# OFDM modulator in LTE

My understanding of what an OFDM modulator does, is that it takes a parallel sequence of QAM symbols of size M, pads it with zeroes corresponding to the zero subcarriers, then passes them through an IFFT block of same size M. IFFT is used because it can digitally create subcarriers.

My questions

1- Is the result output of the IFFT operation, an OFDM symbol of length M too?

2- Is EACH OFDM symbol going to be weighted sum of the ALL the QAM symbol?

3- How do things change if we have two antennas instead of one, do we have an OFDM modulator to each antenna? For example when using the Alamouti scheme? I have no clear vision how things change in this case, i.e what is the input at the IFFT now?

I am looking forward for answers thank you.

1. Yes. Cyclic Prefix and windows(prefix and postfix for pulse shaping) are added to the OFDM symbol, but windows are only for overlap-and-add for pulse shaping, so the effective length is M+CP_length only. I've mentioned Windowing since it is an important thing to take into consideration if you want to design and test an OFDM transmitter.

2. Each OFDM sample is the IFFT of the corresponding column of Resource Elements or in other words weighted sum of modulated subcarriers as @Serj put it.

3. A clear understanding of the sequence of codeword generation->Layer Mapping->Precoding is required to get big picture of LTE MIMO. This documents explains this sequence well. It's a little complicated as this trio-sequence is different for different channels(for example Layer Mapping and Precoding schemes for Broadcast channel and Shared or Data channel can be completely different within a single frame). If you want to know the finer details of this sequence you will have a take a look at 3GPP 36.211 spec from section 6.3.3 onwards. The following is the block diagram which depicts this sequence in a LTE transmitter.

Antennae Mapping depends on the Transmission Mode being used. The following table should give some clarity on this process.

• Thank you @Naveen, for your answer and for the references there in. I have questions regarding layer mapping, is it correct to say, that for transmit diversity there is ONE option available and that is ONE codeword and for spatial multiplexing there is only one option and it is TWO codewords? or can spatial multiplexing have one codeword? Also does precoding the step after the layer mapping, depends on the channel gain conditions? or are they fixed precoding matrices? Thanks – Tyrone Apr 25 '15 at 19:13
• @Tyrone Yes, that is correct. The Transmit Diversity mode serves the purpose of making the transmission more robust my transmitting the same data stream(codeword) through multiple antennae ports. Spatial Multiplexing on the other hand is for increasing throughput, so multiple codewords(here it is 2 since that is the maximum number of allowed codewords) are mapped to multiple antennae ports. Only in case of closed loop spatial multiplexing the precoding matrices are changed based on PMI(Precoding Matrix Indicator) feedback from the UE. – Naveen Apr 25 '15 at 21:31
• cont..The PMI is related to the channel conditions and another UR feedback called Rank Index, but I'm not sure about the exact expression for calculating PMI. – Naveen Apr 25 '15 at 21:32
• thank you very much, so in transmit diversity, do you send DIFFERENT QAM symbols constituting the SAME codeword though multiple antenna OR do you send the same ONE symbol over the multiple antennas?@Naveen – Tyrone Apr 26 '15 at 0:48
• cont.. so for example if we aim for transmit diversity with 4 layers, and we have a codeword: s0s1s3....... sm. Do you send s0 over layer 1 and s2 over layer 2 s3 over layer 3 and s4 over layer 4 and then repeat? – Tyrone Apr 26 '15 at 1:02
1. Definitely yes. But after IFFT operation data block is CP extended before transmission.
2. Each sample of OFDM symbol from the output of IFFT is weighted sum of all QAM/PSK modulated subcarriers from the input of IFFT.
3. In the MIMO case all spatial-time algorithms are applied in the frequency domain. So in transmitter you should do encoding with QAM subcarriers before IFFT and do the distinct IFFT for each spatial channel created. While in receiver you should do decoding after FFT applied separately to each spatial channel again. By doing this you exploit the fact OFDM is multiplexing of the large number (actually M) of narrow band channels and by appropriate processing (actually FFT/IFFT pair and CP insertion technique) we can treat each subcarrier as narrow band. It is very useful in the case of MIMO because MIMO decoding algorithms are much too simpler when dealing with narrow band (so flat fading channel is the case) and for each subcarrier we can define simple MIMO matrix of weights $[W_{ij}]$. That's why OFDM + MIMO is so popular combination today.