CECCO::AWGN Class Reference

Additive White Gaussian Noise channel for complex-valued symbols. More...

#include <blocks.hpp>

Inheritance diagram for CECCO::AWGN:

Public Member Functions
	AWGN (double EbNodB, double a, double b)
	Construct with SNR and constellation parameters.
std::complex< double >	operator() (const std::complex< double > &in)
	Add Gaussian noise to a complex symbol.
double	get_capacity () const noexcept
	Shannon capacity in bits per symbol (real signaling).
Noise Parameters
double	get_variance () const noexcept
	Noise variance σ² (per real component).
double	get_standard_deviation () const noexcept
	Noise standard deviation σ (per real component).
constexpr double	get_pe () const noexcept
	Theoretical hard-decision bit error probability for the configured constellation/SNR.
Public Member Functions inherited from CECCO::details::BlockProcessor< T, ElementType, ElementType >
Vector< ElementType >	operator() (const Vector< ElementType > &in)
	Apply the block element-wise to each vector entry.
Vector< ElementType >	operator() (Vector< ElementType > &&in)
	Apply the block element-wise (rvalue input).
Matrix< ElementType >	operator() (const Matrix< ElementType > &in)
	Apply the block element-wise to each matrix entry.
Matrix< ElementType >	operator() (Matrix< ElementType > &&in)
	Apply the block element-wise (rvalue input).
ElementType	operator() (const U &)
	Catch-all for inputs whose element type differs from InputType.
Vector< ElementType >	operator() (const Vector< U > &)
Matrix< ElementType >	operator() (const Matrix< U > &)

Additional Inherited Members
Protected Member Functions inherited from CECCO::details::BlockProcessor< T, ElementType, ElementType >
const T &	derived () const noexcept
T &	derived () noexcept

Detailed Description

Additive White Gaussian Noise channel for complex-valued symbols.

Adds independent 𝒩(0, σ²) noise to the real and imaginary parts of each input symbol. The noise variance is derived from the SNR Eb/N₀ and the constellation parameters supplied at construction: σ² = Eb / (2 · 10^(EbN0dB/10)).

For NRZ/BPSK input the bit error probability after a hard decision is Pe = ½ · erfc(√( b²·Eb/N₀ / (4·Eb) )), available via get_pe.

BPSKMapper map;
AWGN awgn(6.0, map.get_a(), map.get_b());        // 6 dB Eb/N₀
Vector<Fp<2>> message = {0, 1, 1, 0};
Vector<std::complex<double>> y = message >> map >> awgn;

See also

CECCO::NRZMapper, CECCO::BPSKMapper, CECCO::BI_AWGN, CECCO::LLRCalculator

Definition at line 539 of file blocks.hpp.

Constructor & Destructor Documentation

AWGN()

CECCO::AWGN::AWGN ( double EbNodB, double a, double b )

inline

Construct with SNR and constellation parameters.

Parameters

EbNodB	SNR Eb/N₀ in dB
a	DC offset of the source constellation
b	Constellation distance of the source constellation

Definition at line 550 of file blocks.hpp.

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Member Function Documentation

get_capacity()

double CECCO::AWGN::get_capacity ( ) const

inlinenoexcept

Shannon capacity in bits per symbol (real signaling).

Returns

C = ½·log₂(1 + Eb/σ²) for one real dimension (NRZ/BPSK).

For complex signaling with noise on both I and Q the formula is C = log₂(1 + Eb/(2σ²)).

Definition at line 589 of file blocks.hpp.

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get_pe()

double CECCO::AWGN::get_pe ( ) const

inlineconstexprnoexcept

Theoretical hard-decision bit error probability for the configured constellation/SNR.

Definition at line 569 of file blocks.hpp.

get_standard_deviation()

double CECCO::AWGN::get_standard_deviation ( ) const

inlinenoexcept

Noise standard deviation σ (per real component).

Definition at line 566 of file blocks.hpp.

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get_variance()

double CECCO::AWGN::get_variance ( ) const

inlinenoexcept

Noise variance σ² (per real component).

Definition at line 560 of file blocks.hpp.

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operator()()

std::complex< double > CECCO::AWGN::operator() ( const std::complex< double > & in )

inline

Add Gaussian noise to a complex symbol.

Parameters

in	Input symbol

Returns

Symbol with independent Gaussian noise added to each real component

Definition at line 578 of file blocks.hpp.

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The documentation for this class was generated from the following file:

• blocks.hpp