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/*!
* \file
* \brief Definition of vector (MIMO) modulator classes
* \author Erik G. Larsson and Adam Piatyszek
*
* -------------------------------------------------------------------------
*
* IT++ - C++ library of mathematical, signal processing, speech processing,
* and communications classes and functions
*
* Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
* -------------------------------------------------------------------------
*/
#ifndef MODULATOR_ND_H
#define MODULATOR_ND_H
#include <itpp/base/vec.h>
#include <itpp/base/array.h>
#include <itpp/comm/llr.h>
namespace itpp {
/*!
* \addtogroup modulators
*/
// ----------------------------------------------------------------------
// Modulator_ND
// ----------------------------------------------------------------------
/*!
* \ingroup modulators
* \brief Base class for an N-dimensional (ND) vector (MIMO) modulator.
*
* See \c ND_UPAM class for examples.
*
* \note Can also be used for scalar modulation/demodulation as an
* alternative to \c Modulator_1D or \c Modulator_2D. Mixed use of \c
* Modulator_1D or \c Modulator_2D and \c Modulator_ND is <b>not
* advised</b>.
*/
class Modulator_ND {
public:
//! Soft demodulation method
enum Soft_Demod_Method {
//! Log-MAP demodulation by "brute-force" enumeration of all points
FULL_ENUM_LOGMAP,
//! Zero-Forcing Log-MAP approximated demodulation
ZF_LOGMAP
};
//! Default constructor
Modulator_ND(LLR_calc_unit llrcalc_in = LLR_calc_unit()):
llrcalc(llrcalc_in) {}
//! Destructor
~Modulator_ND() {}
//! Set LLR calculation unit
void set_llrcalc(LLR_calc_unit llrcalc_in) { llrcalc = llrcalc_in; };
//! Get LLR calculation unit
LLR_calc_unit get_llrcalc() const { return llrcalc; }
//! Get number of dimensions
int get_dim() const { return nt; }
//! Get number of bits per modulation symbol per dimension
ivec get_k() const { return k; }
//! Get number of modulation symbols per dimension
ivec get_M() const { return M; }
protected:
//! Number of dimensions
int nt;
//! LLR calculation unit
LLR_calc_unit llrcalc;
//! Number of bits per modulation symbol
ivec k;
//! Number of modulation symbols along each dimension
ivec M;
//! Bit mapping table (one table per dimension)
Array<bmat> bitmap;
//! Bit pattern in decimal form ordered and the corresponding symbols (one pattern per dimension)
Array<ivec> bits2symbols;
//! Convert LLR to log-probabilities
QLLRvec probabilities(QLLR l); // some abuse of what QLLR stands for...
//! Convert LLR to log-probabilities, vector version
Array<QLLRvec> probabilities(const QLLRvec &l);
/*!
* \brief Update LLR (for internal use)
*
* This function updates the numerator and denominator in the expression
* \f[
* \log \left( \frac {\sum_{s:b_k=0} \exp(-x^2) P(s)}
* {\sum_{s:b_k=1} \exp(-x^2) P(s)} \right)
* \f]
*
* \param[in] logP_apriori Vector of a priori probabilities per bit
* \param[in] s Symbol vector
* \param[in] scaled_norm Argument of the exponents in the above
* equation
* \param[out] num Logarithm of the numerator in the above
* expression
* \param[out] denom Logarithm of the denominator in the above
* expression
*/
void update_LLR(const Array<QLLRvec> &logP_apriori, const ivec &s,
QLLR scaled_norm, QLLRvec &num, QLLRvec &denom);
/*!
* \brief Update LLR, for scalar channel (for internal use)
*
* This function updates the numerator and denominator in the expression
* \f[
* \log \left( \frac {\sum_{s:b_k=0} \exp (-x^2) P(s)}
* {\sum_{s:b_k=1} \exp (-x^2) P(s)} \right)
* \f]
*
* \param[in] logP_apriori Vector of a priori probabilities per bit
* \param[in] s Symbol
* \param[in] scaled_norm Argument of the exponents in the above
* equation
* \param[in] j Channel index (dimension)
* \param[out] num Logarithm of the numerator in the above
* expression
* \param[out] denom Logarithm of the denominator in the above
* expression
*/
void update_LLR(const Array<QLLRvec> &logP_apriori, int s,
QLLR scaled_norm, int j, QLLRvec &num, QLLRvec &denom);
};
// ----------------------------------------------------------------------
// Modulator_NRD
// ----------------------------------------------------------------------
/*!
