Wireless Notes

QPSK Quadrature Phase Shift Keying Modulation

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.

Continue the lesson path

Study next in this module

4 connected lessons

01Modulation TechniquesQAM Quadrature Amplitude Modulation Complete GuideLearn QAM with 16-QAM 64-QAM 256-QAM 1024-QAM constellation diagrams, spectral efficiency, BER vs SNR trade-off, adaptive modulation coding AMC, and applications in WiFi 4G 5G cable for engineering students.02Modulation TechniquesPSK Phase Shift Keying in Digital CommunicationLearn PSK Phase Shift Keying with BPSK working, constellation diagram, coherent detection, BER performance, DPSK differential, comparison with ASK FSK, and applications in GPS satellite WiFi for engineering students.03Modulation TechniquesPhase Modulation PM in Wireless CommunicationLearn Phase Modulation PM with working principle, mathematical representation, relationship with FM, modulation index, PM generation methods, and applications in digital PSK systems explained for engineering students.04Modulation TechniquesModulation Techniques Comparison Complete TableComplete comparison of all modulation techniques AM FM PM ASK FSK PSK QPSK QAM with performance metrics, bandwidth efficiency, power efficiency, BER, applications, and selection criteria for engineering students.

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