Signal Processing - September 2017 - 91

time-varying channel conditions due to, e.g., multipath fading
facts, we apply the AOK, and the corresponding IF estimate
and line-of-sight obstruction. Such phenomena are more freis obtained via sparse reconstruction using the OMP algoquently observed in ground GNSS operation in urban envirithm. The resulting TFR is shown in Figure 7(c). It is evironments, such as a city canyon. Missing data may also be a
dent that the reconstructed IF signatures well approximate
result of discarding samples contaminated by impulsive noise
the true ones. With accurate IF estimates secured, the
from, e.g., motor ignition noise and wideband radar emissubspace projection-based jammer mitigation technique
sions using narrow pulse, frequency-hopping, and other types
can proceed to yield the jammer-suppressed GNSS sigof TF-selective waveforms. Consequently, the observed data
nal. The output is the time-domain waveform, and no signal
may be viewed as sparsely sampled and described by misssynthesis is required. The WVD of the yielded signal is
ing samples from Nyquist sampled data. In these situations,
shown in Figure 7(d). In this case, some residual jammer sigmissing samples cause a high level of noise-like artifacts in
nal components are still observed in the WVD result.
the TF analysis [30].
To further improve performance, a total of 11 parallel IF
The combined use of TF kernels and sparse reconstrucsignatures, which equally occupy an instantaneous bandtion is shown in [30] and [31] to eliminate, or at least signifiwidth of 2 KHz, are assumed. Figure 7(e) shows the WVD
cantly reduce, the artifacts due to missing samples as well
of the resulting jammer-suppressed GNSS signal when augas cross terms due to interactions of jammer signal compomented jammer signal IF signatures are used. Effective jamnents. A TF kernel, in essence, is a 2-D low-pass filter mulmer signal suppression is confirmed.
tiplied in the AF domain (time-lag versus frequency-shift)
and represented as 2-D convolution in the TF domain [8].
From single- to multiantenna receivers
As such, the properties of a reduced-interference TFD can
Many GNSS receivers are equipped with a multisensor
be characterized by constraints on kernel design. The basic
array that can add significant antijam capabilities. The
concept behind TF kernels is that signal autoterms are
spatial degrees of freedom, offered by the multisensor
concentrated near the AF origin (small valarray, are employed to place beam patues of time lag and frequency shift), whereas
tern nulls along the jammer directions.
Successful implementation By combining spatial and temporal inforcross terms are generally located away
of STAP for jammer signal
from the origin. On the other hand, noise
mation, space-time adaptive processsuppression requires
and artifact contributions spread over the
ing (STAP) extends the projection-based
entire AF domain. Therefore, placing highjammer suppression, discussed previousaccurate estimation of
er weights to the AF entries around the
ly, to the joint spatiotemporal domain. In
the IF signatures and
origin leads to the enhancement of signal
this case, the joint spatiotemporal signathe associated spatial
autoterms, while cross terms, noise, and
ture of a jammer signal is the Kronecker
signatures of the jammers.
artifacts become diminished.
product of its spatial and temporal sigWhile some TF kernels, such as the
natures. The result is a jammer signal
Choi-Williams, assume fixed (signal-independent) paramesubspace with an extended dimension. This lends itself to
ters, other kernels, such as the adaptive optimal kernel (AOK)
enhanced output signal-to-interference-plus-noise ratio
[36], provide signal-adaptive filtering capability.
performance and improved jammer signal suppression
capabilities [15], [16].
Example
Successful implementation of STAP for jammer signal
For illustrative purposes, we consider two FM jammers
suppression requires accurate estimation of the IF signaimpinging on the receiver along with an L1 band GPS sigtures and the associated spatial signatures of the jammers.
nals with coarse acquisition codes. The chip rate of the
When a clear line-of-sight exists for the jammer signals, the
signals is 1.023 MHz, and a data segment of 256 samples
spatial signatures can be properly represented as the array
is considered. The input signal-to-noise ratio of the GPS
manifold corresponding to the jammer directions of arrival
waveform is -16 dB, and the input jammer-to-noise ratio
(DOAs). It is important to note that the jammer TF and spais assumed to be 25 dB. We consider the case where 50%
tial signatures can interplay and benefit one another in the
of the data samples are randomly missing. The number of
sense that the information collected at multiple antennas
frequencies used in constructing the sparse TFR is set to
can improve the jammer signal IF estimation and subspace
1,024, and the yielding frequency resolution is approximateconstruction. On the other hand, an accurate IF estimate
ly 1 KHz.
permits better selections of TF entries corresponding to
Figure 7(a) shows the real part of the jammed GPS sigeach jammer, leading to an accurate jammer signal spatial
nal waveform with missing samples, where the red dots
signature or DOA.
represent the 128 missing samples. The WVD of the jammed
To underscore the previous argument, [37] shows that the
GPS signal is shown in Figure 7(b). The WVD suffers from
autoterm QTFDs of a signal obtained at each antenna are all
the artifacts due to the missing data samples as well as cross
positive, whereas the cross terms alternate between positive
terms. As a consequence, it becomes difficult to accurately
and negative signs. Because the phase differences between
estimate the IFs of the jammer signals. To suppress the artimultiple jammer signals vary for each antenna, the cross
IEEE SIGNAL PROCESSING MAGAZINE

September 2017

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