Communication Channel Models
Communication Channel Models.
More...
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Classes |
class | itpp::Fading_Generator |
| Fading generator class. More...
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class | itpp::Rice_Fading_Generator |
| Rice type Fading generator class. More...
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class | itpp::FIR_Fading_Generator |
| FIR type Fading generator class. More...
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class | itpp::IFFT_Fading_Generator |
| IFFT type Fading generator class. More...
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class | itpp::Channel_Specification |
| General specification of a time-domain multipath channel. More...
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class | itpp::TDL_Channel |
| Tapped Delay Line (TDL) channel model. More...
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class | itpp::BSC |
| A Binary Symetric Channel with crossover probability p. More...
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class | itpp::AWGN_Channel |
| Ordinary AWGN Channel for cvec or vec inputs and outputs. More...
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Enumerations |
enum | itpp::DOPPLER_SPECTRUM {
itpp::Jakes = 0,
itpp::J = 0,
itpp::Classic = 0,
itpp::C = 0,
itpp::GaussI = 1,
itpp::GI = 1,
itpp::G1 = 1,
itpp::GaussII = 2,
itpp::GII = 2,
itpp::G2 = 2,
itpp::Rice = 3,
itpp::R = 3
} |
| Predefined doppler spectra. More...
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enum | itpp::RICE_METHOD { itpp::MEDS
} |
| Methods calculation of parameters using the Rice fading generation method. More...
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enum | itpp::FADING_GENERATION_METHOD { itpp::IFFT,
itpp::FIR,
itpp::Rice_MEDS
} |
| Fading generation methods. More...
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enum | itpp::CHANNEL_PROFILE {
itpp::ITU_Vehicular_A,
itpp::ITU_Vehicular_B,
itpp::ITU_Pedestrian_A,
itpp::ITU_Pedestrian_B,
itpp::COST207_RA,
itpp::COST207_RA6,
itpp::COST207_TU,
itpp::COST207_TU6alt,
itpp::COST207_TU12,
itpp::COST207_TU12alt,
itpp::COST207_BU,
itpp::COST207_BU6alt,
itpp::COST207_BU12,
itpp::COST207_BU12alt,
itpp::COST207_HT,
itpp::COST207_HT6alt,
itpp::COST207_HT12,
itpp::COST207_HT12alt,
itpp::COST259_TUx,
itpp::COST259_RAx,
itpp::COST259_HTx
} |
| Predefined channel profiles. Includes settings for doppler spectrum. More...
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Functions |
vec | itpp::jake_filter (double NormFDopp, int order=100) |
| Jakes spectrum filter.
|
Detailed Description
Communication Channel Models.
- Author:
- Tony Ottosson
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,
as
where
is the transmitted signal and
is the complex channel coefficient (or fading process). If this process is modeled as a Rayleigh fading process then
is a complex Gaussian process and the envelope
is Rayleigh distributed.
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,
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
where
is the maximum doppler frequency given by
Here
is the speed of light and
is the carrier frequency. Often the maximum doppler frequency is given as the normalized doppler
, where
is the sample duration (often the symbol time) of the simulated system. Instead of specifing the correlation fuction
we can specify the doppler spectrum (the fourier transform of
).
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
where
is the number of channel taps,
is the average amplitude at delay
, and
is the channel phase of the
th channel tap. The average power profile, and the delay profiles are defined as:
and
respectively. We assume without loss of generality that
and
. Now the received signal is simpy a linear filtering (or convolution of the transmitted signal) where,
is impulse response of the filter.
In practise, when simulating a communication link, the impulse response
is sampled with a sample period
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
, and
are positive integers.
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:
where
,
, and
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
and hence typically the doppler of the LOS is expressed relative to its maximum (common is
). 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).
[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
Predefined doppler spectra.
- Enumerator:
-
Jakes |
|
J |
|
Classic |
|
C |
|
GaussI |
|
GI |
|
G1 |
|
GaussII |
|
GII |
|
G2 |
|
Rice |
|
R |
|
Definition at line 172 of file channel.h.
Methods calculation of parameters using the Rice fading generation method.
- Enumerator:
-
Definition at line 178 of file channel.h.
Fading generation methods.
- Enumerator:
-
Definition at line 185 of file channel.h.
Predefined channel profiles. Includes settings for doppler spectrum.
- Enumerator:
-
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 |
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COST207_HT12 |
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COST207_HT12alt |
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COST259_TUx |
|
COST259_RAx |
|
COST259_HTx |
|
Definition at line 191 of file channel.h.
Function Documentation
vec itpp::jake_filter |
( |
double |
NormFDopp, |
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int |
order = 100 | |
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) |
| | |
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::concat(), itpp::elem_mult(), itpp::floor(), itpp::hamming(), itpp::norm(), itpp::pi, itpp::reverse(), and itpp::sqrt().
Referenced by itpp::FIR_Fading_Generator::init().
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