🔬 Virtual Laboratory: QPSK & QAM Modulation

ECE 426-Digital Communications | Department of Electrical & Communication Engineering

1. Introduction to Quadrature Modulation

Quadrature modulation techniques (QPSK and QAM) are widely used in modern digital communication systems including WiFi, LTE, and satellite communications. These schemes modulate both the amplitude and phase of the carrier signal to transmit multiple bits per symbol.

Key Concept: Quadrature modulation uses two orthogonal carriers (sine and cosine) to transmit independent data streams simultaneously over the same bandwidth.

2. QPSK (Quadrature Phase Shift Keying)

QPSK encodes 2 bits per symbol using four phase states spaced 90° apart.

Mathematical Representation

s(t) = A·cos(2πfct + φk)
where φk ∈ {π/4, 3π/4, 5π/4, 7π/4}

In-phase component (I): I = A·cos(φk)
Quadrature component (Q): Q = A·sin(φk)

QPSK Constellation Mapping (Gray Coding)

Bits (b1b0) Phase (φ) I Component Q Component
00 45° (π/4) +1/√2 +1/√2
01 135° (3π/4) -1/√2 +1/√2
11 225° (5π/4) -1/√2 -1/√2
10 315° (7π/4) +1/√2 -1/√2

3. QAM (Quadrature Amplitude Modulation)

QAM varies both amplitude and phase, allowing higher spectral efficiency. 16-QAM transmits 4 bits per symbol.

s(t) = I(t)·cos(2πfct) - Q(t)·sin(2πfct)

Where I(t) and Q(t) take values from: {±1, ±3} (for 16-QAM)
Normalization factor: Eavg = 10 (for 16-QAM)

16-QAM Constellation Characteristics

  • Number of Symbols: 16
  • Bits per Symbol: 4
  • Amplitude Levels: 3 (±1, ±3)
  • Minimum Distance: dmin = 2
  • Average Energy: Eavg = 10

4. Signal Space Representation

The constellation diagram represents:

  • X-axis: In-phase component (I)
  • Y-axis: Quadrature component (Q)
  • Decision Boundaries: Optimal receiver thresholds
  • Noise Effect: Scattered points around ideal positions

5. Error Performance

QPSK BER: Pb = Q(√(2Eb/N0))
16-QAM BER: Pb ≈ (3/2)Q(√(4Eb/(5N0)))
Note: Higher-order QAM (64-QAM, 256-QAM) provides higher data rates but requires higher SNR to maintain the same bit error rate due to reduced distance between constellation points.

🎛️ Modulation Parameters

Status: Ready | Symbols Transmitted: 0 | Errors: 0 | BER: 0.000
Constellation Diagram (I-Q Plane)
Transmitted
Received (with noise)
Time Domain Signal
Eye Diagram
Symbol Mapping
💡 Observation Tip: Increase the SNR to see the received constellation points cluster tighter around the ideal transmitted points. At low SNR (<5 dB), notice how noise causes symbol errors as points cross decision boundaries.

🧪 Laboratory Procedure

Experiment 1: QPSK Constellation Analysis

  1. Set the modulation scheme to QPSK
  2. Set SNR to 30 dB (effectively no noise)
  3. Click Start and observe the constellation diagram
  4. Verify that four distinct points are visible at 45°, 135°, 225°, and 315°
  5. Note the I and Q amplitudes (should be approximately ±0.707)
  6. Gradually decrease SNR to 10 dB and observe the spread of received points
  7. Continue decreasing to 5 dB and identify when decision errors begin

Experiment 2: 16-QAM Modulation

  1. Change modulation to 16-QAM
  2. Observe the rectangular constellation grid (4×4 points)
  3. Measure the minimum distance between adjacent points
  4. Compare the constellation density with QPSK
  5. At SNR = 15 dB, compare the noise immunity with QPSK at same SNR
  6. Calculate the theoretical bandwidth efficiency improvement (4 bits/symbol vs 2 bits/symbol)

Experiment 3: Error Rate Analysis

  1. Reset the simulation
  2. Set modulation to QPSK and SNR to 0 dB
  3. Run simulation for 10,000 symbols (use auto-run feature)
  4. Record the Bit Error Rate (BER) displayed
  5. Repeat for SNR values: 5, 10, 15, 20 dB
  6. Plot BER vs SNR curve (semi-log scale)
  7. Compare with theoretical Q(√(2Eb/N0)) curve
  8. Repeat entire experiment for 16-QAM and compare results

