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Learn QPSK with working principle, I-Q components, constellation diagram, bandwidth efficiency double BPSK, same BER as BPSK, OQPSK pi/4-QPSK variants, and applications in 4G 5G WiFi satellite for engineering students.
In QPSK, 4 different phases (0°, 90°, 180°, 270°) of the carrier are used. Each phase represents 2 bits. This means QPSK provides double the data rate compared to BPSK within the same bandwidth.
🎯 What is QPSK?
QPSK is an extension of BPSK in which 4 phase states are used. Each symbol carries 2 bits, so double the bit rate is achieved at the same baud rate.
| │ BPSK: 2 phases | 1 bit/symbol │ |
| │ QPSK: 4 phases | 2 bits/symbol → DOUBLE the data rate! │ |
| │ Phase = 45° | bits "00" │ |
| │ Phase = 135° | bits "01" │ |
| │ Phase = 225° | bits "11" │ |
| │ Phase = 315° | bits "10" │ |
⭕ QPSK Constellation Diagram
| "01" | "00" |
|---|---|
| ● | ● |
| (135°) | (45°) |
| (225°) | (315°) |
| ● | ● |
| "11" | "10" |
Gray Coding Benefit:
- Adjacent constellation points differ by only 1 bit
- Most errors go to adjacent point (nearest neighbor)
- Single bit error per symbol error (not 2 bits)
- Reduces BER by ~factor of 2
📊 I-Q Components
A QPSK signal can be understood as a combination of 2 independent BPSK signals – one on the In-phase (I) channel and one on the Quadrature (Q) channel (90° apart).
| │ Input bits | b1 b2 b3 b4 b5 b6 b7 b8 ... │ |
| │ Split into | │ |
| │ I-channel (even bits): b1 b3 b5 b7 ... | BPSK on cos(2πfct) │ |
| │ Q-channel (odd bits): b2 b4 b6 b8 ... | BPSK on sin(2πfct) │ |
| │ Combined | s(t) = I(t)×cos(2πfct) - Q(t)×sin(2πfct) │ |
| │ I and Q are ORTHOGONAL (90° apart) | don't interfere! │ |
| │ Total | 2 × (Rb/2) = Rb with HALF the bandwidth of BPSK │ |
📐 Mathematical Representation
| │ Or equivalently | │ |
| │ Where | │ |
| │ I(t) = ±1 (even bits | +1 for "1", -1 for "0") │ |
| │ Q(t) = ±1 (odd bits | +1 for "1", -1 for "0") │ |
| │ Symbol mapping (Gray code) | │ |
| │ "00" | I=+1, Q=+1 → θ = 45° │ |
| │ "01" | I=-1, Q=+1 → θ = 135° │ |
| │ "11" | I=-1, Q=-1 → θ = 225° │ |
| │ "10" | I=+1, Q=-1 → θ = 315° │ |
🔧 QPSK Transmitter & Receiver
Transmitter:
Serial ┌─────────┐ Even bits ──▶ ×cos(2πfct) ──┐
Data ──▶│ Serial │ ├──▶ Σ ──▶ QPSK
│to │ │ Signal
│Parallel │ Odd bits ──▶ ×(-sin(2πfct))─┘
└─────────┘
Receiver:
QPSK ┌──┐×cos(2πfct)┌──────┐ ┌────────┐
Signal──┤ ├───────────▶│∫&Dump│▶│Decision│──▶ Even bits
│ │ └──────┘ └────────┘
│ │
│ │×(-sin(2πfct))┌──────┐ ┌────────┐
│ ├─────────────▶│∫&Dump│▶│Decision│──▶ Odd bits
└──┘ └──────┘ └────────┘
→ Parallel to Serial
📡 Bandwidth & Spectral Efficiency
The bandwidth of QPSK is the SAME as BPSK, but the data rate is DOUBLE! This is the biggest advantage of QPSK.
