One Medium, Many Users
Every budget in Module 9 described one link, alone in its band. That link does not exist. Three ways exist to cut one shared resource — and only three.
Frequency, Time, or Neither
Two transmissions that overlap in both axes collide. A multiple access scheme is a rule for cutting the rectangle. Space is the fourth axis — sectors (M7-L3), MIMO (M10-L3).
A Private Strip, Forever
- 25 MHz at 30 kHz spacing: 25e6/30e3 = 833 channels
- Per 12.5 MHz operator, 10 kHz edge guards: (12.5e6 − 20e3)/30e3 = 416
- Guard bands cost 40 kHz of 25 MHz = 0.16%, not the great waste
- 30 kHz is Carson-full: 2(12 + 3) = 30 kHz exactly (M4-L2)
- With N = 7 reuse (M9-L3), a cell gets 416/7 = 59 channels
The real cost is an idle channel is wasted, and one full RF chain per user.
Take Turns
- 200 kHz carrier, 1625/6 = 270.833 kbit/s gross
- 4.615 ms frame, 8 slots → slot = 4.615/8 = 577 µs
- 1250 bits per frame → 1250/8 = 156.25 bits per slot
- Per user 270.833/8 = 33.85 kbit/s for a 13 kbit/s codec
- Guard 8.25 bits × 3.692 µs = 30.5 µs = 5.28% of the slot
30.5 µs is 9.1 km of propagation. Timing advance stretches it to 34.9 km.
Below the Noise Floor
1.2288 Mcps / 9.6 kbit/s = 128, and 10log₁₀128 = 21.07 dB (2⁷ × 3.0103 ✓). So the in-band SNR is 7 − 21.07 = −14.07 dB — buried, and still recovered.
Cut the Rectangle
User 42 Is Admitted
- 128/5.012 = 25.5 → 26 users, continuous talkers
- Voice activity ν = 0.4 → 63.9, so ≈65
- Other-cell f = 0.6 → 63.9/1.6 = ≈41 per sector
- Same 1.25 MHz as FDMA with reuse 7: 41/7 = 5.9 per cell
123/5.9 = 21× — the optimistic end of a real advantage. Capacity is a target, not a count.
The Near-Far Problem
100 m against 1 km at n = 4 is 10 × 4 × log₁₀(10) = 40 dB. In CDMA the near handset is in your band by design — there is no filter for it (M9-L3).
Two loops, ~1 dB steps. What costs capacity is the residual scatter, not the mean — all users 1 dB high is harmless.
Orthogonal Only When Aligned
- Walsh codes correlate to zero — but only in perfect step
- Downlink: one transmitter, one clock → 64 Walsh codes
- Uplink: many clocks, so alignment is abandoned — long PN codes of period 2⁴²−1, repeating every 41 days
- A chip is 814 ns = 244 m. Aligning uplinks to a fraction of that beats TDMA’s guard time for difficulty
- Echoes desynchronise the downlink against itself → the rake
What you learned
- FDMA splits B, TDMA splits T, CDMA splits neither
- AMPS: 833 channels, 416 per operator, 59 per cell at reuse 7
- GSM: 577 µs slots, 156.25 bits, 30.5 µs of guard = 5.28%
- IS-95: Gp = 128 = 21.07 dB, signal 14 dB under the floor
- Hard capacity refuses; soft capacity admits and degrades