Experiment 4: Time Domain Analysis

  1. Observe the time domain waveform with different modulation schemes
  2. Note the amplitude variations in 16-QAM vs constant amplitude in QPSK
  3. Measure the phase transitions using the time cursor
  4. Analyze the eye diagram for Inter-Symbol Interference (ISI)
  5. Verify that the eye opening decreases with lower SNR
Important: For accurate BER measurements, run each simulation for at least 10,000 symbols or until at least 100 errors are detected, whichever comes first.

📊 Performance Analysis

Spectral Efficiency

Definition: Number of bits transmitted per Hz of bandwidth

  • BPSK: 1 bit/s/Hz
  • QPSK: 2 bits/s/Hz
  • 16-QAM: 4 bits/s/Hz
  • 64-QAM: 6 bits/s/Hz

Trade-off: Higher efficiency requires higher SNR for same BER

Power Efficiency

Definition: Energy required per bit for reliable communication (Eb/N0)

  • QPSK: Requires ~10 dB for BER = 10-5
  • 16-QAM: Requires ~14 dB for BER = 10-5
  • 64-QAM: Requires ~18 dB for BER = 10-5

Each doubling of constellation size requires ~4 dB more power

Theoretical BER Comparison

BER vs SNR (Theoretical Curves)
Q-function: Q(x) = (1/√(2π)) ∫x∞ e(-t²/2) dt
QPSK: Pb = Q(√(2Eb/N0))
M-QAM: Pb ≈ (4/k)(1-1/√M) Q(√(3kEb/((M-1)N0))), where k = log₂(M)

Constellation Distance Analysis

Modulation Min Distance (dmin) Avg Energy (Es) dmin²/Es
QPSK √2 1 2 (0 dB)
16-QAM 2 10 0.4 (-4 dB)
64-QAM 2 42 0.095 (-10.2 dB)
Analysis: The normalized minimum distance decreases with higher-order modulation, explaining the increased SNR requirement. QPSK offers the best power efficiency among these schemes.

📋 Laboratory Report Guidelines

Required Report Sections

1. Title Page

  • Experiment Title: QAM & QPSK Modulation Analysis
  • Course: Digital Communications
  • Date and Student Information

2. Objectives

  • To understand quadrature modulation principles
  • To analyze QPSK and QAM constellation diagrams
  • To evaluate the effect of AWGN on modulation performance
  • To compare theoretical and simulated BER performance
  • To analyze the bandwidth efficiency vs. power efficiency trade-off

3. Theory (Brief Summary)

  • Mathematical representation of QPSK and QAM
  • Signal space concepts and constellation diagrams
  • Gray coding principles
  • Error probability analysis

4. Simulation Results

Include screenshots/observations for:

  • QPSK constellation at SNR = 30 dB, 10 dB, and 5 dB
  • 16-QAM constellation at SNR = 30 dB and 15 dB
  • Time domain waveforms showing amplitude/phase variations
  • Eye diagrams under different SNR conditions
  • Measured BER vs. SNR table (minimum 5 SNR points)

5. Analysis Questions

  1. Why is Gray coding used in QAM constellations?
  2. Calculate the theoretical BER for QPSK at 10 dB SNR and compare with your simulation results.
  3. Explain why 16-QAM requires higher SNR than QPSK for the same BER.
  4. If you need to transmit 10 Mbps in a 5 MHz bandwidth, which modulation scheme would you choose? Justify your answer.
  5. Analyze the effect of phase noise on the constellation diagram (research extension).

6. Conclusion

  • Key findings from the experiments
  • Comparison between theoretical and practical results
  • Practical implications for system design
Submission Requirements:
  • Report length: 8-12 pages maximum
  • Include all plots with proper labels and captions
  • Show sample calculations for theoretical BER
  • Attach signed data sheets from virtual lab
  • Deadline: As per course schedule
Grading Rubric:
Theory Understanding (25%) | Simulation Results (30%) | Analysis (25%) | Presentation (20%)