The Galileo E6 signal is centered at 1278.75 MHz, and comprises three signals: an authorized signal (E6A, the publicly regulated service, PRS plus two civilian signals), a data component (E6B), and a pilot component (E6C). Both E6B and C are modulated using binary-phase shift keying (BPSK) code division multiple access (CDMA) memory codes, having lengths of 5,115 chips and chipping rates of 5.115 Mcps.
The pilot signal further employs a secondary code, at a rate of one ksps, with a length of 100 symbols, while the data signal carries symbols at a rate of one ksps, being a half-rate encoded 500-bps message. This distinguishes the Galileo E6B signal as having the highest symbol rate and the highest data rate of any GNSS signal.
As such, it is quite interesting to study the signal in terms of tracking and data delivery performance. To this end, in this article we will first provide a study of the theoretical bounds on processing the E6 signal and, secondly, examine the behavior of current E6-enabled GNSS receivers.
Theoretical Bounds
We begin with an overview of the theoretical performance of a simplified GNSS receiver processing Galileo E6, either as a data-only signal, or as a data-pilot pair. We will examine the carrier- phase tracking and the data-demodulation performance to estimate the relative benefits of processing the pilot signal.
Carrier Synchronization. We can characterize carrier-phase tracking in a GNSS receiver, when operating in its linear region, by the phase domain model presented in Figure 1. Under this model, the effective noise bandwidth of the phase lock loop (PLL) can be estimated from the closed-loop transfer function:
Equation (1) (see inset photo, above right, for all equations)
where the PLL filter is denoted by F(z), the numerically controlled oscillator is defined by NCO(z), typically modelled as an integrator, and the discriminator gain, in rad/rad, is given by KD.
From this transfer function, the phase tracking jitter can be predicted as:
Equation (2)
where Nθ represents the equivalent noise floor after the discriminator, and accounts for the squaring loss that the nonlinearity of the carrier phase discriminator can induce, such that it increases as the prevailing carrier to noise floor ratio, C/N0 is reduced.
Both KD and Nθ depend on the discriminator used in the PLL, and the received signal characteristics generally influence the choice of discriminator. When an unknown data sequence modulates the signal, a Costas-style discriminator is employed, which is insensitive to BPSK modulation, while a pure-PLL discriminator is used when a pilot signal is available.
The tracking performance of PLLs that use either of these discriminators, although similar under nominal conditions, can diverge significantly under weak-signal conditions. In particular, the effective gain of the discriminator diminishes rapidly, and the region of phase errors over which the discriminator provides a proportional response contracts. These two factors can result in sporadic cycle-slips, or loss of lock, when the receiver experiences any appreciable phase dynamic.
In particular, the linear region plays an important role in determining PLL performance. The linear region of an ideal discriminator would extend from –π to +π, for a pure PLL, and from –π/2 to +π/2, for a Costas PLL. Although this is achieved under high C/N0 conditions, under nominal operating conditions, this region is smaller, and contracts as the received signal power reduces, with the onset of this contraction occurring earlier for the Costas PLL.
Figure 2 depicts the carrier-phase tracking jitter and discriminator linear region for a typical pure-PLL and Costas-PLL for a range of C/N0. The curves depict the 3σ bound for typical PLL configurations for a receiver processing the Galileo E6B and E6C signals, having a 20-hertzbandwidth and a one-kilohertz loop update rate.
The curves represent a static receiver; so, the estimated 3σ bound has been further offset by a phase margin, Δθ. The latter term reflects any residual stress that the PLL might experience, such as receiver dynamics, oscillator phase noise, or physical vibration and shock. Also included is the estimated linear region of the two classes of PLL discriminator, which can be seen to converge to 180 and 90, respectively, for the pure-PLL (E6C) and for the Costas-PLL (E6B).
These curves offer some insight into the performance that might be observed for a receiver that either processes the Galileo E6B signal alone or employs the pilot signal E6C. In terms of thermal noise–induced phase error, a similar level of tracking error will be observed in either case when the prevailing signal strength is high. As this signal quality reduces below 40 dB-Hz, however, the E6B-only receiver probably will perform more poorly.
We may examine the relative magnitude of the tracking jitter curves and the discriminator linear region in terms of cycle-slippag