Combine uplink and downlink C/N ratio
The complete satellite circuit consists of an uplink and a downlink. Noise will be introduced on the uplink at the satellite receiver input. Denoting the noise power per unit bandwidth by $P_{NU}$ and the average carrier at the same point by $P_{RU}$ , the carrier – to – noise ratio on the uplink is:
$\left(\frac{C}{N_0 }\right)_U=\left(\frac{P_{RU}}{P_{NU}}\right)$
It is important to note that power levels, and not decibels, are being used here. The carrier power at the end of the space link is shown asP_R, which of course is also the received carrier power for the downlink. This is equal to γ times the carrier power input to earth station input, as given in the below figure.
It includes the satellite transponder and transmits antenna gains, the downlink losses, and the earth station receives antenna gain and feeder losses. The noise at the satellite input also appears at the earth station input multiplied by γ and in addition, the earth station introduces its own noise which is denoted as $P_{ND}$. Thus the end – of – link noise is
$γP_{NU}+P_{ND}$
The $\frac{C}{N_0}$ ratio for the downlink alone, not counting the $γP_{NU}$ contribution, is $\frac{P_R}{P_{ND}}$ and the combined $\frac{C}{N_0}$ ratio at the ground receiver is ${P_R} (γP_{NU}+P_{ND})$. The power flow diagram is shown figure.
The combined carrier – to – noise ratio can be determined in terms of the individual link values. To show this, it is more convenient to work with the noise – to – carrier ratios rather than the carrier – to – noise ratio, and again, these must be expressed as power ratios, not decibels.
Denoting the combined carrier – to – noise values by $\frac{N_0}{C}$, the uplink value by $\left(\frac{N_0}{C}\right)_U$ and the downlink value by $\left(\frac{N_0}{C}\right)_D$ then,
$\frac{N_0}{C}=\frac{P_N}{P_R}$
$=\frac{\gamma P_{NU}+P_{ND}}{P_R}$
$=\frac{γP_{NU}}{P_R}+\frac{P_{ND}}{P_R}$
$=\frac{γP_{NU}}{γP_{RU}}+\frac{P_{ND}}{P_R}$
$\left(\frac{N_0}{C}\right)=\left(\frac{N_0}{C}\right)_U+\left(\frac{N_0}{C}\right)_D....(1)$
The above derived equation is the combine value of $\frac{C}{N_0}$ , the reciprocals of individual values must be added to obtain the $\frac{N_0}{C}$ ratio and then reciprocal of this taken to get $\frac{C}{N_0}$ .
$∴ \left(\frac{C}{N_0}\right)^2=\frac{1}{\left(\frac{C}{N_0}\right)_U^{-1}+\left(\frac{C}{N_0}\right)_D^{-1}}$
Intermodulation noise is the amplitude modulation of signals containing two or more different frequencies in a system with nonlinearities. The intermodulation between each frequency component will form additional signals at frequencies that are not just harmonic frequencies (integer multiples) of either, but also at the sum and difference frequencies of the original frequencies and at multiples of those sum and difference frequencies.
Intermodulation is caused by non-linear behavior of the signal processing being used. The theoretical outcome of these non-linearities can be calculated by generating a series of the characteristic, while the usual approximation of those non-linearities is obtained by generating a Taylor series.
Intermodulation is rarely desirable in radio or audio processing, as it creates unwanted spurious emissions, often in the form of sidebands. For radio transmissions this increases the occupied bandwidth, leading to adjacent channel interference, which can reduce audio clarity or increase spectrum usage.
In satellite communication systems, this most commonly occurs in the travelling – wave tube high – power amplifier abroad the satellite. Both amplitude and phase non – linearities give rise to this intermodulation noise.
The carrier – to – intermodulation - noise ratio is usually found experimentally or in some cases it may be determined by computer methods.
Ratio can be combined with the carrier –to – thermal noise ratio by the addition of the reciprocals.
$\left(\frac{N_0}{C}\right)=\left(\frac{N_0}{C}\right)_U+\left(\frac{N_0}{C}\right)_D+\left(\frac{N_0}{C}\right)_{IM}....(2)$ (Using equation 1)
$∴ ∴ \left(\frac{C}{N_0}\right)^2=\frac{1}{\left(\frac{C}{N_0}\right)_U^{-1}+\left(\frac{C}{N_0}\right)_D^{-1}+\left(\frac{C}{N_0}\right)_{IM}^{-1}}$
Note: To derive intermodulation noise ratio we need to first derive equation 1 and then write equation 2 directly.
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