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GPS Signal Structure Sources: –GPS Satellite Surveying, Leick –Kristine Larson Lecture Notes http://www.colorado.edu/engineering/ASEN/asen 4519/asen4519.html

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GPS Signal Requirements Method (code) to identify each satellite The location of the satellite or some information on how to determine it Information regarding the amount of time elapsed since the signal left the satellite Details on the satellite clock status

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Important Issues to Consider Methods to encode information Signal power Frequency allocation Security Number and type of codes necessary to satisfy system requirements

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Overview of Satellite Transmissions All transmissions derive from a fundamental frequency of 10.23 Mhz –L1 = 154 10.23 = 1575.42 Mhz –L2 = 120 10.23 = 1227.60 Mhz All codes initialized once per GPS week at midnight from Saturday to Sunday –Chipping rate for C/A is 1.023 Mhz –Chipping rate for P(Y) is 10.23 Mhz

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Schematic of GPS codes and carrier phase

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GPS Signal Characteristics

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Digital Modulation Methods Amplitude Modulation (AM) also known as amplitude-shift keying. This method requires changing the amplitude of the carrier phase between 0 and 1 to encode the digital signal. Frequency Modulation (FM) also known as frequency-shift keying. Must alter the frequency of the carrier to correspond to 0 or 1. Phase Modulation (PM) also known as phase- shift keying. At each phase shift, the bit is flipped from 0 to 1 or vice versa. This is the method used in GPS.

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Modulation Schematics

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Modulo-2 recovery of GPS code Modulo-2 arithmetic: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 0 Bit shifts aligned MUST MOD-2 ADD RECEIVER-GENERATED CODE TO RECOVER

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Superposition of codes - details Superposition of two codes is not unique because the bit transition occurs at the same epoch; remember that both codes and phases are multiples of the fundamental frequency Need to impose an additional constraint to arrive at a solution - quadri-phase-shift keying (QPSK), which puts the two codes 90° ( /2)

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Phase and Quandrature - General General Expression: All spectral components of y 1 (t) are 90° out of phase with those of y 2 (t). This allows this the two signals to be separated in the receiver. 2

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Codes on L1 and L2

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Codes on L1 and L2 (con’t.)

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GPS signal strength - frequency domain Note that C/A code is below noise level; signal is multiplied in the Receiver by the internally calculated code to allow tracking. C/A-code chip is 1.023 Mhz P-code chip is 10.23 Mhz Power = P(t) = y 2 (t) The calculated power spectrum derives from the Fourier transform of a square wave of width 2π and unit amplitude. Common function in DSP called the “sinc” function.

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Digital Signal Processing Techniques Filtering: Allows one to remove some portion of the frequency spectrum that may contain unwanted signal. –Low Pass Filter: lets all frequencies below a cutoff frequency through. –High Pass Filter: lets all frequencies above a cutoff frequency through. –Band Pass Filter: lets all frequencies within a specified window pass through. The window is called the passband

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DSP Techniques, con’t. Frequency Translation and Multiplication: technique to shift frequency spectrum of some signal to another portion of the frequency domain. –Up-conversion: translate signal to higher frequencies. –Down-conversion: translate signal to lower frequencies. Commonly done in GPS receivers. Multiply signal by sine function in a “mixer.” Special case is signal squaring and may be used to recover the pure carrier phase from a bi-phase modulated ranging signal.

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DSP Techniques, con’t. Spread Spectrum: broadly defined as a mechanism by which the bandwidth of the transmitted code is much greater than the baseband information signal (e.g. the navigation message in GPS) –FDMA: Frequency Division Multiple Access. Requires different carriers. Used by GLONASS. –TDMA: Time Division Multiple Access. Several channels share transmission link. Used by many cellular telephone providers and LORAN-C. –CDMA: Code Division Multiple Access. Requires pseudorandom codes by transmitted and also generated for correlation within the receiver. Used by GPS.

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DSP Techniques, con’t. Cross-correlation: Used by GPS receivers to determine what signal is coming from a specific satellite. Can be generalized to extracting information from any multiplexed digital signal.

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PRN Cross-correlation Correlation of receiver generated PRN code (A) with incoming data stream consisting of multiple (e.g. four, A, B, C, and D) codes

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Schematic of C/A-code acquisition Since C/A-code is 1023 chips long and repeats every 1/1000 s, it is inherently ambiguous by 1 msec or ~300 km. Must modulo-2 add the transmitted and received codes after correlation to increase SNR and narrow bandwidth.

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Methods to Cope with Anti-spoofing Anti-spoofing: Implemented in 1994 to make P- code unavailable to non-military users. Encrypted P-code is referred to as Y-code. –Squaring: Yields half-wavelength carrier and greatly reduces SNR. Old technology. –Code-aided squaring: Uses mathematical similarity of the Y-code to P-code. L1 carrier is down-converted and multiplied with a local replica of the P-code, then squared. Results in less reduction of SNR than simple squaring.

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Anti-spoofing Methods, con’t. Cross-correlation: Takes advantage of the fact that both L1 and L2 are modulated with the same P(Y)-code, despite lack of knowledge of the actual P-code. Yields the difference in pseudoranges, P 1 (Y) - P 2 (Y), and the phase difference of L1 and L2. Again less SNR loss compared with squaring. Can be difficult to track at low elevation angles. Technique employed in Trimble 4000SSi/SSE. Z-tracking: Takes advantage of the fact that Y-code is the modulo-2 sum of the P-code with a lower encryption rate. Yields L1 and L2 Y-code pseudoranges and the full carrier phases of L1 & L2. This method yields the best SNR. Multipath performance is better than other methods. Technique employed in Ashtech Z-12 and micro-Z.

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AS Technologies Summary Table Trimble 4000SSi Ashtech Z-12 & µZ From Ashjaee & Lorenz, 1992

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Lecture 3 Data Encoding and Signal Modulation

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