Communication Channel Models

Communication Channel Models. More...


Classes
class	itpp::Fading_Generator
	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::DOPPLER_SPECTRUM { Jakes = 0, J = 0, Classic = 0, C = 0, GaussI = 1, GI = 1, G1 = 1, GaussII = 2, GII = 2, G2 = 2, Rice = 3, R = 3 }
	Predefined doppler spectra. More...
enum	itpp::RICE_METHOD { MEDS }
	Methods calculation of parameters using the Rice fading generation method. More...
enum	itpp::FADING_GENERATION_METHOD { IFFT, FIR, Rice_MEDS }
	Fading generation methods. More...
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 settings for doppler spectrum. More...
Functions
vec	itpp::jake_filter (double NormFDopp, int order)
	Jakes spectrum filter.

Detailed Description

Communication Channel Models.

Author:: Tony Ottosson

Modelling and simulation of communication channels

Introduction

Introduction

When simulating a communication link a model of the channel behaviour is usually needed. These models 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) around the receiver. Mathematically we write the receieved 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 exist of this correlation 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 specifing the correlation fuction $R(\tau)$ we can specify the doppler spectrum (the fourier transform of $R(\tau)$ ).

Frequency-selective channels

Since

affects the transmitted signal as a constant scaling factor at a given time this channel model is often refered 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 sample times) 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 profile, and the 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 simpy a linear filtering (or convolution of the transmitted signal) where, $h(t)$ is impulse response of the filter.

In practise, 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 respone 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 line of sight (LOS) between transmitter and receiver the first component received (shortest delay) will have a static component that only depend on the doppler frequency. In practise the difference in time between the first LOS component and the first refelcted 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 the fading process power (or relative power), often called the Rice factor, is often stated. 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

[Patzold] Matthias Patzold, Mobile fading channels, Wiley, 2002.

[Stuber] Gordon L. Stuber, Principles of mobile communication, 2nd. ed., Kluwer, 2001.

[Rappaport] Theodore S. Rappaport, Wireless communications: principles and practise, Prentice Hall, 1996.

Enumeration Type Documentation

enum DOPPLER_SPECTRUM

Predefined doppler spectra.

Definition at line 172 of file channel.h.
Referenced by itpp::Fading_Generator::get_doppler_spectrum().

enum RICE_METHOD

Methods calculation of parameters using the Rice fading generation method.

Definition at line 178 of file channel.h.

enum FADING_GENERATION_METHOD

Fading generation methods.

Definition at line 185 of file channel.h.

enum CHANNEL_PROFILE

Predefined channel profiles. Includes settings for doppler spectrum.

Definition at line 191 of file channel.h.

Function Documentation

vec itpp::jake_filter ( double NormFDopp,

int order = 100

)

Jakes spectrum filter.
Function that generates the taps in the Jake-filter. order is the number of taps in the filter. NormFdopp is the normalized doppler frequency, i.e. NormFDopp = Fd * Ts, where Fd is the acctual Doppler frequency and Ts is the sampling interval. Returns a vector containing the filter taps of the Jake-filter.
Definition at line 44 of file channel.cpp.
References itpp::besselj(), itpp::floor(), itpp::hamming(), itpp::norm(), itpp::reverse(), and itpp::sqrt().

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