Digital modulation maps bits onto the amplitude, frequency or phase of a carrier, and the main techniques are ASK, FSK, PSK, QAM and multicarrier OFDM. They differ in how many bits each symbol carries, how much signal-to-noise ratio they need for a given bit error rate, and how hard they push the power amplifier. Choosing one is a trade between spectral efficiency, power efficiency and linearity.
This page compares those families with numbers computed from the standard additive white Gaussian noise (AWGN) formulas. Each technique then has its own article, and the transmitter side of the problem is covered in Modulation, EVM and PAPR, part of the Radio Architectures series.
From Analog to Digital Modulation
Analog modulation carries a continuous message. Amplitude modulation varies the envelope, frequency modulation varies the instantaneous frequency, and phase modulation varies the phase directly. Any noise that reaches the demodulator ends up in the output, reduced in FM and PM by bandwidth expansion, but never removed.
Digital modulation restricts the carrier to a finite set of states, called symbols. The receiver only has to decide which state was sent, so moderate noise causes no error at all, and forward error correction can repair the occasional wrong decision. A modulated carrier can always be written in terms of two baseband components:
s(t) = I(t) cos(2πfct) − Q(t) sin(2πfct)
That single equation is why nearly every modern radio uses an IQ modulator and demodulator. A digital baseband generates I and Q, and the same hardware can produce any scheme on this page.
The Main Digital Modulation Techniques
Amplitude shift keying and pulse amplitude modulation
Amplitude shift keying (ASK) switches the carrier between amplitude levels. Its simplest form, on-off keying, needs only a switch and an envelope detector, which suits short-range remote controls and tags. Coherent on-off keying needs about 3 dB more average Eb/N0 than BPSK, and every amplitude level sits on one axis. Pulse amplitude modulation is the baseband equivalent, and it appears in high-speed wired links as PAM4.
Frequency shift keying
Frequency shift keying (FSK) moves the carrier between tones. The envelope is constant, so a saturated, efficient amplifier can be used, and a noncoherent receiver can be built from little more than a discriminator. The cost is occupied bandwidth and about 3.7 dB more Eb/N0 than coherent BPSK at a BER of 10−6. GFSK and GMSK smooth the transitions to tighten the spectrum.
Phase shift keying
Phase shift keying keeps the symbol amplitude constant and encodes data in phase. BPSK carries one bit per symbol, QPSK two, 8-PSK three. QPSK needs the same Eb/N0 as BPSK for twice the spectral efficiency, which is why it is the default for control channels and satellite links. Beyond eight states PSK wastes the interior of the IQ plane, and QAM takes over.
Quadrature amplitude modulation
Quadrature amplitude modulation places points on a grid, varying both amplitude and phase. Each extra bit per symbol adds roughly 3 dB of required SNR, and it also raises the sensitivity to phase noise, IQ imbalance and amplifier compression. Adaptive links step through QPSK, 16-QAM, 64-QAM, 256-QAM and beyond as conditions allow.
Multicarrier modulation
OFDM is a way of arranging symbols, not a new constellation. It spreads QPSK or QAM symbols across many narrow orthogonal subcarriers so that multipath becomes a simple per-subcarrier correction. The price is a high peak-to-average power ratio.
Comparing Bit Error Rate and Spectral Efficiency
The formulas below assume Gray coding, ideal coherent detection unless stated, and no error correction coding. Q(x) is the Gaussian tail function.
- BPSK and QPSK: BER = Q(√(2Eb/N0))
- Square M-QAM, with k = log2M: BER ≈ (4/k)(1 − 1/√M) Q(√(3k/(M−1) · Eb/N0))
- 8-PSK: BER ≈ (2/3) Q(√(6Eb/N0) sin(π/8))
- Noncoherent binary FSK: BER = ½ exp(−Eb/2N0)
Figure 1 shows the familiar waterfall curves. Solving them for a BER of 10−6 gives the table below. Es/N0 is Eb/N0 + 10log10k, and the noise-limited EVM is 10−(Es/N0)/20, the error vector magnitude that noise alone would produce at that operating point.
