BPSK modulator with complex symbols. More...

#include <itpp/comm/modulator.h>

Inheritance diagram for itpp::BPSK_c:

Public Member Functions
	BPSK_c ()
	Constructor.

virtual	~BPSK_c ()
	Destructor.

void	modulate_bits (const bvec &bits, cvec &output) const
	Modulate bits into BPSK symbols in complex domain.

cvec	modulate_bits (const bvec &bits) const
	Modulate bits into BPSK symbols in complex domain.

void	demodulate_bits (const cvec &signal, bvec &output) const
	Demodulate noisy BPSK symbols in complex domain into bits.

bvec	demodulate_bits (const cvec &signal) const
	Demodulate noisy BPSK symbols in complex domain into bits.

virtual void	demodulate_soft_bits (const cvec &rx_symbols, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const
	Soft demodulator for AWGN channel.

vec	demodulate_soft_bits (const cvec &rx_symbols, double N0, Soft_Method method=LOGMAP) const
	Soft demodulator for AWGN channel.

virtual void	demodulate_soft_bits (const cvec &rx_symbols, const cvec &channel, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const
	Soft demodulator for a known channel in AWGN.

vec	demodulate_soft_bits (const cvec &rx_symbols, const cvec &channel, double N0, Soft_Method method=LOGMAP) const
	Soft demodulator for a known channel in AWGN.

void	set_M (int M)
	Change the size of the signal constellation.

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	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 int	get_k () const
	Returns number of bits per symbol.

virtual int	get_M () const
	Returns number of modulation symbols.

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 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

BPSK modulator with complex symbols.

This is a special version of the PSK modulator with $M = 2$ constellation points. The following bit to symbol mapping is used:

$0 \rightarrow 1+0i$
$1 \rightarrow -1+0i$ .

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.

Note: Although constellation points of the BPSK modulator can be represented in the real domain only, this class uses complex signals to be compatible with other PSK and QAM based modulators.

See Also: BPSK

Definition at line 775 of file modulator.h.

Member Function Documentation

void itpp::BPSK_c::demodulate_soft_bits	(	const cvec &	rx_symbols,
		double	N0,
		vec &	soft_bits,
		Soft_Method	method = `LOGMAP`
	)		const

virtual

Soft demodulator for AWGN channel.

This function calculates the log-MAP estimate assuming equally likely bits transmitted:

$\log \left( \frac{P(b=0|r)}{P(b=1|r)} \right) = \frac{4 \Re\{r\}} {N_0}$

Parameters

rx_symbols	The received noisy constellation symbols, (complex but symbols in real part)
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.

Definition at line 264 of file modulator.cpp.

References itpp::real().

Referenced by demodulate_soft_bits().

void itpp::BPSK_c::demodulate_soft_bits	(	const cvec &	rx_symbols,
		const cvec &	channel,
		double	N0,
		vec &	soft_bits,
		Soft_Method	method = `LOGMAP`
	)		const

virtual

Soft demodulator for a known channel in AWGN.

This function calculates the log-MAP estimate assuming equally likely bits transmitted:

$\log \left( \frac{P(b=0|r)}{P(b=1|r)} \right) = \frac{4 \Re\{r c^{*}\}}{N_0}$

Parameters

rx_symbols	The received noisy constellation symbols, (complex but symbols in real part)
channel	The channel coefficients, (complex)
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.

Definition at line 284 of file modulator.cpp.

References itpp::conj(), and itpp::real().

virtual ivec itpp::Modulator< std::complex< double > >::get_bits2symbols ( ) const

inlinevirtualinherited

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));

Definition at line 117 of file modulator.h.

References itpp::Modulator< T >::bits2symbols.

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

virtualinherited

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 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

virtualinherited

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.

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

itpp/comm/modulator.h
itpp/comm/modulator.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Related Functions

Detailed Description

Member Function Documentation