This JavaScript calculates estimated median values for external radio noise based on the spherical harmonic coefficient model of CCIR Report 322-3 and ITU-R P.372, the calculation is according to NTIA Report 87-212 p.11 ff. It can be expected that in 50% of all measurements the noise level is lower than or equal to and in 50% higher than or equal to the estimated median values, and furthermore that in 80% of all measurements the downward or upward deviation from the median values is not higher than Dl or Du. These estimates apply only to background noise, which is white noise generated by many distributed distant sources. In contrast, superimposed impulse noise which sounds crackling or "corny" or rapid amplitude changes are generated by local sources like nearby thunderstorms, rain or snowfall or electrical appliances in the neighborhood. A noise level significantly above the predicted values can be an indicator for such local sources.

ATMOSPHERIC NOISE

Atmospheric noise is caused by electrical discharges in the atmosphere due to e.g. thunderstorms, rain and snow, sandstorms. It can propagate over long distances on shortwave via the ionosphere and depends on location, frequency, time of day and season. In high latitudes only relatively weak noise is to be expected, while in the tropical zone, especially during the rainy season, very strong atmospheric noise is generated.

In the years 1957 to 1966 (19th sunspot cycle maximum to minimum and beginning of the 20th cycle), as part of an international cooperative program of the URSI, the atmospheric noise between 13 KHz and 20 MHz and its statistical distribution was measured by a network of 16 stations equipped with the standardized radio noise recorders ARN-2 at the following locations:

Balboa, Panama Canal Zone
Bill, Wyoming, USA
Boulder, Colorado, USA
Byrd Station, Antarctica
Cook, Australia
Enkoping, Sweden
Front Royal, Virginia, USA
Ibadan, Nigeria
Kekaha, Hawaii, USA
New Delhi, India
Ohira, Japan
Pretoria, South Africa
Rabat, Morocco
San Jose, Brazil
Singapore
Thule, Greenland

The collected noise data was grouped into four seasons ...

Winter in the northern hemisphere =
Summer in the southern hemisphere =
December, January, February

Spring in the northern hemisphere =
Fall in the southern hemisphere =
March, April, May

Summer in the northern hemisphere =
Winter in the southern hemisphere =
June, July, August

Fall in the northern hemisphere =
Spring in the southern hemisphere =
September, October, November ...

... within which there are six 4-hour blocks of local mean time ...

00:00 - 04:00
04:00 - 08:00
08:00 - 12:00
12:00 - 16:00
16:00 - 20:00
20:00 - 24:00

... and converted to a matched and lossless short monopole antenna (length << 0.1 λ) over a perfectly conductive radial network, which to this day is the reference antenna in ITU publications. Finally, a spherical harmonic analysis was applied to this data, which resulted in a set of coefficients from which the median value of the effective antenna noise figure Fam [dB(kTob)] of the reference antenna caused by external noise and its statistical variance can be calculated as a function of geographical latitude and longitude, season, time block and frequency.

As early as 1964, before the measurements were completed, the ITU published CCIR Report 322 "Worldwide Distribution and Characteristics of Atmospheric Radio Noise" with 24 (4 seasons x 6 time blocks) isoline maps and diagrams showing these values for any point on the earth's surface and any frequency between 10 KHz and 30 MHz. Lucas and Harper developed a numerical representation of Report 322 in 1965 based on the 1 MHz maps instead of the original data points from which the maps were created, which resulted in an average error of about 2 dB and a maximum error of about 10 dB compared to the maps. In 1970, Zacharisen and Jones developed numerical maps from the original data and in 1982 Sailors and Brown developed a simplified numerical model for minicomputers. This 1964 report only considered the data collected between July 1957 and October 1961, but it was reprinted in 1983 as CCIR Report 322-2 with revised text and under a different title, but with the same atmospheric noise data.

Later, data from the 16 original stations were available until 1966, and additional data were available for many years from 10 stations in the then USSR and from Thailand until 1968. The new locations were:

Laem Chabang, Thailand
Alma Ata, USSR
Ashkhabad, USSR
Irkutsk, USSR
Khabarovsk, USSR
Kiev, USSR
Moscow, USSR
Murmansk, USSR
Simferopol, USSR
Sverdlovsk, USSR
Tbilisi, USSR

This new data was analyzed, corrected, converted and added to the existing data by David Sailors and his colleagues at the Naval Ocean Systems Center (NOSC) in San Diego, California, and the Institute for Telecommunication Sciences (ITS) in Boulder, Colorado. The result was a new set of 13,056 coefficients as the basis for the CCIR Report 322-3 and the Recommendation ITU-R P.372 (Spaulding, Stewart: "Atmospheric Radio Noise: Worldwide Levels and Other Characteristics", NTIA Report 85-173, 1985). The numerical version of Report 322-3 is now exact, i.e. the numerical and graphical versions provide identical data for all parameters including the median effective noise figure Fam.

