Signal Processing - September 2017 - 105

v Th =

B PLL 1 +
1
c
m.
C /N 0
2T $ C/N 0

(5)

However, longer integration times will have adverse oscillator noise effect on phase and frequency estimation errors
[47], [48]. For signals with data modulation, data bit transitions
introduce additional complexity when integrating over periods
longer than a data bit length. Optimal integration time is determined by specific PLL implementations, oscillator quality,
and signal noise and dynamic characteristics [49]. Kassabian
and Morton [50] demonstrated that increasing integration time
improves tracking accuracy only if the rate of carrier-phase
fluctuation is relatively slow or the PLL update rate is relatively high. In general, for high latitude scintillation dominated
by fast phase fluctuations, an integration time such as 10 ms
is sufficient for proper operation of the receiver. For weak to
moderate equatorial scintillation, longer integration times on
the order of 10~100 ms have been effective. For strong equatorial scintillation, the optimization of integration time alone is
not enough. Other strategies such as changes in fundamental
filter design will be needed to maintain the lock of signals.

by the wider bandwidth and the phase jitter associated with the
scintillation effects. As a result, carrier cycle slips may occur
more frequently.
Equatorial scintillation is often associated with concurrent
amplitude and phase variations, which impose conflicting
requirements on the PLL noise bandwidth selection. Such
conflict is a major challenge for equatorial scintillation mitigation. Nevertheless, a number of algorithms have been developed
to exploit diversities in nontraditional domains to overcome
this conflict, and these will be discussed next.
The variable bandwidth PLL and frequency lock-loopassisted-PLL (FAP) are designed to optimize bandwidth in
response to changes in signal fading and carrier dynamics. Both fixed bandwidth and variable bandwidth Kalman
filter-based PLLs (KFPs) have also been the subject of
investigations.
A variable bandwidth PLL optimizes the noise bandwidth to
minimize the tracking loop phase errors. Skone et al. [17] and
Kondo et al. [53] both implemented a fast adaptive bandwidth
(FAB) PLL. The FAB is based on consideration of phase error
generated by both the thermal noise (5) and dynamic stress:

Discriminators

v Dy = c

Several studies have investigated the performance of different types of carrier discriminators in processing simulated or
real high latitude [17] and equatorial scintillation signals [51],
[52]. These studies indicated that several Costas discriminators ^atan, I # Q, sign ^ I h # Qh had similar performance, with
sign ^ I h # Q discriminator showing a somewhat improved
phase accuracy and reduced phase lock threshold [17], [51].
The atan2 discriminator demonstrated the most robust performance in terms of cycle slips [52]. This result indicates that
when tracking the scintillation signal, the dataless pilot channels will be less affected by scintillation. For channels with
data modulations, the tracking loop performance will be better
if there is external aiding of data bits.

Filter design and filter bandwidth optimization
The most studied subject in scintillation mitigation is the tracking loop filter design. Considering that both high latitude and
equatorial scintillation have a phase dynamics component,
most filter designs intended to mitigate scintillation are thirdorder systems. A commonly manipulated filter parameter is
the bandwidth. Smaller bandwidth will lead to lower thermal
noise phase jitter and therefore is desired when tracking amplitude scintillation signals, as shown in (5). However, narrower
bandwidth is not suitable if the signal is experiencing phase
scintillation. Fast phase fluctuations introduce additional disturbances on carrier frequency. To accommodate the carrier
dynamics due to phase scintillation, the PLL must have a wide
bandwidth comparable to the scintillation signal frequency
deviation range. At high latitudes where phase scintillation is
the dominant effect, a wide-band PLL can be used to mitigate
the scintillation effects. While higher bandwidth improves the
receiver's ability to maintain lock of phase scintillation signals,
it also has higher tracking errors due to both the noise allowed

J LOS
B 3PLL

v PLL = v Th + v Dy,

(6)
(7)

where J LOS is the signal receiver-satellite LOS jerk and can
be estimated from the PLL; c is a constant. Equation (7) can
be used to iteratively solve for an optimal PLL bandwidth that
minimizes v PLL . Skone et al. [17] showed that the FAB has an
improvement of ~5 dB in SNR over a constant bandwidth PLL
for high-latitude scintillation. Kondo et al. [53] used simulated
scintillation signals to conclude that the FAB has improved
phase error performances for C/N 0 over 40 dB-Hz. These
results indicate that the technique is only suitable for high-latitude phase scintillation and mild equatorial scintillation.
An FAP estimates the Doppler frequency error and phase
error simultaneously [54]. These errors pass through two loop
filters separately and are then combined to control the reference-carrier generation. Considering that an FLL is known
to have more robust performance for dynamic signals, while
a PLL is more sensitive to weak signals, an FAP is expected
to offer a good compromise for tracking equatorial scintillation signals. Psiaki et al. [55] and Zhang and Morton [52]
both studied FAP performance in comparison with that of a
conventional PLL and KFP for a wide range of scintillation
levels. Their results show that the FAP does not have noticeable
improvement in steady-state phase tracking errors, number of
cycle slips, or loss-of-lock over the conventional PLL.
KFP has been explored to improve carrier tracking of equatorial scintillation signals. A typical Kalman filter models a
system using a state function with additive noise and estimates
the state variables through an iterative process. Upon obtaining
new measurements at a time epoch, the difference between measurements and a priori estimation of the state vector from the
state function is computed. This difference, also referred to as

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

105

Table of Contents for the Digital Edition of Signal Processing - September 2017