Recommendation ITU-R P.1623¶

This Recommendation provides prediction methods of fade dynamics on Earth-space paths.

Title	PDF	Latest approved in
Recommendation ITU-R P.1623	[PDF]	2005-03
Prediction method of fade dynamics on Earth-space paths
Current recommendation version (In force)		Date
Recommendation ITU-R P.1623-1	[PDF]	03/2005
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.1623-1	[PDF]	03/2005
Recommendation ITU-R P.1623-0	[PDF]	04/2003

Introduction¶

In the design of a variety of telecommunication systems, the dynamic characteristics of fading due to atmospheric propagation are of concern to optimize system capacity and meet quality and reliability criteria. Examples are fixed networks that include a space segment and systems that apply fade mitigation or resource sharing techniques.

Several temporal scales can be defined, and it is useful to have information on fade slope, fade duration and interfade duration statistics for a given attenuation level. Fade duration is defined as the time interval between two crossings above the same attenuation threshold whereas interfade duration is defined as the time interval between two crossings below the same attenuation threshold. Fade slope is defined as the rate of change of attenuation with time.

Of particular interest in the context of availability criteria is the distinction between fades of shorter and longer duration than 10 s. Knowledge of the distribution of fade duration as a function of fade depth is also a prerequisite for the application of risk concepts in the provision of telecommunication services.

In addition, information about the expected fade slope is essential to assess the required minimum tracking rate of a fade mitigation system.

Module description¶

itur.models.itu1623.Qfunc(z)[source]¶

Tail distribution function of the standard normal distribution.

Q(z) is the probability that a normal (Gaussian) random variable will a value larger than z standard deviations

The Q-function can be expressed in terms of the error function as

\[Q(z) = \frac{1}{2} \left(1 - erf\left(\frac{z}{\sqrt{2}}\right)\right)\]

Parameters:	z (float) – Value to evaluate Q at.
Returns:	q – Value of the Q function evaluated at z.
Return type:	float

itur.models.itu1623.change_version(new_version)[source]¶

Change the version of the ITU-R P.1623 recommendation currently being used.

This function changes the model used for the ITU-R P.1623 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

1: Activates recommendation ITU-R P.1623-1 (03/2005) (Current version)

0: Activates recommendation ITU-R P.1623-0 (04/2003) (Superseded)

itur.models.itu1623.get_version()[source]¶

Obtain the version of the ITU-R P.1623 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu1623.fade_duration_probability(D, A, el, f)[source]¶

Compute the probability of occurrence of fades of duration longer than D.

Compute the probability of occurrence of fades of duration d longer than D (s), given that the attenuation a is greater than A (dB).

This probability can be estimated from the ratio of the number of fades of duration longer than D to the total number of fades observed, given that the threshold A is exceeded.

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz)
Returns:	p – Probability of occurence of fade events of duration d longer than D given a>A, P(d > D\|a > A)
Return type:	number, sequence, or numpy.ndarray

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration_cummulative_probability(D, A, el, f)[source]¶

Compute the cumulative probability of exceedance of fades of duration longer than D.

Compute the cummulative exceedance probability F(d > D|a > A), the total fraction (between 0 and 1) of fade time due to fades of duration d longer than D (s), given that the attenuation a is greater than A (dB).

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz)
Returns:	F – Cumulative probability of exceedance, total fraction of fade time due to fades of d > D
Return type:	number, sequence, or numpy.ndarray

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration_number_fades(D, A, el, f, T_tot)[source]¶

Compute the number of fades of duration longer than D.

For a given reference period, the number of fades of duration longer D is estimated by multiplying the probability of occurrence P(d > D|a > A) by the total number of fades exceeding the threshold, Ntot(A).

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz) T_tot (number) – Total fade time from cumulative distribution (P(A)/100)Reference time period. T_tot should be obtained from local data. If this long-term statistic is not available, an estimate can be calculated from Recommendation ITU-R P.618. In this case the procedure consists in calculating the CDF of total attenuation, deriving the percentage of time the considered attenuation threshold A is exceeded and then the associated total exceedance time T_tot for the reference period considered. For a reference period of a year, T_tot = ((100-availability_in_pctg)/100)365.25243600 [s]
Returns:	N – threshold A
Return type:	Total number of fades of duration d longer than D, for a given

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration_total_exceedance_time(D, A, el, f, T_tot)[source]¶

Compute the total exceedance time of fades of duration longer than D.

The total exceedance time due to fade events of duration longer than D is obtained by multiplying the fraction of time F(d > D|a > A) by the total time that the threshold is exceeded, Ttot(A).

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz) T_tot (number) – Total fade time from cumulative distribution (P(A)/100)Reference time period. T_tot should be obtained from local data. If this long-term statistic is not available, an estimate can be calculated from Recommendation ITU-R P.618. In this case the procedure consists in calculating the CDF of total attenuation, deriving the percentage of time the considered attenuation threshold A is exceeded and then the associated total exceedance time T_tot for the reference period considered. For a reference period of a year, T_tot = ((100-availability_in_pctg)/100)365.25243600 [s]
Returns:	T
Return type:	Total fading time due to fades of d > D for A threshold.

