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Two questions sit underneath every Wi-Fi design and every troubleshooting session: how strong is the signal where the client is? and how much data can that signal carry? The first is answered with RF power maths — decibels, EIRP, antenna gain, path loss and link budgets. The second is answered by OFDM, the modulation system every Wi-Fi standard since 802.11a has built on. This post covers both, with enough worked numbers to calculate them by hand.

Part 1 — RF Power

Why Decibels

An AP might transmit 100 mW. A client 20 metres away might receive 0.000000001 mW. Working with numbers that span twelve orders of magnitude is impractical, so RF engineering uses the decibel, a logarithmic ratio. Multiplication becomes addition, division becomes subtraction, and a whole radio link can be worked out with mental arithmetic.

• dB is a ratio between two powers: 10 × log10(P1/P2). Gains are positive, losses negative.
• dBm is an absolute power level relative to 1 milliwatt: 10 × log10(P in mW). 0 dBm = 1 mW, 20 dBm = 100 mW, 30 dBm = 1 W.
• dBi is antenna gain relative to an isotropic radiator (a theoretical antenna radiating equally in all directions).
• dBd is antenna gain relative to a half-wave dipole. A dipole has 2.15 dBi of gain, so dBi = dBd + 2.15.

The rules of 3s and 10s handle nearly every calculation: +3 dB doubles power, −3 dB halves it, +10 dB multiplies by ten, −10 dB divides by ten. Because they combine, +6 dB is four times the power and +13 dB is twenty times. Adding dB values to dBm values is valid (a level plus a ratio gives a new level); adding two dBm values is not — 20 dBm plus 20 dBm is 23 dBm, not 40.

EIRP and ERP

The power radiated from an antenna depends on three things: what the radio delivers, what the cable and connectors lose, and how much the antenna concentrates energy. Equivalent Isotropically Radiated Power (EIRP) combines them into one number — the power an isotropic antenna would need to produce the same signal strength in the antenna’s strongest direction.

EIRP (dBm) = Tx power (dBm) − cable/connector loss (dB) + antenna gain (dBi)
ERP  (dBm) = EIRP − 2.15            (relative to a dipole; used in some regulations)

Example: a radio delivers 20 dBm (100 mW) through a cable losing 2 dB to a 6 dBi antenna. EIRP = 20 − 2 + 6 = 24 dBm (about 250 mW). Regulators limit EIRP, not just transmitter power, which is why attaching a higher-gain antenna can make a previously legal system exceed the limit. Integrated-antenna APs handle this automatically; external-antenna APs must be configured with the antenna gain so they can reduce transmit power to compensate. The actual limits per band and region are covered in Frequency Bands and Channels.

Antennas

An antenna cannot create energy. “Gain” means it focuses energy into some directions at the expense of others, like a reflector on a torch. Higher gain gives a stronger signal in a narrower region.

Type	Typical gain	Beamwidth	Typical use
Integrated omni (ceiling AP)	3–6 dBi	360° horizontal; downward-tilted doughnut	Offices, classrooms — most indoor Wi-Fi
Dipole / “rubber duck”	2–5 dBi	360° horizontal	External-antenna APs, home routers
Patch / panel	6–10 dBi	60–90°	Wall mounting, aisles, outdoor courtyards
Sector	12–18 dBi	60–120° horizontal, narrow vertical	Stadiums, outdoor coverage, high-density seating
Yagi	10–16 dBi	20–40°	Long corridors, short point-to-point links
Parabolic dish	20–30+ dBi	Under 10°	Long-distance point-to-point bridges

• Beamwidth is the angle within which gain stays within 3 dB of the peak. It is specified separately for the horizontal (azimuth) and vertical (elevation) planes.
• Polarization is the orientation of the electric field. Mismatched polarization costs signal on point-to-point links; indoors, reflections scramble polarization and the effect is smaller. MIMO APs often use dual-polarized (slant ±45°) antennas.
• Mounting matters. A ceiling AP’s integrated antennas assume ceiling mounting. Mounting it on a wall turns the doughnut on its side, sending much of the energy into the floor above and below.
• Reciprocity. Antenna gain works in both directions: a high-gain AP antenna helps the AP hear weak clients just as much as it helps clients hear the AP. Transmit power, by contrast, only helps one direction.

Received Signal, Noise and SNR

At the receiver, three numbers matter:

• Received signal strength, in dBm — usually negative: −45 dBm is very strong, −67 dBm is good, −80 dBm is weak. Tools often label this “RSSI”, although strictly RSSI is a vendor-specific relative index that drivers convert to dBm.
• Noise floor — the background energy on the channel, around −90 to −95 dBm on a quiet 20 MHz channel. It rises by 3 dB each time the channel width doubles (more spectrum collects more noise), and rises further with interference.
• Signal-to-noise ratio (SNR) — signal minus noise in dB. A −65 dBm signal over a −92 dBm noise floor gives 27 dB SNR. When the “noise” includes other transmitters, the term is SINR.

