[Basic] Signal Transmission in MATLAB: Understanding Channel Models and Signal Attenuation

# 2.1 Overview of Channel Models

A channel model is a mathematical model describing the characteristics of a channel experienced by signals during transmission. It can be used to analyze signal attenuation, distortion, and noise, providing a theoretical foundation for the design and optimization of communication systems.

### 2.1.1 Channel Classification

Channels can be classified based on their characteristics as follows:

- **Wired Channels:** Signals are transmitted through wires or optical fibers, experiencing lower attenuation and distortion, but are limited by distance and bandwidth.
- **Wireless Channels:** Signals are transmitted through electromagnetic waves in the air, with higher attenuation and distortion, but without distance restrictions.
- **Fiber Optic Channels:** Signals are transmitted through optical fibers, having extremely low attenuation and distortion, but at a higher cost.
- **Acoustic Channels:** Signals are transmitted through sound waves in water or air, experiencing higher attenuation and distortion, suitable for underwater or noisy environments.

### 2.1.2 Channel Characteristics

Channel characteristics can be described using several parameters:

- **Bandwidth:** The range of frequencies a channel can transmit.
- **Attenuation:** The power loss signals experience while traveling through the channel.
- **Distortion:** The shape change signals undergo while traveling through the channel.
- **Noise:** The random interference signals present in the channel.
- **Delay:** The time it takes for signals to travel through the channel.

# 2. Channel Models and Signal Attenuation Theory

### 2.1 Overview of Channel Models

**2.1.1 Channel Classification**

A channel model describes the physical environment and characteristics signals experience during transmission. Channels can be classified based on the transmission medium and the signal propagation method as follows:

- **Wired Channels:** Signals are transmitted through cables or optical fibers, exhibiting stable transmission characteristics and lower attenuation.
- **Wireless Channels:** Signals are propagated through radio waves in the air, influenced by environmental factors, with time-varying and stochastic properties.
- **Fiber Optic Channels:** Signals are transmitted through optical fibers, having extremely low attenuation and very high bandwidth.

**2.1.2 Channel Characteristics**

Channel characteristics are described by the following aspects:

- **Bandwidth:** The maximum frequency range a channel can transmit.
- **Attenuation:** The energy loss signals experience during transmission due to various factors.
- **Delay:** The time it takes for signals to travel from the sender to the receiver.
- **Multipath Effects:** The phenomenon where signals take multiple propagation paths due to reflection or refraction, resulting in multiple delay components when reaching the receiver.
- **Shadow Fading:** The significant reduction in signal strength caused by obstacles or other factors during transmission. Shadow fading is random, and the degree of attenuation depends on the shape, size of obstacles, and the signal frequency.

### 2.2 Mechanisms of Signal Attenuation

Signals can attenuate due to various factors during transmission, mainly including the following mechanisms:

**2.2.1 Path Loss**

Path loss refers to the energy loss signals experience as they propagate through free space due to increased distance. The attenuation formula is:

Path Loss (dB) = 20 log10(f) + 20 log10(d) + 32.45

Where:

- f is the signal frequency (MHz)
- d is the transmission distance (km)

**2.2.2 Multipath Effects**

Multipath effects occur when signals take multiple propagation paths due to reflection or refraction during transmission, resulting in multiple delay components when signals reach the receiver. These delay components, when superimposed, can cause signal distortion and attenuation.

**2.2.3 Shadow Fading**

Shadow fading is the significant reduction in signal strength caused by obstacles or other factors during transmission. Shadow fading is random, and the degree of attenuation depends on the shape, size of obstacles, and the signal frequency.

### 2.2.4 MATLAB Simulation of Signal Attenuation

% Signal frequency
f = 1 GHz;

% Transmission distance
d = 100; % Units: km

% Path loss calculation
path_loss = 20 * log10(f) + 20 * log10(d) + 32.45;

% Multipath effect simulation
num_paths = 10; % Number of multipath routes
path_delays = rand(num_paths, 1) * 100; % ns
path_gains = rand(num_paths, 1); % 0-1

% Shadow fading simulation
shadow_fading = 10 * log10(rand()); % dB

% Total attenuation calculation
total_loss = path_loss + s