itpp::ND_UPAM Class Reference
[Digital Modulation]

Real-valued MIMO channel with uniform PAM along each dimension. More...

#include <modulator_nd.h>

List of all members.

Public Types

enum Soft_Demod_Method { FULL_ENUM_LOGMAP, ZF_LOGMAP }

Soft demodulation method. More...

Public Member Functions

ND_UPAM (int nt=1, int Mary=2)

Constructor.

~ND_UPAM ()

Destructor.

void set_M (int nt=1, int Mary=2)

Set component modulators to M-PAM with Gray mapping.

void set_M (int nt=1, ivec Mary="2")

Set component modulators to M-PAM with Gray mapping, different M per component.

int sphere_decoding (const vec &y, const mat &H, double rmin, double rmax, double stepup, QLLRvec &detected_bits)

Sphere decoding.

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 demodulate_soft_bits (const vec &y, const mat &H, double sigma2, const QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori, Soft_Demod_Method method)

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)

Soft demodulation wrapper function for various methods.

void demodulate_soft_bits (const vec &y, const mat &H, double sigma2, const QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori)

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

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 get_M () const

Get number of modulation symbols per dimension.

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).

QLLRvec probabilities (QLLR l)

Convert LLR to log-probabilities.

Array< QLLRvec > probabilities (const QLLRvec &l)

Convert LLR to log-probabilities, vector version.

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).

int nt

Number of dimensions.

LLR_calc_unit llrcalc

LLR calculation unit.

ivec k

Number of bits per modulation symbol.

ivec M

Number of modulation symbols along each dimension.

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).

Friends

std::ostream & operator<< (std::ostream &os, const Modulator_NRD &m)

Output some properties of the MIMO modulator (mainly to aid debugging).

Detailed Description

Real-valued MIMO channel with uniform PAM along each dimension.

Example: (4 x 3 matrix channel with 4-PAM)

 ND_UPAM chan; // multidimensional channel with uniform PAM
 chan.set_M(3, 4); // 3-dimensional matrix channel, 4-PAM per dimension
 cout << chan << endl;
 bvec b = randb(3*2); // 3*2 bits in total
 vec x = chan.modulate_bits(b);
 mat H = randn(4,3); // 4 x 3 real matrix channel
 double sigma2 = 0.01; // noise variance per real dimension
 vec y = H*x + sqrt(sigma2)*randn(4); // transmit vector x
 QLLRvec llr; // log-likelihood ratios
 QLLRvec llr_ap = zeros_i(3*2);  // a priori equiprobable bits
 chan.demodulate_soft_bits(y, H, sigma2, llr_ap, llr);
 cout << "True bits:" << b << endl;
 cout << "LLRs:" << chan.get_llrcalc().to_double(llr) << endl;

Example: (scalar channel with 8-PAM)

 ND_UPAM chan;
 chan.set_M(1, 8); // scalar channel, 8-PAM (3 bits per symbol)
 cout << chan << endl;
 bvec b = randb(3);
 vec x = chan.modulate_bits(b);
 mat H = "1.0";      // scalar channel
 double sigma2 = 0.01;
 vec y= H*x + sqrt(sigma2)*randn(); // transmit vector x
 QLLRvec llr;
 QLLRvec llr_ap = zeros_i(3);
 chan.demodulate_soft_bits(y, H, sigma2, llr_ap, llr);
 cout << "True bits:" << b << endl;
 cout << "LLRs:" << chan.get_llrcalc().to_double(llr) << endl;

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.
ZF_LOGMAP	Zero-Forcing Log-MAP approximated demodulation.

Member Function Documentation

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

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.

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::Modulator_NRD::symbols, itpp::LLR_calc_unit::to_qllr(), and itpp::Modulator_ND::update_LLR().

void itpp::Modulator_NRD::demodulate_soft_bits	(	const vec &	y,
		const mat &	H,
		double	sigma2,
		const QLLRvec &	LLR_apriori,
		QLLRvec &	LLR_aposteriori
	)			`[inherited]`

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.

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

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.

