GPS Signals-soumyadip

8/14/2019 GPS Signals-soumyadip

1/23

GPS Signal Structure

Sources: GPS Satellite Surveying, Leick Kristine Larson Lecture Noteshttp://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 someinformation on how to determine it

Information regarding the amount of timeelapsed since the signal left the satellite

Details on the satellite clock status


3/23

Important Issues to Consider

Methods to encode information

Signal power

Frequency allocation Security

Number and type of codes necessary tosatisfy system requirements


4/23

Overview of Satellite Transmissions

All transmissions derive from afundamental 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


5/23

Schematic of GPS codes and carrier phase


6/23

GPS Signal Characteristics


7/23

Digital Modulation Methods

Amplitude Modulation (AM) also known asamplitude-shift keying. This method requireschanging the amplitude of the carrier phasebetween 0 and 1 to encode the digital signal.

Frequency Modulation (FM) also known asfrequency-shift keying. Must alter the frequencyof the carrier to correspond to 0 or 1.

Phase Modulation (PM) also known as phase-shift keying. At each phase shift, the bit is flippedfrom 0 to 1 or vice versa. This is the method usedin GPS.


8/23

Modulation Schematics


9/23

Modulo-2 recovery of GPS code

Modulo-2 arithmetic: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 0Bit shifts aligned

MUST MOD-2 ADD RECEIVER-GENERATED CODE TO RECOVER


10/23

Superposition of codes - details

Superposition of two codes is not unique becausethe bit transition occurs at the same epoch;remember that both codes and phases aremultiples of the fundamental frequency

Need to impose an additional constraint to arriveat a solution - quadri-phase-shift keying (QPSK),

which puts the two codes 90 ( /2)


11/23

Phase and Quandrature - General

General Expression:

y(t ) = y1(t ) + y2( t ) = x1(t )cos w t + x2 (t )sin w t

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

All spectral components of y1(t) are 90 out of phasewith those of y2(t). This allows this the two signals tobe separated in the receiver.


12/23

Codes on L1 and L2

S1 p(t ) = A pP

p (t ) D P (t )cos(2 p f 1t ) + AcGP (t ) D P (t )sin(2 p f 1t )

where

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

P P (t ) = pseudorandom P(Y) - code

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

DP ( t ) = navigation data stream

and

S2 p(t ) = B pP

p (t ) D P (t )cos(2 p f 2t )


13/23

Codes on L1 and L2 (cont.)

P p (t ) DP ( t ) and G P ( 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 ) = X 1(t ) X 2(t - pT )

0 p 361T

= 10.23 Mhz


14/23

GPS signal strength - frequency domainNote that C/A code is below noiselevel; signal is multiplied in theReceiver by the internally calculatedcode to allow tracking.C/A-code chip is 1.023 MhzP-code chip is 10.23 Mhz

Power = P(t) = y 2(t)

The calculated power spectrumderives from the Fouriertransform of a square waveof width 2 and unit amplitude.Common function in DSPcalled the sinc function.

sin c( x) =sin( p x)

p x= 1

2 pe iw x w

- p

p

Bandwidth B 1T

whereT is chip duration


15/23

Digital Signal Processing Techniques

Filtering: Allows one to remove someportion of the frequency spectrum that maycontain unwanted signal.

Low Pass Filter: lets all frequencies below acutoff frequency through. High Pass Filter: lets all frequencies above a

cutoff frequency through.

Band Pass Filter: lets all frequencies within aspecified window pass through. The windowis called the passband


16/23

DSP Techniques, cont.

Frequency Translation and Multiplication:technique to shift frequency spectrum of somesignal 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 bysine function in a mixer. Special case is signalsquaring and may be used to recover the pure carrierphase from a bi-phase modulated ranging signal.


17/23


Spread Spectrum: broadly defined as a mechanismby which the bandwidth of the transmitted code ismuch 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 telephoneproviders and LORAN-C.

CDMA: Code Division Multiple Access. Requirespseudorandom codes by transmitted and also generated forcorrelation within the receiver. Used by GPS.


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Cross-correlation: Used by GPS receiversto determine what signal is coming from aspecific satellite. Can be generalized toextracting information from any

multiplexed digital signal.

C ij (Dt ) =1

t yi (t ) y j (t + Dt ) dt =

1

1 -Dt

T 0

t 0

t 0 +t

if Dt = 0if | Dt | T if | Dt | > T

where t denotes the integration time and y

i (t ) and

y j(

t ) are continuous functions (

e.g. PRN codes)


19/23

PRN Cross-correlationCorrelation of receiver generated PRN code (A) with incoming data

stream consisting of multiple (e.g. four, A, B, C, and D) codes


20/23

Schematic of C/A-code acquisition

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


21/23

Methods to Cope with Anti-spoofing

Anti-spoofing: Implemented in 1994 to make P-code unavailable to non-military users. EncryptedP-code is referred to as Y-code. Squaring: Yields half-wavelength carrier and

greatly reduces SNR. Old technology.

Code-aided squaring: Uses mathematicalsimilarity of the Y-code to P-code. L1 carrier isdown-converted and multiplied with a localreplica of the P-code, then squared. Results inless reduction of SNR than simple squaring.


22/23

Anti-spoofing Methods, cont.

Cross-correlation: Takes advantage of the fact that bothL1 and L2 are modulated with the same P(Y)-code, despitelack of knowledge of the actual P-code. Yields thedifference in pseudoranges, P 1(Y) - P 2(Y), and the phasedifference of L1 and L2. Again less SNR loss compared

with squaring. Can be difficult to track at low elevationangles. Technique employed in Trimble 4000SSi/SSE.

Z-tracking: Takes advantage of the fact that Y-code is themodulo-2 sum of the P-code with a lower encryption rate.Yields L1 and L2 Y-code pseudoranges and the full carrierphases 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 & Z

F A hj & L 1992

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