IEEE - Aerospace and Electronic Systems - February 2020 - 45

Peters and Benson
Example 1. For a BPSK modulated signal, at time k,
the filters for the bit sequence (0,0,1,0,0) (and
(1,1,0,1,1)) contained the most energy; then, at time
k þ 1, we expect filters (0,1,0,0,1) or (0,1,0,0,0)
((1,0,1,1,0) and (1,0,1,1,1)) to contain the most
energy. If this is not the case, there is very likely a
bit error in the decoding. The abovementioned bit
sequences are illustrated in Figure 6.
Remark 3. It is worth noting, that the proposed SDR
can be tuned to any modulation scheme. The filters
can be designed manually by curve fitting received
signals. This has, for example, been done for
an amateur satellite that beacons using GFSK-2
modulation.

Figure 7.
Signal over time for two receiving stations located 90 km apart
during a downlink transmission with burst interference. Note that
the interference is independent between the stations.

MULTICHANNEL DEMODULATION
The proposed SDR can blend information from multiple
receivers. This blending can be performed with differing
levels of cost/benefit. For example, our implementation is
dealing with burst interference and time varying polarization, with both colocated antennas and an additional
receiving station on the far end of low-rate Internet connection. Hence, we perform hard detection of the bits
from each antenna (receiver), but flag bits where confidence is low. We then perform simple voting on the
remaining bits. More capable but expensive approaches
suggest themselves for other scenarios.
The bits and the flags from each receiver are collected
and temporally aligned. The temporal alignment is in this
implementation purely done using cross correlation, but
could also use a priori knowledge and/or high-quality
clocks. The coherent mixer/voter delays the processing for
a short amount of time until it ensures that the bits and
flags from most (or all) receivers are received. If the cross
correlation exceeds a threshold, the bits get aligned and
voting commences. If the cross correlation is below the
threshold, the mixer delays the cross correlation for a short
time period. If too many time periods passed, the raw bits
get forwarded to the decoder. The bits from all channels
are taken into account when the voting commences.
Figure 7 illustrates the magnitude of the received signal from two stations during the same time period. The
stations are located 90 km apart. A packet reception commences after 0.1 s. The large spikes are caused by the local
burst interference. It is clear from Figure 7 that the local
burst interference is spatially uncorrelated. Therefore, by
detecting the bursts in the signal, the demodulator at each
station can flag the bits decoded during the bursts with
low confidence. Another effect apparent on the blue trace
on Figure 7 is polarization fading. This occurs since the
satellites spin in the orbit is not synchronized with its
movement over the earth. The polarization fading is compensated for by utilizing two linearly polarized antennas
at each station.
FEBRUARY 2020

IMPLEMENTATION
The presented SDR is computationally expensive to use
due to the large number of cross correlations that are
required to do the Doppler search. However, the realworld implementation cost is not well aligned to a narrow
view of computational complexity. For example, the economies of scale of GPUs drives an appetite for a very large
number of multiply-accumulate units to lower other costs.

Example 2. Consider a satellite in LEO traveling at
7500 m/s that communicates on the UHF band
(450 MHz). From a ground station that communicates
horizon to horizon, this results in a frequency offset
due to the Doppler effect between À11 and 11 kHz.
For a mask covering p ¼ 5 bits, there are N h ¼ 25 ¼
32 masks. If a frequency resolution of 500 Hz is
desired card ðFÞ ¼ 45 frequencies have to be tested.
This results in 32 Á 45 ¼ 1440 convolution per block.
For a GMSK modulated signal with a symbol
rate of 9600 bit/s, (resulting in a signal bandwidth
of 14.4 kHz). With a frequency search resolution of
500 Hz, this results in a remaining Doppler offset of
up to 0.052 Hz/bit, which equals a phase rotation of
0.104 p rad/bit. Recall that GMSK alternatingly
modulates the bits on the in-phase component and
the quadrature-phase component of the carrier, corresponding to a Æ0:5p rad/bit phase rotation. To
avoid ambiguity in the symbol detection, the additional phase rotation due to Doppler offsets should
be less than 0.5p rad/bit. Since this is the case with
a 500 Hz frequency search resolution, the demodulator presented in this work can directly demodulate
the Doppler corrected signal.
The oversampling rate is set to 16 samples/symbol
and FFT length set to 32 768 samples, these 1440 convolutions have to be done within 0.21 s since this is
the block sampling interval. Using the built in FFT
algorithm from the Python package NumPy, a single
32 768 point FFT takes approximately 0.785 ms.

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IEEE - Aerospace and Electronic Systems - February 2020

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