itpp::PSK Class Reference
[Digital Modulation]

M-ary PSK modulator. More...

#include <modulator.h>

List of all members.

Public Member Functions

PSK ()

Default Constructor.

PSK (int M)

Class constructor.

virtual ~PSK ()

Destructor.

void set_M (int M)

Change the size of the signal constellation.

void demodulate_bits (const cvec &signal, bvec &bits) const

Hard demodulation of bits.

bvec demodulate_bits (const cvec &signal) const

Hard demodulation of bits.

virtual void set (const Vec< std::complex< double > > &symbols, const ivec &bits2symbols)

Set the constellation to use in the modulator.

virtual int bits_per_symbol () const

Returns number of bits per symbol.

virtual Vec< std::complex
< double > > get_symbols () const

Get the symbol values used in the modulator.

virtual ivec get_bits2symbols () const

Get the bitmap, which maps input bits into symbols.

virtual void modulate (const ivec &symbolnumbers, Vec< std::complex< double > > &output) const

Modulation of symbols.

virtual Vec< std::complex
< double > > modulate (const ivec &symbolnumbers) const

Modulation of symbols.

virtual void demodulate (const Vec< std::complex< double > > &signal, ivec &output) const

Demodulation of symbols.

virtual ivec demodulate (const Vec< std::complex< double > > &signal) const

Demodulation of symbols.

virtual void modulate_bits (const bvec &bits, Vec< std::complex< double > > &output) const

Modulation of bits.

virtual Vec< std::complex
< double > > modulate_bits (const bvec &bits) const

Modulation of bits.

virtual void demodulate_bits (const Vec< std::complex< double > > &signal, bvec &bits) const

Hard demodulation of bits.

virtual bvec demodulate_bits (const Vec< std::complex< double > > &signal) const

Hard demodulation of bits.

virtual void demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const

Soft demodulator for AWGN channels.

virtual vec demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, double N0, Soft_Method method=LOGMAP) const

Soft demodulator for AWGN channels.

virtual void demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, const Vec< std::complex< double > > &channel, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const

Soft demodulator for fading channels.

virtual vec demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, const Vec< std::complex< double > > &channel, double N0, Soft_Method method=LOGMAP) const

Soft demodulator for fading channels.

Protected Member Functions

void calculate_softbit_matrices ()

This function calculates the soft bit mapping matrices S0 and S1.

Protected Attributes

bool setup_done

Setup indicator.

int k

Number of bits per modulation symbol.

int M

Number of modulation symbols.

bmat bitmap

Bit to symbol mapping table (size: M x k).

ivec bits2symbols

Bit to symbol mapping in decimal form (size: M).

Vec< std::complex< double > > symbols

Corresponding modulation symbols (size: M).

imat S0

Matrix where row k contains the constellation points with '0' in bit position k.

imat S1

Matrix where row k contains the constellation points with '1' in bit position k.

Related Functions

(Note that these are not member functions.)

typedef Modulator< double > Modulator_1D

Definition of 1D Modulator (with real symbols).

typedef Modulator
< std::complex< double > > Modulator_2D

Definition of 2D Modulator (with complex symbols).

Detailed Description

M-ary PSK modulator.

This class implements the M-ary PSK modulator with $M = 2^k$ constellation points, where $k = 1, 2, \ldots$ . The symbol numbering is counter clockwise starting from the real axis, i.e. symbol $(1, 0)$ . The bitmap is Gray encoded. The symbol energy is normalized to 1.

Beside hard demapping, this class can also perform soft demodulation, calculating the log-MAP estimate of the individual bits. To use it properly the received symbols should be equal to:

$r_k = c_k s_k + n_k,$

where $c_k$ is the real or complex channel gain, $s_k$ is the transmitted constellation symbol, and $n_k$ is the AWGN of the channel (with variance $N_0$ ).

It is also assumed that the channel estimates are perfect when calculating the soft bits.

