# OFDM implementation in Detail

A typical OFDM transmitter is shown on the following figure. To reduce the amount of RF hardware required for OFDM the modulation process is split into two parts. A first part uses the inverse discrete Fourier transform (IDFT) or one of its more efficient but equivalent implementations known as Inverse Fast Fourier Transform to modulate all the OFDM subcarriers in the baseband around the center frequency 0. In the second step the signal is then modulated to higher frequencies for transmission over air.

The binary data sequence is put into the bit distribution where each bit is assigned to a subcarrier. This function is highly specific to the system using OFDM. In EUTRAN for instance the scheduler has great influence to this step. For each subcarrier a modulation mapper takes a number of bits from the assigned stream and maps them to a single complex valued data symbol. How many bits will be mapped in one symbol period depends on the selected modulation scheme (e.g. 1 bit of OOK, BPSK; 2 bits for QPSK, 4 bits for 16QAM and 6 bits for 64QAM). Note that each subcarrier can use a different modulation scheme at the same time. Then the complex valued data symbols from the modulation mappers are interpreted as frequency domain signal for one symbol period.

They are fed into the IFFT algorithm which transforms the frequency domain vector into the corresponding time sequence. The number of time symbols (also complex of course) is typically equal to number of carriers. Note also that some subcarriers before the IFFT step begins might be inserted without data symbol (so called virtual subcarriers). They are usually used as guard bands to protect from interference of adjacent radio systems. The time sequence of complex valued samples is next brought to the OFDM symbol generator, which inserts cyclic prefix and if required cyclic suffix.

This is simply done be taking some bits from the end of the symbol and placing them as cyclic prefix in front of the symbol. Similar is the mechanism for cyclic suffixes. This step is equivalent to the insertion of cyclic prefix and suffix for each subcarrier, but it requires lower number of arithmetical operations. Optionally an up-conversion unit can increase the sampling rate now before we go to the DAC. The up-conversion can be used to reduce the amount of hardware required for the anti-aliasing filter after the DAC which translates the signal into an analog waveform such that the digital sampling values before corresponds to voltage or current afterwards.

Because a DAC generates a signal that contains the original spectrum again in mirrored versions in higher bands, a low pass (anti-aliasing filter) filter is required to suppress the unwanted spectrum. The last step is to modulate the signal onto the radio carrier.

This is done using a classical I/Q modulator where the real part of the complex samples goes to the cosine and the imaginary part of the complex samples goes on the sine of the carrier frequency. Then we fed the signal to some spectral filter (to suppress out-of-band emissions) and to the RF amplifier.