Interleaved Z4-Linear Sequences With Low Correlation for Global Navigation Satellite Systems

Global Navigation Satellite Systems (GNSS) employ low-correlation sequences, termed as spreading codes, to distinguish between the signals transmitted by the different satellites. The spreading codes commonly employed have period that is a multiple of 1023, as the fundamental frequency associated with the navigation signals generated onboard all of these systems is 10.23 MHz, derived using highly-stable atomic clocks. The principal contribution of the paper is the construction of a family ${\mathcal{ J}}_{{\text {NAV}}}$ , of low-correlation, binary sequences having period 10230, derived by interleaving a selected set of $5 {\textstyle \mathbb {Z}_{4}}$ -Linear sequences of period 2046 followed by flipping or complementing, a subset of the interleaved sequences. Sequence selection is based on the value of an exponential sum over a Galois ring and interleaving is carried out using the Chinese Remainder Theorem. The period 10230 is of particular interest, as it is the period of the spreading codes employed by major GNSS currently in operation. The ${\mathcal{ J}}_{{\text {NAV}}}$ spreading code family turns in competitive performance when compared to existing designs including a 4.5 dB improvement in worst-case, even-correlation properties. Additional techniques are employed to ensure that Family ${\mathcal{ J}}_{{\text {NAV}}}$ has other desirable attributes of a GNSS spreading code such as low values of odd-correlation, an orthogonality property and a simple, shift-register-based implementation. The construction is shown to be a special instance of a general select, interleave and flip approach to construction that generates families of balanced, low-correlation interleaved ${\textstyle \mathbb {Z}_{4}}$ -linear sequences having period $10(2^{m}-1)$ for $m=2 \pmod {4}$ and $14(2^{m}-1)$ for $m=2,4 \pmod {6}$ . By replacing the constituent ${\textstyle \mathbb {Z}_{4}}$ -linear sequences with Family ${\mathcal{ A}}$ quaternary sequences, the same approach can be used to construct two low-correlation, interleaved quaternary sequence families having period $5(2^{m}-1)$ with $m=2 \pmod {4}$ and $7(2^{m}-1)$ with $m=2,4 \pmod {6}$ , respectively.