# OFDM Receiver and How it work for LTE?

The receiver is like in any other radio system the more complicated part. In radio systems and of course also OFDM there are two special points a receiver has to pay attention to: time/phase and frequency synchronization. Both are crucial for the performance of the receiver. A receiver gets its input from the antenna (or antennas) and the attached low noise amplifier.

A band pass suppresses signals out of the spectrum. The demodulator converts the signal back into the baseband and with this recovers the complex valued data signal. At this step we have the time domain representation of the signal. The time signal is now given to the “De-rotator” which applies to each time sample a phase offset to compensate frequency drifts and global phase offsets. A special unit in the receiver is responsible to determine and track the frequency and phase drifts and calculate the associated correction value for each sample.

This is a quite critical task, as errors made here, apply as additional (receiver intrinsic) noise to all data symbols. The frequency and time synchronization unit uses typically as input the autocorrelation of the input time sequence (especially cyclic prefix) and reference (or pilot) symbol interleaved with the data at predefined positions. The corrected signal is now fed into the Fast Fourier Transform (FFT) which implements a fast and efficient algorithm for the discrete Fourier transform to bring the signal back into the frequency domain representation.

In other words the FFT decodes the complex valued data symbols for each subcarrier. Of course before the FFT is applied, the cyclic prefix has to be removed. The recovered subcarrier data symbols are not useful yet, as there might be still distortion from phase offsets and from the channel propagation (multi-path propagation) on it. Thus the next step is to correct the data according to the known channel response.

The channel estimation uses the pilot and reference signals that are interleaved with the normal data at predefined positions to estimate and permanently correct the channel state information. A nice thing of the frequency domain representation is, that a distortion coming from channel propagation and time offset are in first order simple correction factors to each subcarrier, so that no complex filtering is required here.

After we have corrected our data symbols for each subcarrier, the symbol demapping can take place. Here we recover the original bit sequence either as hard decided bits or as soft decided bits. (Soft bits have some advantages in the further processing, namely in the channel decoding.)