A Cross-Symbol Frequency Discriminator for Carrier Tracking of Weak DSSS Signals

Direct-sequence spread spectrum (DSSS) systems have found wide applications in space missions. The possibility for the receiver to operate at a low symbol energy to noise density ratio (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$E_{S} / N_{0}$</tex>) enabled by error correction coding makes carrier tracking the new processing bottleneck. Robust carrier tracking at low <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$E_{S} / N_{0}$</tex> often involves a frequency-locked loop (FLL), whose transient and steady-state error strongly depend on the noise performance of the frequency discriminator. However, the presence of symbol transitions in the received signal poses a challenge to the frequency discriminator. Despite the availability of various cross-symbol discrimination approaches, most of them assume known symbol transition boundaries and neglect symbol transitions within each coherent integration interval. Without symbol synchronization, the risk of trespassing a symbol transition boundary limits the coherent integration time, thereby restricting the signal-to-noise ratio (SNR) of the coherent integration results. Consequently, the frequency discriminators suffer greater SNR loss from subsequent non-linear processing in low <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$E_{S} / N_{0}$</tex> scenarios, resulting in a degradation in noise performance. To address this issue, this paper proposes a cross-symbol differential correlation frequency discriminator. The proposed discriminator employs an approximate maximum likelihood (ML) approach to jointly discriminate the frequency offset and detect the unknown symbol transition and transition boundaries. Additionally, it utilizes an overlapping secondary integration to extend the coherent integration time without reducing the discrimination range. Numerical simulations are presented to verify its advantage over conventional frequency discriminators.