class sdr.CPM

Implements continuous-phase modulation (CPM).

Variable nomenclature

  • \(k\): Symbol index

  • \(n\): Sample index

  • \(s[k]\): Decimal symbols

  • \(a[k]\) Complex symbols

  • \(x[n]\): Pulse-shaped complex samples

  • \(\tilde{x}[n]\): Received (noisy) pulse-shaped complex samples

  • \(\tilde{a}[k]\): Received (noisy) complex symbols

  • \(\hat{a}[k]\): Complex symbol decisions

  • \(\hat{s}[k]\): Decimal symbol decisions

Constructors

CPM(order: int, index: float = 0.5, ...)

Creates a new continuous-phase modulation object.

Methods

modulate(s: ArrayLike) → NDArray[complex128]

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

demodulate(x_tilde: ArrayLike) → NDArray[int_]

Demodulates the pulse-shaped complex samples into decimal symbol decisions.

abstract ber(ebn0: ArrayLike | None = None) → ndarray

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

abstract ser(esn0: ArrayLike) → ndarray

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 coded bits per symbol \(k = \log_2 M\).

property index : float

The modulation index \(h\).

property phase_offset : float

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

property sps : int

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

property pulse_shape : ndarray

The pulse shape \(h[n]\) of the instantaneous frequency of the 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 \(h[-n]^*\).