MAN-MADE NOISE

Artificial or "man-made" noise is caused by electrical devices, equipment and networks. The NTIA Report 87-212 also provided an improved model for this noise component, which was developed by Spaulding and Disney in 1974 and is based primarily on measurements taken in the United States. The measurements for quiet rural areas were carried out worldwide. The model for man-made noise is based on the following equation:

Fam = c - d log(f)

with f = frequency [MHz] and the constants c and d from the following table:

Environmental category: c / d
*****
Business: 76.8 / 27.7
Inter-state highways: 73.0 / 27.7
Residential: 72.5 / 27.7
Parks and university campuses: 69.3 / 27.7
Rural: 67.2 / 27.7
Quiet rural: 53.6 / 28.6


Normally, only the categories business (city, industrial area), residential (residential area), rural (rural area) and quiet rural (quiet rural area, remote and uninhabited) are used. The analysis of the measured data has shown that the following statistical parameters provide acceptable results for all four categories and all frequencies, but are most suitable for the shortwave range:

Du = 9.7 dB
σ Du = 1.5 dB
Dl = 7.0 dB
σ Dl = 1.5 dB
σ Fam = 5.4 dB

While in the past ignition systems of motor vehicles and overhead power lines also for low-voltage contributed a lot to the artificial noise, today's ignition systems and the low-voltage lines that we have now mostly laid in the ground are no longer an issue. Instead, new technologies (e.g. switch-mode power supplies, PLC, power-saving and LED lights, solar systems) and the cumulative interference caused by the rapid increase in the number of devices in use is very problematic. In recent years, several studies have been conducted with contradictory results. A large-scale measurement campaign by the BNetzA between 2007 and 2009 at over 100 locations in Germany at frequencies of 5, 12 and 20 MHz even came to the conclusion that the artificial noise was usually lower than predicted by the model (Report ITU-R SM.2155, result on p.29 Table 4).

For the artificial noise, the GENOIS procedure in the NTIA report calculates with σ Fam = 3.0 dB instead of the correct value given in the report as 5.4 dB, in the old program NOIS1.FOR with Dl = 6.0 dB instead of the correct value given in the report as 7.0 dB and in the new program GH_NOISE again with all correct values according to the report.

GALACTIC NOISE

Galactic noise is only significant when highly directive antennas are pointed toward the sun or other regions of the sky, such as the center of the Milky Way, and due to ionospheric absorption only above approximately 15 MHz. The following parameters apply to this noise component:

Fam = 52.0 - 23.0 log(f)

Du = 9.7 dB
σ Du = 0.2 dB
Dl = 2.0 dB
σ Dl = 0.2 dB
σ Fam = 0.5 dB

COMBINED NOISE

External electromagnetic noise ("radio noise") is composed of the three components atmospheric, artificial or man-made and galactic noise, which must be summed correctly. The normal distribution (Gaussian distribution, bell curve) is the most important probability distribution. Examples: intelligence, body height, income (if it is logarithmized) are normally distributed. The "logarithmic normal distribution" (abbreviated "log-normal" distribution) describes the distribution of a random variable x if ln(x) or log(x) is normally distributed. Conversely, if y is normally distributed, then e^y or 10^y is log-normally distributed. While a normally distributed random variable can be understood as the sum of many independent random variables, a log-normally distributed random variable is the product of many random variables and therefore the log-normal distribution is the simplest distribution for multiplicative models. This includes atmospheric, galactic, and artificial noise, because their noise factors fa are log-normally distributed and thus their noise figures Fa = 10 log (fa) are normally distributed. Therefore, the mean value can be directly calculated from two noise figures Fa in dB and linear interpolation can be performed directly between them.

Spaulding & Stewart showed in NTIA Report 87-212 that the previously applied method of determining the distribution of the combination of the three noise components was not correct and developed a statistically more correct method. Simply adding up the average values for the atmospheric, artificial and galactic noise power into a resulting average value would be correct, but the model provides median values and adding these up into a resulting median value would produce an error. Therefore, the noise components must be combined using split log-normal distributions.