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

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

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

References itpp::Modulator_NRD::demodulate_soft_bits().

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
	)			`[inherited]`

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
`[out]`	LLR_aposteriori	Vector of a posteriori LLR values
`[in]`	method	Soft demodulation method

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

Referenced by itpp::Modulator_NRD::demodulate_soft_bits().

int itpp::ND_UPAM::sphere_decoding	(	const vec &	y,
		const mat &	H,
		double	rmin,
		double	rmax,
		double	stepup,
		QLLRvec &	detected_bits
	)

Sphere decoding.

This function solves the integer-constrained minimization problem

$\mbox{min} |y - Hs|$

with respect to $s$ using a sphere decoding algorithm and the Schnorr-Eucner search strategy (see the source code for further implementation notes). The function starts with an initial search radius and increases it with a factor (stepup) until the search succeeds.

Parameters:

`[in]`	y	received data vector ( $n_r\times 1$ )
`[in]`	H	channel matrix ( $n_r\times n_t$ )
`[in]`	rmax	maximum possible sphere radius to try
`[in]`	rmin	sphere radius in the first try
`[in]`	stepup	factor with which the sphere radius is increased if the search fails
`[out]`	detected_bits	result of the search (hard decisions only, QLLR for a sure "1" is set to 1000)

Returns:: status of the decoding: 0 if the search suceeds, -1 otherwise

References itpp::Modulator_ND::bitmap, it_assert, itpp::Modulator_ND::k, itpp::length(), itpp::Modulator_ND::M, itpp::Modulator_ND::nt, and itpp::sum().

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

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

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

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

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

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 itpp::Modulator_NCD::demodulate_soft_bits(), and itpp::Modulator_NRD::demodulate_soft_bits().

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

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

References itpp::length(), itpp::sqr(), and itpp::Modulator_NRD::symbols.

Referenced by itpp::Modulator_NRD::demodulate_soft_bits().

Friends And Related Function Documentation

std::ostream & operator<<	(	std::ostream &	os,
		const Modulator_NRD &	m
	)			`[friend, inherited]`

Output some properties of the MIMO modulator (mainly to aid debugging).

Print some properties of the MIMO modulator (mainly to aid debugging).

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


Public Types
enum	Soft_Demod_Method { FULL_ENUM_LOGMAP, ZF_LOGMAP }
	Soft demodulation method. More...
Public Member Functions
	ND_UPAM (int nt=1, int Mary=2)
	Constructor.
	~ND_UPAM ()
	Destructor.
void	set_M (int nt=1, int Mary=2)
	Set component modulators to M-PAM with Gray mapping.
void	set_M (int nt=1, ivec Mary="2")
	Set component modulators to M-PAM with Gray mapping, different M per component.
int	sphere_decoding (const vec &y, const mat &H, double rmin, double rmax, double stepup, QLLRvec &detected_bits)
	Sphere decoding.
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	demodulate_soft_bits (const vec &y, const mat &H, double sigma2, const QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori, Soft_Demod_Method method)
	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)
	Soft demodulation wrapper function for various methods.
void	demodulate_soft_bits (const vec &y, const mat &H, double sigma2, const QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori)
	Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.
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	get_M () const
	Get number of modulation symbols per dimension.
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).
QLLRvec	probabilities (QLLR l)
	Convert LLR to log-probabilities.
Array< QLLRvec >	probabilities (const QLLRvec &l)
	Convert LLR to log-probabilities, vector version.
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).
int	nt
	Number of dimensions.
LLR_calc_unit	llrcalc
	LLR calculation unit.
ivec	k
	Number of bits per modulation symbol.
ivec	M
	Number of modulation symbols along each dimension.
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).
Friends
std::ostream &	operator<< (std::ostream &os, const Modulator_NRD &m)
	Output some properties of the MIMO modulator (mainly to aid debugging).

itpp::ND_UPAM Class Reference [Digital Modulation]

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Member Enumeration Documentation

Member Function Documentation

Friends And Related Function Documentation

itpp::ND_UPAM Class Reference
[Digital Modulation]