# Analyzing Digital Communication Systems with MATLAB: BER Performance in AWGN Channel

October 05, 2023 Dr. David Mitchell
United States of America
MATLAB Simulation
Dr. David Mitchell is a distinguished expert in the field of digital communication systems and MATLAB simulation from Columbia University. He has made significant contributions to the study of communication systems in the presence of Additive White Gaussian Noise (AWGN) with 10 years of experience.

In the realm of digital communication systems, understanding how different modulation schemes perform under the influence of noise is crucial, especially when you need to complete your Communication Systems assignment. Engineers and students alike often need to simulate and analyze the Bit Error Rate (BER) of these systems to ensure reliable data transmission. MATLAB, with its powerful computational capabilities, is a popular choice for such simulations. In this blog post, we will delve into the theoretical aspects of designing a MATLAB program to simulate the performance of a digital communication system in the presence of Additive White Gaussian Noise (AWGN). We will explore various modulation schemes such as Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), and 16-Quadrature Amplitude Modulation (16-QAM) while focusing on BER performance analysis.

## Understanding Digital Communication Systems

Before we dive into the details of our MATLAB simulation, let's grasp the fundamental concepts of digital communication systems and why they are susceptible to noise.

Digital Communication Basics

At its core, a digital communication system aims to transmit digital data (usually represented as bits) from one point to another. These systems utilize various modulation techniques to encode the digital information onto an analog carrier signal, making it suitable for transmission over communication channels.

The key components of a digital communication system include: 1. Transmitter

The transmitter is the starting point of the digital communication system. Its primary function is to prepare the digital data for transmission. Here's a more detailed explanation of its role:

• Digital Data Modulation: In the transmitter, digital data is transformed into an analog signal suitable for transmission over a communication channel. Modulation techniques, such as Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), or Phase Shift Keying (PSK), are employed to map the digital bits to analog signal parameters.
• Carrier Signal Generation: A carrier signal at a specific frequency is generated to carry the modulated digital data. The choice of carrier frequency depends on factors like available bandwidth and the communication medium.
• Signal Amplification and Processing: The transmitter often includes components for signal amplification, filtering, and shaping to ensure that the transmitted signal meets regulatory requirements and can effectively propagate through the channel.

2. Channel

The channel represents the physical medium through which the modulated signal travels from the transmitter to the receiver. In practical scenarios, channels introduce various impairments, with AWGN being a common factor. Here's a more detailed look at the channel's role and the impact of AWGN:

• Transmission Medium: The channel can take many forms, such as wired (e.g., copper cables, optical fibers) or wireless (e.g., radio waves, microwave). Each medium introduces its own characteristics, including attenuation, dispersion, and noise.
• AWGN Introduction: In many communication scenarios, the channel introduces noise, and this noise is often modeled as AWGN. AWGN is characterized by its randomness, being statistically Gaussian (following a normal distribution), and having a constant power spectral density across all frequencies. It represents background noise that is independent of the transmitted signal.
• Signal Degradation: The presence of AWGN in the channel leads to signal degradation. As the signal propagates through the medium, it gets corrupted by the added noise. The higher the noise level relative to the signal power (expressed as the Signal-to-Noise Ratio or SNR), the more challenging it becomes to recover the original data at the receiver.

The receiver is the final stage of the digital communication system and plays a critical role in ensuring that the transmitted data is accurately recovered. Here's a deeper exploration of its functions:

• Signal Detection and Reception: The receiver captures the incoming signal, which has been affected by noise and other channel impairments. It processes the received signal to extract the information contained within it.
• Demodulation: Demodulation is the process of reversing the modulation applied at the transmitter. Depending on the modulation scheme used, the receiver employs appropriate demodulation techniques to recover the digital data from the analog signal.
• Error Correction and Data Recovery: The receiver implements error correction algorithms and techniques to mitigate the effects of noise and interference introduced by the channel. These techniques can include Forward Error Correction (FEC) codes, interleaving, and error detection schemes.
• Signal Quality Assessment: The receiver assesses the quality of the received signal and evaluates its suitability for further processing. This assessment often involves measuring the Bit Error Rate (BER) or other performance metrics to determine the reliability of the received data.

Additive White Gaussian Noise (AWGN) in Context

AWGN is a ubiquitous challenge in digital communication systems. It represents the inherent noise present in communication channels due to a variety of sources, including electronic components, thermal noise, and environmental factors. Understanding and dealing with AWGN is essential for communication system engineers and designers because it affects the system's performance.

In the presence of AWGN, the receiver's task becomes particularly challenging. The random nature of AWGN means that some of the transmitted bits may be corrupted during transmission. Hence, the receiver must employ error correction and detection techniques to recover the original data accurately.

Furthermore, the Signal-to-Noise Ratio (SNR) plays a pivotal role in determining the effectiveness of communication in the presence of AWGN. A higher SNR results in a lower probability of bit errors, making communication more reliable. Conversely, a lower SNR increases the likelihood of errors, necessitating more advanced error correction and detection strategies.

