# LTE: where are my 100 Mbps?

I want to share my thoughts on speed in LTE networks. I think that many of you have seen colorful advertising by operators about how cool it is to use modern mobile Internet at a huge speed of 100 Mbit per second. But this number 100 should be with an asterisk.

Why with an asterisk? Let's figure it out. So, how do you calculate the maximum speed in an LTE network? First, let's dig a little deeper. How is data transmission arranged on the network? In the time domain, the LTE structure consists of 10 ms radio frames. Each frame consists of 10 subframes, 1 ms long each. Each frame consists of two slots of 0.5 ms. Each slot can contain either 7 (more often) or 6 (less often) OFDM symbols.

Now let's move on to the frequency domain. Everything is simpler here. One OFDM symbol occupies 15 kHz. Thus, the number of these symbols is limited only by the size of the frequency band allocated to the operator.

So, how to calculate the maximum speed in the LTE network? Yes, very simple. One OFDM symbol (or one resource element, RE) may contain 2, 4 or 6 information bits, depending on the type of modulation. We already know that in one time slot (0.5 ms) contains 7 REs, respectively, in one millisecond of such elements 14, in a second - 14000.

Move on. In the frequency domain, the RE occupies 15 kHz. Let us assume that the operator was lucky and he was allocated the maximum possible frequency range - 20 MHz. Given that 10% of this range needs to be left behind guard intervals, 18,000 kHz is useful, into which 1200 OFDM symbols can fit. We multiply 1200 * 14000 and we get 16.8 Megacharacters per second. Each of these characters is modulated either by two (QPSK), or four (QAM-16), or six (QAM-64) bits. Thus, in the best scenario, using QAM-64 modulation, we get: 16.8 Msymbols * 6 = 100.8 Mbit / s. Here they are, the very ones, advertising, 100 megabits. However, what do we have in practice?

The Big Three operators are allocated two frequency ranges: 10 MHz in the 2.5-2.6 GHz region and 7.5 MHz in the 800 MHz band. As far as I know, the 7.5 MHz band is now practically not used by our operators. Which conclusion is that? This condition alone already cuts the maximum speed in an LTE network by half, up to 50 Mbps. To obtain it, ideal conditions are needed: the antenna of the base station in direct visibility, the absence of interference, a smartphone capable of operating at this speed. In addition, no one should use the Internet except you at this moment. Unfortunately, even if all these conditions are met, it will not be possible to achieve a speed of 50 Mbit / s, because, in addition to useful information for you, the base station also exchanges service signals (signaling).

Now let's go down from heaven and imagine that you are not sitting next to the base station, but in your living room or office. There can be no talk about the direct visibility of the antenna, respectively, the signal level entering the smartphone is low. Under such conditions, part of the received data will come with errors and, to avoid this, the LTE network will be forced to lower the modulation scheme to QAM-16 or even to QPSK. Also, we must not forget that due to interference in the radio channel, redundant coding is used.

So what speed can you expect on your smartphone? The situation is quite real when, sitting at home on the couch, a KAM-16 modulation scheme will work for you (I recall, under this condition, one resource element contains 4 rather than 6 information bits, as in QAM-64) and the code speed R will take value 1 \ 2. Let's calculate: due to noise-resistant coding, the maximum speed will decrease from 50 to 25 Mbps. Given that the modulation scheme has changed to QAM-16, the speed will drop another 2/3 times, to 16.6 Mbit / s. And this is provided that the base station serves only one subscriber - you. Of course, for mobile devices these speeds are more than enough, but these are far from the 100 Megabits per second that appear on posters.