Constellations

class Constellations.BaseConstellation

Base class for constellations such as QAM or PSK.

Notes

• Other constellations should be derived from this class. They need to initialize self._alphabet, which is returned by the alphabet property, self._bit_matrix, which is returned by the bit_matrix property, and self._str, which is returned by the str property.
• Bits are represented by the numbers zero and one.

alphabet

Vector of constellation points. The number of points has to be a power of two.

Type:numpy.array (complex)

bit_matrix

Matrix of bit patterns.

The size of the matrix should be N x M, where N is the size of the alphabet and M is the number of bits per symbol. The n-th row of the matrix contains the bit pattern of the n-th symbol in the alphabet. The allowed values in the matrix are zero and one.

Type:numpy.array(int)

gray_code(m, n)

Gray code bit matrix.

Parameters:

• m (int) –
• n (int) –

Returns:

Matrix as described in the bit_matrix property. The number of bit patterns (rows) is m*n. The number of bits per pattern (columns) is ceil(log2(m*n)).

Return type:

numpy.array(int)

idx2bits(idx)

Translates a vector of indices into a bit pattern.

Parameters:idx (numpy.array(complex)) – Vector of indices Returns:Vector of bits Return type:numpy.array(complex)

idx2symbol(idx)

Translates a vector of indices into a vector of symbols.

Parameters:idx (numpy.array(integer)) – Vector of indices. Returns:A array with the same length as idx whose n-th element is self.alphabet[idx[n]]. Return type:numpy.array(complex)

name

Identifcation string for the constellation, should also specify parameters.

Type:str

show(new_fig=False)

Shows the constellation alphabet together with the bit patterns.

Parameters:new_fig (bool) – Always creates a new figure if True, reuses existing figures if False. Returns:matplotlib figure handle (only if new_fig=True) Return type:Figure

size()

int : Number of elements in the alphabet.

symbol2idx(symbols)

Translates a vector of symbols into a vector of indices.

Parameters:symbols (numpy.array(complex)) – Vector of symbols. Returns:A vector with the same length as symbols whose n-th element is the integer number i=i(n) in 0,…,numpy.size(symbols)-1 that minimizes the Eucledian distance |symbols[n] - self.alphabet[i]|. Return type:numpy.array(integer)

class Constellations.MPSKConstellation(m, rotate_by_delta_half=False)

Phase shift keying (PSK) modulation. Implements BaseConstellation.

__init__(m, rotate_by_delta_half=False)

Contructor for a PSK constellation.

Parameters:

• m (int) – Number of constellation points
• rotate_by_delta_half (Boolean) – Rotate constellation by 2pi/m

class Constellations.QAMConstellation(m, n)

Quadrature amplitude modulation (QAM) constellation (implements BaseConstellation).

__init__(m, n)

Constructor for a m x n QAM constellation.

Parameters:

• m (int) – Number of rows in the constellation.
• n (int) – Number of columns in the constellation.

class Constellations.ReshapedQAMConstellation(m, n, b0_fun, Ed, bnds)

Reshaped quadrature amplitude modulation (QAM) constellation (implements BaseConstellation).

The goal of the reshaping procedure is to fit the average (normalized) energy of the generated pulses to a desired value Ed. For details, see Gui et al., Opt. Express 26(21), 2018.

__init__(m, n, b0_fun, Ed, bnds)

Constructor for a reshaped m x n QAM constellation.

Parameters:

• m (int) –
• n (int) –
• b0_fun (function) – Carrier waveform. The function should maps any input vector of the type numpy.array(float), which represents a vector of nonlinear frequencies xi, to a output vector of the type numpy.array(complex), which represents the values of the carrier waveform at these xi.
• Ed (float) – Desired average energy of the generated pulses (with respect to normalized units). Should be positive.
• bnds (numpy.array(float)) – Vector with two entries [a,b], which are used as initial bounds in the bisection produdure based on which the constellation is reshaped. It should be 0<a<b.