Base class for N-dimensional vector (MIMO) channel modulators/demodulators with real-valued components. More...

#include <itpp/comm/modulator_nd.h>

Inheritance diagram for itpp::Modulator_NRD:

Public Types
enum	Soft_Demod_Method { FULL_ENUM_LOGMAP, FULL_ENUM_MAXLOG, ZF_LOGMAP }
	Soft demodulation method. More...

Public Member Functions
	Modulator_NRD ()
	Constructor.

virtual	~Modulator_NRD ()
	Destructor.

Array< vec >	get_symbols () const
	Get modulation symbols per dimension.

void	modulate_bits (const bvec &bits, vec &symbols) const
	Modulate `bits` into `symbols`.

vec	modulate_bits (const bvec &bits) const
	Modulate `bits` vector. Symbols are returned.

void	init_soft_demodulator (const itpp::mat &H, const double &sigma2)
	Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.

void	demodulate_soft_bits (const vec &y, const QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori, Soft_Demod_Method method=FULL_ENUM_LOGMAP)
	Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.

void	demodulate_soft_bits (const vec &y, const mat &H, double sigma2, const QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori, Soft_Demod_Method method=FULL_ENUM_LOGMAP)
	Soft demodulation wrapper function for various methods.

QLLRvec	demodulate_soft_bits (const vec &y, const mat &H, double sigma2, const QLLRvec &LLR_apriori, Soft_Demod_Method method=FULL_ENUM_LOGMAP)
	Soft demodulation wrapper function for various methods.

void	demodulate_soft_bits (const vec &y, const vec &h, double sigma2, const QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori)
	Soft MAP demodulation for parallelchannels without crosstalk.

void	set_llrcalc (LLR_calc_unit llrcalc_in)
	Set LLR calculation unit.

LLR_calc_unit	get_llrcalc () const
	Get LLR calculation unit.

int	get_dim () const
	Get number of dimensions.

ivec	get_k () const
	Get number of bits per modulation symbol per dimension.

ivec	bits_per_symbol () const
	Get number of bits per modulation symbol per dimension.

ivec	get_M () const
	Get number of modulation symbols per dimension.

Array< ivec >	get_bits2symbols () const
	Get bit pattern in decimal.

Array< bmat >	get_bitmap () const
	Get Bit mapping table.

Protected Member Functions
void	update_norm (double &norm, int k, int sold, int snew, const vec &ytH, const mat &HtH, const ivec &s)
	Update residual norm (for internal use).

void	hxnormupdate (itpp::vec &Hx, unsigned &bitstring, unsigned &ind, unsigned bit)
	Calculation of the part of the norms that depends on H.

void	yxnormupdate (double &yx, itpp::QLLR &lapr, unsigned &bitstring, unsigned &ind, unsigned bit)
	Calculation of the remaining part of the norms that depends both on H and y.

QLLRvec	probabilities (QLLR l)
	Convert LLR to log-probabilities.

Array< QLLRvec >	probabilities (const QLLRvec &l)
	Convert LLR to log-probabilities, vector version.

void	marginalize_bits (itpp::QLLRvec &llr, Soft_Demod_Method method) const
	Marginalize (sum) over the bits.

void	demodllrbit0 (itpp::QLLR &llr) const
	Hardcoded implementation of 1:st bit demodulation.

void	demodllrbit1 (itpp::QLLR &llr) const
	Hardcoded implementation of 2:nd bit demodulation.

void	demodllrbit2 (itpp::QLLR &llr) const
	Hardcoded implementation of 3:rd bit demodulation.

void	demodmaxbit0 (itpp::QLLR &maxllr) const
	Hardcoded implementation of 1:st bit demodulation.

void	demodmaxbit1 (itpp::QLLR &maxllr) const
	Hardcoded implementation of 2:nd bit demodulation.

void	demodmaxbit2 (itpp::QLLR &maxllr) const
	Hardcoded implementation of 3:rd bit demodulation.

void	update_LLR (const Array< QLLRvec > &logP_apriori, const ivec &s, QLLR scaled_norm, QLLRvec &num, QLLRvec &denom)
	Update LLR (for internal use)

void	update_LLR (const Array< QLLRvec > &logP_apriori, int s, QLLR scaled_norm, int j, QLLRvec &num, QLLRvec &denom)
	Update LLR, for scalar channel (for internal use)

Protected Attributes
Array< vec >	symbols
	Vectors of modulation symbols (along each dimension)

itpp::mat	H
	Real channel matrix.

itpp::Array< itpp::Array < itpp::vec > >	hspacings
	The spacing between different constellation points multiplied by the different H columns.

itpp::Array< itpp::vec >	yspacings
	The spacing between different constellation points scaled by different y elements.

int	nt
	Number of dimensions.

int	nb
	Number of bits in the symbol vector.