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration(D, A, el, f, T_tot)[source]¶

Compute the probability of occurrence of fades of duration longer than D.

Compute the probability of occurrence of fades of duration d longer than D (s), given that the attenuation a is greater than A (dB) and F(d > D|a > A), the cumulative exceedance probability, or, equivalently, the total fraction (between 0 and 1) of fade time due to fades of duration d longer than D (s), given that the attenuation a is greater than A (dB).

The function also returns other parameters associated to the fade duration prediction method. See ITU-R P.1623 Annex 1 Section 2.2

Parameters:

D (number, sequence, or numpy.ndarray) – Event durations, array, (s)
A (number) – Attenuation threshold, scalar, (dB)
el (number) – Elevation angle towards the satellite, deg (5 - 60)
f (number) – Frequency, GHz (between 10 and 50 GHz)
T_tot (number) –
Total fade time from cumulative distribution (P(A)/100)*Reference time period. T_tot should be obtained from local data. If this long-term statistic is not available, an estimate can be calculated from Recommendation ITU-R P.618. In this case the procedure consists in calculating the CDF of total attenuation, deriving the percentage of time the considered attenuation threshold A is exceeded and then the associated total exceedance time T_tot for the reference period considered.

For a reference period of a year, T_tot = ((100-availability_in_pctg)/100)*365.25*24*3600 [s]

Returns:

p (probability of occurence of fade events of) – duration d longer than D given a>A, P(d > D|a > A)
F (cumulative probability of exceedance, total) – fraction of fade time due to fades of d > D
N (total number of fades of duration d longer than D, for a given) – threshold A
T (total fading time due to fades of d > D for A threshold)

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_slope(z, A, f_B, delta_t)[source]¶

Compute the probability of exceeding a valueo f fade slope.

Fade slope is defined as the rate of change of attenuation with time information about the expected fade slope is essential to assess the required minimum tracking rate of a fade mitigation system. The model is valid for the following ranges of parameters:

frequencies from 10 to 30 GHz

elevation angles from 10° to 50°.

See ITU-R P.1623 Annex 1 Section 3.2

Parameters:

z (number, sequence, or numpy.ndarray) – array of fade slope values (dB/s)
A (number) – attenuation threshold, scalar, dB (range 0 - 20 dB)
f_B (number) – 3 dB cut-off frequency of the low pass filter (Hz, range 0.001 - 1) used to remove tropospheric scintillation and rapid variations of rain attenuation from the signal. Experimental results show that a 3 dB cut-off frequency of 0.02 Hz allows scintillation and rapid variations of rain attenuation to be filtered out adequately.
delta_t (number) – Time interval length over which fade slope is calculated (s), 2-200 s

Returns:

p (conditional probability (probability density function)) – that the fade slope is equal to the fade slope for a given attenuation value, A
P (conditional probability (complementary cumulative) – distribution function)that the fade slope is exceeded for a given attenuation value, A
P2 (conditional probability that the absolute value of) – the fade slope is exceeded for a given attenuation value, A
sigma_z (standard deviation of the conditional fade slope)
Remark
——
The output is an array of 4 elements.

Example

import itur.models.itu1623 as itu1623

z = np.linspace(-2,2,100)
A = 10
f_B = 0.02
delta_t = 1
p, P, P2, sigma_z = itu1623.fade_slope(z, A, f_B, delta_t)

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_depth(N_target, D_target, A, PofA, el, f)[source]¶

Compute the maximum fade a link must tolerate given a target outage intensity value (number of events) and a target duration of event.

The fade depth is computed by numerical solution of the fade_duration problem.

See ITU-R P.1623 Annex 1 Section 3.2

Parameters:

N_target (int) – Target outage intensity (scalar)
D_target (int) – Event duration (scalar)
A (number, sequence, or numpy.ndarray) – Attenuation distribution (CDF, A) for the link under analysis
PofA (number, sequence, or numpy.ndarray) – Probability that A is exceeded (CDF, probability)
el (number) – Elevation angle (deg)
f (number) – Frequency (GHz)

Returns:

a_min (number) – Minimum attenuation the link must tolerate to meet the OI target
Remark
——
This function uses scipy’s fsolve as optimizer.

Example

import itur.models.itu1623 as itu1623

N_target = 25
D_target = 60
PofA = np.array([50, 30, 20, 10, 5, 3, 2, 1, .5, .3, .2, .1, .05, .03,
                 .02, .01, .005, .003, .002, .001])
A = np.array([0.4, 0.6, 0.8, 1.8, 2.70, 3.5, 4.20, 5.7, 7.4, 9, 10.60,
              14, 18.3, 22.3, 25.8, 32.6, 40.1, 46.1, 50.8, 58.8])
el = 38.5
f = 28
itu1623.fade_depth(N_target, D_target, A, PofA, el, f) # 21.6922280

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en