VBM

Velocity bin masking (VBM) electronic attack slow-time modulations.

Provides slow-time phase noise functions that a DRFM jammer can apply to spread energy across Doppler bins, masking the true target velocity. Includes LFM, random-phase, and sinusoidal modulation strategies.

logger = logging.getLogger(__name__) module-attribute

calc_f_delta(fcar, rdot_delta)

Calculates the Doppler frequency spread from a range-rate spread.

This function converts a spread in target radial velocities (range-rate delta) into a corresponding Doppler frequency bandwidth.

Parameters:

Name	Type	Description	Default
fcar	float	The carrier frequency of the radar in Hertz.	required
rdot_delta	float	The spread in range-rates (radial velocities) in meters/second.	required

Returns:

Type	Description
float	The corresponding frequency spread (f_delta) in Hertz.

Source code in src/rad_lab/vbm.py

def calc_f_delta(fcar: float, rdot_delta: float) -> float:
    """Calculates the Doppler frequency spread from a range-rate spread.

    This function converts a spread in target radial velocities (range-rate delta)
    into a corresponding Doppler frequency bandwidth.

    Args:
        fcar: The carrier frequency of the radar in Hertz.
        rdot_delta: The spread in range-rates (radial velocities) in meters/second.

    Returns:
        The corresponding frequency spread (f_delta) in Hertz.
    """
    return 2 * fcar / c.C * rdot_delta

slowtime_noise(N_pulses, fcar, rdot_delta, prf, noise_fun=_lfm_phase)

Generates a slow-time noise sequence for Velocity Band Modulation (VBM).

This function acts as a wrapper to generate various types of complex noise sequences applied across pulses (slow-time). It first calculates the required Doppler frequency spread from the given range-rate spread and then calls the specified noise generation function.

Parameters:

Name	Type	Description	Default
N_pulses	int	The total number of pulses in the coherent processing interval.	required
fcar	float	The radar's carrier frequency in Hertz.	required
rdot_delta	float	The desired spread in range-rates (radial velocities) in m/s, which defines the VBM bandwidth.	required
prf	float	The Pulse Repetition Frequency in Hertz.	required
noise_fun	Callable	The function to use for generating the noise sequence. Defaults to _lfm_phase.	_lfm_phase

Returns:

Type	Description
ndarray	A 1D numpy array representing the complex slow-time noise sequence.

Notes

Available noise_fun choices include: - _random_phase: Broadband random phase noise. - _uniform_bandwidth_phase: Noise with a uniform spectral distribution. - _gaussian_bandwidth_phase: Noise with a Gaussian spectral distribution. - _gaussian_bandwidth_phase_normalized: Gaussian noise with time-domain normalization. - _lfm_phase: A deterministic LFM sweep across the Doppler band (cleanest).

Source code in src/rad_lab/vbm.py

def slowtime_noise(
    N_pulses: int, fcar: float, rdot_delta: float, prf: float, noise_fun: Callable = _lfm_phase
) -> np.ndarray:
    """Generates a slow-time noise sequence for Velocity Band Modulation (VBM).

    This function acts as a wrapper to generate various types of complex noise
    sequences applied across pulses (slow-time). It first calculates the required
    Doppler frequency spread from the given range-rate spread and then calls the
    specified noise generation function.

    Args:
        N_pulses: The total number of pulses in the coherent processing interval.
        fcar: The radar's carrier frequency in Hertz.
        rdot_delta: The desired spread in range-rates (radial velocities) in m/s,
            which defines the VBM bandwidth.
        prf: The Pulse Repetition Frequency in Hertz.
        noise_fun: The function to use for generating the noise sequence.
            Defaults to `_lfm_phase`.

    Returns:
        A 1D numpy array representing the complex slow-time noise sequence.

    Notes:
        Available `noise_fun` choices include:
        - `_random_phase`: Broadband random phase noise.
        - `_uniform_bandwidth_phase`: Noise with a uniform spectral distribution.
        - `_gaussian_bandwidth_phase`: Noise with a Gaussian spectral distribution.
        - `_gaussian_bandwidth_phase_normalized`: Gaussian noise with time-domain normalization.
        - `_lfm_phase`: A deterministic LFM sweep across the Doppler band (cleanest).
    """
    f_delta = calc_f_delta(fcar, rdot_delta)
    slowtime_noise = noise_fun(N_pulses, f_delta, prf)

    logger.debug("\nBand Noise:")
    logger.debug(f"\t{norm(slowtime_noise)=}")
    logger.debug(f"\t{slowtime_noise.size=}")
    logger.debug(f"\t{np.mean(abs(slowtime_noise))=}")
    logger.debug(f"\t{np.var(abs(slowtime_noise))=}")
    logger.debug(f"\t{np.mean(np.angle(slowtime_noise))=}")
    logger.debug(f"\t{np.sqrt(np.var(np.angle(slowtime_noise)))=}")

    return slowtime_noise