LLR_calc_unit	llrcalc
	LLR calculation unit.

ivec	k
	Number of bits per modulation symbol.

ivec	M
	Number of modulation symbols along each dimension.

bool	demod_initialized
	Flag indicating whether the demodulator has been initialized.

Array< bmat >	bitmap
	Bit mapping table (one table per dimension)

Array< ivec >	bits2symbols
	Bit pattern in decimal form ordered and the corresponding symbols (one pattern per dimension)

double	gaussnorm
	The normalization factor in the exponent (in front of the square norm) in the Gaussian distribution.

itpp::vec	hnorms
	Norms part dependent on H.

itpp::QLLRvec	Qnorms
	Norms part depending on both H and y.

itpp::QLLRvec	llrapr
	A prioi information.

itpp::ivec	bpos2cpos
	The bit to column mapping.

itpp::ivec	bitcumsum
	The cumulative sum of bits in the symbol vector.

itpp::Array< itpp::Vec < unsigned > >	gray2dec
	The Gray to decimal mapping.

Friends
ITPP_EXPORT std::ostream &	operator<< (std::ostream &os, const Modulator_NRD &m)
	Output some properties of the MIMO modulator (mainly to aid debugging)

Related Functions
(Note that these are not member functions.)
ITPP_EXPORT std::ostream &	operator<< (std::ostream &os, const Modulator_NRD &m)
	Print some properties of the MIMO modulator (mainly to aid debugging)

Detailed Description

Base class for N-dimensional vector (MIMO) channel modulators/demodulators with real-valued components.

This class can be used to perform modulation and demodulation for a matrix (MIMO) channel of the form

$y = Hx+e$

, where H is the channel matrix of dimension $n_r\times n_t$ , $y$ is a received vector of length $n_r$ , $x$ is a transmitted vector of length $n_t$ and $e$ is a noise vector.

The class supports soft-input soft-output demodulation. It can also be used for scalar modulation to take advantage of this feature.

Complex MIMO channels can be handled by using the Modulator_NCD class. Alternatively, if the signal constellation is separable in I/Q then the complex channel can be first transformed to a real channel

$G = \left[ \begin{array}{cc} H_r & -H_i \\ H_i & H_r \end{array} \right]$

See ND_UPAM for examples.

Note: For issues relating to the accuracy of LLR computations, please see the documentation of LLR_calc_unit

Definition at line 248 of file modulator_nd.h.

Member Enumeration Documentation

enum itpp::Modulator_ND::Soft_Demod_Method

inherited

Soft demodulation method.

Enumerator:

FULL_ENUM_LOGMAP	Log-MAP demodulation by "brute-force" enumeration of all points.
FULL_ENUM_MAXLOG	Max-Log demodulation by "brute-force" enumeration of all points.
ZF_LOGMAP	Zero-Forcing Log-MAP approximated demodulation.

Definition at line 67 of file modulator_nd.h.

Member Function Documentation

void itpp::Modulator_NRD::init_soft_demodulator	(	const itpp::mat &	H,
		const double &	sigma2
	)

Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.

This function precomputes the norms

$\frac{|Hs|^2}{2\sigma^2}$

used to compute the LLR values

$LLR(k) = \log \left( \frac {\sum_{s:b_k=0} \exp \left( -\frac{|y - Hs|^2}{2\sigma^2} \right) P(s)} {\sum_{s:b_k=1} \exp \left( -\frac{|y - Hs|^2}{2\sigma^2} \right) P(s)} \right)$

without approximations. It is assumed that H is real-valued. Complex-valued channels can be handled using the Modulator_NCD class.

Definition at line 486 of file modulator_nd.cpp.