* \ingroup modulators
* \brief 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
* \f[ y = Hx+e \f],
* where H is the channel matrix of dimension \f$n_r\times n_t\f$, \f$y\f$
* is a received vector of length \f$n_r\f$, \f$x\f$ is a transmitted vector
* of length \f$n_t\f$ and \f$e\f$ 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 \c 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
* \f[
* G = \left[ \begin{array}{cc} H_r & -H_i \\ H_i & H_r \end{array} \right]
* \f]
*
* See \c ND_UPAM for examples.
*/
class Modulator_NRD : public Modulator_ND {
public:
//! Constructor
Modulator_NRD() {}
//! Destructor
~Modulator_NRD() {}
//! Get modulation symbols per dimension
Array<vec> get_symbols() const { return symbols; }
//! Modulate \c bits into \c symbols
void modulate_bits(const bvec &bits, vec &symbols) const;
//! Modulate \c bits vector. Symbols are returned.
vec modulate_bits(const bvec &bits) const;
/*!
* \brief 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
*
* \param[in] y Received vector
* \param[in] H Channel matrix
* \param[in] sigma2 Noise variance per real dimension
* (typically \f$N_0/2\f$)
* \param[in] LLR_apriori Vector of a priori LLR values per bit
* \param[out] LLR_aposteriori Vector of a posteriori LLR values
* \param[in] method Soft demodulation method
*/
void demodulate_soft_bits(const vec &y, const mat &H, double sigma2,
const QLLRvec &LLR_apriori,
QLLRvec &LLR_aposteriori,
Soft_Demod_Method method);
/*!
* \brief 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
*
* \param[in] y Received vector
* \param[in] H Channel matrix
* \param[in] sigma2 Noise variance per real dimension
* (typically \f$N_0/2\f$)
* \param[in] LLR_apriori Vector of a priori LLR values per bit
* \param[in] method Soft demodulation method
* \return Vector of a posteriori LLR values
*/
QLLRvec demodulate_soft_bits(const vec &y, const mat &H, double sigma2,
const QLLRvec &LLR_apriori,
Soft_Demod_Method method);
/*!
* \brief Soft MAP demodulation for multidimensional channel, by
* "brute-force" enumeration of all constellation points.
*
* This function computes the LLR values
* \f[
* 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)
* \f]
*
* without approximations. It is assumed that H, y and s are
* real-valued. Complex-valued channels can be handled using the \c
* Modulator_NCD class.
*
* \param[in] y Received vector
* \param[in] H Channel matrix
* \param[in] sigma2 Noise variance per real dimension
* (typically \f$N_0/2\f$)
* \param[in] LLR_apriori Vector of a priori LLR values per bit
* \param[out] LLR_aposteriori Vector of a posteriori LLR values
*
* The function performs an exhaustive search over all possible points
* \c 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 demodulate_soft_bits(const vec &y, const mat &H, double sigma2,
const QLLRvec &LLR_apriori,
QLLRvec &LLR_aposteriori);
/*!
* \brief Soft MAP demodulation for parallelchannels without crosstalk.
*
* This function is a much faster equivalent to \c demodulate_soft_bits
* with \f$H = \mbox{diag}(h)\f$. Its complexity is linear in the number
* of subchannels.
*/
void demodulate_soft_bits(const vec &y, const vec &h, double sigma2,
const QLLRvec &LLR_apriori,
QLLRvec &LLR_aposteriori);
//! Output some properties of the MIMO modulator (mainly to aid debugging)
friend std::ostream &operator<<(std::ostream &os, const Modulator_NRD &m);
protected:
//! Vectors of modulation symbols (along each dimension)
Array<vec> symbols;
/*!
* \brief Update residual norm (for internal use).
*
* Update the residual norm \f$|y-Hs|\f$ when moving from one
* constellation point to an adjacent point.
*
* \param[in,out] norm Norm to be updated
* \param[in] k Position where s changed
* \param[in] sold Old value of s[k]
* \param[in] snew New value of s[k]
* \param[in] ytH y'H vector
* \param[in] HtH Grammian matrix H'H
* \param[in] s Symbol vector
*/
void update_norm(double &norm, int k, int sold, int snew, const vec &ytH,
const mat &HtH, const ivec &s);
};
/*!
