IEEE - Aerospace and Electronic Systems - February 2020 - 41

Peters and Benson
To mitigate the abovementioned problem, we propose
a SDR receiver that finds the signal carrier in real time,
and thereby the Doppler offset. This makes the radio
robust for internal oscillator offsets, inaccurate TLEs and
propagations. In fact, as long as the modulation scheme,
approximate code rate, and approximate center frequency
are known, the carrier offset can be found. The proposed
radio is illustrated in Figure 1(b).
Doppler search is, however, not a new idea, since it is
frequently used, for example for GPS/global navigation
satellite system (GNSS) signal acquisition [14], [15], [16],
[17]. However, a brute force Doppler search is computationally expensive [16]. In the proposed design, the Doppler search is made feasible by taking advantage of
noncausal signal processing techniques, such as the fast
convolution algorithm that utilizes FFTs. However, a central processing unit (CPU) implementation of the proposed
algorithm was still an order of magnitude too slow for
real-time processing. To address this performance issue,
we demonstrate a GPU implementation, that supports
real-time Doppler search and acquisition for data rates in
excess of 1 Mbaud. Additionally, the demodulator also
performs a code rate and code phase search for accurate
symbol synchronization.
Another advantage of the proposed approach is that the
Doppler search algorithm can be tuned to any modulation
scheme by merely replacing a set of filters. This allows one
to switch between different modulation schemes without
redesigning the entire algorithm. These filters are also used
for subsequent demodulation of the signal. In addition, if
the signal has embedded markers, the cost of the Doppler
search can be reduced by limiting the number of matched
filters employed. This makes the proposed SDR highly
flexible.
A customizable decoder is integrated in the SDR that
finds packetized data in the bit stream. This decoder is
compatible with the AX.25 protocol [18], and can easily
be altered to support different protocols.

SDR BLOCKS
This section introduces and explains the modules that
make up the SDR in detail.

DOPPLER SEARCH AND COMPENSATION
The SDR utilizes an universal software radio peripheral
(USRP) that downmixes the RF signal and samples the
base band (BB) in a selected bandwidth. We perform a
coarse Doppler search by cross correlating the received signal with templates of the modulated carrier with different
Doppler offsets. The coarse Doppler shift can then be found
from the magnitude of the cross correlations. Figure 2 provides an overview of the Doppler search.
FEBRUARY 2020

Figure 2.
Illustration of the computations in the Doppler search. The blocks
in the blue box are executed for each combination of Doppler offset and filter template. This can be done sequentially or in
parallel.

For a received signal xðkÞ 2 C and filter hðkÞ 2 C, the
cross correlation is given by
cðk; hÞ ¼ xcorrðxðkÞ; hðkÞÞ
, xðkÞ Ã hðkÞ
1
X
¼
xðk À tÞhðtÞ

(1)

t¼À1

or in the frequency domain as
Cðf; HÞ ¼ XðfÞHðfÞ
where
XðfÞ ,

1
X

xðkÞe2pjT f

k¼À1

is the Fourier transform of xðkÞ and T is the sample
interval.
Let the signal xðkÞ be given by
xðkÞ ¼ rðkÞ þ vðkÞ
where rðkÞ is a BB signal with unknown carrier remnants
due to the Doppler shift (While the Doppler frequency fd
is time-varying during a satellite pass, it can be assumed
constant during the processing window, which generally
is less than 500 ms long.)
k

rðkÞ ¼ sðkÞej2pfd T

and vðkÞ representing other disturbances, such as white
Gaussian noise and sporadic bursts. While the carrier remnants fd are unknown, the upper and lower bounds are
usually known, i.e., fd 2 ½fdÀ ; fdþ , F. The upper and
lower bounds on the frequency offset due to Doppler, can

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