This is a first attemtp to provide statistics about CML networks in CZ. It is ment to have some concrete material to discuss. We have currently complete data set describing CML network of T-Mobile which is one of the three dominant Cellular providers who operates biggest network of CMLs. This statistics concerns only T-Mobile network.

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MWL network of T-Mobile in CZ looks like this:

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You can clearly see hotspots with high cml density:

basic CML statistics I

This is frequency(x)-length(y) relationship

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There is a clear trend that CMLs with lower frequencies are longer, except 10 GHz. Also 80 GHz links are typicaly slightly longer than 38 GHz.

basic CML statistics II

CML sensitivity to rain rate can be estimated using ITU parameters. This is resolution of CMLs [mm/h] assuming quantization 1 dB and rain rate 10 mm/h. 5 % of least sensitive CMLs of each class were excluded form the analysis.

Interestingly even low frequency CMLs under 20 GHz have reasonable quantization for rainfall estimation as they are typicaly significantly longer than CMLs of higher frequencies.

Spatial statistics (mowing window)

This is a statistics calculated for moving window 10x10 km^2 which is moved with 2 km step both in S-N and E-W direction.

Number of CMLS

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One can see huge concentration of CMLs in cities. The highest density around 600 CMLs/(10x10 km^2), is in the Prague city center. In contrast, biggest spot with less than one CMLs/(10x10 km^2) (near the west-north border) belongs to military trianing area.

Total length of CMLs

This statistics descibes how many km of CMLs are in the 10x10 km^2 moving window

Total length of T-Mobile CMLS in Czech Republic is 36 485 km, i.e. cca 0.5 km of CMLs for km^2. In contrast to CML counts total lenghts of CMls are distributed more uniformly within CZ. This is because outside of cities there are less CMLs but they are usually significantly longer. This can be nicely seen below.

Median length of CMLs

Average length of CMLs

It is interesting that typical CML length differs around cities. E.g. Pilsen (which is fifth biggest city in CZ) have significantly longer CMLs than the other cities.

How far it is to the nearest CML?

This analysis evaluates each square km of CZ regarding how far this square is from CMLs. Two different measures of “remotness” are used:

Distance of a cell to the nearest CML path

Avout 50 % of area places are closer than 1 km to the nearest CML path. There are no places in CZ which would be further than 8 km from the path of at least one CML. This statistics however does not consider length of CMLs, i.e. relatively high coverage even in remote areas can be caused by few long CMLs which average rain rates along long path.

Distance of a cell to the nearest CML end nodes

Distance to end nodes of CML represent statistics which considers both distance of cell to the CML path but also CML length, i.e. along how long path the rain rate is integrated.

By comparison of this image with the previous one we can clearly see that significant part of coverage is provided by long CMLs. This counts especially for non urban areas.

Long CMLs however detect rain rates integrated over longer path which can lead to underestimation of peaks especially by strong convective rainfalls.

Population and CML coverage

High concentration of CMLs in cities indicate (not surprisingly) that there is strong connection between population density and CML coverage. This statistics investigates this connection using demographic data for CZ districts.

Visual inspectin of data indicates that connection between population density and number of CMLs is very strong. Let’s look at this connection in detail.

Relation between population and CML coverage

One can see that density of CMLs and population density is extremely strongly correalted (r=0.97), on the contrary there is no correlation between area of district and number of CMLs in there. Interestingly, area of ditrict and total length of CMLs in there is correlated. There is also week negative correlation between population density and total length of CMLs which indicates that less popoulated districts could have longer CMLs. However this negative correlation is really week.

Note, that most of the T-Mobile’s backhaul network is operated by CMLs. Some operators (esp. those who acquired old telecom. companies) use much more optical fiber conections. This can significantly influence CML topology of their networks and relations between population and CML coverage.