Aerospace and Electronic Systems Magazine June 2017 - 10
State-of-the-Art Space Mission Telecommand Receivers
Figure 6.
Figure 5.
FSE probability with hard and soft correlations and with the S-LRT for
the original 16-bit and a 64-bit start sequence. The decision thresholds
are optimum for Es/N0 = 2 dB.
cally inserted sync marker, in which the receiver searches for the
most likely position within one frame [16], in our case synchronization has to be achieved before reception of the entire CLTU,
whose length is variable and unknown a priori.
For this reason, we must resort to one-shot frame synchronization which compares, for each position of the observation window,
the computed metric to a predefined threshold in order to decide
whether or not the current position corresponds to the start of the
CLTU. In this scenario, two types of error can occur:
C
C
False alarm: The metric exceeds the threshold, but the samples in the observation window do not correspond to the start
sequence.
Missed detection: The start sequence is in the observation
window, but the metric is below the threshold.
The optimum approach for computing the metric is given by
the likelihood ratio test (LRT), derived for the given scenario by
Chiani and Martini [17]. Interestingly, this metric for one-shot
frame synchronization is equivalent to Massey's metric, derived in
[16] for the periodic case.
Since for TC a binary modulation scheme is applied which
is not differentially encoded, the receiver needs to determine
the sign of the received symbols. The frame synchronizer has
to account for this sign ambiguity, while it can provide the correct sign once the correct position of the start sequence has been
found.
A near-optimum metric [18], derived with the approach outlined in [17], is given by the simplified LRT (S-LRT), defined as
Λ S-LRT (r ) =
Ns
Ns
rs − r
i =1
i i
i =1
i
(1)
This metric provides, as a by-product, the sign of the received symbols, which is given by
sgn
10
(
Ns
rs
i =1 i i
)
CLTU termination: Pmd vs. SNR for Pfa = 10−6.
and is required for decoding unless differential modulation is
used. The optimum threshold, providing the best trade-off between
missed detection and false alarm probabilities, is found by simulations and generally depends on the operating SNR. In Figure 5,
we plot the FSE probability as a function of the ratio Es/N0, for the
S-LRT metric and, as a reference, for the hard and soft correlation.
The S-LRT provides significant gains compared to the still widely
applied correlation metrics. It is also clearly appreciable that, with
the 16-bit sequence, the FSE is much higher than the desired target
of 10−3 at Es/N0 = 2 dB while, with a 64-bit start sequence, this
requirement is satisfied for all metrics.
After detecting the CLTU start, the decoder processes each
block of n bits. To recognize the CLTU end, the receiver exploits
the 64-bit tail sequence. For the current standard, an "uncorrectable pattern" approach is typically used: when a block is marked
as incorrect, the receiver declares the end of the CLTU. The 64-bit
pattern is a pseudo-random sequence designed to be uncorrectable by the single-error-correction BCH(63, 56) decoder, because
its distance from any codeword is larger than one. Without noise,
when the tail sequence is processed, the decoder fails, marks the
block as uncorrectable, and forces the CLTU end. With noise, this
approach may fail if the number of errors is high, making the pattern correctable (actually, three wrong bits may be sufficient to induce this problem).
If the code is much more powerful, as the new LDPC codes
are, it is difficult to find an uncorrectable pattern. Moreover, the
approach fails for complete decoders (like those based on the most
reliable basis (MRB) algorithm, that we will consider in the following), which always return a codeword. The "natural" approach
for CLTU termination is then the application of a detector, which
looks for the 64-bit tail sequence after each codeword.
Like for the start sequence, the optimal LRT is characterized
by higher complexity, with respect to the other methods, and requires estimation of the SNR value. This makes its application to
high data-rate implementation more difficult. Soft and hard correlations are then often used, although they are highly suboptimal.
In our study, we have focused on the simplified Massey detector
[16] which, given the pattern symbols pi and the received symbols
IEEE A&E SYSTEMS MAGAZINE
JUNE 2017
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