Signal Processing - September 2017 - 64

for weaker GNSS signal acquisition. In the literature, the mean
acquisition computation (MAC) (n C, i.e., the expected computational cost for a signal acquisition) is used for a measure
of the mean computational cost of acquisition [11]. Note that,
in practice, X * can be pregenerated and stored in a memory of
a receiver, and fast Fourier transform (FFT) and inverse FFT
(IFFT) are used instead of DFT and IDFT, respectively, which
effectively reduces the computational cost. Figure 3 shows the
FFT-based hybrid search technique (FFT-based technique, for
short), where, due to the circular convolution in the FFT-based
correlation [12], x is padded with N co (or more) zeros to make
the length of X equal to an integer power of two, and y of the
same size should be used to obtain Y. The circular shifting
of Y in Figure 3 is to shift the Doppler-frequency hypothesis
to the next one. As a result, the overall amount of complex
multiplications for the FFT-based technique has an order of
O ^ N co log 2N co h .
Note that, while an acquisition function can employ the serial,
parallel, or hybrid search strategy depending on the available
receiver capacity, the multiple-dwell search can be used in
combination to the search strategy to speed up the acquisition.
When the detection variable is found to be larger than the
threshold, the verification function additionally tests the detected
hypothesis multiple times to verify the acquisition. Since the
detected code phase and Doppler frequency by the acquisition
function have errors as large as ∆ x /2 and ∆ f /2, respectively,
the pull-in search process is employed to find a finer-Dopplerfrequency estimate, and then the signal tracking function estimates
and tracks the precise code phase and Doppler frequency of the
incoming signal to produce measurements for positioning.

Detection schemes
In GNSSs, a detection scheme involves a detection variable
and a detection rule for reliable signal detection from the
search result. In practice, the selection of the detection variable
may depend on the employed search strategy as discussed next.

Threshold crossing
In the serial search, the integration function G ($) output resulting from the current hypothesis test is used as the detection
variable, and a detection is declared when the detection variable is found to be larger than the detection threshold c. This
detection rule is called the threshold crossing (TC) [10] and
is used only for the serial search strategy. The overall system performance of the acquisition function using TC can be
expressed with the system probabilities [13]: the detection PD,
misdetection PM, and false alarm PF probabilities. Note that
the system probabilities are different from those ( Pd, Pm, and
P f ) of the individual hypothesis test, since the system probabilities represent the performance of the overall acquisition
function, while Pd, Pm, and P f are related to the detection performance of each individual hypothesis test.

Maximum TC and maximum-to-second-maximum ratio
For acquisition functions employing the hybrid or parallel search
strategy, the maximum of the integration function G ($) output
64

(in other words, the maximum of the current search result) is
often used as the detection variable and is compared to the detection threshold, which is the maximum TC (MTC) scheme [14]
shown in Figures 2 and 3. Note that, in the hybrid search strategy,
the maximum of the integration function output is only a local
maximum. In practice, the maximum-to-second-maximum ratio
[15] (MTSMR) of the search result can be used as the detection
variable, where the second maximum should be at least one chip
apart from the maximum. In [16], the system probabilities, i.e.,
PD, PM, and PF, of the acquisition function using MTC are very
similar to those using MTSMR.

K-largest
The K-largest detection rule has been used successfully in practice [17], where an acquisition function selects K (2 1) hypotheses that produce the K-largest integration function outputs. To
verify the detection, a receiver tests the selected K hypotheses
again to identify the true hypothesis. This detection rule can be
used for both hybrid and parallel search strategies and has been
found useful for detecting the GNSS signal in noise, since the
probability that the true hypothesis H 1 is included within the
K-largest hypotheses is higher than the probability that H 1 is at
the maximum of the integration function output.

Detection threshold
The detection threshold c has a critical effect on the acquisition performance, since it affects both the probabilities (i.e., Pd,
Pm, and P f ) of the individual hypothesis testing and the system
probabilities (i.e., PD , PM, and PF, ) of the acquisition function. The conventional technique for determining the detection
threshold is to find a c that limits P f under a tolerable small
constant level (e.g., 0.01 or less), known as the constant false
alarm rate (CFAR) [4]. This rule is effective, since the false
alarm costs a large penalty in the acquisition time, and the
detection threshold for a low CFAR leads to the optimal acquisition performance (i.e., minimum MAT n T or MAC n C) for
GNSS signals with moderate and high SNR. Note that the
MAT n T and MAC n C are functions of c , Pd, Pm, P f , penalty time, N Hc, N Hf , N i, and Tco, and that the minimum n T,min
and the minimum n C,min can be found by letting the derivative
of n T and n C with respect to c be equal to zero, respectively.
However, in [16], it is found that the algebraically determined
optimal detection threshold c achieves smaller MAT n T and
MAC n C than the CFAR-based detection threshold for weak
GNSS signals. Note that, to determine c for all of the detection
variables except MTSMR, knowledge of the average integration function output at incorrect hypotheses E 6Z | H 0@ (in other
words, noise power in the integration output) is required.

