This question appears in Mumbai University > Satellite Communication and Network subject

Marks: 6 M

Year: May 2015

A measure of the performance of a satellite link is the ratio of carrier power to noise power at the receiver input, and link-budget calculations are often concerned with determining this ratio.

Conventionally, the ratio is denoted by $\frac{C}{N}$ (or CNR), which is equivalent to $\frac{P_R}{P_N}$ . In terms of decibels,

$\frac{C}{N}=(P_R )-(P_N ) (1)$

Evaluating the values for $\frac{P_R}{P_N}$ , we get

$\frac{C}{N}=(EIRP)+(G_R )-(LOSSES)-(k)-(T_S )-(B_N) (2)$

The $\frac{G}{T}$ ratio is a key parameter in specifying the receiving system performance. The antenna gain $G_R$ and the system noise temperature $T_S$ can be combined in eq. (2) as

$[\frac{G}{T}]=[G_R ]-[T_S ]dBK^- (3)$

Therefore, the link equation becomes

$\frac{C}{N}=(EIRP)+(\frac{G}{T})-(LOSSES)-(k)-(T_S )-(B_N) (4)$

The ratio of carrier power to noise power density $\frac{P_R}{N_0}$may be the quantity actually required.

Since $P_N=kT_N B_N=N_0 B_N$, then

$[\frac{C}{N}]=[\frac{C}{N_0 B_N }]$

$= [\frac{C}{N_0 }]-[B_N ]$

…and therefore,

$[\frac{C}{N_0} ]=[\frac{C}{N}]+[B_N ] (5)$

$\frac{C}{N}$ is a true power ratio in units of decibels, and $B_N$ is in decibels relative to 1 Hz, or dBHz. Thus, the units for $[\frac{C}{N_0} ]$ are dBHz. Substituting eq. (5) for $[\frac{C}{N}]$ gives

$\frac{C}{N_0} =(EIRP)+(\frac{G}{T})-(LOSSES)-(k) (6)$