Applied Research Laboratories The University of Texas at Austin Applied Research Laboratories The University of Texas at Austin Interfacing GPSTk to Existing Software Receiver Michael Davis 08/13/08 (512)

2 The University of Texas at Austin ARL Objective To integrate GPS Creations GPS1A software defined gnss receiver with the existing tools in the GPSTk.

3 The University of Texas at Austin ARL Topics  GPS1A Specifications  Updates to GPSTk Simulator Program  Hilbert Transform (Real to I&Q)  Acquisition  Tracking  Performance  Next Steps

4 The University of Texas at Austin ARL GPS1A Block Diagram

5 The University of Texas at Austin ARL Output Format  SiGe SE4110L outputs 2-bit real samples on sign/mag pins.  MHz sample rate.  MHz intermediate frequency (L1 at MHz is mixed with 96 * clock).  ogusb-lite program included with the board handles USB interface and outputs samples in 8-bit format...inefficient but easy to work with.

6 The University of Texas at Austin ARL Updates to GPSTk swrx Simulator  Previous input parameters: band, offset, Doppler, noise and quantization.  Added Intermediate Frequency and Sample Rate parameters. Example: gpsSim -c c:1:4:50:4000:c -x r q 2 -n 2  All applications in the swrx section of the toolkit now have adjustable sample rate and IF.  The software receiver tools in the GPSTk are located in dev/apps/swrx.

7 The University of Texas at Austin ARL Inphase and Quadrature Components  Typical hardware method of generating complex I and Q samples --->  Recall from the GPS1A block diagram that we only mix with the oscillator frequency to generate IF – no Q component.  Second part of my project involved writing a Hilbert transform in C++ to pull quadrature samples from the SiGe output.

8 The University of Texas at Austin ARL Frequency Domain  Fourier Transform:  Discrete Fourier Transform:  Fast Fourier Transforms (FFT) compute the Discrete Fourier transform with O(N log N) operations. (Equation above is O(N^2))

9 The University of Texas at Austin ARL Hilbert Transform  Generates Inphase and Quadrature samples from Real samples. – Allows code/algorithm reuse. – Can improve acquisition time by cutting effective sampling rate in half.  Input: real 8 bit data from GPS1A output file.  Output: IQ2Stream class, a complex two bit stream that can be used as input to the other swrx tools. For each data point, the inphase sample is the real part and the quadrature sample is the imaginary part.  Algorithm: – Take N data points to frequency domain using FFT. – Only use frequency components from 0 to N/2-1 – Perform inverse FFT on those N/2 points – Result is N/2 points of complex data in the time domain.

1010 The University of Texas at Austin ARL Hilbert Example: Sin Wave

1 The University of Texas at Austin ARL FFTW  C library for performing FFT's.  Free under the terms of the GNU General Public License.  O(N log N)  The Hilbert transform and Acquisition programs both link to FFTW.  Programs that link to FFTW are not currently included in the jamfile. Linkage commands for GCC can be found at the top of each.cpp file.

1212 The University of Texas at Austin ARL Acquisition  We generate a local code/carrier replica and correlate it with the received signal from a satellite.  Signal search attributes: PRN, Doppler, Code Shift. – PRN is used to select SV. – Doppler is change in signal frequency caused by SV velocity and local clock error. – Code Shift is caused by changing distance to satellite. Height Doppler Code Shift

1313 The University of Texas at Austin ARL Time Based / Brute Force  Correlate a local replica with incoming code by multiplying each data point and adding the results.  Local replicas must be created and correlated for each possible code and Doppler shift  (# data points * # code shifts * # frequency bins) + time to generate local replica  Slow......several minutes for only one C/A period.  Typically about 1.3 billion floating point multiplies and replicas generated (again for one period).

1414 The University of Texas at Austin ARL FFT Based Acquisition  Parallel Code Phase Search eliminates need to shift local replicas.  Algorithm: – Generate local code/carrier replicas for each frequency bin. – Use an FFT to take input and replicas to frequency domain. – Multiply the frequency components of the local codes by the complex conjugate of the input frequency components. – Convert the result back to the time domain using an inverse FFT.

1515 The University of Texas at Austin ARL Mathematical Explanation (Valid for non-circular correlation as well, not limited to short codes)

1616 The University of Texas at Austin ARL Acquisition Example - Samples

1717 The University of Texas at Austin ARL Acquisition Example – Frequency Domain

1818 The University of Texas at Austin ARL Acquisition Example – Correlation Peaks Using one C/A period Using five periods

1919 The University of Texas at Austin ARL Acquisition Example – 3D Results Five periods One period

2020 The University of Texas at Austin ARL Commands hilbert | acquire -c 4 -p 1 -q 2 -b 1 -x r w f 50 -c 4PRN 4 -p 1 One period -q 2 Two bit quantization -b 1One band -x 4.13Intermediate Frequency (MHz) -r Sample Rate (MHz) -w 20000Frequency search width (Hertz) -f 50Bin Width (Hertz) Output: PRN 4: Bin 160 = Doppler: Offset Height data for graphing correct frequency bin

2121 The University of Texas at Austin ARL Frequency Separation

2 The University of Texas at Austin ARL Frequency Bin Width Selection  We need smaller bins for longer data lengths.  If the “frequency separation” between two signals is more than one cycle over a given data length, there will be no correlation.  A 1 kHz change in frequency will cause a 1 cycles separation over 1 ms (one code period)  Arbitrarily picked max of 0.5 cycle separation to ensure peak is found and improve signal to noise ratio.

2323 The University of Texas at Austin ARL Bin Width Selection Examples

2424 The University of Texas at Austin ARL Verification  SiGe data is noisy, but we see some similarity.  gpsSim data with noise turned off matches very well. SiGe Data gpsSim with noise off gpsSim zoomed  Red Line = Theoretical C/A code autocorrelation.  Blue Line = Data acquired and correlated using acquire.cpp

2525 The University of Texas at Austin ARL CW Acquisition Method (Carrier Wave) Especially useful for GLONASS, only one spreading code. “Parallel Frequency Space Search”

2626 The University of Texas at Austin ARL Tracking  Early Minus Late Code Tracker  Costas Carrier Tracker  Includes NavFramer class to find preamble and HOW (hand over word) of potential subframes.  Uses EngNav class to check subframe parity.

2727 The University of Texas at Austin ARL Tracker Algorithm  Code and Carrier phases and frequency offsets are then adjusted by selected multiples of these errors, and tracker moves to next code period.  Phase of remaining carrier wave is checked, nav bit is assigned based on positive or negative real component.

2828 The University of Texas at Austin ARL Tracker Output (verbose mode)

2929 The University of Texas at Austin ARL Subframes

3030 The University of Texas at Austin ARL Performance  Time domain / brute force acquisition is linear, but very steep. ~ 1.3 billion multiplies + time to generate replicas for one period of C/A code. Replicas are expensive in memory if pre-generated, or performance if on the fly.  FFT based acquisition is O(N log N), replicas are pre- generated.  We can acquire one period of data digitized at MHz in less than a second. That is fast enough for real-time transfer to tracker.  Tracker is the bottleneck, currently takes about 5 minutes to track 1 minute of data. This could easily be improved by updating the tracker less often (e.g. Every 10 ms instead of every 1) and/or using fixed point arithmetic.

3131 The University of Texas at Austin ARL To Do:  Generate RINEX obs – Get estimated pseudoranges (based on beginning of subframes), all with “clock error” from estimation since we have no local time. – Correct using nav data.  RINEX nav just needs to be formatted.  Real-Time Operation  Parallel Frequency Space Acquisition (CW)