Channel Modeling
[Communications Module]

Communication Channel Models. More...


Classes

class  itpp::Fading_Generator
 Fading generator class. More...
class  itpp::Independent_Fading_Generator
 Independent (random) fading generator class. More...
class  itpp::Static_Fading_Generator
 Static fading generator class. More...
class  itpp::Correlated_Fading_Generator
 Correlated (random) fading generator class. More...
class  itpp::Rice_Fading_Generator
 Rice type fading generator class. More...
class  itpp::FIR_Fading_Generator
 FIR type Fading generator class. More...
class  itpp::IFFT_Fading_Generator
 IFFT type Fading generator class. More...
class  itpp::Channel_Specification
 General specification of a time-domain multipath channel. More...
class  itpp::TDL_Channel
 Tapped Delay Line (TDL) channel model. More...
class  itpp::BSC
 A Binary Symetric Channel with crossover probability p. More...
class  itpp::AWGN_Channel
 Ordinary AWGN Channel for cvec or vec inputs and outputs. More...

Enumerations

enum  itpp::CHANNEL_PROFILE {
  ITU_Vehicular_A, ITU_Vehicular_B, ITU_Pedestrian_A, ITU_Pedestrian_B,
  COST207_RA, COST207_RA6, COST207_TU, COST207_TU6alt,
  COST207_TU12, COST207_TU12alt, COST207_BU, COST207_BU6alt,
  COST207_BU12, COST207_BU12alt, COST207_HT, COST207_HT6alt,
  COST207_HT12, COST207_HT12alt, COST259_TUx, COST259_RAx,
  COST259_HTx
}
 Predefined channel profiles. Includes LOS and Doppler spectrum settings.
enum  itpp::FADING_TYPE { Independent, Static, Correlated }
 Fading generator type: Independent (default), Static or Correlated.
enum  itpp::CORRELATED_METHOD { Rice_MEDS, IFFT, FIR }
 Correlated fading generation methods: Rice_MEDS (default), IFFT or FIR.
enum  itpp::RICE_METHOD { MEDS }
 Rice fading generation methods: MEDS.
enum  itpp::DOPPLER_SPECTRUM {
  Jakes = 0, J = 0, Classic = 0, C = 0,
  GaussI = 1, Gauss1 = 1, GI = 1, G1 = 1,
  GaussII = 2, Gauss2 = 2, GII = 2, G2 = 2
}
 Predefined Doppler spectra.

Detailed Description

Communication Channel Models.

Author:
Tony Ottosson, Pal Frenger, Adam Piatyszek and Zbigniew Dlugaszewski

Table of Contents

Introduction

When simulating a communication link, a model of the channel behaviour is usually needed. Such a model typically consist of three parts: the propagation attenuation, the shadowing (log-normal fading) and the multipath fading (small scale fading). In the following we will focus on the small scale (or multipath) fading.

Multipath fading is the process where the received signal is a sum of many reflections, each with different propagation time, phase and attenuation. The sum signal will vary in time if the receiver (or transmitter) moves, or if some of the reflectors move. We usually refer to this process as a fading process and try to model it as a stochastic process. The most common model is the Rayleigh fading model where the process is modeled as a sum of infinitely many (in practise it is enough with only a few) received reflections from all angles (uniformly distributed) around the receiver. Mathematically we write the received signal, $ r(t) $ as

\[ r(t) = a(t) * s(t), \]

where $ s(t) $ is the transmitted signal and $ a(t) $ is the complex channel coefficient (or fading process). If this process is modeled as a Rayleigh fading process then $ a(t) $ is a complex Gaussian process and the envelope $ \|a(t)\| $ is Rayleigh distributed.

Doppler

The speed by which the channel changes is decided by the speed of the mobile (transmitter or receiver or both). This movement will cause the channel coefficient $ a(t) $ to be correlated in time (or equivalently in frequency). Different models of this correlation exist, but the most common is the classical Jakes model where the correlation function is given as

\[ R(\tau) = E[a^*(t) a(t+\tau)] = J_0(2 \pi f_\mathrm{max} \tau), \]

where $ f_\mathrm{max} $ is the maximum Doppler frequency given by

\[ f_\mathrm{max} = \frac{v}{\lambda} = \frac{v}{c_0} f_c. \]

Here $ c_0 $ is the speed of light and $ f_c $ is the carrier frequency. Often the maximum Doppler frequency is given as the normalized Doppler $ f_\mathrm{max} T_s $ , where $ T_s $ is the sample duration (often the symbol time) of the simulated system. Instead of specifying the correlation function $ R(\tau) $ one can specify the Doppler spectrum (the Fourier transform of $ R(\tau) $).

Frequency-selective Channels

Since $ a(t) $ affects the transmitted signal as a constant scaling factor at a given time, this channel model is often referred to as flat-fading (or frequency non-selective fading). On the other hand, if time arrivals of the reflections are very different (compared to the sampling time), we cannot model the received signal only as a scaled version of the transmitted signal. Instead we model the channel as frequency-selective but time-invariant (or at least wide-sense stationary) with the impulse response

\[ h(t) = \sum_{k=0}^{N_\mathrm{taps}-1} a_k \exp (-j \theta_k ) \delta(t-\tau_k), \]

where $ N_\mathrm{taps} $ is the number of channel taps, $ a_k $ is the average amplitude at delay $ \tau_k $, and $ \theta_k $ is the channel phase of the $ k^{th} $ channel tap.

The average power and delay profiles are defined as:

\[ \mathbf{a} = [a_0, a_1, \ldots, a_{N_\mathrm{taps}-1}] \]

and

\[ \mathbf{\tau} = [\tau_0, \tau_1, \ldots, \tau_{N_\mathrm{taps}-1}], \]

respectively. We assume without loss of generality that $ \tau_0 = 0 $ and $ \tau_0 < \tau_1 < \ldots < \tau_{N_\mathrm{taps}-1} $. Now the received signal is simply a linear filtering (or convolution) of the transmitted signal, where $ h(t) $ is the impulse response of the filter.

In practice, when simulating a communication link, the impulse response $ h(t) $ is sampled with a sample period $ T_s $ that is related to the symbol rate of the system of investigation (often 2-8 times higher). Hence, the impulse response of the channel can now be modeled as a time-discrete filter or tapped-delay line (TDL) where the delays are given as $ \tau_k = d_k T_s $, and $ d_k $ are positive integers.

Line of Sight (LOS) or Rice Fading

If there is a line of sight (LOS) between the transmitter and receiver the first component received (or a few first) will have a static component that depends only on the Doppler frequency. In practice the difference in time between the first LOS component(s) and the reflected components is small and hence in a discretized system the first tap is usually modeled as a LOS component and a fading component. Such a process is usually called a Rice fading process.

The LOS component can be expressed as:

\[ \rho \exp(2 \pi f_\rho t + \theta_\rho), \]

where $ \rho $, $ f_\rho $, and $ \theta_\rho $ are the amplitude, Doppler frequency and phase of the LOS component, respectively. Instead of stating the amplitude itself, the ratio of the LOS power and total fading process power, called the Rice factor (or relative power), is often used. The Doppler frequency is limited by the maximum Doppler frequency $ f_\mathrm{max} $ and hence typically the Doppler of the LOS is expressed relative to its maximum (common is $ f_\rho = 0.7 f_\mathrm{max} $). The phase is usually assumed to be random and can without loss of generality be set to 0 (does not affect the statistics of the process).

References

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