Wireless 101
M06 · L02
Module 6 · Lesson 2

How Fast Can You Signal?

Shannon capped the bits. Nyquist (1928) caps the symbols: how many you can push through a band before they smear into each other — inter-symbol interference.

01 / 11
Wireless 101
M06 · L02
The limit

The Nyquist Rate

Signalling Rate
R_s \le 2W

A baseband channel of width W carries at most 2W symbols/s without ISI. So Rs baud needs at least Rs/2 of bandwidth. Symbols/s is called baud.

02 / 11
Wireless 101
M06 · L02
Don’t confuse them

Baud ≠ Bits/s

Bit Rate from Symbol Rate
R_b = R_s \times \log_2 M

One symbol carries several bits (Module 5). A 1 Mbaud link is 1 Mbps with BPSK, 2 with QPSK, 6 with 64-QAM — same baud, different bit rates.

03 / 11
Wireless 101
M06 · L02
The catch

The Ideal Can’t Be Built

Reaching exactly 2W needs a brick-wall filter — a flat-then-vertical spectrum. In time that is a sinc pulse: it rings forever, is non-causal, and is brutally sensitive to timing error. Real links spend a little extra bandwidth to be realizable.

04 / 11
Wireless 101
M06 · L02
The fix

Raised-Cosine Shaping

Occupied Bandwidth — Baseband, One-Sided
W = \tfrac{R_s}{2}\,(1 + \alpha)

Keep the pulse zero at every other symbol instant (no ISI), but soften the wall into a cosine roll-off α. Bandwidth grows from the Nyquist minimum by (1 + α). On the air the same signal occupies twice this: BRF = 2W = Rs(1 + α).

05 / 11
Wireless 101
M06 · L02
The knob

Roll-off α

α = 0: minimum band, but long fragile pulses. α = 1: double the band, but short forgiving pulses. Real systems pick a small α — ~0.22 in 3G, 0.1–0.25 in LTE — tight spectrum, practical filter.

06 / 11
Wireless 101
M06 · L02
Try it

Widen the Skirt

The curve is the raised-cosine spectrum for a fixed 1 Mbaud. Drag α and watch the occupied baseband bandwidth W (one-sided) and the excess over Nyquist.

Roll-off α α=0.25 · W = 625 kHz
07 / 11
Wireless 101
M06 · L02
Two jobs, one filter

Root Raised Cosine

Split the shape in half — an RRC filter at TX and an identical one at RX. Cascaded they make a full raised cosine (zero ISI); and being a copy of the transmit pulse, the RX filter is also the matched filter that maximizes SNR.

08 / 11
Wireless 101
M06 · L02
Two levers

Put It Together

RF (passband) bandwidth and roll-off buy symbols: Rs = BRF / (1 + α) — that B is twice the baseband W of slide 5. Modulation order buys bits per symbol: log₂M. Multiply for the bit rate.

20 MHz RF, α=0.1
18.2 Mbaud
× 256-QAM
145 Mbps
09 / 11
Wireless 101
Knowledge Check

Check what stuck

Four questions from this lesson. Answer to see why — the explanation appears whether you were right or wrong. Nothing is scored or saved.

Question 1 of 0
Score 0/0

10 / 11
Wireless 101
M06 · L02
Recap

What you learned

  • Nyquist: a band of width W carries at most 2W symbols/s without ISI
  • Baud ≠ bits/s: Rb = Rs × log₂M
  • The brick-wall sinc is unbuildable; raised-cosine shaping keeps zero ISI
  • Roll-off α widens the band by (1 + α); RRC also gives the matched filter
Up next in Module 6
Spectral Efficiency →
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