IEEE - Aerospace and Electronic Systems - February 2020 - 44

A Doppler Correcting Software Defined Radio Receiver Design for Satellite Communications

Figure 6.
Figure 5.
Flow diagram of the demodulator. The green box presents the
timing recovery module, which is illustrated in Figure 4.

h ðiÞ ¼ arg max maxk¼½ÀW;...;W Š jcði þ kÞj2

Few examples of templates of waveforms used for demodulation.
Note that for GMSK, the inverse bit sequences (i.e., (0,0,1,0,0)
and (1,1,0,1,1)) are related through complex conjugation, whereas
the BPSK inverse bit sequences are related through sign reversal.

?

h2H

i 2 ½f; f þ r; f þ 2r; . . . ; f þ nrŠ

(10)

where W is smaller than or equal to half the search window width. It is worth noting that (10) only depends on
the estimated symbol index, allowing a parallel implementation of the demodulator. This is illustrated as the yellow
box in Figure 5.
A flow diagram of the demodulator is presented in
Figure 5. First, the Doppler corrected signal that is received
from the Doppler search is cross correlated with each mask.
Next, the code rate and code offset from the timing recovery
module are used to estimate the locations of the symbols in
the over-sampled cross correlation output. Each symbol location is then fine synchronized independently using the inner
maximization in (10) (the yellow box in Figure 5). Finally,
the symbol that corresponds to the largest peak magnitude in
the local search domain for each symbol is selected, which is
formally described in the outer maximization in (10).
Finally, the demodulator utilizes a lookup table to map
the detected masks to symbols, and/or bits. Since the template is multiple symbols long, any symbol in the template
can be chosen to "represent" the decoded bits. However, if
the templates are weighted using a windowing function, the
symbol in the center of the template is usually selected.

FILTER TEMPLATE DESIGN
The filter templates are designed as a set of matched filters
of the modulated wave form. These templates can span
multiple symbols to achieve stronger correlations for signals with inter symbol interference and to avoid high frequency artifacts at the edges of the waveform.
The filter templates have two purposes: First, they are
used for signal detection during the Doppler search, and
second, they are used for symbol synchronization and detection in the demodulator. There are multiple ways to utilize
44

the symbol detection in the demodulator. Depending on the
modulation waveform, one can directly map the center symbol in the template to an encoded symbol and discard the
other symbols in the template. This works very well for continuous phase modulation schemes such as FSK and minimum shift keying (MSK). In this case, it is recommended to
use a windowing/weighting function on the matched filters
to reduce the contribution of high frequency artifacts and
possible distortion on the edges of the filters. Figure 6 illustrates unweighted Gaussian MSK (GMSK) and BPSK waveforms for a few length 5 bit sequences. It is worth noting,
that for GMSK, the waveform for the inverse bit sequence,
i.e., (0,0,1,0,0) and (1,1,0,1,1) are complex conjugates. The
reason for this is that the phase in MSK schemes increases or
decreases by p2 rad depending on the bit. However, for
BPSK, the filter for the inverse bit sequence is merely a sign
change of the filter for the original bit sequence. This results
in a detection ambiguity when purely the magnitude is used,
since both filters will result in the same correlation energy.
The ambiguity can, however, be resolved by observing the
phase of the detection. Another approach to resolve the
ambiguity is to interpret the filters as sliding windows. This
means that the previous symbol is taken into account when
detecting the current symbol. The advantage of this method
is, that for a modulation scheme with n symbols, there are
from each previous template only n templates that can cover
the next symbol. Additionally, only half of the filters have to
be tested on the signal. Using this, it is possible to detect
potential bit errors in case consecutive templates do not
match. One issue that remains is to resolve the ambiguity of
the first bit. Encoding schemes such as nonreturn to zero
(NRZ) coding or the error control system [cyclic redundancy
check (CRC) or forward error correction (FEC)] could be
used to resolve this issue [19]. If no non-return to zero
(NRZ) coding is used, the ambiguity can be removed in the
decoder by detecting packets in both the decoded and flipped
bit sequence and performing a CRC or FEC on the bits, as is
done in GPS [19].

IEEE A&E SYSTEMS MAGAZINE

FEBRUARY 2020



IEEE - Aerospace and Electronic Systems - February 2020

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