How can a 4G phone or a Wi-Fi router squeeze many bits into every wave cycle? The answer is visible in a single picture — the constellation diagram. It shows each digital symbol as a point on a plane of amplitude and phase. Constellation diagrams are a regular topic in digital-communication papers for BCS (Telecom/EEE), BTCL, Teletalk, BTRC and university exams. This post explains how to read one, with an animation of BPSK, QPSK, 8-PSK and 16-QAM.
- A constellation diagram plots each modulation symbol as a point in the I–Q (in-phase / quadrature) plane.
- Distance from the origin = amplitude; angle = phase of the carrier for that symbol.
- M points ⇒ log₂M bits per symbol: BPSK 1, QPSK 2, 8-PSK 3, 16-QAM 4, 64-QAM 6, 256-QAM 8.
- More points = higher data rate in the same bandwidth, but points are closer together, so more SNR is needed for the same error rate.
- Neighbouring points are labelled with Gray code so a small error usually corrupts only one bit.
1. I and Q: the Basis of the Diagram
Any sinusoidal carrier with amplitude A and phase φ can be written as the sum of a cosine and a sine of the same frequency:
s(t) = A cos(ωct + φ) = I cos ωct − Q sin ωct, I = A cos φ, Q = A sin φThe cosine part is the in-phase (I) component and the sine part the quadrature (Q) component (90° apart). Each symbol is therefore just a pair of numbers (I, Q) — a point on a plane. That plane is the constellation diagram.
2. How to Read a Constellation Diagram
- Horizontal axis = I, vertical axis = Q.
- Radius √(I² + Q²) = carrier amplitude; points on one circle → constant-envelope (PSK) schemes.
- Angle tan⁻¹(Q/I) = carrier phase.
- Each point carries a bit label; the number of points M decides bits per symbol.
- In a real receiver, received points form clouds around each ideal point because of noise; the tighter the clouds, the better the link (measured as EVM, error vector magnitude).
3. Common Constellations (Animation)
- BPSK: two points at 0° and 180° — very robust.
- QPSK: four points 90° apart — twice the bit rate of BPSK in the same bandwidth with the same bit-error performance (in terms of Eb/N0).
- 8-PSK: eight points on a circle — 3 bits/symbol.
- 16-QAM: a 4 × 4 grid — both amplitude and phase vary.
4. Comparison of Modulation Schemes
| Scheme | Points M | Bits/symbol | Amplitude levels | Robustness to noise |
|---|---|---|---|---|
| BPSK | 2 | 1 | 1 | Highest |
| QPSK (4-QAM) | 4 | 2 | 1 | High |
| 8-PSK | 8 | 3 | 1 | Medium |
| 16-QAM | 16 | 4 | 3 | Medium–low |
| 64-QAM | 64 | 6 | 9 | Low |
| 256-QAM | 256 | 8 | many | Lowest (needs high SNR) |
Symbol rate Rs = Rb / log₂M. Since bandwidth depends on symbol rate, higher-order modulation increases spectral efficiency (bits/s/Hz).
5. Noise, Decision Regions and Minimum Distance
The receiver divides the plane into decision regions — each received sample is assigned to the nearest ideal point. An error occurs when noise pushes a sample across a boundary. The key figure is the minimum distance dmin between points (for the same average energy):
| Scheme (unit average energy) | dmin |
|---|---|
| BPSK | 2 |
| QPSK | √2 ≈ 1.414 |
| 8-PSK | 2 sin(π/8) ≈ 0.765 |
| 16-QAM | 2/√10 ≈ 0.632 |
Smaller dmin ⇒ more errors at a given SNR. That is why modern systems use adaptive modulation: 256-QAM close to the tower, dropping to QPSK at the cell edge or in rain.
6. Gray Coding
In Gray code, adjacent constellation points differ in only one bit (e.g. QPSK: 00, 01, 11, 10 around the circle). The most likely error — choosing a neighbouring point — therefore causes only one bit error instead of several, so BER ≈ SER / log₂M.
