# Calculate communications window for LEO

I am designing a communication system for a small satellite. One of the major constraints is the duration of communication between the satellite and the ground station. I did link budget calculations and the minimum SNR required is 15 dB. I also understand that path loss depends on distance between the transmitter and the receiver, and increasing the SNR will require increasing the power transmitted.

To get to the question, my constraints are :
1- Max. data rate 9600 bps.
2- Amount of data to be sent is 3.9MB.
3- My SNR is 10 dB.
4- Maximum transmit power = 1 W
5- Altitude = 667km

From the above values, how can I calculate the communications window (duration). At what elevation angle should communication start? Is there a way to graph the relationship between SNR, path loss and elevation angle?

• Seems like a homework question. Have you attempted to answer these questions yourself? Are you stuck on some particular concept? – Chris May 23 '16 at 13:48
• I'm happy to answer but we need some more information: Which direction(s) are you transmitting and if bidirectional are the requirements the same? Does this need to be analytical or can you use a computer to help out? What are the antenna gains? Note that Free Space Path Loss (FSPL) is a function of distance and frequency. Is the frequency the same in both directions? Lastly note that FSPL does not include atmospheric losses, pointing inaccuracies, or antenna gain variations. Short Answer: YES, you can graph SNR vs FSPL vs elevation angle, etc, we just need some more information. – Andrew W. May 23 '16 at 18:17
• @Chris no it is not a homework, it is a research am working on and supervisor ask me if i can do it. i did a research before asking, the only paper i found was comparing between elevation angle and amount of data rate that can be transferred. all am asking is to guide me with steps and i will do it by my self. – user5564784 May 23 '16 at 18:57
• @AndrewW. it is down-link from satellite to ground-station, yes bidirectional is requirement since the ground station need to send command to satellite . However they use different frequency (MHz,MHz). am fine with any method as long as i can understand how the calculation is done and graph it. hope i get help on this. – user5564784 May 23 '16 at 19:07

Thanks for the clarification. Your problem has two parts. 1) What is the spacial relationship between the ground station and the satellite and 2) given a spacial relationship between two radios, how 'good' is the connection between them.

Problem 1: Taking the Easy Efficient Route

The spacial relationship between a satellite and a receiver can be calculated by hand (a common home work assignment in aerospace classes, and another discussion in itself), but the fastest way to find satellite coverage windows is to use a computer. There is plenty of free software available that can do this, but I'll recommend the free version of STK. Here is what you can do with the free version, and here is where you can download it.

Problem 2: Elevation Angle

The system could be designed in various ways. Data is often broken into packets, which can be transmitted individually. The satellite needs to know which packets the ground station has received successfully and vice versa. Successful reception of a packet is acknowledged with an 'ACK' transmission. To downlink, the satellite could be commanded to transmit a packet repeatedly until it is received successfully, then commanded to transmit the next packet. To uplink data, the ground station would transmit a command or packet and wait for an ACK, then transmit another packet. These methods are agnostic of communication angle and path loss. You simply start when the satellite is approaching the window.

Problem 3: Relating SNR and Path Loss to Elevation Angle

First, Power. Free Space Path Loss (FSPL) is used in conjunction with the Friss Transmission Equation to compute signal power at the input of the receiver (not the receivers antenna, the actual receiver). Given the location of the radios and some information about the receivers this is straight forward. Including atmospheric and other effects can be done if you want a more realistic model (let me know if you're curious).

Next, Noise. Noise is a little complicated since it involves the actual noise of the transmitter and receiver, as well as external noise. Let's ignore external noise and look at thermal noise. Electrical noise is often measure in temperature because thermal energy translates to electron motion, which is electrical noise. Noise power density (noise power per unit bandwidth) is found as $N_0=kT$ where $N_0$ is in watts, $k$ is the Boltzmann constant in joules/kelvin, and $T$ is the receiver system noise temperature in kelvin. A simple approximation of $T$ on Earth is 290 K. (This is ignoring a few things, but it's an okay first attempt).

Noise power spectral density is found as $\frac{E_b}{N_0}=\frac{S/R}{N_0}=\frac{S}{kTR}$ (not in dB) where $S$ is signal power, and $R$ is the bit rate. This is the Energy per bit over the noise density, or the SNR per bit. Defining this in terms of bits will help us relate it to data rate. Further, $SNR = \frac{S}{R}=\frac{E_bR}{N_0B}$ where $B$ is the bandwidth of the signal. Changing your encoding will give different relationships between noise and bit error rate.

increasing the SNR will require increasing the power transmitted

Remember decreasing system noise also will increase SNR.

Final Thought: Data Rate

The Shannon-Hartley theorem defines the maximum possible information rate over any (AWGN) channel. $I<B \log_2{\left(1+\frac{S}{N}\right)}$.

You can now relate elevation angle with path loss, SNR, and even maximum data rate. Hurray!

I'm not sure I understand, but I'm going to try to explain. I'm an astronautical engineer, so I'm gonna explain this in orbital mechanics instead of electronics. Hope it helps!

Basically, in orbital mechanics we assume that you can communicate with your sat between the time that it enters to G/S's horizon and the time when it leaves it. You know your altitude and Earth's radius so you can evaluate the central angle related to your orbit using basic trigonometric calculations. Then you can calculate your period in that altitude. Now you know your communication time.

For further analysis, communication time depends on satellite's attitude capability. Also you need to perform an orbital analysis to know that satellite passes directly above GS or at an angle, and when it will pass above GS.

Good luck.