Dear All
As we know any flying object like LEO Satellite or UAV its elevation angle of antenna of a ground(Earth) receiver starts from some value reaches a peak (maximum value) when flying object is just above your head then it starts decreasing and decreasing after some time it reaches below the earth surface and or elevation reaches zero .
Now we take an example of a signal tracking of low earth orbit satellite satellite. suppose we have a signal receiver at ground and trying to receive the satellite signal. as the elevation angle increases the received signal strength increases, this strength keep increasing as the elevation angle keep increasing . the strength of signal reaches maximum value when the satellite is just above our head after that satellite elevation decreases so the receive signal strength reaches a minimum value at minimum elevation.
the requirement is mathematical formula which provide relation between receive signal strength and elevation angle.
I found paper attached which derived probability density function of elevation angle .how can I use this pdf function in order to get the receive signal strength(or SNR) from this pdf formula. do we need another formula or some changes is required to this formula.
I shall be very grateful for help.
Regards
Hello Shakeel,
The K in my equation is for Kelvin. I was trying to indicate that TA the result of the calculation is a temperature in Kelvin. I'm afraid this text box does not work well for equations.
For a reference I recommend
Satellite communications systems / Gerard Maral, Michel Bousquet
This equation for Noise Figure will allow you to derive the relationship between the elevation angle (α) in my first equation to S/N. Again, this text box does not work well for equations. However, you should be able to find this equation in any EM or antenna text.
F= (Si/Ni)/(So/No) = No/(GNi) = No/(GkTAB) = 〖GkTA B + N)+R]/(GkTA B)
• Ni = kTOB is the available noise power at the input
• F is the Noise Figure of the receiver
• Si is the available signal power at the input
• So is the available signal power at the output
• TA is the temperature of the antenna in Kelvin
• NO is the available noise power at the output
• NR is the noise added by the receiver
• G is the available gain of the receiver
• B is the effective noise bandwidth of the receiver
Work out the signal-to-noise ratio for each elevation angle, from the geometry, generate a curve of SNR vs elevation. You could multiply this by the curve in the pdf and integrate to get average SNR. I am not sure this is a useful number to have, though. You can also use the two curves to plot probability density vs SNR, which is probably more useful.
I didn't read the document yet, but I would run the link budget, it will give us the relation between the power or density of power transmitted and the SNR, there we must include the dependence of the receiver G/T with the elevation angle. Depending on the type of receiver's antenna, T could depend on the elevation angle or both G and T depend on it. E.g. in an old parabolic antenna only the system temperature (T) depends on the elevation angle, in a new flat phase array the receiver antenna gain (G) and the system temperature (T) both depend on the elevation angle.
Dear Shakeel,
Your question itself speaks about the answer.
Dr Daniel and Dr Malcolm have highlighted main concepts
Dear All
I need SNR formula which shows dependence on the elevation angle for low earth orbit satellite. or in any generalized form for any flying object.e.g
SNR=(channel_Square) x Es/No.here channel is any wireless channel fading like rayleigh fading or rician fading.
Shakeel,
You ask "What is Mathematical relation between Signal to Noise Ratio and Satellite Elevation angle? " but then you talk about changes in received signal strength.
The changes in received signal strength that you describe are partly due to a change in distance as the elevation angle increases. Also the gain of the antenna changes as the satellite moves through its beam.
As for you original question, Daniel Moreno is on the right track when he talked about the dependence of the receiver Gain/Temperature with the elevation angle.
Atmospheric attenuation, precipitation, ground radiation and cosmic sources all effect antenna noise temperature.
The elevation dependent part of the antenna noise temperature due to losses from water and oxygen in the atmosphere can be approximated by the following formula:
TA= Tc+ Tm (1– β0cosec α ) K
where:
TA : antenna noise temperature
Tc : constant part of the noise temperature
Tm : mean radiating temperature of the absorbing medium
β0 : transmission coefficient of the atmosphere in the zenith direction
α : angle of elevation of the antenna.
Dear David thanks for answering
What is k in your formula. How to relate your formula with signal strength. The effect of elevation angle increase is the effect of increase in Snr. I need to know how this is happening. What is reference of your formula. Thanks
Hello Shakeel,
The K in my equation is for Kelvin. I was trying to indicate that TA the result of the calculation is a temperature in Kelvin. I'm afraid this text box does not work well for equations.
For a reference I recommend
Satellite communications systems / Gerard Maral, Michel Bousquet
This equation for Noise Figure will allow you to derive the relationship between the elevation angle (α) in my first equation to S/N. Again, this text box does not work well for equations. However, you should be able to find this equation in any EM or antenna text.
F= (Si/Ni)/(So/No) = No/(GNi) = No/(GkTAB) = 〖GkTA B + N)+R]/(GkTA B)
• Ni = kTOB is the available noise power at the input
• F is the Noise Figure of the receiver
• Si is the available signal power at the input
• So is the available signal power at the output
• TA is the temperature of the antenna in Kelvin
• NO is the available noise power at the output
• NR is the noise added by the receiver
• G is the available gain of the receiver
• B is the effective noise bandwidth of the receiver
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