7. Where It Is Used
- Mobile: 4G LTE and 5G NR use QPSK, 16-QAM, 64-QAM and 256-QAM (5G also 1024-QAM in some cases); GSM uses GMSK.
- Wi-Fi: BPSK to 1024-QAM (Wi-Fi 6) and 4096-QAM (Wi-Fi 7).
- Satellite (DVB-S2): QPSK, 8-PSK, 16-APSK, 32-APSK — ring-shaped constellations that tolerate non-linear amplifiers.
- Cable modems, microwave backhaul, digital TV.
- Test equipment: vector signal analysers display constellations to diagnose transmitters.
8. Solved Problems
Problem 1. A 10 Mb/s stream is sent using 16-QAM. Find the symbol rate. Rs = 10/4 = 2.5 Mbaud.
Problem 2. A link carries 3 Mbaud. What bit rate is possible with QPSK, 8-PSK and 64-QAM? QPSK: 6 Mb/s; 8-PSK: 9 Mb/s; 64-QAM: 18 Mb/s.
Problem 3. A QPSK symbol has I = −1/√2 and Q = +1/√2. Find its amplitude and phase. A = 1; φ = tan⁻¹(Q/I) in the second quadrant = 135°.
9. Practice MCQs (click to see answer)
1. In a constellation diagram, the horizontal axis represents: (a) Frequency (b) In-phase component (c) Time (d) Power
2. Number of bits per symbol in 16-QAM is: (a) 2 (b) 4 (c) 8 (d) 16
3. In a PSK constellation all points lie on a: (a) Straight line (b) Circle (c) Square grid (d) Spiral
4. The distance of a point from the origin represents: (a) Phase (b) Amplitude (c) Frequency (d) Bit rate
5. Gray coding ensures that adjacent symbols differ by: (a) 0 bits (b) 1 bit (c) 2 bits (d) All bits
6. Which needs the highest SNR for the same bit-error rate? (a) BPSK (b) QPSK (c) 16-QAM (d) 256-QAM
7. QPSK has how many constellation points? (a) 2 (b) 4 (c) 8 (d) 16
8. A 12 Mb/s signal with 64-QAM has symbol rate: (a) 12 Mbaud (b) 6 Mbaud (c) 2 Mbaud (d) 64 Mbaud
9. QAM varies: (a) Only amplitude (b) Only phase (c) Both amplitude and phase (d) Only frequency
10. Spreading of points along arcs in a constellation indicates: (a) Phase noise (b) DC offset (c) Perfect link (d) Low bit rate
10. বাংলায় দ্রুত রিভিশন
- কনস্টেলেশন ডায়াগ্রাম হলো I (ইন-ফেজ) ও Q (কোয়াড্রেচার) অক্ষে প্রতিটি ডিজিটাল সিম্বলের বিন্দু-চিত্র।
- মূলবিন্দু থেকে দূরত্ব = বিস্তার (amplitude), কোণ = দশা (phase)।
- M বিন্দু হলে প্রতি সিম্বলে log₂M বিট: BPSK ১, QPSK ২, 8-PSK ৩, 16-QAM ৪, 64-QAM ৬।
- বিন্দু বেশি হলে ডেটা রেট বাড়ে, কিন্তু বিন্দুগুলো কাছাকাছি থাকায় বেশি SNR লাগে।
- পাশাপাশি বিন্দুতে গ্রে কোড ব্যবহার করা হয় — একটি বিট মাত্র বদলায়।
- সিম্বল রেট = বিট রেট ÷ log₂M।
Related Posts
- Advantages and Disadvantages of Digital Communication
- Eye Pattern (Eye Diagram) in Digital Communication
- Line Coding in Digital Communication
- Why Is Modulation Needed?
References: John G. Proakis, Digital Communications; Simon Haykin, Digital Communication Systems; B. Sklar, Digital Communications. Images and animations: original work by Totalecer.
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