References itpp::Modulator_ND::bitcumsum, itpp::Modulator_ND::bits2symbols, itpp::Modulator_ND::bpos2cpos, itpp::cumsum(), itpp::Modulator_ND::demod_initialized, itpp::Modulator_ND::gaussnorm, itpp::Modulator_ND::gray2dec, itpp::Modulator_ND::hnorms, it_assert, itpp::Modulator_ND::k, itpp::Modulator_ND::M, itpp::Modulator_ND::nb, itpp::Modulator_ND::nt, itpp::pow2i(), itpp::prod(), itpp::Modulator_ND::Qnorms, itpp::reverse(), itpp::Array< T >::set_size(), and itpp::sum().

void itpp::Modulator_NRD::demodulate_soft_bits	(	const vec &	y,
		const QLLRvec &	LLR_apriori,
		QLLRvec &	LLR_aposteriori,
		Soft_Demod_Method	method = `FULL_ENUM_LOGMAP`
	)

Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.

This function computes the LLR values

$LLR(k) = \log \left( \frac {\sum_{s:b_k=0} \exp \left( -\frac{|y - Hs|^2}{2\sigma^2} \right) P(s)} {\sum_{s:b_k=1} \exp \left( -\frac{|y - Hs|^2}{2\sigma^2} \right) P(s)} \right)$

without approximations. It is assumed that H, y and s are real-valued. Complex-valued channels can be handled using the Modulator_NCD class. Currently the following two demodulation methods are supported:

FULL_ENUM_LOGMAP - exact demodulation, which use "brute-force" enumeration of all constellation points
FULL_ENUM_MAXLOG - max-log approximate demodulation, which use "brute-force" enumeration to find the constellation points that give the smallest euclidian distances

Parameters

[in]	y	Received vector (typically )
[in]	LLR_apriori	Vector of a priori LLR values per bit
[out]	LLR_aposteriori	Vector of a posteriori LLR values
[in]	method	Soft demodulation method

The function performs an exhaustive search over all possible points s in the n-dimensional constellation. This is only feasible for relatively small constellations. The Jacobian logarithm is used to compute the sum-exp expression.

void itpp::Modulator_NRD::demodulate_soft_bits	(	const vec &	y,
		const mat &	H,
		double	sigma2,
		const QLLRvec &	LLR_apriori,
		QLLRvec &	LLR_aposteriori,
		Soft_Demod_Method	method = `FULL_ENUM_LOGMAP`
	)

Soft demodulation wrapper function for various methods.

Currently the following three demodulation methods are supported:

FULL_ENUM_LOGMAP - exact demodulation, which use "brute-force" enumeration of all constellation points
FULL_ENUM_MAXLOG - max-log approximate demodulation, which use "brute-force" enumeration to find the constellation points that give the smallest euclidian distances
ZF_LOGMAP - approximated methods with Zero-Forcing preprocessing, which sometimes tends to perform poorly, especially for poorly conditioned H

Parameters

[in]	y	Received vector
[in]	H	Channel matrix
[in]	sigma2	Noise variance per real dimension (typically )
[in]	LLR_apriori	Vector of a priori LLR values per bit
[out]	LLR_aposteriori	Vector of a posteriori LLR values
[in]	method	Soft demodulation method

Definition at line 560 of file modulator_nd.cpp.

References itpp::inv(), it_assert, itpp::Modulator_ND::k, itpp::ones(), itpp::sqrt(), itpp::sum(), itpp::zeros_i(), and itpp::Modulator_ND::ZF_LOGMAP.

QLLRvec itpp::Modulator_NRD::demodulate_soft_bits	(	const vec &	y,
		const mat &	H,
		double	sigma2,
		const QLLRvec &	LLR_apriori,
		Soft_Demod_Method	method = `FULL_ENUM_LOGMAP`
	)

Soft demodulation wrapper function for various methods.

