itpp::ND_UPAM

itpp::ND_UPAM Class Reference

Multidimensional channel with uniform PAM along each dimension. More...

#include <itpp/comm/modulator_nd.h>

Inheritance diagram for itpp::ND_UPAM:


Public Member Functions
	ND_UPAM (int nt_in=1, int Mary=2)
	Constructor.
	~ND_UPAM ()
	Destructor.
void	set_Gray_PAM (int nt_in=1, int Mary=2)
	Set component modulators to M-PAM with Gray mapping.
void	set_Gray_PAM (int nt_in=1, ivec Mary="2")
	Set component modulators to M-PAM with Gray mapping, different M per component.
int	sphere_decoding (vec &y, mat &H, double rmin, double rmax, double stepup, QLLRvec &detected_bits)
	Sphere decoding.
void	ZF_demod (QLLRvec &detected_bits, double sigma2, mat &H, vec &y)
	ZF demodulation (NOT IMPLEMENTED YET).
void	MMSE_demod (QLLRvec &detected_bits, double sigma2, mat &H, vec &y)
	MMSE demodulation (NOT IMPLEMENTED YET).
Vec< vec >	get_symbols ()
	Get modulation symbols per dimension.
vec	modulate_bits (const bvec &bits) const
	Modulation of bits.
void	map_demod (QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori, double sigma2, mat &H, vec &y)
	Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.
void	map_demod (QLLRvec &LLR_apriori, QLLRvec &LLR_aposteriori, double sigma2, vec &h, vec &y)
	Soft MAP demodulation for parallel channels without crosstalk.
int	get_dim ()
	Get number of dimensions.
LLR_calc_unit	get_llrcalc () const
	Get LLR calculation unit.
ivec	get_k ()
	Get number of bits per modulation symbol.
ivec	get_M ()
	Get number of modulation symbols per dimension.
Protected Member Functions
void	update_norm (double &norm, int k, int sold, int snew, vec &ytH, mat &HtH, ivec &s)
	For internal use only.
QLLRvec	probabilities (QLLR l)
	Convert LLR to log-probabilities.
Vec< QLLRvec >	probabilities (QLLRvec &l)
	Convert LLR to log-probabilities, vector version.
void	update_LLR (Vec< QLLRvec > &logP_apriori, QLLRvec &numerator, QLLRvec &denominator, ivec &s, QLLR x)
	Update LLR (for internal use).
void	update_LLR (Vec< QLLRvec > &logP_apriori, QLLRvec &numerator, QLLRvec &denominator, int s, QLLR scaled_norm, int j)
	Update LLR, for scalar channel (for internal use).
Protected Attributes
Vec< vec >	symbols
	Vector 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.
Vec< bmat >	bitmap
	Bit mapping table (one table per dimension).
Vec< 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 &mod)
	Print some properties of the MIMO modulator in plain text (mainly to aid debugging).

Detailed Description

Multidimensional channel with uniform PAM along each dimension.

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

  ND_UPAM chan;            // Multidimensional channel with uniform PAM 
  chan.set_Gray_PAM(3,4);  // 3-dimensional matrix channel, 4-PAM (2 bits) per dimension
  cout << chan << endl;   
  bvec b=randb(3*2);  // 3*2 bits in total    
  vec x=chan.modulate_bits(b); 
  QLLRvec llr = zeros_i(3*2);
  QLLRvec llr_ap = zeros_i(3*2);  // apriori equiprobable bits
  mat H = randn(4,3);      // 4*3 matrix channel
  double sigma2=0.01; // noise variance
  vec y= H*x + sqrt(sigma2)*randn(4); // add noise
  chan.map_demod(llr_ap, llr, sigma2, H, y);
  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_Gray_PAM(1,8);  // scalar channel, 8-PAM (3 bits)
  cout << chan << endl;   
  bvec b=randb(3);
  vec x=chan.modulate_bits(b);     
  QLLRvec llr = zeros_i(3);
  QLLRvec llr_ap = zeros_i(3);
  mat H = "1.0";      // scalar channel
  double sigma2=0.01; 
  vec y= H*x + sqrt(sigma2)*randn(1); // add noise
  chan.map_demod(llr_ap, llr, sigma2, H, y);
  cout << "True bits:" << b << endl;
  cout << "LLRs:" << chan.get_llrcalc().to_double(llr) << endl;

Definition at line 336 of file modulator_nd.h.

Constructor & Destructor Documentation

itpp::ND_UPAM::ND_UPAM	(	int	nt_in = `1`,
		int	Mary = `2`
	)

Constructor.

Definition at line 405 of file modulator_nd.cpp.

References itpp::Modulator_ND::nt, and set_Gray_PAM().

itpp::ND_UPAM::~ND_UPAM ( ) [inline]

Destructor.

Definition at line 341 of file modulator_nd.h.

Member Function Documentation

void itpp::ND_UPAM::set_Gray_PAM	(	int	nt_in = `1`,
		int	Mary = `2`
	)

Set component modulators to M-PAM with Gray mapping.

Definition at line 411 of file modulator_nd.cpp.

References itpp::Modulator_ND::nt.

Referenced by ND_UPAM().

void itpp::ND_UPAM::set_Gray_PAM	(	int	nt_in = `1`,
		ivec	Mary = `"2"`
	)

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

Definition at line 421 of file modulator_nd.cpp.

