Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 238

of input data will be used in an example to illustrate the operation. The input
is down-converted to baseband and then divided into 10 groups. Each group
contains 1 ms of data (5000 points). Since the C/A code is periodic, each ms
of data can be correlated with the same specific C/A code. The detail of this
correlation operation is the same as described in Section 7.9. Each ms of data
generates 2,500-point outputs. This operation can be further explained through
Figure 7.4, which is redrawn as Figure 10.5. In this figure, each input data point
and the corresponding point of the local code is multiplied and summed together
to generate one output point. The procedure is equivalent to multiplying the input
and C/A and summing 5000 points into one output point. The local code rotates
two data points instead of one and performs the multiplication and summation
again. Thus there are a total of 2500 output points to cover all the possible
positions of the local C/A code.
Ten ms of input data generate ten 2500-point outputs. The ten outputs are
the correlation results in 10 ms time. These results can be converted into the
frequency domain. To convert to the frequency domain, a FFT is performed on
every 10 corresponding points in the time domain. This operation is performed
2500 times. The final result is a 10 by 2500 point matrix with 2500 points in the
time domain and 10 points in the frequency domain with a resolution of 100 Hz.
This procedure can be illustrated in Figure 10.6. The index for the maximum
amplitude of the matrix represents the initial phase of the C/A code and the
carrier frequency at 100 Hz resolution. Since in the 1-ms coherent integration,
5000 points are summed into one point, the output sample time is 1 ms; thus this
entire operation covers a frequency range of only 1 kHz. Alternatively, one can
consider that there are 10 frequency components with a resolution of 100 Hz.
The overall frequency coverage is 1 kHz.
closest to beginning of C/A code
input data
beginning of C/A code
local code with carrier
frequency component i
FIGURE 10.5 Illustration of acquisition with periodic correlation.