SNR, not raw signal strength, decides which data rates a link can sustain. A −60 dBm signal in a noisy hall may perform worse than a −70 dBm signal in a quiet office. Common design targets:

Use	Signal at cell edge	SNR
Basic data / browsing	−70 to −72 dBm	≥ 20 dB
Voice and video	−65 to −67 dBm	≥ 25 dB
High-density, high-throughput	−60 to −65 dBm	≥ 30 dB
Location services (RTLS)	Several APs heard at ≥ −75 dBm	—

Receiver Sensitivity and MCS

Each data rate needs a minimum signal to be decoded. The 802.11 standard specifies worst-case minimum sensitivities; real radios are usually 5–10 dB better, but the relative steps are the same. For a 20 MHz channel:

MCS	Modulation	Coding	Minimum sensitivity (20 MHz)
0	BPSK	1/2	−82 dBm
1	QPSK	1/2	−79 dBm
2	QPSK	3/4	−77 dBm
3	16-QAM	1/2	−74 dBm
4	16-QAM	3/4	−70 dBm
5	64-QAM	2/3	−66 dBm
6	64-QAM	3/4	−65 dBm
7	64-QAM	5/6	−64 dBm
8	256-QAM	3/4	−59 dBm
9	256-QAM	5/6	−57 dBm
10	1024-QAM	3/4	−54 dBm
11	1024-QAM	5/6	−52 dBm

Each doubling of channel width makes every figure 3 dB worse (40 MHz MCS0 needs −79 dBm, 80 MHz −76 dBm), because the same transmit power is spread over twice the spectrum and twice the noise is collected. That is the hidden cost of wide channels: at the cell edge a client may get a lower MCS on 80 MHz than on 40 MHz, partly cancelling the extra width.

Path Loss and Attenuation

Even with nothing in the way, a signal weakens as it spreads out. Free space path loss (FSPL):

FSPL (dB) = 20·log10(distance in km) + 20·log10(frequency in MHz) + 32.44

At 1 m:   2.4 GHz ≈ 40 dB    5.5 GHz ≈ 47 dB    6.5 GHz ≈ 49 dB
At 10 m:  2.4 GHz ≈ 60 dB    5.5 GHz ≈ 67 dB
At 20 m:  2.4 GHz ≈ 66 dB    5.5 GHz ≈ 73 dB

Two rules fall out of the formula: doubling the distance adds 6 dB of loss, and at the same distance, 5.5 GHz loses about 7 dB more than 2.4 GHz. Indoors, walls, furniture and people add more. Approximate attenuation at 5 GHz:

Material	Approximate loss
Interior drywall / plasterboard	3–4 dB
Clear glass window, cubicle wall	2–4 dB
Wooden door	3–6 dB
Human body	3–5 dB
Brick wall	8–15 dB
Concrete wall, floor slab	15–25+ dB
Low-E / metallized glass	20–40 dB
Metal (elevator shaft, cold room, racking)	30 dB to near-total

These are rules of thumb; real values vary widely with construction. That is why serious designs use survey measurements or predictive tools calibrated with on-site attenuation measurements.

Link Budgets

A link budget adds every gain and subtracts every loss between transmitter and receiver to predict the received signal, then compares it with what the receiver needs. The difference is the fade margin — headroom against everyday variation (people walking past, doors closing).

Downlink (AP → laptop, 20 m, 5.5 GHz, two drywall walls)
  AP transmit power            +18 dBm
  AP antenna gain               +4 dBi   → EIRP 22 dBm
  Free space path loss, 20 m   −73 dB
  Two drywall walls             −6 dB
  Body / device loss            −3 dB
  Client antenna gain            0 dBi
  Received signal              −60 dBm
  Noise floor                  −92 dBm   → SNR 32 dB (supports MCS 9 at 20 MHz)

Uplink (laptop → AP, same path)
  Client transmit power        +15 dBm
  Client antenna gain            0 dBi
  Path, walls, body            −82 dB
  AP antenna gain               +4 dBi
  Received at AP               −63 dBm

The uplink is 3 dB weaker because the client transmits at lower power than the AP. Phones often transmit at 12–15 dBm, some IoT devices less. If an AP transmits at a high power that clients cannot match, clients hear the AP well, associate, and then fail to get their frames back reliably — one-way coverage. This is why AP power in a well-designed network is usually set near typical client power, not at the maximum, and why “turn the power up” rarely fixes coverage complaints.

