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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
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QPSK Baseline (4-PSK)
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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.

Read why they are identical →


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Further Reading 




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