Member Function Documentation

virtual void itpp::Modulator< std::complex< double > >::demodulate_soft_bits	(	const Vec< std::complex< double > > &	rx_symbols,
		const Vec< std::complex< double > > &	channel,
		double	N0,
		vec &	soft_bits,
		Soft_Method	method = `LOGMAP`
	)			const `[virtual, inherited]`

Soft demodulator for fading channels.

This function calculates the log-likelihood ratio (LLR) of the received signal from fading channels. Depending on the soft demodulation method chosen, either full log-MAP calculation is performed (default method), according to the following equation:

$\log \left( \frac{P(b_i=0|r)}{P(b_i=1|r)} \right) = \log \left( \frac{\sum_{s_i \in S_0} \exp \left( -\frac{|r_k - c_k s_i|^2}{N_0} \right)} {\sum_{s_i \in S_1} \exp \left( -\frac{|r_k - c_k s_i|^2}{N_0} \right)} \right)$

or approximate, but faster calculation is performed.

The approximate method finds for each bit the closest constellation points that have zero and one in the corresponding position. Let $d_0 = |r_k - c_k s_0|$ denote the distance to the closest zero point and $d_1 = |r_k - c_k s_1|$ denote the distance to the closest one point for the corresponding bit respectively. The approximate algorithm then computes

$\frac{d_1^2 - d_0^2}{N_0}$

When this function is to be used together with MAP-based turbo decoding algorithms then the channel reliability factor $L_c$ of the turbo decoder shall be set to 1. The output from this function can also be used by a Viterbi decoder using an AWGN based metric calculation function.

Parameters:

	rx_symbols	The received noisy constellation symbols
	channel	The channel values
	N0	The spectral density of the AWGN noise
	soft_bits	The soft bits calculated using the expression above
	method	The method used for demodulation (LOGMAP or APPROX)

Note:: For soft demodulation it is suggested to use the N-dimensional modulator (Modulator_ND) instead, which is based on the QLLR (quantized) arithmetic and therefore is faster. Please note, however, that mixed use of Modulator_1D/Modulator_2D and Modulator_ND is not advised.

virtual void itpp::Modulator< std::complex< double > >::demodulate_soft_bits	(	const Vec< std::complex< double > > &	rx_symbols,
		double	N0,
		vec &	soft_bits,
		Soft_Method	method = `LOGMAP`
	)			const `[virtual, inherited]`

Soft demodulator for AWGN channels.

This function calculates the log-likelihood ratio (LLR) of the received signal from AWGN channels. Depending on the soft demodulation method chosen, either full log-MAP calculation is performed (default method), according to the following equation:

$\log \left( \frac{P(b_i=0|r)}{P(b_i=1|r)} \right) = \log \left( \frac{\sum_{s_i \in S_0} \exp \left( -\frac{|r_k - s_i|^2}{N_0} \right)} {\sum_{s_i \in S_1} \exp \left( -\frac{|r_k - s_i|^2}{N_0} \right)} \right)$

or approximate, but faster calculation is performed.

The approximate method finds for each bit the closest constellation points that have zero and one in the corresponding position. Let $d_0 = |r_k - s_0|$ denote the distance to the closest zero point and $d_1 = |r_k - s_1|$ denote the distance to the closest one point for the corresponding bit respectively. The approximate algorithm then computes

$\frac{d_1^2 - d_0^2}{N_0}$

This function can be used on channels where the channel gain $c_k = 1$ .

When this function is to be used together with MAP-based turbo decoding algorithms then the channel reliability factor $L_c$ of the turbo decoder shall be set to 1. The output from this function can also be used by a Viterbi decoder using an AWGN based metric calculation function.

Parameters:

	rx_symbols	The received noisy constellation symbols
	N0	The spectral density of the AWGN noise
	soft_bits	The soft bits calculated using the expression above
	method	The method used for demodulation (LOGMAP or APPROX)

Note:: For soft demodulation it is suggested to use the N-dimensional modulator (Modulator_ND) instead, which is based on the QLLR (quantized) arithmetic and therefore is faster. Please note, however, that mixed use of Modulator_1D/Modulator_2D and Modulator_ND is not advised.

virtual ivec itpp::Modulator< std::complex< double > >::get_bits2symbols ( ) const [inline, virtual, inherited]

Get the bitmap, which maps input bits into symbols.

