Signal Processing - September 2017 - 44

RxFilt1

∗

Coherent R1
Integrator

∗

Coherent R2
Integrator

CFilt1
RxFilt2
CFilt2
RxFiltN

.
.
.
.

Noncoherent
Unambiguous
Combiner
Correlation
or Other
Postprocessing

Coherent RN
Integrator

∗

Unambiguous Processing

ain

M
ning

Lob

Wid

0.2
0.4
0.6
0.8
1

-1

ing

Delay Error (Chips)

arr

Delay Error (Chips)

Ambiguous Correlation Envelope

Correlation Envelope

Ambiguities

-0.8
-0.6
-0.4
-0.2
0

Correlation Envelope

False Peaks
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1

Unambiguous Shapes

CFiltN

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1

PRN
Code

Correlation Envelope

Rx Signal

Delay Error (Chips)

FIGURE 4. A generic block diagram of unambiguous processing, including examples of the two types of unambiguous shapes: with wide main lobe and
with narrow main lobe.

found in [16]. Table 3 provides a snapshot of the exact mathematical expressions of the combiner/noncoherent processor and filters
for eight unambiguous algorithms to provide an idea of how the
different unambiguous algorithms can be easily modeled with the
unique block diagram in Figure 4. The N nc factor in Table 3 stands
for the number of noncoherent blocks used in the postintegration,
and a ! (0, 1) is a variable parameter of the model, to be empirically chosen. The detailed mathematical derivations for all of the
algorithms are, however, not within the scope of this article; interested readers are directed to the references shown in Table 4 for
the mathematical details of other unambiguous algorithms. Additionally, the following sections provide a more detailed description
of some of the most known unambiguous algorithms and their
main characteristics.

Principal dichotomy of unambiguous solutions:
Wide main lobe versus narrow main lobe
There are basically two approaches in trying to get rid of the
ambiguities (illustrated in Figure 4): 1) we either try to
44

recover a BPSK-like correlation envelope, or, equivalently to
widen the main lobe width of any BOC modulated signal
from subchip level (see Table 1) to two-chip width, which is
the width of the BPSK modulation, or 2) we try to cancel
most or all of the sidelobes and keep mainly or only the
main correlation lobe. These two categories are referred to
as wide main lobe unambiguous methods and narrow main
lobe unambiguous methods. A combined or hybrid approach
that mixes wide and narrow main lobe solutions is also
possible and discussed next. These three classes (wide, narrow, and hybrid) are shown with three different colors
in Figure 5.

Wide main lobe unambiguous processing
From the category of wide main lobe unambiguous methods, we
have, for example: the Betz and Fishman (BF) methods, also
known as sideband processing methods [4], [18], the Martin and
Heiries (MH) methods, the unambiguous adjacent sidelobe
(UAL) methods, the Benedetto methods [19], the zero-forcing

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

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