The strength of all three noise components decreases with increasing frequency. Atmospheric noise is usually stronger than artificial noise at electrically quiet locations at low latitudes below 20 MHz, while galactic noise can only become the dominant component at electrically very quiet, remote locations and at high latitudes.

The non-local background noise received by an antenna is generated by a very large number of sources and comes from a correspondingly large number of random directions and elevation angles. It can therefore be assumed that concerning noise any antenna behaves like an isotropic radiator. It can also be assumed that noise coming via sky wave from distant sources or via line-of-sight from very nearby sources is randomly polarized and that noise coming via ground wave is mostly vertically polarized. Noise coming via ground wave is therefore strongly suppressed by horizontal antennas and, as a result, more artificial noise is received by vertical antennas than in electrically quiet areas, where there is hardly any noticeable difference between vertical and horizontal antennas.

The noise power supplied by an antenna is the sum of all the power received from individual sources with their own Poynting vectors and polarization planes and therefore cannot be calculated with the antenna gain over the field strength in the deterministic physical sense as we do for a singular radio signal. In order to create a basis that can be applied to all noise components and that also allows a comparison of their strength, in the relevant ITU documents of the ITU a noise power Pn is assumed, which the reference antenna delivers from external sources.

THERMAL NOISE

Thermal or Johnson-Nyquist noise limits the sensitivity and determines the minimum detectable Signal MDS of a receiver. It is white noise caused by the thermal movement of charge carriers in conductive media at a temperature above zero Kelvin. Every Ohmic resistance R is a noise source, and the effective noise voltage across its terminals is ...

Un [V] = √ (4 k T R b)

... with the Boltzmann constant k = 1.387 x 10^-23 J/K, temperature T [K], resistance R [Ω] and bandwidth b [Hz]. In short-circuit operation, the noise power ...

Pn [W] = Un² / R = 4 k T b

... is dissipated by R. A load resistance matched to this noise source has the same value R for maximum power extraction. Due to voltage division, only half the noise voltage drops across it, so the extracted noise power is a quarter of that value or ...

Pn [W] = (Un / 2)² / R = k T b

In contrast to noise voltage, noise power is therefore independent of R, regardless of whether it is a megaOhm carbon film resistor or a short piece of copper wire with a few milliOhms. The values for a bandwidth of 1 Hz are referred to as the spectral noise voltage density [V/√Hz] and noise power density [V/Hz]. The noise voltage increases with √b and the noise power with b, where b stands for the equivalent noise bandwidth of an ideal bandpass filter with a rectangular "brick wall" frequency response. For a resonant circuit b = π fo / (2 Q). At a reference temperature of To = 290 K = 17° C any Ohmic resistance at the input of a radio receiver thus generates a noise power density of k To = 4.02 x 10^-21 W/Hz = -204 dBW/Hz = -174 dBm/Hz. This value represents the theoretically achievable minimum noise floor and thus the absolute sensitivity limit of an ideal receiver at that temperature.

EFFECTIVE ANTENNA NOISE FIGURE

The effective antenna noise figure is the ratio of the noise power Pn received by the reference antenna to the thermal noise power of a resistor at the reference temperature, i.e. the ratio of the effective antenna temperature to the reference temperature:

fa = Pn / (k To b) = Ta / To
Fa = 10 log (fa)

where:

fa = effective antenna noise figure
Fa = effective antenna noise figure [dB(kTob)]
Pn = available noise power [W]
k = Boltzmann constant (1.387 x 10^-23 J/K)
b = effective noise bandwidth [Hz]
To = reference temperature (290 K / 17° C)
Ta = effective antenna temperature due to external noise [K]

So it is:

Pn [W] = fa k To b = 10^Fa/10 k To b

and with B = 10 log (b) and 10 log (k To) = -204 dBW we get:

Pn [dBW] = Fa + B - 204

This results in the effective noise voltage delivered by the reference antenna to a receiver with input resistance Ri [Ω]:

Un [V] = √ (Pn Ri)

For the effective length he and the radiation resistance Rs of the reference antenna (a lossless short monopole above perfect ground-plane) with length l [m] and wavelength λ [m], the following applies:

he [m] = l / 2
Rs [Ω] = 40 π² (l / lambda)² = 395 (l / λ)²

In the electric field E [V/m] and matched to Rs it delivers the voltage Ur and the maximum available receive power Pr:

Ur [V] = E he / 2
Pr [W] = (Ur / 2)² / Rs
= (E l / 4)² / 395 l² / λ²
= E² l² / 6320 l² / λ²
= E² λ² / 6320
= E² λ² / 640 π²

