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

CMOS Logic Gates: Inverter, NAND, and NOR

CMOS Logic Gates: Inverter, NAND, and NOR Complementary metal–oxide–semiconductor (CMOS) technology forms the backbone of modern digital IC design. Patented by Frank Wanlass in 1963 ( US patent 3,356,858 ), CMOS enables low-power, high-speed, and noise-immune logic circuits. CMOS gates, including inverters, NAND, and NOR, are widely used in both large-scale and small-scale integrated circuits due to their efficiency and versatility. CMOS Inverter A CMOS inverter consists of a complementary pair of PMOS and NMOS transistors. The PMOS transistor connects to the supply voltage V DD , while the NMOS connects to ground. The input voltage V IN controls both gates, and the output voltage V OUT is taken from the connected drains. CMOS inverters are highly energy-efficient and produce minimal heat due to their comple...

UGC NET Electronic Science Previous Year Question Papers with Solutions

Download Papers and Solutions Exam Pattern Preparation Tips FAQs More Home / Engineering & Other Exams / UGC NET 2026 PYQ 📊 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 2026 - Question Paper Download PDF June 202...

Linear vs Circular Convolution

Linear vs Circular Convolution Linear convolution vs circular convolution Linear convolution (what nature does) If: x[n] = transmitted signal h[n] = channel impulse response (multipath) Then the received signal is: y[n] = x[n] * h[n] This means: Past symbols spill into future symbols Causes inter-symbol interference (ISI) DFT of y[n] is not a simple product Circular convolution (what DFT assumes) The DFT assumes periodic signals : y[n] = x[n] ⊛ h[n], where indices wrap around modulo N Only under circular convolution does the DFT satisfy: Y[k] = X[k] · H[k] This is what enables one-tap frequency-domain equalization . What happens in the real channel (linear convolution) The channel performs linear convolution: y[n] = Σ l=0 Lh−1 h[l] x[n-l] But because: CP absorbs the “spillover” Receiver discards CP before DFT The useful part of the received symbol becomes: y[n] = Σ l=0 Lh−1 h[l] x[(n-l) mod N] Modulo inde...

Online Simulator for ASK, FSK, and PSK Signal Generation

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 Demodulation More Topics 1. ASK (Ampli...

Flat vs Frequency Selective Online Simulator

Flat vs Frequency Selective Online Simulator Channel Type Without Fading Flat Fading Multipaths Nakagami m SNR(dB) Run Simulation Input Signal Signal After Fading Constellation Diagram BER vs SNR Explore Advanced Flat vs Frequency-Selective Fading Simulator Want to see these equations in action? Visualize it. Launch Simulator Tool Interactive Rayleigh Fading Simulator Want to see Rayleigh fading in action? Visualize it. Launch Simulator Tool Return to DSP Simulations Main Page →

Design of CMOS XOR/XNOR Gates

Design of CMOS XOR/XNOR Gates The semiconductor industry has experienced rapid integration of multimedia applications into mobile electronics, leading to very high integration density in CMOS VLSI. As operating frequencies increase, power consumption, speed, silicon area, and reliability become critical considerations. The XOR-XNOR circuits are fundamental building blocks in arithmetic circuits (Full Adders, Multipliers), compressors, comparators, parity checkers, code converters, error-detecting/correcting codes, and phase detectors. Their performance directly impacts the complex circuits they are used in. Design goals include full output voltage swing, low power consumption, reduced transistor count, minimal delay, and simultaneous non-skewed outputs. Static Logic (Static CMOS) Stat...

MUSIC Algorithm Explained (with MATLAB + Simulator)

Practical Implementation of the MUSIC Algorithm The focus is on how the algorithm works computationally , not just theory, and it explains the denominator (a H E n E n H a) mathematically and intuitively. 1. Introduction The MUSIC (Multiple Signal Classification) algorithm is a high-resolution method used in signal processing and array processing to estimate the Direction of Arrival (DOA) of signals received by a sensor array. Unlike classical beamforming methods, MUSIC uses eigenvector decomposition of the covariance matrix to separate the signal subspace and noise subspace , allowing it to achieve much higher angular resolution. In practical implementations, MUSIC works by: Simulating or collecting array signals Computing the covariance matrix Performing eigenvalue decomposition Separating signal and noise subspaces Scanning possible angles using a steering vector Constructing a pseudo-spectrum where peaks indicate signal directions 2. Signal Mo...

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSK, BPSK (with Simulation)

🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together 🧮 MATLAB Code for M-ary QAM 🧮 MATLAB Code for M-ary PSK 📚 Further Reading MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK % Written by Salim Wireless clc; clear; close all; snr_db = -5:2:25; psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); for i = 1:length(psk_orders) ber_psk_results(i, :) = berawgn(snr_db, 'psk', psk_orders(i), 'nondiff'); end for i = 1:length(qam_orders) ber_qam_results(i, :) = berawgn(snr_db, 'qam', qam_orders(i)); end figure; semilogy(snr_db, ber_psk_results(1, :), 'o-', 'LineWidth', 1.5, 'DisplayName', 'BPSK'); hold on; for i = 2:length(psk_orders) semilogy(snr_db, ber_psk_results(i, :), 'o-', 'DisplayName', sprintf('%d-PSK', psk_or...