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# Satellite Communication - Link Budget

In satellite communication systems, there are two types of power calculations. Those are transmitting power and receiving power calculations. In general, these calculations are called as **Link budget calculations**. The unit of power is **decibel**.

First, let us discuss the basic terminology used in Link Budget and then we will move onto explain Link Budget calculations.

## Basic Terminology

An **isotropic radiator** (antenna) radiates equally in all directions. But, it doesn’t exist practically. It is just a theoretical antenna. We can compare the performance of all real (practical) antennas with respect to this antenna.

### Power flux density

Assume an isotropic radiator is situated at the center of the sphere having radius, r. We know that power flux density is the ratio of power flow and unit area.

**Power flux density**,$\Psi_i$ of an isotropic radiator is

$$\Psi_i = \frac{p_s}{4\pi r^2}$$

Where, $P_s$ is the power flow. In general, the power flux density of a practical antenna varies with direction. But, it’s **maximum value** will be in one particular direction only.

### Antenna Gain

The **gain** of practical antenna is defined as the ratio of maximum power flux density of practical antenna and power flux density of isotropic antenna.

Therefore, the Gain of Antenna or **Antenna gain**, G is

$$G = \frac{\Psi_m}{\Psi_i}$$

Where, $\Psi_m$ is the maximum power flux density of practical antenna. And, $\Psi_i$ is the power flux density of isotropic radiator (antenna).

### Equivalent Isotropic Radiated Power

Equivalent isotropic radiated power (EIRP) is the main parameter that is used in measurement of link budget. **Mathematically**, it can be written as

$$EIRP = G\:\:P_s$$

We can represent EIRP in **decibels** as

$$\left [ EIRP \right ] = \left [ G \right ] + \left [ P_s \right ]dBW$$

Where, **G** is the Gain of Transmitting antenna and $P_s$ is the power of transmitter.

### Transmission Losses

The difference between the power sent at one end and received at the receiving station is known as **Transmission losses**. The losses can be categorized into 2 types.

- Constant losses
- Variable losses

The losses which are constant such as feeder losses are known as **constant losses**. No matter what precautions we might have taken, still these losses are bound to occur.

Another type of loses are **variable loss**. The sky and weather condition is an example of this type of loss. Means if the sky is not clear signal will not reach effectively to the satellite or vice versa.

Therefore, our procedure includes the calculation of losses due to clear weather or clear sky condition as 1^{st} because these losses are constant. They will not change with time. Then in 2^{nd} step, we can calculate the losses due to foul weather condition.

## Link budget calculations

There are two types of link budget calculations since there are two links namely, **uplink** and **downlink**.

### Earth Station Uplink

It is the process in which earth is transmitting the signal to the satellite and satellite is receiving it. Its **mathematical equation** can be written as

$$\left(\frac{C}{N_0}\right)_U = [EIRP]_U+\left(\frac{G}{T}\right)_U - [LOSSES]_U -K$$

Where,

- $\left [\frac{C}{N_0}\right ]$ is the carrier to noise density ratio
- $\left [\frac{G}{T}\right ]$ is the satellite receiver G/T ratio and units are dB/K

Here, Losses represent the satellite receiver feeder losses. The losses which depend upon the frequency are all taken into the consideration.

The EIRP value should be as low as possible for effective UPLINK. And this is possible when we get a clear sky condition.

Here we have used the (subscript) notation “U”, which represents the uplink phenomena.

### Satellite Downlink

In this process, satellite sends the signal and the earth station receives it. The equation is same as the satellite uplink with a difference that we use the abbreviation “D” everywhere instead of “U” to denote the downlink phenomena.

Its **mathematical** equation can be written as;

$$\left [\frac{C}{N_0}\right ]_D = \left [ EIRP \right ]_D + \left [ \frac{G}{T} \right ]_D - \left [ LOSSES \right ]_D - K$$

Where,

- $\left [\frac{C}{N_0}\right ]$ is the carrier to noise density ratio
- $\left [\frac{G}{T}\right ]$ is the earth station receiver G/T ratio and units are dB/K

Here, all the losses that are present around earth stations.

In the above equation we have not included the signal bandwidth B. However, if we include that the equation will be modified as follows.

$$\left [\frac{C}{N_0}\right ]_D = \left [ EIRP \right ]_D + \left [ \frac{G}{T} \right ]_D - \left [ LOSSES \right ]_D -K-B$$

### Link Budget

If we are taking ground satellite in to consideration, then the free space spreading loss (FSP) should also be taken into consideration.

If antenna is not aligned properly then losses can occur. so we take **AML** (Antenna misalignment losses) into account. Similarly, when signal comes from the satellite towards earth it collides with earth surface and some of them get absorbed. These are taken care by atmospheric absorption loss given by **“AA”** and measured in db.

Now, we can write the loss equation for free sky as

$$Losses = FSL + RFL+ AML+ AA + PL$$

Where,

RFL stands for received feeder loss and units are db.

PL stands for polarization mismatch loss.

Now the **decibel equation** for received power can be written as

$$P_R = EIRP + G_R + Losses$$

Where,

- $P_R$ stands for the received power, which is measured in dBW.
- $G_r$ is the receiver antenna gain.

The designing of down link is more critical than the designing of uplink. Because of limitations in power required for transmitting and gain of the antenna.