Digital Modulation Compared: ASK, FSK, PSK and QAM with Examples
Digital modulation puts bits onto a sine-wave carrier by switching its amplitude, frequency or phase between a fixed set of values. A 433 MHz remote control uses on-off keying, Bluetooth uses frequency shift keying, and Wi-Fi and 4G use QAM with dozens of amplitude-phase combinations. The choice decides how many bits fit into a hertz of bandwidth and how much signal power is needed for a given error rate.
This article explains each scheme, introduces the constellation diagram, and works through symbol rate and bandwidth calculations you will meet in exams and datasheets.
Bits, Symbols and Baud
A symbol is one state of the carrier held for a fixed time Ts. If the modulator has M possible symbols, each symbol carries log2(M) bits.
Bits per symbol: k = log2(M)
Symbol rate: Rs = Rb / k (symbols/s, or baud)
Nyquist bandwidth with raised-cosine filtering (roll-off alpha):
B = Rs x (1 + alpha) (passband)
Spectral efficiency = Rb / B (bit/s/Hz)So a modem that sends 2400 baud with 16 symbols carries 9600 bit/s. Baud and bit rate are only equal when M = 2.
The Basic Schemes
ASK and OOK
Amplitude shift keying changes carrier amplitude. Its simplest form, on-off keying (OOK), sends carrier for 1 and nothing for 0. Cheap 433 MHz transmitter and receiver modules and infrared remotes use OOK because the receiver is just an envelope detector. The drawback is that noise and fading change amplitude directly, so ASK has the poorest noise performance.
FSK
Frequency shift keying uses one frequency for 1 and another for 0. Since amplitude is constant, the transmitter can use an efficient non-linear amplifier and the receiver can use a limiter. Variants like GFSK, which smooths the frequency transitions with a Gaussian filter, are used by Bluetooth Low Energy and many sub-GHz radio chips.
PSK
Phase shift keying keeps amplitude and frequency fixed and changes phase. BPSK uses 0 and 180 degrees for one bit per symbol. QPSK uses four phases, 45, 135, 225 and 315 degrees, for two bits per symbol, so it carries twice the data of BPSK in the same bandwidth with the same bit error rate for a given Eb/N0. PSK needs a coherent receiver that recovers the carrier phase, or a differential version (DPSK) that compares each symbol with the previous one.
QAM
Quadrature amplitude modulation changes both amplitude and phase. It is built from two carriers 90 degrees apart, the in-phase (I) and quadrature (Q) components, each amplitude-modulated. 16-QAM arranges 16 points in a 4 by 4 grid; 64-QAM uses 8 by 8. More points means more bits per symbol but less distance between points, so more signal-to-noise ratio is needed.
Reading a Constellation Diagram
A constellation plots each symbol as a point on the I-Q plane. Distance from the origin is amplitude; angle is phase. Noise turns each point into a fuzzy cloud. Errors happen when a cloud crosses into the decision region of a neighbouring point.
BPSK QPSK (Gray coded) 16-QAM
01 Q 00 . . | . .
1 ----+---- 0 x | x . . | . .
| -----+----- I ------+------- I
x | x . . | . .
11 10 . . | . .Gray coding labels neighbouring points so they differ in only one bit. When noise pushes a symbol to its nearest neighbour, which is the most likely error, only one bit is wrong instead of two.
Side-by-Side Comparison
| Scheme | Bits/symbol | Ideal spectral efficiency (alpha = 0) | Noise robustness | Where you meet it |
|---|---|---|---|---|
| OOK / ASK | 1 | 1 bit/s/Hz | Poor | 433 MHz remotes, IR remotes |
| BFSK / GFSK | 1 | Below 1 bit/s/Hz | Good | Bluetooth, many ISM-band radios |
| BPSK | 1 | 1 bit/s/Hz | Very good | GPS, deep-space links, low-rate modes |
| QPSK | 2 | 2 bit/s/Hz | Very good (same BER vs Eb/N0 as BPSK) | Satellite TV, Wi-Fi low rates, LTE |
| 16-QAM | 4 | 4 bit/s/Hz | Moderate | Wi-Fi, LTE at good signal |
| 64-QAM | 6 | 6 bit/s/Hz | Needs high SNR | Wi-Fi, cable modems, LTE |
A widely quoted reference point: coherent BPSK reaches a bit error rate of 10^-5 at an Eb/N0 of about 9.6 dB. Each step up in QAM order needs several dB more for the same error rate. Adaptive systems such as Wi-Fi and LTE measure the channel and switch between QPSK, 16-QAM and 64-QAM on the fly.
Worked Examples
Example 1: Bandwidth for 10 Mbit/s
Rb = 10 Mbit/s, roll-off alpha = 0.25 BPSK: Rs = 10 Mbaud B = 10 x 1.25 = 12.5 MHz QPSK: Rs = 5 Mbaud B = 5 x 1.25 = 6.25 MHz 16-QAM: Rs = 2.5 Mbaud B = 2.5 x 1.25 = 3.125 MHz 64-QAM: Rs = 1.67 Mbaud B = 1.67 x 1.25 = 2.08 MHz
Example 2: What Order Fits a Channel?
A 2 MHz channel must carry 6 Mbit/s with alpha = 0.35.
Maximum symbol rate Rs = B / (1 + alpha) = 2 / 1.35 = 1.48 Mbaud Bits needed per symbol k = 6 / 1.48 = 4.05 k = 4 (16-QAM) gives 5.93 Mbit/s, just short. Choose 32-QAM (k = 5): 7.4 Mbit/s, or reduce alpha.
Example 3: Eb/N0 and SNR
SNR = (Eb/N0) x (Rb / B) In dB: SNR = Eb/N0(dB) + 10 log10(Rb / B) QPSK at Rb = 2 Mbit/s in B = 1 MHz, Eb/N0 = 10 dB: SNR = 10 + 10 log10(2) = 13 dB
Common Mistakes
- Treating baud and bit rate as the same number for multi-level schemes.
- Comparing schemes by SNR instead of Eb/N0 when bit rates differ.
- Assuming QPSK is noisier than BPSK. Per bit, their error performance is the same.
- Forgetting the filter roll-off when calculating occupied bandwidth.
Summary
ASK, FSK and PSK change one property of the carrier; QAM changes amplitude and phase together. Each symbol carries log2(M) bits, the symbol rate is Rb/log2(M), and the bandwidth is roughly Rs(1 + alpha). Higher-order schemes save bandwidth but need more SNR, which is why real radios adapt their modulation to the channel. Use these relations together with the noise and link-budget articles to choose a scheme for your own project.