Wireless Lab · Lecture 14

Received power against distance (log scale)

received powerreceiver sensitivitydot = your distance

Working

Will the signal arrive?

Frequency (MHz)Distance (m)

Tx power (dBm)Sensitivity (dBm)

Tx antenna (dBi)Rx antenna (dBi)

Path-loss exponent n

Path lossReceivedMarginMax range

n = 2 is free space (Friis). Walls and bodies make n larger: 3 to 4 indoors.

Direct + reflected path: received strength across the channel

|direct + echo| in dBthe channel you use

Working

Two copies of one signal

Extra path length of the echo (m) Echo strength (fraction of direct)

Centre (MHz)Channel width (MHz)

Symbol rate (Msymbols/s)

Echo delayNotch spacingDelay ÷ symbol

Where the echo arrives half a cycle late it cancels the direct signal: a fade. OFDM (Wi-Fi, 4G) splits the channel into many narrow subcarriers so each sees an almost flat channel.

Hexagonal cells; same number = same frequency group

Reuse the frequencies

Reuse factor N Two-way channels for the operator Cell radius R (km)

Channels per cellReuse distance DD / R

D = R √(3N). Larger N keeps same-frequency cells farther apart (less interference) but gives each cell fewer channels.

Earth and orbit to scale

Working

Kepler's law

Altitude above Earth (km)

Period (Forouzan)Period (exact)Up + down delay

Forouzan: period = (1/100) × distance^1.5, distance from Earth's centre in km, result in seconds.