* \relatesalso Modulator_NRD
* \brief Print some properties of the MIMO modulator (mainly to aid debugging)
*/
std::ostream &operator<<(std::ostream &os, const Modulator_NRD &m);
// ----------------------------------------------------------------------
// Modulator_NCD
// ----------------------------------------------------------------------
/*!
* \ingroup modulators
* \brief Base class for vector (MIMO) channel modulator/demodulators
* with complex valued components.
*
* This class is equivalent to \c Modulator_NRD except for that all
* quantities are complex-valued.
*
* See \c ND_UPAM for examples.
*/
class Modulator_NCD : public Modulator_ND {
public:
//! Constructor
Modulator_NCD() {}
//! Destructor
~Modulator_NCD() {}
//! Get modulation symbols per dimension
Array<cvec> get_symbols() const { return symbols; }
//! Modulate \c bits into \c symbols
void modulate_bits(const bvec &bits, cvec &symbols) const;
//! Modulation of bits
cvec modulate_bits(const bvec &bits) const;
//! Soft demodulation wrapper function for various methods
/*!
* \brief 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
*
* \param[in] y Received vector
* \param[in] H Channel matrix
* \param[in] sigma2 Noise variance per complex dimension,
* i.e. the sum of real and imaginary parts
* (typically \f$N_0\f$)
* \param[in] LLR_apriori Vector of a priori LLR values per bit
* \param[out] LLR_aposteriori Vector of a posteriori LLR values
* \param[in] method Soft demodulation method
*/
void demodulate_soft_bits(const cvec &y, const cmat &H, double sigma2,
const QLLRvec &LLR_apriori,
QLLRvec &LLR_aposteriori,
Soft_Demod_Method method);
/*!
* \brief 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
*
* \param[in] y Received vector
* \param[in] H Channel matrix
* \param[in] sigma2 Noise variance per complex dimension,
* i.e. the sum of real and imaginary parts
* (typically \f$N_0\f$)
* \param[in] LLR_apriori Vector of a priori LLR values per bit
* \param[in] method Soft demodulation method
* \return Vector of a posteriori LLR values
*/
QLLRvec demodulate_soft_bits(const cvec &y, const cmat &H, double sigma2,
const QLLRvec &LLR_apriori,
Soft_Demod_Method method);
/*!
* \brief Soft MAP demodulation for multidimensional channel, by
* "brute-force" enumeration of all constellation points.
*
* This function computes the LLR values
* \f[
* LLR(k) = \log \left( \frac
* {\sum_{s:b_k=0} \exp \left( -\frac{|y - Hs|^2}{\sigma^2} \right) P(s)}
* {\sum_{s:b_k=1} \exp \left( -\frac{|y - Hs|^2}{\sigma^2} \right) P(s)}
* \right)
* \f]
*
* without approximations. It is assumed that H, y and s are
* complex-valued.
*
* \param[in] y Received vector
* \param[in] H Channel matrix
* \param[in] sigma2 Noise variance per complex dimension, i.e.
* the sum of real and imaginary parts
* (typically \f$N_0\f$)
* \param[in] LLR_apriori Vector of a priori LLR values per bit
* \param[out] LLR_aposteriori Vector of a posteriori LLR values
*
* The function performs an exhaustive search over all possible points
* \c 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 demodulate_soft_bits(const cvec &y, const cmat &H, double sigma2,
const QLLRvec &LLR_apriori,
QLLRvec &LLR_aposteriori);
/*!
* \brief Soft MAP demodulation for parallelchannels without crosstalk.
*
* This function is a much faster equivalent to \c demodulate_soft_bits
* with \f$H = \mbox{diag}(h)\f$. Its complexity is linear in the number
* of subchannels.
*/
void demodulate_soft_bits(const cvec &y, const cvec &H, double sigma2,
const QLLRvec &LLR_apriori,
QLLRvec &LLR_aposteriori);
//! Print some properties of the MIMO modulator (mainly to aid debugging)
friend std::ostream &operator<<(std::ostream &os, const Modulator_NCD &m);
protected:
//! Vectors of modulation symbols (along each dimension)
Array<cvec> symbols;
/*!