The key components of a digital communication system—the transmitter, channel, and receiver—work in tandem to ensure the successful transmission and reception of digital data. The presence of AWGN in the channel adds complexity to the system, making it crucial to employ modulation schemes, error correction, and detection techniques that can mitigate the effects of noise and ensure reliable communication. Engineers and researchers continue to explore innovative methods and technologies to improve the performance of digital communication systems, especially in the presence of challenging noise conditions like AWGN.

## Additive White Gaussian Noise (AWGN)

Noise in communication systems is often modeled as Additive White Gaussian Noise (AWGN). This noise is characterized by being independent at each point in time (white), having a Gaussian probability distribution, and being added to the transmitted signal as it propagates through the channel. AWGN is a suitable model for many real-world communication channels where noise sources are diverse and unpredictable.

MATLAB Simulation for BER Analysis

Now that we have a solid understanding of the basics, let's discuss how to design a MATLAB program for simulating digital communication systems in the presence of AWGN. We will focus on the following aspects:

1. Generation of Modulated Signals: Creating modulated signals corresponding to different modulation schemes (BPSK, QPSK, and 16-QAM).
2. AWGN Channel Modeling: Simulating the channel by adding AWGN to the transmitted signal.
4. BER Calculation: Analyzing the Bit Error Rate to evaluate the system's performance.

## Modulation Schemes

Binary Phase Shift Keying (BPSK)

BPSK is a simple modulation scheme where binary '1' and '0' are represented by phase shifts of 0 and π radians, respectively. In MATLAB, you can create a BPSK modulated signal using the following code:% Generate random binary data data = randi([0 1], 1, numBits); % Modulate using BPSK bpskSignal = 2 * data - 1; 

QPSK employs four phase shifts to represent two bits at a time. It's more bandwidth-efficient than BPSK. Generating a QPSK modulated signal in MATLAB can be done as follows:% Generate random data for QPSK (2 bits per symbol) data = randi([0 3], 1, numBits/2); % Modulate using QPSK qpskSignal = exp(1j * pi/4 * data); 

16-QAM is a more complex modulation scheme that uses both phase and amplitude variations to transmit four bits at a time. Here's how you can generate a 16-QAM signal in MATLAB:% Generate random data for 16-QAM (4 bits per symbol) data = randi([0 15], 1, numBits/4); % Modulate using 16-QAM qamSignal = qammod(data, 16); 

Once the modulated signals are generated, we simulate the channel by adding AWGN to the transmitted signal. The power of the noise is determined by the Signal-to-Noise Ratio (SNR), which is defined as the ratio of the signal power to the noise power.

% Calculate noise power based on SNR (assuming unit signal power) noisePower = 10^(-SNRdB/10); % Generate AWGN noise = sqrt(noisePower/2) * (randn(size(signal)) + 1j * randn(size(signal))); % Add noise to the signal receivedSignal = signal + noise;

The receiver's role is to demodulate the received signal back into digital data. The demodulation process depends on the modulation scheme used. For instance, in BPSK, you can detect the phase to distinguish between '0' and '1'. In QPSK and 16-QAM, you need to analyze both phase and amplitude.% Calculate BER numErrors = sum(data ~= receivedData); BER = numErrors / numBits;

## BER Calculation

Finally, the Bit Error Rate (BER) is calculated by comparing the original data with the demodulated data. The BER represents the ratio of incorrectly received bits to the total number of bits transmitted. In MATLAB, you can calculate BER as follows:

Analyzing BER Performance

The main objective of our MATLAB simulation is to analyze the BER performance of different modulation schemes under varying SNR conditions. The BER gives us insights into how well the communication system copes with noise. Typically, lower BER values indicate better performance.

Impact of SNR on BER

By running the simulation for different SNR values, we can create a BER vs. SNR curve for each modulation scheme. These curves help us understand how robust each scheme is in the presence of noise. For instance, we might observe that BPSK outperforms QPSK and 16-QAM at low SNR values, but as SNR increases, the performance of the more complex schemes improves.

Comparing Modulation Schemes

To aid university students in solving assignments, let's briefly compare the three modulation schemes we discussed:

• BPSK: Simple to implement and robust in noisy environments, but has limited data rate efficiency.
• QPSK: Offers higher data rate efficiency compared to BPSK but requires more complex receiver design.
• 16-QAM: Provides even higher data rate efficiency but is more susceptible to noise and requires more advanced receiver algorithms.

MATLAB as a Learning Tool

MATLAB serves as an excellent learning tool for students studying digital communication systems. It allows them to experiment with various modulation schemes, understand the impact of noise, and gain practical insights into real-world challenges. Additionally, MATLAB's visualization capabilities enable students to create BER vs. SNR curves, facilitating a deeper understanding of system performance.

## Conclusion

In this theoretical discussion, we've explored the design of a MATLAB program for simulating the performance of a digital communication system in the presence of AWGN. We've covered the generation of modulated signals, the addition of AWGN to the signal, receiver design, and BER calculation. Through this simulation, university students can gain valuable insights into the behavior of different modulation schemes under noisy conditions. Understanding how to analyze BER performance equips students with essential skills for solving assignments and tackling real-world communication challenges. Digital communication is a dynamic field, and mastering these concepts will undoubtedly prove beneficial in the ever-evolving world of technology.