Other factors affecting the GNSS acquisition performance
In addition to the detection variable, search strategy, and detection scheme, the acquisition performance depends on a number of other factors. There are receiver-dependent factors, such
as front-end filtering, sampling rate fs, oscillator stability, and
quantization levels, and there are receiver-independent factors
such as multipath and NLOS, interference signals, user dynamics,

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

Signal Processing - September 2017 - Cover1
Signal Processing - September 2017 - Cover2
Signal Processing - September 2017 - 1
Signal Processing - September 2017 - 2
Signal Processing - September 2017 - 3
Signal Processing - September 2017 - 4
Signal Processing - September 2017 - 5
Signal Processing - September 2017 - 6
Signal Processing - September 2017 - 7
Signal Processing - September 2017 - 8
Signal Processing - September 2017 - 9
Signal Processing - September 2017 - 10
Signal Processing - September 2017 - 11
Signal Processing - September 2017 - 12
Signal Processing - September 2017 - 13
Signal Processing - September 2017 - 14
Signal Processing - September 2017 - 15
Signal Processing - September 2017 - 16
Signal Processing - September 2017 - 17
Signal Processing - September 2017 - 18
Signal Processing - September 2017 - 19
Signal Processing - September 2017 - 20
Signal Processing - September 2017 - 21
Signal Processing - September 2017 - 22
Signal Processing - September 2017 - 23
Signal Processing - September 2017 - 24
Signal Processing - September 2017 - 25
Signal Processing - September 2017 - 26
Signal Processing - September 2017 - 27
Signal Processing - September 2017 - 28
Signal Processing - September 2017 - 29
Signal Processing - September 2017 - 30
Signal Processing - September 2017 - 31
Signal Processing - September 2017 - 32
Signal Processing - September 2017 - 33
Signal Processing - September 2017 - 34
Signal Processing - September 2017 - 35
Signal Processing - September 2017 - 36
Signal Processing - September 2017 - 37
Signal Processing - September 2017 - 38
Signal Processing - September 2017 - 39
Signal Processing - September 2017 - 40
Signal Processing - September 2017 - 41
Signal Processing - September 2017 - 42
Signal Processing - September 2017 - 43
Signal Processing - September 2017 - 44
Signal Processing - September 2017 - 45
Signal Processing - September 2017 - 46
Signal Processing - September 2017 - 47
Signal Processing - September 2017 - 48
Signal Processing - September 2017 - 49
Signal Processing - September 2017 - 50
Signal Processing - September 2017 - 51
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Signal Processing - September 2017 - 53
Signal Processing - September 2017 - 54
Signal Processing - September 2017 - 55
Signal Processing - September 2017 - 56
Signal Processing - September 2017 - 57
Signal Processing - September 2017 - 58
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Signal Processing - September 2017 - 60
Signal Processing - September 2017 - 61
Signal Processing - September 2017 - 62
Signal Processing - September 2017 - 63
Signal Processing - September 2017 - 64
Signal Processing - September 2017 - 65
Signal Processing - September 2017 - 66
Signal Processing - September 2017 - 67
Signal Processing - September 2017 - 68
Signal Processing - September 2017 - 69
Signal Processing - September 2017 - 70
Signal Processing - September 2017 - 71
Signal Processing - September 2017 - 72
Signal Processing - September 2017 - 73
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Signal Processing - September 2017 - 85
Signal Processing - September 2017 - 86
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Signal Processing - September 2017 - 88
Signal Processing - September 2017 - 89
Signal Processing - September 2017 - 90
Signal Processing - September 2017 - 91
Signal Processing - September 2017 - 92
Signal Processing - September 2017 - 93
Signal Processing - September 2017 - 94
Signal Processing - September 2017 - 95
Signal Processing - September 2017 - 96
Signal Processing - September 2017 - 97
Signal Processing - September 2017 - 98
Signal Processing - September 2017 - 99
Signal Processing - September 2017 - 100
Signal Processing - September 2017 - 101
Signal Processing - September 2017 - 102
Signal Processing - September 2017 - 103
Signal Processing - September 2017 - 104
Signal Processing - September 2017 - 105
Signal Processing - September 2017 - 106
Signal Processing - September 2017 - 107
Signal Processing - September 2017 - 108
Signal Processing - September 2017 - 109
Signal Processing - September 2017 - 110
Signal Processing - September 2017 - 111
Signal Processing - September 2017 - 112
Signal Processing - September 2017 - 113
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Signal Processing - September 2017 - 116
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Signal Processing - September 2017 - 125
Signal Processing - September 2017 - 126
Signal Processing - September 2017 - 127
Signal Processing - September 2017 - 128
Signal Processing - September 2017 - 129
Signal Processing - September 2017 - 130
Signal Processing - September 2017 - 131
Signal Processing - September 2017 - 132
Signal Processing - September 2017 - 133
Signal Processing - September 2017 - 134
Signal Processing - September 2017 - 135
Signal Processing - September 2017 - 136
Signal Processing - September 2017 - 137
Signal Processing - September 2017 - 138
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Signal Processing - September 2017 - 140
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Signal Processing - September 2017 - 143
Signal Processing - September 2017 - 144
Signal Processing - September 2017 - 145
Signal Processing - September 2017 - 146
Signal Processing - September 2017 - 147
Signal Processing - September 2017 - 148
Signal Processing - September 2017 - 149
Signal Processing - September 2017 - 150
Signal Processing - September 2017 - 151
Signal Processing - September 2017 - 152
Signal Processing - September 2017 - 153
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Signal Processing - September 2017 - 193
Signal Processing - September 2017 - 194
Signal Processing - September 2017 - 195
Signal Processing - September 2017 - 196
Signal Processing - September 2017 - Cover3
Signal Processing - September 2017 - Cover4
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