pam#

sionna.phy.mapping.pam(num_bits_per_symbol: int, normalize: bool = True, precision: Literal['single', 'double'] | None = None) → numpy.ndarray[source]#

Generates a PAM constellation.

This function generates a real-valued vector, where each element is a constellation point of an M-ary PAM constellation. The bit label of the n th point is given by the length-num_bits_per_symbol binary representation of n.

Parameters:

  • num_bits_per_symbol (int) – Number of bits per constellation point. Must be positive.

  • normalize (bool) – If True, the constellation is normalized to have unit power. Defaults to True.

  • precision (Literal['single', 'double'] | None) – Precision used for internal calculations and outputs. If set to None, precision is used.

Outputs:

c – np.ndarray, shape [2**num_bits_per_symbol]. PAM constellation symbols.

Notes

The bit label of the nth constellation point is given by the binary representation of its position within the array and can be obtained through np.binary_repr(n, num_bits_per_symbol).

The normalization factor of a PAM constellation is given in closed-form as:

\[\sqrt{\frac{1}{2^{n-1}}\sum_{i=1}^{2^{n-1}}(2i-1)^2}\]

where \(n= \text{num\_bits\_per\_symbol}\) is the number of bits per symbol.

This algorithm is a recursive implementation of the expressions found in Section 5.1 of [3GPPTS38211]. It is used in the 5G standard.

Examples

from sionna.phy.mapping import pam

# Generate 4-PAM constellation
constellation = pam(2)
print(constellation.shape)
# (4,)
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