How far does a signal reach? How many users fit in a cell? This module gives you the formulas and rules of thumb that RF engineers use every day.
1. Decibels — the unit you cannot avoid
| Unit |
Meaning |
| dB |
Ratio on a log scale: 10·log₁₀(P₂/P₁). +3 dB = ×2 power, +10 dB = ×10, −3 dB = half |
| dBm |
Power relative to 1 mW: 0 dBm = 1 mW, 20 dBm = 100 mW, 30 dBm = 1 W, 43 dBm = 20 W, 46 dBm = 40 W |
| dBW |
Relative to 1 W (0 dBW = 30 dBm) |
| dBi / dBd |
Antenna gain over isotropic / over dipole (dBi = dBd + 2.15) |
| dBc |
Relative to the carrier |
| EIRP |
Effective Isotropic Radiated Power = transmit power + antenna gain − cable loss |
| ERP |
EIRP − 2.15 dB |
Handy: adding powers in dB = multiply, so gain/loss chains are simply added: Rx power = Tx power + gains − losses.
Typical powers: GSM phone 33 dBm (2 W) max at 900 MHz, 30 dBm at 1800 MHz; LTE/5G phone class 3: 23 dBm (200 mW); macro cell sector 40–46 dBm per carrier (10–40 W); small cell 24–30 dBm; Wi-Fi AP ~20 dBm (EU limit 20 dBm EIRP at 2.4 GHz).
2. Propagation
Free-space path loss (FSPL)
FSPL (dB) = 32.45 + 20·log₁₀(d in km) + 20·log₁₀(f in MHz)
Doubling the distance costs 6 dB; doubling the frequency also costs 6 dB. So a 3.5 GHz signal loses ≈ 12 dB more than 900 MHz over the same distance (20·log₁₀(3500/900)).
Example: 1 km at 2100 MHz → 32.45 + 0 + 66.4 = 98.9 dB.
Real-world effects
| Effect |
Meaning |
| Path loss exponent |
In free space power falls with d²; in cities more like d³–d⁴ |
| Shadowing (slow fading) |
Buildings and hills block the signal; log-normal, σ ≈ 6–10 dB |
| Multipath / fast fading |
Reflections add and cancel over a wavelength; Rayleigh (no line of sight) / Rician (with LOS) |
| Penetration loss |
Walls, glass, cars: 10–25 dB at 2 GHz, higher on 3.5 GHz and mmWave; low-E glass 25–40 dB |
| Diffraction |
Bending around edges (knife-edge) — why signals appear behind buildings |
| Reflection, scattering |
Bounce from surfaces |
| Fresnel zone |
Ellipsoid around the line of sight that must be ~60% clear for a microwave link |
| Doppler shift |
f_d = v·f/c: 100 km/h at 2.1 GHz ≈ 194 Hz |
| Delay spread |
Spread of arrival times; OFDM cyclic prefix must exceed it |
| Coherence bandwidth/time |
How far apart in frequency/time the channel stays similar |
| Rain attenuation |
Strong above 10 GHz (Module 17) |
| Atmospheric absorption |
Oxygen absorption peak at 60 GHz; water vapour at 22 and 183 GHz |
| Ducting |
Temperature inversions carry signals unexpectedly far, causing interference |
Propagation models
| Model |
Typical use |
| Free space |
Line-of-sight, microwave, satellite |
| Okumura-Hata |
Macro cells, 150–1500 MHz |
| COST 231-Hata |
1500–2000 MHz |
| COST 231 Walfisch-Ikegami |
Urban street canyons |
| 3GPP TR 38.901 |
Models for 0.5–100 GHz: UMa, UMi, RMa, InH (urban macro/micro, rural macro, indoor hotspot) |
| Ray tracing / 3D models |
Dense urban, indoor, mmWave |
| Machine learning |
Fitting measurement data to predict coverage |
3. Noise, sensitivity and Shannon
| Formula |
Meaning |
| Thermal noise = −174 dBm/Hz + 10·log₁₀(B) |
At room temperature; for 20 MHz: −174 + 73 = −101 dBm |
| Noise floor with NF |
+ receiver Noise Figure (phone ≈ 7–9 dB, base station ≈ 2–5 dB) |
| SNR = Signal − Noise (dB) |
|
| SINR |
Signal ÷ (Interference + Noise) — the number that actually sets the bit rate |
| Receiver sensitivity |
= Noise floor + required SNR (e.g. LTE 20 MHz QPSK: ≈ −100 dBm) |
| Shannon limit |
C = B · log₂(1 + SNR) — maximum bit rate: 20 MHz and 20 dB SNR (100×) → 20·6.66 ≈ 133 Mbit/s per stream |
| Spectral efficiency |
bit/s per Hz; 4G ≈ 2–5, 5G with massive MIMO much higher |
| MIMO capacity |
Scales roughly with min(Tx, Rx) streams |
| Eb/N0 |
Energy per bit over noise density |
| MCS |
Modulation and Coding Scheme chosen from CQI: low SINR → QPSK + strong coding, high SINR → 256QAM |
Rough LTE/NR signal levels (RSRP)
| RSRP |
Quality |
| ≥ −80 dBm |
Excellent |
| −80 to −90 dBm |
Good |
| −90 to −100 dBm |
Fair |
| −100 to −110 dBm |
Poor (cell edge) |
| < −110 dBm |
