# LTE questions (subcarriers and cyclic prefix)

Assume we have transmission bandwidth of 10 MHz, in this case the total number of subcarriers (FFT size) present is 1024. According to LTE standards, 600 out of 1024 subcarriers are data subcarriers.

data subcarriers= total number of subcarriers- pilot/null subcarriers

Moreover, 0.07 % of 1024 are used as Cyclic Prefix extension

1) Is it correct that we have 1024-600 are therefore unused subcarriers?
(where 600 = total number of Resource Blocks (RB) * number of subcarriers/RB = 50*12)

2) An OFDM symbol is made up of data part and CP part. Is it correct to say that the number of QAM symbols for each OFDM symbol is then 600 (equal to number of data subcarriers) and the number of CP symbols are 72? How is the actual transmission over the subcarriers taking place. For example in downlink, does the transmitter allocate a certain number of subcarriers over which it transmits?

I hope I can get some feedback! Thanks

• What exactly are "Cyclic Prefix subcarriers"? The CP is inserted in time domain. Do you have a reference for this type of subcarriers in LTE?
– Deve
Commented Apr 21, 2015 at 7:06
• Actually I got this from a book called Fundamentals of LTE, in that book some constant G defined as Guard fraction is 0.07% of 2048 for CP. So I thought these are for the CP subcarriers. @Deve Commented Apr 21, 2015 at 14:21
• Does the book mention "CP subcarriers"? I'm sure the "guard fraction" means the ratio of guard interval and OFDM symbol length.
– Deve
Commented Apr 21, 2015 at 14:24
• I see your point, I will edit the question accordingly so as to not confuse people. By guard interval do you mean Cyclic Prefix?@Deve Commented Apr 21, 2015 at 14:30
• Yes, the guard interval is usually implemented by a cyclic prefix.
– Deve
Commented Apr 21, 2015 at 14:43

## 1 Answer

1. The FFT size in LTE is defined as 2^(nextpow2(Nsubcarriers/2)+1) or the nearest power of two that is also higher than the number of subcarriers for a given bandwidth. For the 10 Mhz case, for example, this means that 424 FFT bins(1024-600) are zero padded apart including the DC bin. The usual practice is to zero pad the central 423+DC bins and use the rest for filling the data so that you get a continous spectrum of 10 MHz around DC. You can also fill the central 600 FFT bins with data and do a fftshift. See table 1 in this document.

2. Yes. Each Resource Element(i.e.1 subcarrier and 1 OFDM system in the Time- Frequency Grid) has one QAM Symbol in shared channel.

Check out this visualization to get a better clarity about the LTE resource grid. The resource is allocated both in time and frequency domain and in the case of Multi User MIMO(MU-MIMO) transmission mode, spatial resource allocation of resource elements to different user equipment in the downlink also take place. To keep things simple, let's just focus on a single-antennae transmission. The following diagram will give you a better idea of the whole transmission process.

• Thank you very much for the clear explanation. Shouldn't the output of the FFT inverse operation be also parallel symbols? As I see in this figure its a serial output of symbols? Also does this figure shown, where is the actual allocation of resource elements taking place to send the QAM symbols? Commented Apr 22, 2015 at 23:09
• The output of IFFT is a complex sinusoidal waveform. You can see the real and imaginary parts that are multiplied by sin and cosine components of the carrier. This waveform is transmitter at a sampling rate commensurate to the bandwidth (Fs=15.34 Mhz for BW of 10 MHz) as shown in table 3.1.1-1 in this document. Commented Apr 22, 2015 at 23:31
• Thank you again, so do you mean to say that the output of the IFFT is not serial symbols but actually a complex waveform? then how come we have a digital to analog converter after the inverse FFT? I thought the inverse FFT would transform the frequency domain symbols into time domain symbols and thats it? Commented Apr 22, 2015 at 23:37
• @Deve Edited the answer. Thanks for pointing out the error. Commented Apr 23, 2015 at 10:05
• @Tyrone I think he is referring to shift registers in hardware buffers into which IFFT output is pushed before further processing. In software we work with arrays, but the underlying logic is the same. Commented Apr 23, 2015 at 10:58