In the OFDM example, we have described the OFDM modulation and demodulation, including channel estimation and CP insertion. On the significance of the CP we have already elaborated in another article. However, in all these works, we have assumed that the receiver knows, at which point in time the OFDM symbol is received and hence on which received samples to perform the FFT.
However, in reality this information is not available by default. Instead, the receiver needs to perform a synchronization procedure to obtain the start of the OFDM symbol. When talking about OFDM, the most fundamental work was published by Timothy Schmidl and Donald Cox in their paper Robust Frequency and Timing Synchronization for OFDM. In this notebook, we are going to illustrate their algorithm presented in this paper concerning the estimation of the frame start in the time domain. In addition, the authors propose a method for frequency offset estimation, which we silently ignore in the present description.
So, to summarize, here's the task of synchronization:
Given a received OFDM signal, how can we obtain knowledge about where in the signal the OFDM symbols are located?
In what follows we will describe the proposal by Schmidl&Cox and implement this algorithm for timing synchronization. However, before we dive into the implementation, we need to setup the system model.