Part 2 — OFDM

The Problem OFDM Solves

Indoors, a signal reaches the receiver along many paths — directly and by reflection from walls, floors, furniture and people. The reflected copies arrive a few hundred nanoseconds late. If each data symbol is very short (as it must be to send many symbols per second on a single carrier), those late copies overlap the next symbol and corrupt it: inter-symbol interference. Making a single carrier faster makes the problem worse.

Orthogonal Frequency Division Multiplexing turns the problem around. Instead of one fast carrier, it uses many slow ones: the channel is divided into dozens or hundreds of narrow subcarriers, each carrying a small share of the data at a low symbol rate. Each symbol lasts long enough that echoes are a small fraction of it.

How It Works

1. Coding — user bits get forward error correction (convolutional coding in older standards, LDPC in newer ones), adding redundancy at the chosen coding rate.
2. Interleaving — coded bits are spread across subcarriers, so a narrowband fade or interferer damages scattered bits that the error correction can repair rather than a burst it cannot.
3. Mapping — groups of bits are mapped onto each subcarrier’s constellation (BPSK, QPSK or QAM) — the modulation part of the MCS.
4. IFFT — an inverse fast Fourier transform converts the set of subcarrier values into a single time-domain waveform: one OFDM symbol.
5. Guard interval — a copy of the end of the symbol is added to its front (a cyclic prefix) to absorb echoes.
6. Receiver — the receiver strips the guard interval, runs an FFT to recover each subcarrier, corrects each one using the known pilot subcarriers and the channel estimate from the preamble, then de-maps, de-interleaves and decodes.

The subcarriers overlap in frequency, which looks wasteful, but they are spaced exactly so that each subcarrier’s peak falls where all others are zero — they are orthogonal, and the FFT separates them perfectly. That spacing is 312.5 kHz in 802.11a/g/n/ac (64 subcarriers per 20 MHz) and 78.125 kHz in Wi-Fi 6 and 7 (256 subcarriers per 20 MHz).

Subcarrier Roles

• Data subcarriers carry user bits.
• Pilot subcarriers carry known values so the receiver can track phase and frequency drift during the frame.
• Null subcarriers — the centre (DC) subcarrier and guard bands at the channel edges — are left empty to avoid DC offset problems and to keep energy out of neighbouring channels.

In an 802.11a/g 20 MHz channel: 48 data, 4 pilot and 12 null subcarriers. 802.11n/ac squeezed in 52 data subcarriers. Wi-Fi 6 uses 234 data and 8 pilot subcarriers per 20 MHz — more than four times as many — because the subcarriers are four times narrower and edge overhead is relatively smaller.

Guard Intervals and Symbol Times

The guard interval trades efficiency for robustness. A longer guard interval tolerates larger delay spread (big warehouses, outdoor links, halls with reflective surfaces) but spends more time not carrying data. Wi-Fi 4/5 offered 0.8 µs and a 0.4 µs “short GI”; Wi-Fi 6’s symbols are four times longer (12.8 µs), so it can afford 0.8, 1.6 or 3.2 µs guard intervals with less relative overhead — improving outdoor and high-multipath performance as well as efficiency.

Calculating a Data Rate

Every Wi-Fi data rate comes from one formula:

Rate = data subcarriers × bits per subcarrier × coding rate × spatial streams ÷ symbol time

Case	Data subcarriers	Bits	Coding	Streams	Symbol	Rate
802.11a, 6 Mbps	48	1 (BPSK)	1/2	1	4.0 µs	6 Mbps
802.11a, 54 Mbps	48	6 (64-QAM)	3/4	1	4.0 µs	54 Mbps
802.11ac, 80 MHz MCS 9, short GI	234	8 (256-QAM)	5/6	2	3.6 µs	867 Mbps
802.11ax, 80 MHz MCS 11, 0.8 µs GI	980	10 (1024-QAM)	5/6	2	13.6 µs	1,201 Mbps
802.11be, 320 MHz MCS 13, 16 streams	3,920	12 (4096-QAM)	5/6	16	13.6 µs	≈ 46 Gbps

Working the 54 Mbps case: 48 × 6 × 3/4 = 216 data bits per symbol; 216 bits ÷ 4 µs = 54 Mbps. The last row is the theoretical Wi-Fi 7 maximum — no shipping client has 16 spatial streams, which is why headline rates are never seen in practice.

From OFDM to OFDMA

In OFDM, every subcarrier in a transmission belongs to one client. Wi-Fi 6 introduced OFDMA, which assigns groups of subcarriers — resource units, from 26 tones upward — to different clients within the same transmission. Small frames no longer need a whole channel, which cuts contention and latency in busy networks. WLAN Fundamentals compares OFDM, OFDMA and MU-MIMO.

