Implements linear phase/amplitude modulation with arbitrary symbol mapping.

Constructors¶

LinearModulation(symbol_map: ArrayLike, ...)

Creates a new linear phase/amplitude modulation object.

String representation¶

__repr__() → str

Returns a code-styled string representation of the object.

__str__() → str

Returns a human-readable string representation of the object.

Methods¶

map_symbols(s: ArrayLike) → NDArray[complex_]

Converts the decimal symbols \(s[k]\) to complex symbols \(a[k]\).

decide_symbols(a_hat: ArrayLike) → NDArray[int_]

Converts the received complex symbols \(\hat{a}[k]\) into decimal symbol decisions \(\hat{s}[k]\) using maximum-likelihood estimation (MLE).

modulate(s: ArrayLike) → NDArray[complex_]

Modulates the decimal symbols \(s[k]\) into pulse-shaped complex samples \(x[n]\).

demodulate(x_hat) → tuple[NDArray[int_], NDArray[complex_]]

Demodulates the pulse-shaped complex samples \(\hat{x}[n]\) into decimal symbol decisions \(\hat{s}[k]\) using matched filtering and maximum-likelihood estimation.

abstract ber(ebn0: ArrayLike) → NDArray[float_]

Computes the bit error rate (BER) at the provided \(E_b/N_0\) values.

abstract ser(esn0: ArrayLike) → NDArray[float_]

Computes the symbol error rate (SER) at the provided \(E_s/N_0\) values.

Properties¶

property order : int

The modulation order \(M = 2^k\).

property bps : int

The number of bits per symbol \(k = \log_2 M\).

property phase_offset : float

The phase offset \(\phi\) in degrees.

property symbol_map : NDArray[np.complex_]

The symbol map \(\{0, \dots, M-1\} \mapsto \mathbb{C}\). This maps decimal symbols from \(0\) to \(M-1\) to complex symbols.

property sps : int

The number of samples per symbol \(f_s / f_{sym}\).

property pulse_shape : NDArray[np.float_]

The pulse shape \(h[n]\) of the modulated signal.

property tx_filter : Interpolator

The transmit interpolating pulse shaping filter. The filter coefficients are the pulse shape \(h[n]\).

property rx_filter : Decimator

The receive decimating matched filter. The filter coefficients are matched to the pulse shape \(h[-n]^*\).