Skip to main content

BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc (MATLAB + Simulator)


 

QPSK provides twice the data rate compared to BPSK. However, the bit error rate (BER) is approximately the same as BPSK at low SNR values when gray coding is used. On the other hand, QPSK exhibits similar spectral efficiency to 4-QAM and 16-QAM under low SNR conditions. In very noisy channels, QPSK can sometimes achieve better spectral efficiency than 4-QAM or 16-QAM. In practical wireless communication scenarios, QPSK is commonly used along with QAM techniques, especially where adaptive modulation is applied.


Modulation Bits/Symbol Points in Constellation Usage Notes
BPSK 1 2 Very robust, used in weak signals
QPSK 2 4 Balanced speed & reliability
4-QAM 2 4 Equivalent to QPSK
16-QAM 4 16 Higher data rate, less robust in noise

Interactive Modulation Comparison (QPSK vs Others)

Adjust parameters to see how your scheme compares to QPSK in real-time.

Selected Scheme
---
QPSK Baseline (4-PSK)
---
Reference

 QPSK vs BPSK and QAM: A Comparison of Modulation Schemes in Wireless Communication

1. Spectral Efficiency

Higher-order QAM increases data rate but demands a higher SNR, making it vulnerable to noise and interference. Ideal for high-speed internet but less so in environments with fading or interference.

2. Robustness

BPSK is the most robust, but offers the lowest throughput. It's ideal for scenarios where communication reliability is more important than speed, such as in space missions, military communication, or IoT devices.

3. Flexibility

QPSK strikes a balance, offering more data per symbol than BPSK, while still providing good noise immunity. It's widely used in cellular networks (e.g., 3G, 4G LTE), satellite communication, and Wi-Fi.

4. Power Efficiency

Higher-order QAM schemes, due to their complex modulation, require higher power for reliable transmission, especially in noisy environments. This makes it less ideal for battery-powered devices or long-distance communication.

Real-World Example:

5G NR: In high-density urban areas, 256-QAM may be used to support high throughput for smartphones and IoT devices. However, in rural areas with poor signal quality, the system might drop down to QPSK or 16-QAM to ensure connectivity.


Error Probability Formulas for Digital Modulation Schemes

Bit Error Rate (BER) Formulas

BPSK

\[ P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right) \] 

  Q-function or erfc (Click here)

QPSK (Gray Coded)

\[ P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right) \]

8-PSK (Approximation)

\[ P_b \approx \frac{2}{\log_2(8)} Q\left( \sqrt{\frac{2E_s}{N_0}} \sin\left(\frac{\pi}{8}\right) \right) \]

16-QAM (Gray Coded Approximation)

\[ P_b \approx \frac{3}{4} Q\left( \sqrt{\frac{4}{5}\frac{E_b}{N_0}} \right) \]

64-QAM (Gray Coded Approximation)

\[ P_b \approx \frac{7}{12} Q\left( \sqrt{\frac{2}{7}\frac{E_b}{N_0}} \right) \]

256-QAM (Gray Coded Approximation)

\[ P_b \approx \frac{15}{32} Q\left( \sqrt{\frac{8}{85}\frac{E_b}{N_0}} \right) \]

Symbol Error Rate (SER) Formulas

BPSK

\[ P_s = Q\left(\sqrt{\frac{2E_b}{N_0}}\right) \]

QPSK (Approximation)

\[ P_s \approx 2Q\left(\sqrt{\frac{2E_b}{N_0}}\right) \]

8-PSK (Approximation)

\[ P_s \approx 2Q\left( \sqrt{\frac{2E_s}{N_0}} \sin\left(\frac{\pi}{8}\right) \right) \]

16-QAM (Approximation)

\[ P_s \approx 3Q\left( \sqrt{\frac{4}{5}\frac{E_b}{N_0}} \right) \]

64-QAM (Approximation)

\[ P_s \approx \frac{7}{2} Q\left( \sqrt{\frac{2}{7}\frac{E_b}{N_0}} \right) \]

256-QAM (Approximation)

\[ P_s \approx \frac{15}{4} Q\left( \sqrt{\frac{8}{85}\frac{E_b}{N_0}} \right) \]

Notes

  • BER formulas assume Gray coding for QPSK and QAM constellations.
  • All formulas assume transmission over an AWGN (Additive White Gaussian Noise) channel.
  • For BPSK, the BER and SER are identical because each symbol carries only one bit.
  • The QAM expressions are commonly used high-SNR approximations for communication-system analysis and simulations.
  • \(E_b\) = Energy per bit, \(E_s\) = Energy per symbol, and \(N_0\) = Noise power spectral density.
  • \(Q(x)\) denotes the Gaussian Q-function.

QPSK vs. 4-QAM: Why They Should Have Same BER?

In digital communications, QPSK and 4-QAM exhibit identical Bit Error Rate (BER) performance. Although they are categorized differently, they share the same constellation geometry and power efficiency.


Try Interactive Online Simulators


Further Reading 




Contact Us

Name

Email *

Message *

Popular Posts

Constellation Diagram of FSK in Detail

📘 Overview 🧮 Simulator for constellation diagram of FSK 🧮 Theory 🧮 MATLAB Code 📚 Further Reading 📚 BER vs SNR from Constellation   Binary bits '0' and '1' can be mapped to 'j' and '1' to '1', respectively, for Baseband Binary Frequency Shift Keying (BFSK) . Signals are in phase here. These bits can be mapped into baseband representation for a number of uses, including power spectral density (PSD) calculations. For passband BFSK transmission, we can modulate signal 'j' with a lower carrier frequency and signal '1' with a higher carrier frequency while transmitting over a wireless channel. Let's assume we are transmitting carrier signal fc1 for the transmission of binary bit '1' and carrier signal fc2 for the transmission of binary bit '0'. Simulator for 2-FSK Constellation Diagram Simulator for 2-FSK Constellation Diagram ...

