Receiver Hardware Considerations - Fundamentals of Global Positioning System Receivers: A Software Approach - page 121

FIGURE 6.11 Aliasing of L1 and L2 bands to baseband.

1217.6 - 1237.6 MHz for L1 and L2 bands, respectively. It is tedious to solve
the desired sampling frequency. It is easier to solve the sampling frequency f s
through trial and error. The output frequency can be obtained from Equation (6.5)
by increasing the sampling frequency in 100 kHz steps starting from 100 MHz.
When the two output frequency ranges are properly aliased into the baseband, the
sampling frequency is the desired one. There are many sampling frequencies that
can fulfill this requirement. One of the lower sampling frequencies is arbitrarily
selected, such as f s 107 . 8 MHz. With this sampling frequency, the L1 band

is aliased to 2.32 - 22.32 MHz, and the L2 band is aliased to 31.8 - 51.8 MHz.
These two bands are not overlapped and they are within the baseband of 0 - 53.9
( f s /2) MHz. Figure 6.11 shows such an arrangement.
In the second example, the same two bands are allowed to partially overlap
after they are aliased into the baseband. The sampling frequency can be found
through the same approach. The output bandwidth can be as narrow as 20 MHz,
when the input bands are totally overlapped. Therefore, the minimum sampling
frequency is about 50 MHz. if the sampling frequency f s

=

57 . 8MHz,theL1
frequency aliases to 3.8 - 23.8 MHz and L2 aliases to 4.82 - 24.82 MHz and they
are partially overlapped. The output bandwidth is from 0 to 28.9 ( f s /2) MHz.
The third example is to alias the C/A band of the GPS signal and Russia's
GLONASS signal into separate bands in the baseband. The GLONASS is Rus-
sia's standard position system, which is equivalent to the GPS system of the
United States. The GLONASS uses bi-phase coded signals with 24 channels
at frequencies 1602

=

0 . 5625 n where n is an integer representing the chan-
nel number. A future plan to revise the frequency channels used will eliminate
a number of the upper channels. Therefore, only the 1 - 12 channels will be
considered. The center frequency of these 12 channels is at 1605.656 (1602

+

+

0 . 5625 13) MHz. For sim-

plicity let us use a 7.5 MHz bandwidth, the signal frequency is approximately
1601.9 - 1609.4 MHz. Including the C/A code of the GPS signal, the overall band-
width is about 9.5 MHz. The minimum sampling frequency can be 23.75 (9 . 5

× 6 . 5) MHz. The total bandwidth is 7.3125 (0 . 5625 ×

×

35 . 1 MHz, the GPS channel is aliased to 12.47 - 14.47 MHz,
the GLONASS to 4.8 - 12.35 MHz, and both signals are within the 0 to 17.55
( f s /2) MHz baseband. Hardware has been built to test this idea. The collected
data contain both the GPS and the GLONASS signals.

2 . 5) MHz. If f s =