Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 232

the overall outputs from 1 ms of data can be represented by a 20 2500 matrix.

If the input signal is not strong enough to be detected, a subsequent 1 ms of data
will be processed using the same process and another 20

×

2500 matrix will be
generated. These two metrics can be summed, and the result is a new 20 × 2500
matrix. This addition process is the noncoherent integration, which sums the
output of the same frequency. Since in the adjacent ms of data the initial C/A
codes are at about the same location, this process will enhance the output in
the time domain. The number of noncoherent integration can be increased by
summing subsequent 1 ms outputs.
The same process can be applied to 10 ms coherent integration instead of
1 ms. Ten ms of data can produce 2500 time domain outputs and 200 frequency
domain outputs, separated by 100 Hz. Thus the output is a 200

×

2500 matrix.
Subsequent 10 ms of data can be coherently processed and summed together to
perform the noncoherent integration.
When adding the time domain outputs together, one must take into consider-
ation the Doppler frequency. During acquisition the locally generated C/A code
does not take the Doppler frequency into consideration. Thus the initial phase
of the C/A code in the input signal may change position slightly with respect to
the locally generated C/A code. If the Doppler is zero, then there is no initial
point shift. A higher Doppler frequency causes more initial phase shift. When the
results obtained in time domain are summed together, a proper time shift needs
to be added according to the frequency component. This problem will be further
discussed in Section 10.12.
In obtaining the amplitude of the output, a squaring operation is required,
which is equivalent to the video detector in radar. Based on this similarity, the
concept of noncoherent integration, discussed in radar topics, is used to process
GPS signal.

×

10.7 NONCOHERENT INTEGRATION LOSS AND GAIN ( 1,3,11 )

In this section the gain of the noncoherent integration will be obtained. This
discussion is based on Barton ( 3 ) . The procedure is to find two factors: the coherent
integration gain and the noncoherent integration loss. The noncoherent integration
gain equals the coherent integration gain minus the noncoherent integration loss.
The coherent integration gain is given by Equation (10.6). Therefore the main
goal of this section is to find the noncoherent integration loss.
If the probability of detection and probability of false alarm are given, the
integration loss factor can be found from curves in Skolnik ( 1 ) and Barton ( 3 ) .

Here a Matlab program will be used to find the integration loss.
The ideal detectability factor D c (1) is a function of probability of detection
P d and probability of false alarm P fa , which can be written as

= [ erfc − 1 ( 2 P fa ) − erfc − 1 ( 2 P d ) ] 2

D c ( 1 ) ( 10 . 7 )

where erfc − 1 ( y ) is the inverse complimentary error function. The inverse error
function is available in the Matlab program, but the complimentary inverse