Digital Modulation
Once symbols are points in a plane, bit rate and noise immunity are both geometry — and 256-QAM's need for a clean channel stops being a separate fact.
Skip to the animationDigital modulation switches a carrier's amplitude, frequency or phase between discrete values, and drawing those symbols as points in a plane makes the central trade geometric: more points means more bits per symbol and less distance between them, hence less noise before an error.
The three families
| Scheme | What varies | Bits/symbol | Used in |
|---|---|---|---|
| OOK / ASK | Amplitude | 1+ | Optical fibre, simple remotes |
| FSK | Frequency | 1+ | Bluetooth (GFSK), early modems |
| BPSK | Phase, 2 states | 1 | Deep space, GPS |
| QPSK | Phase, 4 states | 2 | Satellite, LTE control channels |
| 16/64/256-QAM | Amplitude and phase | 4/6/8 | Wi-Fi, LTE, cable, DSL |
The constellation
Plot each symbol by its amplitude and phase and you get a constellation. Two facts then become geometric: the number of points sets the bits per symbol, and the distance between them sets the noise immunity.
Total power fixes the size of the constellation, so adding points necessarily brings them closer. A noise spike that was harmless with QPSK pushes a 256-QAM point across a decision boundary. Every step up the ladder makes the same trade.
Adaptive modulation
Rather than choosing one scheme, modern links measure the channel and adapt, walking up the constellation ladder when conditions allow and down when they do not — thousands of times per second.
That is why moving away from a Wi-Fi access point reduces throughput smoothly instead of dropping the connection. Wi-Fi, LTE and DSL all do it.
The receiver's decision
The receiver correlates the incoming signal against each possible symbol and picks the best match. A matched filter does this optimally — it provably maximises SNR at the sampling instant for white noise.
This is why performance is quoted against Eb/N0, energy per bit rather than raw power. It puts schemes with different rates on a comparable footing.
The waterfall curve
Plotted against Eb/N0, bit error rate falls in a waterfall: a few extra decibels drop errors by orders of magnitude. One extra dB can be worth a hundredfold reduction in errors.
That steepness is why link designers fight for every decibel from antenna gain, low-noise amplifiers and coding gain. It also means a link is usually either working well or not working at all.
Coding gain
Error-correcting codes add redundancy so the receiver can repair errors rather than merely detect them, buying fewer decibels for the same error rate. You pay in bandwidth or rate and buy back transmit power — usually a very good deal.
A deep-space probe cannot get a bigger antenna, so it spends everything it has on coding. Modern LDPC and turbo codes come within a fraction of a decibel of Shannon's 1948 limit.
The numbers you will be asked for
- Bits per symbol
n = log₂(M)
M points in the constellation
- Symbol rate
R_s = R_b / n
in baud
- BPSK error rate
P_e = Q(√(2Eb/N0))
- Bandwidth efficiency
R_b / B, in bit/s/Hz
- Matched filter
h(t) = s(T − t)
the time-reversed symbol
Watch it work
Check yourself
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