* \brief Update residual norm (for internal use).
*
* Update the residual norm \f$|y-Hs|\f$ when moving from one
* constellation point to an adjacent point.
*
* \param[in,out] norm Norm to be updated
* \param[in] k Position where s changed
* \param[in] sold Old value of s[k]
* \param[in] snew New value of s[k]
* \param[in] ytH y'H vector
* \param[in] HtH Grammian matrix H'H
* \param[in] s Symbol vector
*/
void update_norm(double &norm, int k, int sold, int snew, const cvec &ytH,
const cmat &HtH, const ivec &s);
};
/*!
* \relatesalso Modulator_NCD
* \brief Print some properties of the MIMO modulator (mainly to aid debugging)
*/
std::ostream &operator<<(std::ostream &os, const Modulator_NCD &m);
// ----------------------------------------------------------------------
// ND_UPAM
// ----------------------------------------------------------------------
/*!
* \ingroup modulators
* \brief Real-valued MIMO channel with uniform PAM along each dimension.
*
* <b>Example: (4 x 3 matrix channel with 4-PAM)</b>
* \code
* 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;
* \endcode
*
* <b>Example: (scalar channel with 8-PAM)</b>
* \code
* 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;
* \endcode
*/
class ND_UPAM : public Modulator_NRD {
public:
//! Constructor
ND_UPAM(int nt = 1, int Mary = 2);
//! Destructor
~ND_UPAM() {}
//! Set component modulators to M-PAM with Gray mapping
void set_M(int nt = 1, int Mary = 2);
//! Set component modulators to M-PAM with Gray mapping, different M per component
void set_M(int nt = 1, ivec Mary = "2");
/*!
* \brief Sphere decoding
*
* This function solves the integer-constrained minimization problem
* \f[
* \mbox{min} |y - Hs|
* \f]
* with respect to \f$s\f$ 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 (\c stepup) until the search
* succeeds.
*
* \param[in] y received data vector (\f$n_r\times 1\f$)
* \param[in] H channel matrix (\f$n_r\times n_t\f$)
* \param[in] rmax maximum possible sphere radius to try
* \param[in] rmin sphere radius in the first try
* \param[in] stepup factor with which the sphere radius is
* increased if the search fails
* \param[out] detected_bits result of the search (hard decisions only,
* QLLR for a sure "1" is set to 1000)
* \return status of the decoding: 0 if the search suceeds, -1 otherwise
*/
int sphere_decoding(const vec &y, const mat &H, double rmin, double rmax,
double stepup, QLLRvec &detected_bits);
private:
// Sphere decoding search with Schnorr Eucner strategy.
int sphere_search_SE(const vec &y, const mat &H, const imat &zrange,
double r, ivec &zhat);
vec spacing; // spacing between the constellation points
inline int sign_nozero_i(int a) { return (a > 0 ? 1 : -1); }
inline int sign_nozero_i(double a) { return (a > 0.0 ? 1 : -1); }
};
// ----------------------------------------------------------------------
// ND_UQAM
// ----------------------------------------------------------------------
/*!
* \ingroup modulators
* \brief Complex MIMO channel with uniform QAM per dimension
*/
class ND_UQAM : public Modulator_NCD {
public:
//! Constructor
ND_UQAM(int nt = 1, int Mary = 4);
//! Destructor
~ND_UQAM() {}
//! Set component modulators to M-QAM with Gray mapping
void set_M(int nt = 1, int Mary = 4);
//! Set component modulators to M-QAM with Gray mapping, different M per component
void set_M(int nt = 1, ivec Mary = "4");
protected:
ivec L; //!< the square root of M
};
// ----------------------------------------------------------------------
// ND_UPSK
// ----------------------------------------------------------------------
/*!
* \ingroup modulators
* Complex MIMO channel with uniform PSK per dimension
*/
class ND_UPSK : public Modulator_NCD {
public:
//! Constructor
ND_UPSK(int nt = 1, int Mary = 4);
//! Destructor
~ND_UPSK() {}
//! Set component modulators to M-QAM with Gray mapping
void set_M(int nt = 1, int Mary = 4);
//! Set component modulators to M-QAM with Gray mapping, different M per component
void set_M(int nt = 1, ivec Mary = "4");
};
} // namespace itpp
#endif // #ifndef MODULATOR_ND_H
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