The Global Positioning System: A Shared National Asset (1995)
Chapter: OLD TECHNOLOGY (100,000 GATE ASIC)
Appendix K
Direct Y-Code Acquisition
Below are calculations showing the time for direct Y-code acquisition with older application specific integrated circuit (ASIC) technology and current ASIC technology. In the analysis, the following assumptions were made:
-
(1)
Receivers have limited knowledge of their current position.
-
(2)
Receivers are using the latest satellite ephemerides.
-
(3)
Time is known to ± 1 second.
Old Technology (100,000 Gate ASIC)
The Y-code has 107 chips to search, given a 1-second uncertainty in clock offset (10.23 million chips per second). A well-designed receiver can obtain a signal-to-noise ratio of 12.6 dB in 0.001 seconds, based on the following derivation:
Noise power = kTB,
where k is Boltzman's constant, k = -198.6 dBm/Hz/Kelvin or 10-19.86 milliwatts/Hz/K. Assume the system temperature, T, is 100 Kelvin, then B, the noise bandwidth, is taken to be 1/0.001 seconds, or 1,000 Hz. Thus:
Noise power = (10.-19.86 milliwatts/Hz/K)(1,000 Hz)(100 K)
= 10-14.86 milliwatts or -148.6 dBm
Given the minimum received power level for the L2 signal, which is -136 dBm, the ratio of signal-to-noise can be calculated:
Signal-to-noise = received power - noise power
= -136 dBm -(-148.6 dBm)
= 12.6 dB.
