Abstract
We investigate the autocorrelation properties of timing synchronization waveforms that are generated by embedded frequency domain pilot tones in orthogonal frequency division multiplex (OFDM) systems. The waveforms are composed by summing a selected number of OFDM subcarriers such that the autocorrelation function (ACF) of the resulting time waveform has desirable sidelobe behavior. Analytical expressions for the periodic and aperiodic ACF sidelobe energy are derived. Sufficient conditions for minimum and maximum aperiodic ACF sidelobe energy for a given number of pilot tones are presented. Several useful properties of the pilot design problem, such as invariance under transformations and equivalence of complementary sets are demonstrated analytically. Pilot tone design discussion is expanded to the ACF sidelobe peak minimization problem by including various examples and simulation results obtained from a genetic search algorithm.
Highlights
Timing synchronization is an essential task of an orthogonal frequency division multiplex (OFDM) receiver, which requires alignment of the discrete Fourier transform (DFT) segments with OFDM symbol boundaries
We explore the relation between pilot phases, the autocorrelation function (ACF) sidelobe peak and the PAPR of synchronization waveforms
Synchronization waveforms composed of a sum of orthogonal complex exponentials are considered for timing synchronization of OFDM systems
Summary
Timing synchronization is an essential task of an orthogonal frequency division multiplex (OFDM) receiver, which requires alignment of the discrete Fourier transform (DFT) segments with OFDM symbol boundaries. Timing alignment errors may occur in cases where the DFT aperture contains part of the guard interval that has been distorted by intersymbol interference (ISI) This results in loss of orthogonality due to spectral leakage [1], leading to performance degradation. Data-aided techniques offer the advantage of superior performance in low SNR applications at the expense of reduced spectral efficiency These techniques benefit from the correlation gain of a synchronization waveform embedded into the transmitted signal, which can be maximized by a judicious design of the waveform. Waveforms have to be spectrally shaped to meet given bandwidth requirements to mitigate leakage to/from neighboring channels After spectral shaping, both CAZAC and Barker sequences lose their optimal properties [10]. For ease of exposition most of our proofs are relegated to Appendices A, B, and C
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