| Technique | Bits per symbol | Eb/N0 (dB) | Es/N0 (dB) | Noise-only EVM (%) | Single-carrier peak/average of constellation (dB) |
|---|---|---|---|---|---|
| BPSK | 1 | 10.53 | 10.53 | 29.7 | 0 |
| QPSK | 2 | 10.53 | 13.54 | 21.0 | 0 |
| 8-PSK | 3 | 13.95 | 18.72 | 11.6 | 0 |
| 16-QAM | 4 | 14.40 | 20.42 | 9.5 | 2.55 |
| 64-QAM | 6 | 18.78 | 26.56 | 4.7 | 3.68 |
| 256-QAM | 8 | 23.51 | 32.54 | 2.4 | 4.23 |
| 1024-QAM | 10 | 28.50 | 38.50 | 1.2 | 4.50 |
The peak/average column describes the constellation points only. Pulse shaping adds to it, and OFDM replaces it with a much larger figure. These are uncoded results; a modern error correction code moves the operating point several dB closer to the Shannon limit, shown in Figure 2.
Every point sits to the right of the Shannon curve, and the gap is what coding is designed to close. Figure 2 also shows why 16-QAM replaced 16-PSK: for the same four bits per symbol it needs about 4 dB less Eb/N0, because its points fill the IQ plane more evenly.
Worked Example: Rate Against Sensitivity in a 20 MHz Channel
Take a 20 MHz channel with root-raised-cosine filtering at a roll-off of α = 0.25, and a receiver noise figure of 6 dB. The aim is to compare QPSK with 64-QAM at an uncoded BER of 10−6.
- Symbol rate: Rs = 20 MHz / 1.25 = 16 Msym/s.
- Bit rates: QPSK gives 2 × 16 = 32 Mbit/s and 64-QAM gives 6 × 16 = 96 Mbit/s.
- Noise floor in the symbol-rate bandwidth: −174 + 10log10(16 × 106) + 6 = −95.96 dBm, using the thermal noise density of −174 dBm/Hz.
- Sensitivity for QPSK: −95.96 + 13.54 = −82.42 dBm.
- Sensitivity for 64-QAM: −95.96 + 26.56 = −69.40 dBm.
Tripling the rate costs 13.0 dB of received signal. On a free-space path, where power falls 6 dB for each doubling of distance, 13.0 dB shortens the range by a factor of about 4.5. That single calculation explains adaptive modulation, and it feeds directly into an RF link budget. See SNR and Eb/N0 for the conversions used here.
How Modulation Choice Drives the RF Hardware
The modulation choice sets three hardware budgets.
- Noise. Required Es/N0 sets the noise figure and antenna gain needed for a given range.
- Linearity. Constellations and OFDM with high peak/average ratios need back-off or PA linearization, and compression shows up as ACLR and EVM degradation. Constant-envelope FSK and PM avoid most of this.
- Phase purity. Dense constellations need low phase noise. One degree RMS of phase error alone contributes about 1.75% EVM, a small part of an 8% 64-QAM budget but half the magnitude of a 3.5% 256-QAM budget.
A short rule of thumb follows. Use FSK or GMSK when cost, battery life and a simple saturated amplifier dominate. Use QPSK when range is what matters and bandwidth is available. Use adaptive QAM with coding when spectrum is expensive, and OFDM when the channel is wideband with multipath. Measurements of the finished link are covered in Measuring Radio Performance.
Frequently asked questions
What are the main types of digital modulation?
The main types are amplitude shift keying, frequency shift keying, phase shift keying and quadrature amplitude modulation. OFDM is a multicarrier method that carries those constellations on many subcarriers. Most current wideband systems use QPSK and QAM on OFDM subcarriers.
Which digital modulation technique is the best?
No single technique wins on every measure. QPSK offers a good balance of noise tolerance and rate, high-order QAM gives the most bits per hertz at high SNR, and FSK allows the simplest, most power-efficient transmitter. Most modern links change modulation order as signal quality changes.
Why is QPSK no worse than BPSK in bit error rate?
QPSK is two independent BPSK signals on orthogonal carriers, so each bit sees the same noise and has the same energy. It needs the same Eb/N0 as BPSK and carries twice the bits in the same bandwidth, although its required Es/N0 is 3.01 dB higher because each symbol holds two bits.
What is the difference between modulation and multiplexing?
Modulation maps data onto a carrier. Multiplexing shares a channel between several streams. OFDM does both: it modulates each subcarrier with QAM or PSK and multiplexes the subcarriers in frequency.
Related topics
Continue with PSK, QAM, OFDM and phase modulation, then read Modulation, EVM and PAPR for the transmitter view. The RF fundamentals hub and RF calculators cover the supporting decibel arithmetic.