Costs of OFDM

• Peak-to-average power ratio — summing many subcarriers produces occasional high peaks, which demand linear (and less efficient) power amplifiers. High-order QAM is especially sensitive, which is one reason 1024-QAM and 4096-QAM often run at slightly reduced transmit power.
• Frequency accuracy — subcarriers 78 kHz apart require very precise oscillators; small errors break orthogonality.
• Overhead — preambles, pilots, guard intervals and null subcarriers all consume capacity.

How Power and OFDM Connect

• Transmit power is spread across all subcarriers. Doubling the channel width halves the power per subcarrier, costing 3 dB of SNR per subcarrier — which is why wider channels need a stronger signal for the same MCS.
• 6 GHz regulations express limits as power spectral density (dBm per MHz) precisely because of this: wider channels are allowed more total power, keeping power per subcarrier constant.
• The SNR at the receiver, set by the link budget, decides which constellation each subcarrier can use — and therefore, through the rate formula, how fast the link runs.

Exercises

1. Convert to dBm: 200 mW, 25 mW, 2 W. Convert to mW: 23 dBm, 7 dBm.

Show answer

200 mW = 100 mW × 2 → 20 + 3 = 23 dBm. 25 mW = 100 ÷ 2 ÷ 2 → 20 − 6 = 14 dBm. 2 W = 1 W × 2 → 30 + 3 = 33 dBm. 23 dBm = 20 + 3 → 100 × 2 = 200 mW. 7 dBm = 10 − 3 → 10 ÷ 2 = 5 mW.

2. An outdoor AP transmits 17 dBm into a cable with 3 dB of loss and a 14 dBi sector antenna. What is the EIRP? If the limit in that band is 30 dBm EIRP, by how much must transmit power change?

Show answer

EIRP = 17 − 3 + 14 = 28 dBm, which is within a 30 dBm limit with 2 dB to spare; transmit power could rise to 19 dBm. (Point-to-point links can have different rules in some bands.)

3. A client measures −71 dBm with a noise floor of −95 dBm. What is the SNR, and is it adequate for voice?

Show answer

SNR = −71 − (−95) = 24 dB. That is just below the common voice target of 25 dB and the signal is weaker than the usual −67 dBm target, so the location is marginal for voice — workable for data.

4. A client at 10 m from an AP receives −55 dBm. Approximately what would it receive at 40 m in free space?

Show answer

40 m is two doublings of 10 m, each adding about 6 dB, so about −67 dBm. Indoors, walls along the way would make it weaker.

5. An AP runs at 23 dBm in an office of phones that transmit at 12 dBm. Users report full bars but poor performance at the far end of rooms. Explain.

Show answer

An 11 dB power imbalance: phones hear the AP strongly (full bars) but the AP hears the phones 11 dB more weakly, so uplink frames fail or use low rates. The cells are also oversized, keeping phones associated too far away. Reduce AP power towards client power (and add APs if coverage then falls short).

6. Calculate the 802.11a data rate for 16-QAM with coding rate 1/2.

Show answer

48 data subcarriers × 4 bits × 1/2 = 96 bits per symbol; 96 ÷ 4 µs = 24 Mbps.

7. Why does Wi-Fi 6 use subcarriers four times narrower than Wi-Fi 5?

Show answer

Narrower subcarriers mean four-times-longer symbols (12.8 µs), so guard intervals are a smaller fraction of symbol time (less overhead) and longer guard intervals become affordable (better outdoor and high-multipath tolerance). More, finer subcarriers also enable OFDMA resource units and slightly more data tones per MHz.

Summary

Decibels turn RF power into simple arithmetic: +3 dB doubles, +10 dB multiplies by ten, dBm is power relative to 1 mW. EIRP — transmit power minus losses plus antenna gain — is what regulators limit and what receivers see, while antennas shape coverage rather than create power. At the receiver, SNR determines the achievable MCS; each MCS step needs a few dB more, and each doubling of channel width costs 3 dB. Free space loss grows 6 dB per doubling of distance and is about 7 dB higher at 5 GHz than at 2.4 GHz; walls add more, and link budgets must balance both directions, which is why AP power should match client power. OFDM carries Wi-Fi data on many slow, orthogonal subcarriers protected by guard intervals; data rate equals data subcarriers × bits × coding rate × streams ÷ symbol time, and Wi-Fi 6 refined it with narrower subcarriers, longer symbols and OFDMA.

Next: Channel Bonding and Frame Types looks at how channels are combined into wider ones, and at the frames the 802.11 MAC sends over them.