A model for time and frequency spreading of radio signals
propagating through the equatorial ionosphere.

The ITU-R Study Group 3 has a need to provide a method suitable for prediction of the performance of digital signals propagating between terrestrial locations via the ionosphere.

A method already exists for predictions for analogue systems in Recommendation ITU-R P.533-8, and proposals are being made to extend this method. The basis of the method is to predict the transmission loss for individual modes and to take account of the differential time delay due to the time-of–flight of each active mode. Differential frequency shift (Doppler) due to ionospheric bulk movement is small and would be ignored.

This approach may be appropriate in benign mid-latitude conditions, but it is highly desirable to include terms due to ionospheric scattering for both equatorial and high latitude conditions.

The Annex below is a proposal for a hypothetical model for equatorial scattering (a proposal for high latitudes is still being sought). There seems to be no quantitative data available, although some information may be gained from gain-calibrated ionosondes, and some inferences may be drawn for trans-ionospheric observations. What is presented here is an intuitive impression of what may be the situation, with the intention of seeking criticism and suggestions from the participants in WG4 and from other experts for improving either the whole model or any of the parameters.

Question 1

As indicated above individual modes are predicted to have time delays given by:

where:

c : velocity of light (km/s).

and p' : virtual slant range (km), for the predicted ray path for the mode.

Observations have been made by Shepherd, Tupper and Lomax, “HF Data Compendium: Power Spectra and Oblique Ionograms” (SRI, July 1965) for the average frequency shift on paths to California from New Jersey and Greenland. These had a median of the average frequency shift of 0.22 Hz and an upper decile of 0.74 and 0.81 Hz respectively.

Is it adequate to assume a differential time delay based on the above equation, and to ignore Doppler shift? If not what better models may be used?

Question 2:

Caldwell et al (Caldwell J D, Stevens E E and Warren E S “The reflection coefficient of an ionosphere containing large scale irregularities” in “Oblique ionospheric radiowave propagation at frequencies near the LUF” ed T B Jones, AGARD Conf Proc 13, 1969) suggest that in extreme spread-F conditions, the peak signal power decreases by 3 – 4 dB for 100μs pulses, and less for longer pulses; and that the overall reflection coefficient, including the scatter, increases by as much as 7 dB.

The model presented here assumes that, for each mode where the reflection control point is in the defined area, the specular return due to ionospheric refraction will continue to exist with an unaltered transmission loss, but that time delayed scattered returns may also occur. It is also assumed that the maximum power of the time and frequency scattered components occurs at the same time and frequency as the specular component, 6 dB below the specular component. However, it is also assumed that the maximum of the scattered component decreases with the sunspot number.

Is there a better model for the maximum amplitude of the scattered and specular signals, suitable for use in a probabilistic prediction procedure?

Question 3:

The SRI results showed that the median of the observed standard deviation of frequency scattering was 0.27 and 3.01 Hz, respectively, for the two paths referred to above, with upper decile values of 1.98 and 7.3 Hz. No results for the equatorial region have been found.

Some qualitative information on equatorial scattering may be seen in ionograms.

In the model the time spread is assumed to start at the time of the reflected mode and to extend to greater times with a half-normal distribution with a σ of 1 ms. The frequency spread is assumed to be centered on the transmitted centre frequency with a standard deviation of 3 Hz.

Are there experimental or theoretical results to support or improve these assumptions?

Question 4:

By consideration of the latitudinal extent of the equatorial anomaly, and taking into account trans-ionospheric observations, a model for the size of the equatorial scattering region has been suggested. It is assumed that time and frequency spreading due to scatter occurs in the evening, at a constant level between 19 and 23 hours local time and between ±15° dip latitude. It does not occur between the hours of 03 and 18 local time, nor beyond dip latitudes of 25°. The transition between these two regimes is made with a cubic expression to avoid discontinuities.

Can an improved model be developed?

Question 5:

Cole and McNamara (D G Cole & L F McNamara "Variations of Spread-F Occurrence Rates at Near-equatorial Stations in the Australasian Zone" Aust J Phys, v27 pp249-257, 1974" have shown that in general the occurrence of spread-F is a maximum in equinoctial months at high sunspot numbers. It is assumed in the model that the probability that scattering will occur (i.e. the number of evenings per month when scattering would be observed) varies with sunspot number, from 10% of the month when R₁₂=0, to 90% when R₁₂=100, and that the equinoctial peaks in occurrence may be modeled with a sine function.

Does the probability of occurrence behave in this way?

Question 6:

Can models be proposed for these or any other variables?

Question 7:

What is the model for high latitude scattering?

Annex

The proposed scattering model

1. The time scattering model for the available power from the scattered component is given by a half-normal distribution:

   

   for

   where p_m is the available received power from specular reflection of the mode

   R_factor is (0.2+0.008R₁₂) or 1 whichever is the smaller, and R₁₂ is the sunspot number

   is the time delay being considered

   is the time delay of the specular mode

   T_spread is the standard deviation of the time spread in this half distribution, taken as 1ms

   

   where |λ_d| is the magnetic dip latitude

   

   where T_l, is the local time at the control point in hours.

2. For frequency spreading the scatter is symmetrical around the frequency of the specular component with a similar form of variation as for time spreading:

   

   f is the frequency being considered

   f_m is the centre frequency of the specular mode

   F_spread is the standard deviation of the frequency spread, taken as 3 Hz

3. The probability of occurrence of scattering on a day within a month, prob_occ, is given by:

   

   

   

   where m is the month number

4. The prediction procedure would be to determine the levels of the time and frequency scattered components at the limits of the time and frequency windows specified for the modulation system in use. If the ratio of the greater of these two levels to the level of the specular component of the dominant mode falls within the limits specified for inter-symbol interference for the system, then the system is predicted to fail with a probability given by the probability of scattering occurrence.

Responses

Please send your criticisms, comments and suggestions on any of the questions above to:

wg4@ips.gov.au

lesbarclay@iee.org and john@ips.gov.au

Further topics for this page.

• data sets wg4 encourages people to use as tests
• discussions of methodology that may, or may not evolve from discussions in the mail list
• discussions of the problems, key work areas, etc
• links to papers, software etc of direct interest to the project area
• links to meetings of direct interest to the project area
• and generally anything that seems likely to stimulate the project further.