Very poor / no service |
| SINR: > 20 dB excellent, 13–20 good, 0–13 fair, < 0 poor. |
|
4. Link budget — a worked example (LTE downlink, 1800 MHz)
| Item |
Value |
| eNB transmit power (per antenna port, 20 MHz) |
43 dBm |
| Antenna gain |
+17 dBi |
| Cable/connector loss |
−2 dB |
| EIRP |
58 dBm |
| UE antenna gain / body loss |
0 dBi / −3 dB |
| Penetration loss (indoor) |
−15 dB |
| Shadowing margin (90% edge) |
−8 dB |
| Interference margin |
−3 dB |
| UE sensitivity (QPSK 1/3 at 20 MHz, noise −101 + NF 8 + SNR −3) |
−96 dBm |
| Maximum allowed path loss (MAPL) |
58 − 3 − 15 − 8 − 3 + 96 = 125 dB |
| Then use a propagation model to turn 125 dB into a distance (e.g. ~2–3 km in suburban 1800 MHz). Uplink usually limits coverage because phones transmit only 23 dBm. |
|
5. Cell planning and capacity
| Concept |
Explanation |
| Coverage vs capacity |
Coverage-limited (rural, low bands) or capacity-limited (cities, many sites) |
| Frequency reuse |
GSM: reuse patterns of 3/9, 4/12; LTE/NR: reuse-1 with interference coordination |
| Cell radius |
Rural macro 5–30 km, suburban 1–5 km, urban 0.3–1 km, small cell 50–200 m, mmWave 50–200 m |
| PCI |
Physical Cell Identity (504 in LTE, 1008 in NR) — must not clash between neighbours (mod-3/mod-30 planning) |
| Neighbour lists / ANR |
Automatic Neighbour Relations (SON) |
| Tilt |
Down-tilt reduces overshoot and interference; electrical (RET) vs mechanical |
| Azimuth, sectorisation |
3-sector sites at 0°/120°/240°; 6-sector in dense areas |
| Site spacing / ISD |
Inter-Site Distance |
| Handover margins, hysteresis, TTT |
Parameters to avoid ping-pong |
| Load balancing / MLB |
Offloading busy cells |
| Traffic models |
Busy hour traffic, Erlang, throughput per user |
| Erlang B |
Blocking probability of circuits; 1 Erlang = one channel used continuously for an hour |
| Dimensioning |
Estimate sites needed from subscribers × usage ÷ cell capacity |
| CAPEX/OPEX |
Tower rent, power, backhaul, spectrum |
| Indoor coverage |
DAS, small cells, repeaters, Wi-Fi calling |
| Passive Intermodulation (PIM) |
Interference from bad connectors/rusty metal on antennas |
| VSWR / return loss |
Antenna system quality (VSWR < 1.5) |
| Tower-mounted amplifier (TMA) |
Boosts uplink sensitivity |
| Electromagnetic exposure (EMF) |
ICNIRP limits; Croatia and EU recommendation 1999/519/EC; measurements near sites |
Radio KPIs operators watch
| KPI |
Meaning |
| RRC setup success rate |
Radio connections established |
| E-RAB/ERAB (or 5G PDU) setup success |
Bearers established |
| CSSR / CDR (call setup success / drop rate) |
Call quality |
| VoLTE drop rate, SRVCC success |
Voice quality |
| Handover success rate |
Mobility |
| Throughput (user, cell), PRB utilisation |
Capacity |
| Latency, jitter, packet loss |
Experience |
| Accessibility, Retainability, Integrity, Availability, Mobility |
The five standard KPI families |
| Drive test, walk test, crowd-sourced data (e.g. Ookla) |
Measuring in the field |
| MOS, POLQA, ITU-T P.863 |
Voice quality scoring |
6. Microwave links (backhaul)
| Item |
Details |
| Bands |
6–42 GHz (traditional), E-band 71–76 / 81–86 GHz (multi-Gbit/s, 1–3 km), W/D-band emerging |
| Needs |
Clear line of sight, Fresnel-zone clearance, alignment |
| Rain |
Rain fade grows with frequency: design with fade margin (99.99%) |
| Adaptive modulation |
Drops from 4096QAM to QPSK in rain to stay up |
| XPIC, MIMO, aggregation |
Double capacity with cross-polar cancellation |
| Protection |
1+1 hot standby, space or frequency diversity |
Spectrum analyser, scanner (Rohde & Schwarz, Keysight), drive-test software (TEMS, Nemo, QualiPoc), VNA/Site Master for antenna lines, OTDR for fibre, PIM tester, EMF meter, Wireshark/tshark, iperf3, ping/traceroute/mtr, crowd-sourced apps.
Remember this: path loss rises 6 dB per distance doubling (free space) and per frequency doubling; coverage is set by the weaker link (usually the uplink, 23 dBm); capacity by SINR and bandwidth (Shannon). Low bands for reach, high bands for capacity, small cells to densify.