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## Appendix KDirect 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.

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