Signal Processing - September 2017 - 45

shaping (ZFS) [20], and the minimum mean square error shap■ the general removing ambiguity via sidepeak suppression
ing (MMSES) [20]. BF, MH, and UAL all have either single
(GRASS) [21]
sideband or dual sideband implementation, according to whether
■ the improved GRASS (IGRASS) [22]
only one side frequency lobe (upper or lower) or both are used in
■ the simultaneous perturbation stochastic approximation
the noncoherent combiner, i.e., N = 1 for single sideband and
(SPSA) [23]
N = 2 for dual sideband processing. The differences between
■ the sidelobe cancelation method (SCM) [24]
the BF, MH, and UAL algorithms lie mainly in the way the sig■ the sidelobe cancelation (SLC) algorithm [25]
nal and the reference codes are filtered. For example, in BF
■ QBOC [26]
approaches, only the main frequency lobes of both the received
■ Ren et al. [27]
signal and reference codes are used; in MH approaches, both
■ Huihua et. al [28].
main frequency lobes and everything in between are used, while
PCF/PUDLL, GRASS, IGRASS, and SPSA are based on
in UAL approaches, there is no lobe selector applied on the
the generic block diagram of Figure 4 with N = 2. For example,
received signal; in this latter approach, only a frequency shift filPCF and PUDLL use the unfiltered received signal (i.e., RxFilt 1
ter is used to align the main frequency lobes (occurring at
and RxFilt 2 are absent), and they filter the reference codes with
! N B fc /2) to zero frequency and to be able to correlate them
several subcorrelation shapes filters, (CFilt 1 ! CFilt 2), to get
with a BPSK reference code, whose main spectral energy is also
rid of the ambiguities. A similar approach as for PCF/PUDLL
around zero frequency. Also, modified approaches mBF and
is used in the GRASS and SPSA, with the main differences in
mMH have been proposed [18] for a lowerthe subcorrelation shapes filters and in the
complexity implementation of BF and MH,
combining rule. The difference between
The more ambiguities we
respectively, but the performance remains the
IGRASS and GRASS lie in the fact that
have, the more challenging IGRASS works for all types of BOC modusame as with BF and MH. The Benedetto
it is to mitigate them in
methods rely on filtering the ambiguous corlations, while GRASS is limited to even BOC
acquisition and tracking.
relation function with two types of filters:
modulation orders. Nevertheless, since cureither with a low-complexity three-tap filter
rently in GNSS we only have even BOC
(Benedetto method 1) or with a seven-tap filter (Benedetto methmodulation orders and since IGRASS complexity is higher than
od 2), which also eliminates the unwanted BOC spectrum repliGRASS complexity, the IGRASS algorithm is (despite its name)
cas [19]. The ZFS and MMSES rely on equalization in the
is outperformed by GRASS.
frequency domain and aim at recreating a BPSK-like correlation
The SCM starts from the ambiguous correlation and applies
shape through zero-forcing or MMSE equalization [20]. It was
a nonlinear pulse subtraction filter to the noncoherent ambigushown in [20] that such methods are very sensitive to noise; their
ous BOC correlation to diminish or remove the sidelobes. The
complexity is also quite high.
pulse subtraction filter is designed according to the BOC modulation order [24]. The SLC, despite its close name to the SCM,
Narrow main lobe unambiguous processing
uses a completely different approach: it filters the reference
In this category, we have, for example,
code with N $ 2 subcorrelation shape filters, with N depend■ the pseudocorrelation function (PCF) or PCF-based unaming on BOC modulation order and the sine/cosine type (N can
biguous delay lock loop (PUDLL) algorithms [11], [21]
be up to 24), and it correlates the filtered reference code with
Table 3. A snapshot of linear time-variant filters and combiner rules in the generic block diagram of Figure 4 for eight unambiguous algorithms: dual
BF, single BF, dual UAL, GRASS, PUDLL/PCF, ZFS, MMSES, and quadratic BOC (QBOC); see the section "Principal Dichotomy of Unambiguous Solutions:
Wide Main Lobe Versus Narrow Main Lobe" for explanations on the abbreviations.
Technique

RxFilt1 (f, t)

CFilt1 (f, t)

RxFilt2 (f, t)

CFilt2 (f, t)

Combiner

BF dual

Upper main lobe
selector

Same as RxFilt1

Lower main lobe selector

same as RxFilt2

1 Nnc ^ R 2 + R 2h
1
2
2N nc /

BF single

Upper main lobe
selector

Same as RxFilt1

0 (i.e., absent)

0

1 Nnc ^ R 2h
1
N nc /

UAL dual

Frequency shift
with + N B fc /2

Hold filter

Frequency shift with
- N B fc /2

Hold filter

1 Nnc ^ R 2 + R 2h
1
2
2N nc /

GRASS

1

BOC filter

1

Subcorrelation shape
filter

1 Nnc ^ R - a R h
1
2
N nc /

PUDLL/PCF

1

Subcorrelation shape
filter 1

1

Subcorrelation shape
filter 2

1 Nnc ^ R + R - R - R h
1
2
1
2
N nc /

ZFS and
MMSES

1

BOC filter and ZF or
MMSE filter

0

0

1 Nnc ^ R h
1
N nc /

QBOC

1

BOC filter

1

QBOC filter

1 Nnc ^ R - a R h2
1
2
N nc /

IEEE SIGNAL PROCESSING MAGAZINE

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September 2017

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