BER vs SNR

Defines the number of repetitions as a function of \(Eb/N0\), using linear interpolation between reference points, given by the expression below.

\[ r = r_{i} + \frac{(EBN0 - EBN0_{i})}{(EBN0_{i+1} - EBN0_{i})} \cdot (r_{i+1} - r_{i}) \]

Where

• \(r\): Number of repetitions.
• \(EBN0\): \(Eb/N_0\) ratio in decibels.
• \(r_i\) and \(r_{i+1}\): Number of repetitions at the nearest reference points.
• \(EBN0_i\) and \(EBN0_{i+1}\): \(Eb/N_0\) ratios at the nearest reference points.

Parameters:

Name	Type	Description	Default
positions	int	Total number of points to be generated.	required
ref_points	array - like	Reference points.	required
ref_values	array - like	Values corresponding to the reference points.	required

Returns:

Name	Type	Description
interpolated_values	ndarray	Array of interpolated values, rounded to integers.

__init__(EbN0_values=np.arange(0, 10, 1), num_workers=56, numblocks=8, max_repetitions=2000, error_values=None)

Simulates the BER vs Eb/N0 for the ARGOS-3 standard.

Parameters:

Name	Type	Description	Default
EbN0_values	array - like	Values of Eb/N0 for which the simulation will be performed.	arange(0, 10, 1)
num_workers	int	Number of threads for parallelization.	56
numblocks	int	Number of data blocks for each datagram.	8
max_repetitions	int	Maximum number of repetitions for each Eb/N0 value.	2000
error_values	array - like	Maximum number of errors for each Eb/N0 value.	None

Raises:

Type	Description
ValueError	If the number of errors is not the same as the number of Eb/N0 values.

Examples:

• BER vs Eb/N0 Plot Example:

run()

Runs the BER vs Eb/N0 simulation for the ARGOS-3 standard.

Returns:

Name	Type	Description
ber_results	list	List of tuples (Eb/N0, BER) for each Eb/N0 value.

__init__(EbN0_values=np.arange(0, 10, 1), num_workers=8, num_bits=10000, max_repetitions=2000, error_values=None)

Implements the BER vs Eb/N0 simulation for the QPSK standard.

Parameters:

Name	Type	Description	Default
EbN0_values	array - like	Values of Eb/N0 for which the simulation will be performed.	arange(0, 10, 1)
num_workers	int	Number of threads for parallelization.	8
num_bits	int	Number of bits for each simulation.	10000
max_repetitions	int	Maximum number of repetitions for each Eb/N0 value.	2000
error_values	array - like	Maximum number of errors for each Eb/N0 value.	None

Raises:

Type	Description
ValueError	If the number of errors is not the same as the number of Eb/N0 values.

run()

Runs the BER vs Eb/N0 simulation for the QPSK standard.

Returns:

Name	Type	Description
ber_results	list	List of tuples (Eb/N0, BER) for each Eb/N0 value.

teorical_qpsk()

Calculates the theoretical BER vs Eb/N0 curve for QPSK, according to the expression below.

\[ P_b(x) = Q \left(x\right) \mapsto P_b(x) = Q\left(\sqrt{2 \cdot \frac{E_b}{N_0}}\right) \]

Where

• \(P_b(x)\): Error probability.
• \(Q(x)\): Complementary error function.
• \(x\): Argument of the \(Q(x)\) function.
• \(E_b\): Energy per bit.
• \(N_0\): Noise power.

Returns:

Name	Type	Description
ber_teorico	ndarray	Array of theoretical BER values for each Eb/N0 of the class.