References itpp::bin2dec(), itpp::Modulator_ND::bitmap, itpp::Modulator_ND::bits2symbols, itpp::graycode(), it_assert, itpp::Modulator_ND::k, itpp::length(), itpp::log2(), itpp::Modulator_ND::M, itpp::Modulator_ND::nt, itpp::round_i(), itpp::Vec< Num_T >::set_size(), itpp::sqrt(), and itpp::Modulator_NRD::symbols.

int itpp::ND_UPAM::sphere_decoding	(	vec &	y,
		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 sphere the decoding algorithm and the Schnorr-Eucner search strategy (see 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:

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

The function returns 0 if the search suceeds, and -1 otherwise.

Definition at line 552 of file modulator_nd.cpp.

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::ND_UPAM::ZF_demod	(	QLLRvec &	detected_bits,
		double	sigma2,
		mat &	H,
		vec &	y
	)

ZF demodulation (NOT IMPLEMENTED YET).

void itpp::ND_UPAM::MMSE_demod	(	QLLRvec &	detected_bits,
		double	sigma2,
		mat &	H,
		vec &	y
	)

MMSE demodulation (NOT IMPLEMENTED YET).

Vec<vec> itpp::Modulator_NRD::get_symbols ( ) [inline, inherited]

Get modulation symbols per dimension.

Definition at line 154 of file modulator_nd.h.

References itpp::Modulator_NRD::symbols.

vec itpp::Modulator_NRD::modulate_bits ( const bvec & bits ) const [inherited]

Modulation of bits.

Returns a vector of modulated symbols.

Parameters:

bits

vector of the bits to be modulated

Definition at line 338 of file modulator_nd.cpp.

References itpp::bin2dec(), itpp::Modulator_ND::bits2symbols, it_assert, itpp::Modulator_ND::k, itpp::length(), itpp::Modulator_ND::nt, itpp::sum(), and itpp::Modulator_NRD::symbols.

void itpp::Modulator_NRD::map_demod	(	QLLRvec &	LLR_apriori,
		QLLRvec &	LLR_aposteriori,
		double	sigma2,
		mat &	H,
		vec &	y
	)			`[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 via the Modulator_NCD class.

Parameters:

	H	channel matrix (m*n)
	y	received vector (m*1)
	sigma2	noise variance, per real dimension
	LLR_apriori	vector of a priori LLR values per bit
	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.

Definition at line 192 of file modulator_nd.cpp.

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(), and itpp::Modulator_NRD::update_norm().

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

Soft MAP demodulation for parallel channels without crosstalk.

This function is equivalent to map_demod with $H=\mbox{diag}(h)$ . However, it is much faster (the complexity is linear in the number of subchannels).

Definition at line 138 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::Modulator_NRD::symbols, 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,
		vec &	ytH,
		mat &	HtH,
		ivec &	s
	)			`[protected, inherited]`

For internal use only.

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

Parameters:

	norm	The norm to be updated
	k	The position where s changed
	sold	Old value of s[k]
	snew	New value of s[k]
	ytH	The vector y'H
	HtH	The Grammian matrix H'H
	s	The s-vector

Definition at line 111 of file modulator_nd.cpp.

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

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

int itpp::Modulator_ND::get_dim ( ) [inline, inherited]

Get number of dimensions.

Definition at line 57 of file modulator_nd.h.

References itpp::Modulator_ND::nt.

LLR_calc_unit itpp::Modulator_ND::get_llrcalc ( ) const [inline, inherited]

Get LLR calculation unit.

Definition at line 60 of file modulator_nd.h.

References itpp::Modulator_ND::llrcalc.

ivec itpp::Modulator_ND::get_k ( ) [inline, inherited]

Get number of bits per modulation symbol.

Definition at line 63 of file modulator_nd.h.

References itpp::Modulator_ND::k.

ivec itpp::Modulator_ND::get_M ( ) [inline, inherited]

Get number of modulation symbols per dimension.

Definition at line 66 of file modulator_nd.h.

References itpp::Modulator_ND::M.

QLLRvec itpp::Modulator_ND::probabilities ( QLLR l ) [protected, inherited]

Convert LLR to log-probabilities.

Definition at line 44 of file modulator_nd.cpp.

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

Referenced by itpp::Modulator_NCD::map_demod(), itpp::Modulator_NRD::map_demod(), and itpp::Modulator_ND::probabilities().

Vec< QLLRvec > itpp::Modulator_ND::probabilities ( QLLRvec & l ) [protected, inherited]

Convert LLR to log-probabilities, vector version.

Definition at line 58 of file modulator_nd.cpp.

References itpp::length(), and itpp::Modulator_ND::probabilities().

void itpp::Modulator_ND::update_LLR	(	Vec< QLLRvec > &	logP_apriori,
		QLLRvec &	numerator,
		QLLRvec &	denominator,
		ivec &	s,
		QLLR	x
	)			`[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:

	logP_apriori	vector of a priori probabilities per bit
	numerator	the logarithm of the numerator in the above expression
	denominator	the logarithm of the denominator in the above expression
	s	the symbol vector

Definition at line 87 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 itpp::Modulator_NCD::map_demod(), and itpp::Modulator_NRD::map_demod().

void itpp::Modulator_ND::update_LLR	(	Vec< QLLRvec > &	logP_apriori,
		QLLRvec &	numerator,
		QLLRvec &	denominator,
		int	s,
		QLLR	scaled_norm,
		int	j
	)			`[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:

	logP_apriori	vector of a priori probabilities per bit
	numerator	the logarithm of the numerator in the above expression
	denominator	the logarithm of the denominator in the above expression
	s	the symbol vector