DFTs-OFDM vs OFDM: Why DFT-Spread OFDM Reduces PAPR Effectively (with MATLAB Code)

Understanding PAPR in DFT-spread OFDM vs. Standard OFDM In modern wireless communications like 4G LTE and 5G NR, managing the Peak-to-Average Power Ratio (PAPR) is critical for hardware efficiency. While OFDM is the gold standard for high-speed data, its high PAPR poses significant challenges for mobile devices. This is where DFTs-OFDM (also known as SC-FDMA) comes in. DFT-spread OFDM (DFTs-OFDM) has lower Peak-to-Average Power Ratio (PAPR) because it "spreads" the data in the frequency domain before applying IFFT, making the time-domain signal behave more like a single-carrier signal rather than a multi-carrier one like OFDM. Deeper Explanation: Aspect OFDM DFTs-OFDM Signal Type Multi-carrier Single-carrier-like Process IFFT of QAM directly QAM → DFT → IFFT PAPR Level High (due to many...

Simulation of ASK, FSK, and PSK using MATLAB Simulink (with Online Simulator)

📘 Overview 🧮 How to use MATLAB Simulink 🧮 Simulation of ASK using MATLAB Simulink 🧮 Simulation of FSK using MATLAB Simulink 🧮 Simulation of PSK using MATLAB Simulink 🧮 Simulator for ASK, FSK, and PSK 🧮 Digital Signal Processing Simulator 📚 Further Reading 📚 BER vs SNR Simulation 📚 Constellation Simulation ASK, FSK & PSK HomePage MATLAB Simulation Simulation of Amplitude Shift Keying (ASK) using MATLAB Simulink In Simulink, we pick different components/elements from MATLAB Simulink Library. Then we connect the components and perform a particular operation. Result A sine wave source, a pulse generator, a product block, a mux, and a scope are shown in the diagram above. The pulse generator generates the '1' and '0' bit sequences. Sine wave sources produce a specific amplitude and frequency. The scope displays the modulated signal as well as the...

UGC NET Electronic Science Previous Year Question Papers with Solutions

Home / Engineering & Other Exams / UGC NET 2026 PYQ ⬇️ Download Papers and Solutions 📋 Exam Pattern 💡 Preparation Tips ❓ FAQs 📊 Exam Highlights: Electronic Science (88) Feature Details Junior Research Fellowship (JRF) ₹37,000 + HRA per month Eligibility M.Sc/M.Tech in Electronics (55%) Validity of Certificate JRF (3 Years) | Lectureship (Lifetime) 📥 Download UGC NET Electronics PDFs Complete collection of previous year question papers, answer keys and explanations for Subject Code 88. Start Downloading 📂 View All Question Papers June 2025 - Question Paper Download PDF June 2025 - Solved Paper + Explanation ...

Online Simulator for ASK, FSK, and PSK

Interactive Digital Signal Processing (DSP) Tutorial and Simulator for ASK, FSK, and BPSK modulation techniques. Try our new Digital Signal Processing Simulator!   •   Interactive ASK, FSK, and BPSK tools updated for 2025. Start Now Digital Modulation Visualizer: ASK, FSK, & BPSK Simulator Learn and visualize binary modulation techniques (ASK, FSK, BPSK) in real-time with adjustable carrier and sampling parameters. Perfect for DSP students and engineers. 📡 ASK Simulator 📶 FSK Simulator 🎚️ BPSK Simulator 📚 More Topics ASK Modulator FSK Modulator BPSK Modulator More Topics 1. ASK (Amplitude Shift Keying) Simulat...

What is Frequency Resolution?

  Formula for Frequency Resolution (in general) The frequency resolution is the smallest frequency difference between two adjacent frequency points in your sampling range. It is determined by the total frequency range and the number of frequency samples  N . The formula for the frequency resolution (or step size)  Δf  is: Δf = (f max  - f min ) / (N - 1) Where: f min  is the minimum frequency in the range (in this case, -50 Hz). f max  is the maximum frequency in the range (in this case, 50 Hz). N  is the number of frequency points / frequency bins. Using the Given Values: From the function: f min  = -50 Hz f max  = 50 Hz N  = 1000 The frequency resolution is: Δf = (50 - (-50)) / (1000 - 1) = 100 / 999 ≈ 0.1001 Hz   Understanding Frequency Resolution in Signal Processing Alternative Formula Using Time Duration Another common way to define frequency resolution, especially in time-domain signal processing, is: Δf = 1 / T W...

Ph.D. admissions in IITs without a GATE score

PhD Admission in IITs With Low CGPA approximately 6.5 – 7.0 / 10 No valid GATE score Willing to strengthen research proposal, contact faculty, apply to multiple institutes Expanded List of IITs: Eligibility & Links IIT Eligibility & Notes PhD Info Link IIT Gandhinagar Minimum: 60% marks or 6.0 CGPA (General) or 55%/5.5 (SC/ST/PD) in qualifying degree.  GATE/NET may be waived in certain cases; but short‑listing criteria likely higher. iitgn.ac.in/admissions/phd IIT Kharagpur Minimum eligibility: 60% marks or 6.5 CGPA in qualifying exam for many branches.  However brochure notes “for test & interview this minimum must be met and higher cut‑offs may apply”. iitkgp.ac.in/phd_brochure.pdf IIT Bhubaneswar Minimum: Engineering Schools – M.Tech/ME with minimum 60% marks or 6.5 CGPA....