Currently the following two demodulation methods are supported:

FULL_ENUM_LOGMAP - exact demodulation, which use "brute-force" enumeration of all constellation points
ZF_LOGMAP - approximated methods with Zero-Forcing preprocessing, which sometimes tends to perform poorly, especially for poorly conditioned H

Parameters

[in]	y	Received vector
[in]	H	Channel matrix
[in]	sigma2	Noise variance per real dimension (typically )
[in]	LLR_apriori	Vector of a priori LLR values per bit
[in]	method	Soft demodulation method

Returns: Vector of a posteriori LLR values

Definition at line 591 of file modulator_nd.cpp.

void itpp::Modulator_NRD::demodulate_soft_bits	(	const vec &	y,
		const vec &	h,
		double	sigma2,
		const QLLRvec &	LLR_apriori,
		QLLRvec &	LLR_aposteriori
	)

Soft MAP demodulation for parallelchannels without crosstalk.

This function is a much faster equivalent to demodulate_soft_bits with $H = \mbox{diag}(h)$ . Its complexity is linear in the number of subchannels.

Definition at line 601 of file modulator_nd.cpp.

References it_assert, itpp::Modulator_ND::k, itpp::length(), itpp::Modulator_ND::llrcalc, itpp::Modulator_ND::M, itpp::Modulator_ND::nt, itpp::ones_i(), itpp::Modulator_ND::probabilities(), itpp::sqr(), itpp::sum(), itpp::LLR_calc_unit::to_qllr(), and itpp::Modulator_ND::update_LLR().

void itpp::Modulator_NRD::update_norm	(	double &	norm,
		int	k,
		int	sold,
		int	snew,
		const vec &	ytH,
		const mat &	HtH,
		const ivec &	s
	)

protected

Update residual norm (for internal use).

Update the residual norm $|y-Hs|$ when moving from one constellation point to an adjacent point.

Parameters

[in,out]	norm	Norm to be updated
[in]	k	Position where s changed
[in]	sold	Old value of s[k]
[in]	snew	New value of s[k]
[in]	ytH	y'H vector
[in]	HtH	Grammian matrix H'H
[in]	s	Symbol vector

void itpp::Modulator_ND::update_LLR	(	const Array< QLLRvec > &	logP_apriori,
		const ivec &	s,
		QLLR	scaled_norm,
		QLLRvec &	num,
		QLLRvec &	denom
	)

protectedinherited

Update LLR (for internal use)

This function updates the numerator and denominator in the expression

$\log \left( \frac {\sum_{s:b_k=0} \exp(-x^2) P(s)} {\sum_{s:b_k=1} \exp(-x^2) P(s)} \right)$

Parameters

[in]	logP_apriori	Vector of a priori probabilities per bit
[in]	s	Symbol vector
[in]	scaled_norm	Argument of the exponents in the above equation
[out]	num	Logarithm of the numerator in the above expression
[out]	denom	Logarithm of the denominator in the above expression

Definition at line 94 of file modulator_nd.cpp.

References itpp::Modulator_ND::bitmap, itpp::LLR_calc_unit::jaclog(), itpp::Modulator_ND::k, itpp::Modulator_ND::llrcalc, and itpp::Modulator_ND::nt.

Referenced by demodulate_soft_bits(), and itpp::Modulator_NCD::demodulate_soft_bits().

void itpp::Modulator_ND::update_LLR	(	const Array< QLLRvec > &	logP_apriori,
		int	s,
		QLLR	scaled_norm,
		int	j,
		QLLRvec &	num,
		QLLRvec &	denom
	)

protectedinherited

Update LLR, for scalar channel (for internal use)

This function updates the numerator and denominator in the expression

$\log \left( \frac {\sum_{s:b_k=0} \exp (-x^2) P(s)} {\sum_{s:b_k=1} \exp (-x^2) P(s)} \right)$

Parameters

[in]	logP_apriori	Vector of a priori probabilities per bit
[in]	s	Symbol
[in]	scaled_norm	Argument of the exponents in the above equation
[in]	j	Channel index (dimension)
[out]	num	Logarithm of the numerator in the above expression
[out]	denom	Logarithm of the denominator in the above expression

Definition at line 68 of file modulator_nd.cpp.

References itpp::Modulator_ND::bitmap, itpp::LLR_calc_unit::jaclog(), itpp::Modulator_ND::k, and itpp::Modulator_ND::llrcalc.

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

itpp/comm/modulator_nd.h
itpp/comm/modulator_nd.cpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Related Functions

Detailed Description

Member Enumeration Documentation

Member Function Documentation