The mapping is done as follows. An input bit sequence in decimal notation is used for indexing the bits2symbols table. The indexing result denotes the symbol to be used from the symbols table, e.g.:

 PSK mod(8); // assume 8-PSK modulator
 cvec sym =  mod.get_symbols();
 ivec bits2sym = mod.get_bits2symbols();
 bvec in_bits = "100" // input bits
 int d = bin2dec(in_bits); // decimal representation of in_bits = 4
 // mapping of d into PSK symbol using bits2sym and sym tables
 std::complex<double> out_symbol = sym(bits2sym(d));

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


Public Member Functions
	PSK ()
	Default Constructor.
	PSK (int M)
	Class constructor.
virtual	~PSK ()
	Destructor.
void	set_M (int M)
	Change the size of the signal constellation.
void	demodulate_bits (const cvec &signal, bvec &bits) const
	Hard demodulation of bits.
bvec	demodulate_bits (const cvec &signal) const
	Hard demodulation of bits.
virtual void	set (const Vec< std::complex< double > > &symbols, const ivec &bits2symbols)
	Set the constellation to use in the modulator.
virtual int	bits_per_symbol () const
	Returns number of bits per symbol.
virtual Vec< std::complex < double > >	get_symbols () const
	Get the symbol values used in the modulator.
virtual ivec	get_bits2symbols () const
	Get the bitmap, which maps input bits into symbols.
virtual void	modulate (const ivec &symbolnumbers, Vec< std::complex< double > > &output) const
	Modulation of symbols.
virtual Vec< std::complex < double > >	modulate (const ivec &symbolnumbers) const
	Modulation of symbols.
virtual void	demodulate (const Vec< std::complex< double > > &signal, ivec &output) const
	Demodulation of symbols.
virtual ivec	demodulate (const Vec< std::complex< double > > &signal) const
	Demodulation of symbols.
virtual void	modulate_bits (const bvec &bits, Vec< std::complex< double > > &output) const
	Modulation of bits.
virtual Vec< std::complex < double > >	modulate_bits (const bvec &bits) const
	Modulation of bits.
virtual void	demodulate_bits (const Vec< std::complex< double > > &signal, bvec &bits) const
	Hard demodulation of bits.
virtual bvec	demodulate_bits (const Vec< std::complex< double > > &signal) const
	Hard demodulation of bits.
virtual void	demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const
	Soft demodulator for AWGN channels.
virtual vec	demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, double N0, Soft_Method method=LOGMAP) const
	Soft demodulator for AWGN channels.
virtual void	demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, const Vec< std::complex< double > > &channel, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const
	Soft demodulator for fading channels.
virtual vec	demodulate_soft_bits (const Vec< std::complex< double > > &rx_symbols, const Vec< std::complex< double > > &channel, double N0, Soft_Method method=LOGMAP) const
	Soft demodulator for fading channels.
Protected Member Functions
void	calculate_softbit_matrices ()
	This function calculates the soft bit mapping matrices S0 and S1.
Protected Attributes
bool	setup_done
	Setup indicator.
int	k
	Number of bits per modulation symbol.
int	M
	Number of modulation symbols.
bmat	bitmap
	Bit to symbol mapping table (size: M x k).
ivec	bits2symbols
	Bit to symbol mapping in decimal form (size: M).
Vec< std::complex< double > >	symbols
	Corresponding modulation symbols (size: M).
imat	S0
	Matrix where row k contains the constellation points with '0' in bit position k.
imat	S1
	Matrix where row k contains the constellation points with '1' in bit position k.
Related Functions
(Note that these are not member functions.)
typedef Modulator< double >	Modulator_1D
	Definition of 1D Modulator (with real symbols).
typedef Modulator < std::complex< double > >	Modulator_2D
	Definition of 2D Modulator (with complex symbols).

itpp::PSK Class Reference [Digital Modulation]

Public Member Functions

Protected Member Functions

Protected Attributes

Related Functions

Detailed Description

Member Function Documentation

itpp::PSK Class Reference
[Digital Modulation]