# OFDM numerical example

Am I correct in this example? For example, I have data a data stream like this 101100011100...11001001 .... . Let say a symbol is 64 bits. I will use 16 qam-ofdm. For this, I separate a symbol to 16 subsymbols (means each is 4 bits) and It converted serial to parallel. Then each parallel item is my ofdm symbol mapped as to qam. Then I take IFFT this ofdm symbols and then I add cp and then parallel to serial and then DA then transmit the signal. So I need to 16 subcarriers and I transmit only one symbol (64bits) with 16 subcarriers. Am I right? Am I correct in this example? For example, I have data a data stream like this 101100011100...11001001 .... . Let say a symbol is 64 bits. I will use 16 qam-ofdm. For this, I separate a symbol to 16 subsymbols (means each is 4 bits) and It converted serial to parallel...

If it was serial to start with, yes. At this stage, you've collected together 64 bits for a symbol, and divided those into 16 subsymbols of 4 bits

Then each parallel item is my ofdm symbol mapped as to qam.

Each subsymbol is going to represent one subcarrier, one frequency, within your OFDM symbol. You've chosen to map the 4 bits as QAM onto that carrier.

Then I take IFFT this ofdm symbols...

The QAM coding on each subcarrier gives you one of 16 constellation points, that is one of 16 phase/amplitude pairs, for the relative phase and amplitude of that subcarrier. You assemble all 16 subcarriers as a complex frequency vector that goes into an IFFT

The output of the IFFT is a compex time vector that represents the time duration of exactly the reciprocal carrier spacing. On reception, it's not possible to detect the start and end of this symbol accurately, and the channel is likely to have a delay spread. Increasing the length of the symbol by adding a cyclic prefix, typically taking the end 25% of the time record and tacking it on the other end, allows for looser synchronisation at the receiver, and for delay spread in the channel

and then parallel to serial and then DA

the output of the FFT is logically a time vector, and depending on the hardware it may be serial, parallel, or chunks. Just think of this bit as taking the logical time vector and presenting it one sample at a time to the RF conversion hardware. How this hardware is built will determine whether it's two DACs and analogue mixers, or more likely these days, digital mixers to an IF and to a single high speed DAC

then transmit the signal.

eventually. The complex baseband, or the IF signal, is upconverted to RF and radiated.

So I need to 16 subcarriers and I transmit only one symbol (64bits) with 16 subcarriers. Am I right?

More or less. A working system will have a few extra tweaks. For instance, a few empty subcarriers at the edge are often defined to mitigate interference to adjacent channels. The centre carrier, or the centre few, are often not used for data so that poor DC performance in the IQ modulators, and close to carrier phase noise from the LOs (you get both when you design a real system down to a price) doesn't degrade real data. Some subcarriers, or at least some time slots in them, are often used for pilot signals for synchronisation and channel sounding. Finally, the relative phase of the subcarriers - relative to what? It's usually relative to the previous subsymbol on that carrier, or the mean of the previous few symbols. The phase of one symbol is like the sound of one hand clapping. So we're usually sending several symbols sequentially. So you'll need a few more subcarriers, but only 16 will be carrying your data payload. And you'll need a few more symbols, but you'll get 64 bits from each.