┌──────────────────────────────────────────────────────┐
│ │
│ QPSK Symbol Rate = Rb / 2 (half the bit rate) │
│ │
│ Bandwidth = Symbol Rate × (1+r) = (Rb/2)×(1+r) │
│ │
│ Spectral Efficiency = 2 bps/Hz (double BPSK!) │
│ │
│ Example: Rb = 10 Mbps, r = 0.25 │
│ BW = (10/2) × 1.25 = 6.25 MHz │
│ (BPSK would need: 10 × 1.25 = 12.5 MHz) │
│ │
└──────────────────────────────────────────────────────┘
| Scheme | Bits/Symbol | Spectral Efficiency | BW for 10 Mbps |
|---|---|---|---|
| BPSK | 1 | 1 bps/Hz | 12.5 MHz |
| QPSK | 2 | 2 bps/Hz | 6.25 MHz |
| 8-PSK | 3 | 3 bps/Hz | 4.17 MHz |
📉 BER Performance
Surprisingly, the BER performance of QPSK is the SAME as BPSK (on a per-bit basis)! This is because the I and Q channels are independent.
┌──────────────────────────────────────────────────────┐
│ │
│ QPSK BER = (1/2) × erfc(√(Eb/N₀)) │
│ │
│ Same as BPSK! (per bit) │
│ │
│ At BER = 10⁻⁶: Eb/N₀ ≈ 10.5 dB │
│ │
│ QPSK gives 2× data rate at same BER as BPSK! │
│ This is why QPSK is so popular. │
│ │
└──────────────────────────────────────────────────────┘
This is the magic of QPSK – double data rate, half bandwidth, and the same BER as BPSK. Best of both worlds!
🔄 QPSK Variants
1. OQPSK (Offset QPSK)
- Q channel delayed by half symbol (Tb)
- Maximum phase change = 90° (not 180°)
- Reduces amplitude fluctuation
- Better for non-linear amplifiers
- Used in: Satellite communication
2. π/4-QPSK
- Constellation rotates 45° every symbol
- Max phase change = 135° (less than QPSK's 180°)
- Can use differential detection
- Used in: IS-136 (old 2G), TETRA
3. DQPSK (Differential QPSK)
- Information in phase change (not absolute phase)
- No coherent detection needed
- ~2 dB worse than coherent QPSK
- Simpler receiver
| Variant | Max Phase Jump | Envelope Variation | Used In |
|---|---|---|---|
| QPSK | 180° | High | WiFi, 4G, 5G |
| OQPSK | 90° | Low | Satellite, ZigBee |
| π/4-QPSK | 135° | Medium | TETRA, old 2G |
| DQPSK | 135° | Medium | DECT |
🌐 Applications
| Application | Why QPSK? |
|---|---|
| 4G LTE (baseline) | Good balance of efficiency & robustness |
| 5G NR | Starting modulation, cell-edge |
| WiFi (802.11) | Adaptive modulation starting point |
| DVB-S (satellite TV) | Power-limited, need efficiency |
| GPS L2C signal | Robust demodulation |
| Cable modems (DOCSIS) | Starting modulation level |
| Deep space | When link margin tight |
| Satellite communication | Power-constrained environment |
📝 Summary
| Parameter | QPSK |
|---|---|
| Phase states | 4 (45°, 135°, 225°, 315°) |
| Bits/symbol | 2 |
| Symbol rate | Rb/2 |
| Bandwidth | (Rb/2)(1+r) – half of BPSK! |
| Spectral efficiency | 2 bps/Hz |
| BER | Same as BPSK per bit |
| Eb/N₀ at 10⁻⁶ | 10.5 dB |
| Equivalent to | Two orthogonal BPSK (I + Q) |
| Key advantage | 2× capacity, same BER |
| Used in | WiFi, 4G, 5G, satellite, GPS |
❓ FAQ
Q: Are QPSK and 4-QAM the same? A: Yes! QPSK and 4-QAM are mathematically identical. Same constellation, same performance. Only the names differ.
Q: Why is 8-PSK used less than QPSK? A: In 8-PSK, the constellation points are closer together (at the same power), so BER becomes worse. The trade-off is not worth it. Instead, 16-QAM is used (which adds amplitude variation for better distance between points).
Q: How is QPSK's BER the same as BPSK? A: QPSK is essentially 2 independent BPSK signals (on I and Q). Each performs like BPSK. Per bit energy is the same, so per bit BER is the same.
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