 (5dB)	Sensitivity MCS0	+ SNR MCS11 (33dB)	Sensitivity MCS11	Notes
1 MHz (HaLow)	-174+60=-114 dBm	-114+8	-106 dBm	-106+5	-101 dBm	-106+33	-73 dBm	802.11ah sub-1GHz. Best sensitivity due to narrow BW.
2 MHz (HaLow)	-174+63=-111 dBm	-111+8	-103 dBm	-103+5	-98 dBm	-103+33	-70 dBm
4 MHz (HaLow)	-174+66=-108 dBm	-108+8	-100 dBm	-100+5	-95 dBm	-100+33	-67 dBm
20 MHz	-174+73=-101 dBm	-101+8	-93 dBm	-93+5	-88 dBm	-93+33	-60 dBm	Standard Wi-Fi channel reference.
40 MHz	-174+76=-98 dBm	-98+8	-90 dBm	-90+5	-85 dBm	-90+33	-57 dBm	3 dB higher noise vs 20 MHz.
80 MHz	-174+79=-95 dBm	-95+8	-87 dBm	-87+5	-82 dBm	-87+33	-54 dBm
160 MHz	-174+82=-92 dBm	-92+8	-84 dBm	-84+5	-79 dBm	-84+33	-51 dBm
320 MHz (802.11be)	-174+85=-89 dBm	-89+8	-81 dBm	-81+5	-76 dBm	-81+33	-48 dBm	Widest channel = worst sensitivity floor.

Shannon Capacity Reference - C = B·log₂(1+SNR) | Theoretical maximum spectral efficiency8 rows#

SNR (dB)	SNR (linear)	Capacity @ 20 MHz	Capacity @ 40 MHz	Capacity @ 80 MHz	Capacity @ 160 MHz	Capacity @ 320 MHz	802.11 PHY Rate @ ~this SNR	Notes
5	3.16	66 Mbps	132 Mbps	264 Mbps	528 Mbps	1056 Mbps	~29 Mbps (BPSK 1/2, MCS0)	802.11 uses ~50% of Shannon limit at low SNR.
10	10	133 Mbps	266 Mbps	532 Mbps	1064 Mbps	2128 Mbps	~65 Mbps (QPSK 3/4, MCS2)
15	31.6	196 Mbps	392 Mbps	784 Mbps	1568 Mbps	3136 Mbps	~130 Mbps (16-QAM 1/2, MCS3)
20	100	266 Mbps	532 Mbps	1064 Mbps	2128 Mbps	4256 Mbps	~200 Mbps (64-QAM 2/3, MCS5)
25	316	331 Mbps	662 Mbps	1324 Mbps	2648 Mbps	5296 Mbps	~287 Mbps (64-QAM 5/6, MCS7)
30	1000	398 Mbps	796 Mbps	1592 Mbps	3184 Mbps	6368 Mbps	~344 Mbps (256-QAM 3/4, MCS8)	Approaching 802.11ax single-stream limit at 160 MHz
35	3162	465 Mbps	930 Mbps	1860 Mbps	3720 Mbps	7440 Mbps	~480 Mbps (1024-QAM 5/6, MCS11)
40	10000	532 Mbps	1064 Mbps	2128 Mbps	4256 Mbps	8512 Mbps	~575 Mbps (4096-QAM 5/6, MCS13)	802.11be MCS13 reaches ~70% Shannon efficiency