Understanding Wireless Channel Models: AWGN, Rayleigh, Rician

This page describes various channel models, including AWGN, Rayleigh, Rician, and others used in WiMAX, WLAN, and LTE systems. A channel represents the path between a transmitter and a receiver, whether wired or wireless. A channel model is a mathematical representation or equation that describes the channel’s behavior between the transmitter and receiver.

There are two primary types of channels:

• Time-Invariant Channel: The characteristics of the channel do not change over time. This occurs when both the transmitter and receiver are stationary. An example is a cable connecting a transmitter and receiver or a fixed WiMAX system where both the base station and subscriber equipment are fixed.

• Time-Varying Channel: The characteristics of the channel change over time. This occurs when either the transmitter, receiver, or both are in motion. An example is a mobile WiMAX or cellular system where the base station is fixed, but the mobile devices (tablets, laptops, etc.) are moving.

Basic Channel Models

Several basic channel models, such as AWGN, Rayleigh, and Rician, are commonly used by communication engineers to validate transmitter and receiver designs. More complex communication systems often require custom-designed channel models. These models consider various parameters like:

• Number of paths
• Delays at each path
• Terrain type
• Doppler frequency and/or speed

AWGN (Additive White Gaussian Noise)

AWGN is a channel model that primarily applies to semi-flexible or coaxial cables between the transmit and receive paths, and also space communication. It accounts for thermal noise present in the channel or generated by electronic devices at the transmitter and receiver.

MATLAB provides functions like awgn, rand, and randn to model this type of channel.

• randn: Generates random numbers with a normal (Gaussian) distribution, a mean of zero, and a variance of one.
• rand: Generates random numbers with a uniform distribution.

The following AWGN equation is frequently used:

R = awgn(T, SNR, 'measured')

Where:

• T is the transmit vector.
• R is the received vector with noise added according to the specified SNR (Signal-to-Noise Ratio) in dB.

Rayleigh Channel

The Rayleigh channel model is applied to channels where there are only non-line-of-sight (NLOS) paths between the transmitter and receiver, meaning no dominant or direct line-of-sight (LOS) path exists. The MATLAB model for this channel is rayleighchan.

Rician Channel

The Rician channel model is applied to channels that have both line-of-sight (LOS) and non-line-of-sight (NLOS) paths between the transmitter and receiver. The MATLAB model for this channel is ricianchan.

Other Channel Models

In addition to the basic channel models, various channel models are designed specifically for particular communication systems:

1. SUI Channel Model: Designed for fixed WiMAX system implementations as per the IEEE 802.16-2004 OFDM specifications.

2. ITU-T Channel Model: Designed for mobile WiMAX system implementations as per the IEEE 802.16e-2005 OFDMA specifications (defined in ETSI UMTS specifications). It includes channel coefficients for indoor, pedestrian, and vehicular environments.

3. JTC Channel Model: Designed for WLAN channels as per IEEE 802.11 specifications, and one proposed by Naftali Chayat. Used for 802.11a, 802.11b, and 802.11g.

4. TGn Channel Model: For WLAN channels according to the IEEE 802.11n specifications.

5. UWB Channel Model: For IEEE 802.15.3 and IEEE 802.15.4 system specifications.

Channel Emulators

Several hardware equipments are available from leading test and measurement companies such as Anritsu, Spirent communications, Agilent technologies, azimuth systems and more which emulate channel models for various wireless technologies for test and measurement purpose.

These include channel emulators for wireless technologies such as WiMAX, WLAN, LTE, LTE-Advanced, GSM, CDMA, HSPA and more.