17.12.2018

- As already mentioned, the OFDM signal is created by a set of subcarriers – i.e. sine waves of different frequencies carying separate QPSK/QAM symbols.
- The individual subcarrier is simply a sinewave of at the certain frequency – and of a given duration – corresponding to a whole OFDM symbol duration – being long
- So e.g. we have a single subcarrier of 2Hz, and a symbol duration of 0.5s, in which a single cycle is carying it
- Then the next subcarrier is separated by 2Hz – being a sine wave of 4 Hz, so 2 cycles are within 0.5s
- The next one is again separated by 2Hz – 6Hz – 3 cycles and so on.
- Now if we sum all of them, we get 4 consecutive carriers being four taps with a frequency separation of 2Hz and the resulting symbol is 0.5s. So the frequency separation is Fsc= 1/Tsym

- So what do we actually do is we get our bits through the modulation mapper and out of this we get complex samples (as shown in our previous chapter on modulation mapping) with examples shown here – amp = 1 and phase of 45deg
- Then this is fed to the reousrce mapper, that maps those to the individual subcarriers – i.e. we put X1 to the first subvarrier – and what that means, is we modify the corresponding sine wave (subcarrier) amplitudę and phase by this.

- This was the case without data on those subcarriers – i.e. we had a pure sinewaves of a continouus transmission –
- Now when we put actual data – .e.g a symbol of constant value 1 of duration 0.5s, the resulting single subcarrier frequency response is a sinc (f) function that we also discussed in the beginnig of the signal processing chapter.
- When we put the data on all the subcarriers – we get a consecutive sinc subcarriers separated by Fc =2Hz. This shows that where one of the subcarrier has its maximum – all the others have their zeros, so the receiver when synchronized to the particular subcarrier frequency is able to receive the transmittted symbol values perfectly, if there is a small missmatch – the interference from other subcarriers shows up and distorts the transmission (Inter carrier/subcarrier interference)
- So to maintain the orthogonality of the subcarrier seaparation (i.e. that the different sybcarriers are orthoghonal to each other – ie.. Separable/recognizable), the subcarrier separation has to be exactly 1/Tsym
- The actual generated OFDM spectrum with random data is shown here, where we have the DC subcarrier that is empty – this is to decrease the impact of the power used for the carrrier frequency (as we’ve seen in the introduction to AM modulation, it had a very high power of with respect to the rest of the symbol frequency response). So DC is not carying any useful data (DC stands for direct current – i.e. frequency 0Hz)

- Now, let’s take a look on the signalin the time domain
- In our example we have 2 consecutive OFDM symbols in te time domain with 4subcarriers (as in our previous cases) of 0.5s each.
- As we already discussed in the previous chapter – the symbols shallbe much longer than the channel dispersion.
- But in order to completely avoid ISI, in OFDM we add a guard interval to capture the interference from previous symbols. In the same time, we should not make this guard interval too long , to decrease the throughput too much
- But we do a bit mor than that – we copy the last part of the symbol to the begining, to avoid char changes in the symbol, and to not make the transmitter be switching on and off due to this, and to exploit self similiarty of the symbol – i.e. at the receiver we can compare the two parts and know where the symbol starts

Now, let’s take a look on the signalin the time domain:

- In our example we have 2 consecutive OFDM symbols in te time domain with 4subcarriers (as in our previous cases) of 0.5s each.
- As we already discussed in the previous chapter – the symbols shallbe much longer than the channel dispersion.
- But in order to completely avoid ISI, in OFDM we add a guard interval to capture the interference from previous symbols. In the same time, we should not make this guard interval too long , to decrease the throughput too much
- But we do a bit mor than that – we copy the last part of the symbol to the begining, to avoid char changes in the symbol, and to not make the transmitter be switching on and off due to this, and to exploit self similiarty of the symbol – i.e. at the receiver we can compare the two parts and know where the symbol starts

- So to sum up the processing, the OFDM transmitter itself is composed of:
- the de serializer to get the input bits from serial to paralel set
- The symbol mapper to get the complex modulation symbols out of bits
- The pilot generator and nulls inserter -to put the relevant subcarriers with zeros and plitos
- The IFFT block, to switch from frequency domain taps to time domain IQ samples
- The P/S / serializer – to get the samples in the serial/row manner
- And the guard interval/ cyclic prefix inserter to get the last samples to the beginning
- And to sum up To sum up the OFDM transmission (maybe add a slide with summary)
- A type of multi-carrier modulation
- Single high-rate bit stream is converted to low-rate N parallel bit streams
- Each parallel bit stream is modulated on one of N sub-carriers
- Each sub-carrier can be modulated differently, e.g. BPSK, QPSK or QAM
- To achieve high bandwidth efficiency, the spectrum of the sub-carriers are closely spaced and overlapped
- Nulls in each sub-carrier’s spectrum land at the center of all other sub-carriers (orthogonal)
- OFDM symbols are generated using IFFT

- Lets now see this from wider perspective – the wholde transmission chain using OFDM technology
- We have info bits that are channel encoded – that gives us more bits
- Then we switch from serial to paralel, and modulate
- Then the modulation symbls goe throught IFFT and we obtain time domain samples in the paralel way, so they are moved to serial by P/S converter – this is where we get sampled/digital OFDM symbol samples, after which for each OFDM symbol we add CP
- Then this is fed into D/A converter to get analogue waveform in the baseband domain (ie.e. around 0frequency) we can see that in the time and in freq domain – how the signal looks like (e.g. in wifi it is 4us and 20MHz)
- Then we upconvert it using carrier frequency (e.g. 2.4GHz or 5.8GHz) so the overall signal that is fed into the antenna is a multiplication of the baseband is gial with the carrier frequency – which is also shown – the signal is not of constant amplitudę (like FM, PM) or not with regular amp change (like in AM), but very irregular
- In the frequency domain we see the shift from baseband to the target frequency of the shape of the original signal.

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