GPS Signals (1)

GPS Signal Structure

• Sources: – GPS Satellite Surveying, Leick– Kristine Larson Lecture Notes

http://www.colorado.edu/engineering/ASEN/asen4519/asen4519.html

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

Important Issues to Consider

• Methods to encode information

• Signal power

• Frequency allocation

• Security

• Number and type of codes necessary to satisfy system requirements

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

Schematic of GPS codes and carrier phase

GPS Signal Characteristics

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.

Modulation Schematics

Modulo-2 recovery of GPS codeModulo-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

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)

Phase and Quandrature - General

General Expression:

y(t) y1(t) y2( t) x1(t)cost x2 (t)sint

where

y1(t) is in phase (I) and y1(t) is in quandrature (Q)

All spectral components of y1(t) are 90° out of phase with those of y2(t). This allows this the two signals to be separated in the receiver.

2

Codes on L1 and L2

S1p(t) ApP

p (t)DP (t)cos(2f1t) AcGP (t)DP (t)sin(2f1t)

where

Ap,Ac amplitudes (power) of P(Y) - code and C / A- code

PP (t) pseudorandom P(Y) - code

G P( t) C / A- code (Gold code)

DP( t) navigation data stream

and

S2p(t) BpP

p (t)DP (t)cos(2f2t)

Codes on L1 and L2 (con’t.)

P p (t)DP (t) and GP (t)DP (t) imply modulo - 2 addition

and the P(Y) - code is also a modulo - 2 sum of two

pseudorandom data streams:

P p (t) X1(t)X

2(t pT)

0 p36

1T

10.23 Mhz

GPS signal strength - frequency domain

Note that C/A code is below noise level; signal is multiplied in the Receiver by the internally calculatedcode to allow tracking. C/A-code chip is 1.023 MhzP-code chip is 10.23 Mhz

Power = P(t) = y2(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.

sin c(x) sin(x)x

12

e ix

Bandwidth B1

TwhereT is chip duration

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

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.

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.

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.

C ij(t) 1

y i(t)y j (t t)dt

1

1tT

0

t0

t 0

if t = 0if | t | Tif | t | > T

where denotes the integration time andyi(t) and y j(t) are continuous functions (e.g. PRN codes)

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

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.

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.

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, P1(Y) - P2(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.

AS Technologies Summary Table

Trimble 4000SSi

Ashtech Z-12 & µZ

From Ashjaee & Lorenz, 1992