The receive power Pr therefore gives the electric field strength with the wavelength λ [m] or frequency f [MHz]:

E [V/m] = √ (Pr 640 π² / λ²)
= √ (Pr 640 π² f² / 300²)

Replacing Pr with the thermal noise power density Pnd = k To = 4.02 x 10^-21 W/Hz yields the equivalent electric noise field strength density:

End(kTo) [V/(m√Hz)] = √ (4.02 x 10^-21 640 pi² f² / 300²)
= √ (2.82 x 10^-22 f²)
= 1.68 x 10^-11 f
End(kto) [uV/(m√Hz)] = 1.68 x 10^-5 f
End(kto) [dB(uV/(m√Hz))] = 20 log (f) - 95.5

For the effective antenna noise figure Fa [dB(kTob)] this results in the electrical noise field strength:

En [dB(uV/m)] = Fa + 20 log (f) + B - 95.5

Illuminated by this this electric field a lossless matched monopole delivers:

Pn [W] = fa k To b = 10^Fa/10 k To b
Un [V] = √ (Pn Ri)

However, a lossless matched dipole delivers twice the power or +3 dB, because half of the effective area of the monopole lies in the ground and cannot extract any energy from the field. This result can also be obtained by taking a different approach: the dipole picks up twice the voltage U of a half-length monopole from the electric field and its radiation resistance R is twice as high, so a matched load resistance absorbs the power (2 U)²/ (2 R) = 2 U² / R, in contrast to U² / R for the monopole. This applies to all non-monopole antennas if they are matched and lossless, because in terms of external noise they can be regarded as isotropic radiators.

fa and Fa are independent of the receive bandwidth b, because the noise power supplied by the antenna and that supplied by a resistor are both proportional to the bandwidth, and therefore the valid units for Fa are dB(kTo) and dB(kTob). By contrast, the noise power Pn and noise field strength En are dependent on the bandwidth. Background noise does not come from a single source and therefore does not correlate. Pn and En therefore increase with the measurement bandwidth by 10 log (b) or 3 dB when doubled. Most digital signals are similar to noise. Correlated signals, on the other hand, come from a single source and as long as the measurement bandwidth is less than the signal bandwidth, Pn and En increase with 20 log (b) or 6 dB when doubled.

The above considerations refer exclusively to background noise, which is white noise generated by many non-local sources. On the other hand, superimposed impulse disturbances or rapid amplitude changes are generated by local sources, e.g. nearby thunderstorms or filthy electrical equipment in the neighborhood. A noise level significantly above the predicted value indicates local artificial sources.

ANTENNA POLARIZATION AND LOCAL NOISE

Radio propagates via sky wave, which enables long-distance ionospheric propagation on shortwave, and via ground wave. The sky wave has two components: the direct wave propagates along a straight line from the transmit antenna towards the ionosphere, the ground-reflected wave bounces off the earth's surface and heads in the same direction. The sky wave also exists for local propagation, with the direct wave travelling in a straight line-of-sight between the transmit and receive antennas and the ground-reflected wave taking a midpoint bounce. Because the ground reflection from a horizontally polarized antenna causes phase reversal, the less the difference in path length between the direct and reflected wave (the lower the antenna and the higher the wavelength) the more they cancel. That's why a horizontal antenna is unable to radiate into the far-field at very low elevation angles.

What makes local communication passible is a third wave, namely the surface wave, that exists only near the earth's surface for antennas close to ground and diminishes with antenna height. Surface wave intensity increases with wavelength and ground conductivity, but it is much weaker for hoizontal than for vertical electric fields. On the other hand, the vertical component of a wave's electric field is reflected at grazing angles of incidence approximately in phase, providing a boost of up to 6 dB for low elevation angles. The combination of the direct wave, the ground-reflected wave and the surface wave is called the ground wave. The ground wave makes local radio communication possible and because of the poor ground wave propagation of horizontally polarized waves, AM broadcasters on mediumwave universally used vertical antennas.

The same phenomena cause vertical antennas to pick up much more local noise than horizontal antennas do. Even if a noise source has a stronger horizontal component, by the time the field reaches the receive antenna, the vertical component almost always dominates. However, this does not apply to sky wave but only to ground wave propagated noise which comes from sources within a radius of typically a few tens of kilometers around the receiving site. The noise generated by very close sources within a distance of a few tens of meters is not propagated by radiation but electrically or magnetically coupled into the receiving antenna by the reactive near field.