Synchronization Signal Design for OFDM Based On Time-Frequency Hopping Patterns

In an OFDM system, channel estimation can be considered as sampling the time-frequency response of the channel through a number of known pilot symbols placed across the time-frequency plane. Sampling theory dictates that the pilot insertion frequency must be above the Nyquist rates in both time and frequency to avoid aliasing of the delay-Doppler response. Based on the regularly spaced pilot pattern, we can derive alternative patterns that preserve the non-aliasing property by hopping the scan lines in either time domain or frequency domain, but not both. From this extended set of patterns, we find ones with properties that, in addition to channel estimation, can achieve responsively other synchronization tasks such as initial time-frequency offset estimation and device identification. The ambiguity function analysis frequently used in radar signal design leads to a periodic time-hopping pattern based on the costas array that has minimal coincidences with its circular time-frequency shifts, which can be used for the identification of multiple devices. The hopping in time also greatly increases the pilot´s time support, thus enabling the quick initial acquisition of timing and frequency offset with very short observation.