Wireless – Calculating Maximum Distance for Receiving LTE Signal

wireless

I work for a large retailer who recently started adding outdoor Yagi antennas to try to boost their LTE signal for their LTE based modems at each store. I wanted to see if there was a way to calculate the maximum distance a cellular tower could be from us and still maintain a usable signal.

Here is what I know:

Our received signal with a 1dBi (built in antenna) is, for example -80dBm.
I know that our Yagi antenna supposedly grants us a gain of 11dBi, assuming we mount it properly/get polarity correct, etc.
I also have the SNR, if that is necessary. In this case, SNR is 2dB.
I can find out how many kilometers away the nearest cell tower is for my carrier.
I know the carrier frequency is LTE band 13 (verizon) which is 700 Mhz.

Is there a way to use a formula to extrapolate the signal strength all else staying the same, given that we use an antenna with 11 dBi gain instead of the existing antenna? Or are there too many variables? Even a ballpark figure would help.

Best Answer

Let's assume that the EIRP from the cell tower is about 30 dBm, and it's about 2 kms away. Making yet another strong assumption that the path loss can be characterised by just free space -

Free Space Loss = 20 log (4 * pi * d * f / c) ~ 95.37 dB

That means the received power would be = 30-95.37+11 = -54.37 dBm

However, this is far from being accurate, since the path loss can much greater than ~95 dBm, and you would have to know the thermal noise at the receiver (and possibly interference) to properly estimate the SNR.

Related Solutions

WLAN – Maximum Data Transfer Rate for Data Sharing

I'm afraid that on the network point of view this is a somewhat impossible question.

In wired Ethernet if you have a Gigabit switch and 2 clients with GB NICs, you can expect to get a stable ~1GB/s throughput rate. In the wireless world the advertised max throughput rates can only be achieved in a strictly controlled lab environment, in any real live environment many factors affect your throughput:

- Wireless is a half duplex medium
- Wireless is a shared medium. The more clients you have on the same radio, the less bandwidth is available for each client.
- The point above is theoretical, distance affects. If your clients are both 2m from the AP, you get throughput n. When one of the clients moves to 4m away from the AP, your throughput drops.
- There's background noise, and there's interference from both WiFi and non-WiFi devices. This means that if you get average throughput of n Mb/s, I won't get the same throughput even using exactly same equipment and drivers you use due to only different noise floors. Even you may see different throughput in the afternoon compared to the morning. If you use a wired mouse and mine is btooth, we're likely to get different results. Lighting fixtures can interfere wireless throughput. And so on.
- You're using n, where "max throughput" becomes a complicated matter. It depends on what modulation scheme is used, how many spatial streams you have, guard interval etc., answer being somewhere between 6.5 Mb/s and 600Mb/s... same applies to ac-networks.
- If you have legacy clients on your wireless network, the average throughput will drop

I'd suggest you put this question to Stack Overflow. The coders might be able to give you a more meaningful answer as someone is likely to have tackled similar situation in the past.

Of course you can just take the expected average throughput rates for example from http://www.speedguide.net/faq/what-is-the-actual-real-life-speed-of-wireless-374, but those tend to depend on whom you're asking. Here's a discussion from Superuser concerning wless average throughput on 802.11n: https://superuser.com/questions/187485/average-transit-speed-for-802-11n-wireless-ap. Still you should ask about calculating appropriate buffer size in Stack Overflow.

Wireless IEEE 802.11 – Minimum Signal Level for Co-Channel Interference

A CCI signal of -80dBm is high enough to cause problems. If the APs hear each other at around -80, then a client in between the two APs would hear both APs at a higher level. That's where co-channel interference happens.

The problem is not the APs, but the clients. CCI doesn't just corrupt frames (any noise will do that). CCI interferes with the clear channel assessment (CCA) function in each client. When a client is ready to transmit, it checks to see that the channel is clear (that no one else is transmitting). If the signal strength is strong enough that a radio can decode signals as 802.11, then it will fail the CCA test and the radio will defer transmitting. A nearby transmitter on the same channel will make the client wait for a clear channel even though the AP it's associated is ready to listen, reducing throughput.

The co-channel signal strength should be 20 dB below the AP strength at edge of the cell. Since the cell boundary is usually -67 dBm, CCI should be -87 dB or less.