Faster GPS via the Sparse Fourier Transformgroups.csail.mit.edu › netmit › sFFT ›...
Transcript of Faster GPS via the Sparse Fourier Transformgroups.csail.mit.edu › netmit › sFFT ›...
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Faster GPS via the Sparse Fourier Transform
Haitham HassaniehFadel AdibDina KatabiPiotr Indyk
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Faster GPS benefits many applicationsFaster GPS benefits many applications
GPS Is Widely Used
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How Do We Improve GPS?
Need to Improve GPS Synchronization
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100s of millions of multiplications[Team, Kaplan]
100s of millions of multiplications[Team, Kaplan]
GPS Synchronization
Synchronization is locking onto a satellite’s signal• Consumes 30%‐75% of GPS receiver’s power [ORG447X datasheet, Venus 6 datasheet]
GPS signals are very weak, less than ‐20dB SNR
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Goal
Faster Synchronization Algorithm Reduce number of operations
Reduction in power consumption and delay
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Rest of this Talk
GPS Primer
Our GPS Synchronization Algorithm
Empirical Results
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How Does GPS Work?
Compute the distance to the GPS satellites
d1
d3
d2
distance = propagation delay speed of lightdistance = propagation delay speed of light
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How to Compute the Propagation Delay?
Satellite Transmits CDMA code
CDMA code
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How to Compute the Propagation Delay?CDMA code
delay
Code arrives shifted by propagation delay
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How to Compute the Propagation Delay?CDMA code
delay
Receiver knows the code and when the satellite starts transmitting
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How to Compute the Propagation Delay?
Correlation Spike
delay
Spike determines the delay
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GPS Synchronization is a convolution with CDMA code
Convolution in Time
Multiplication in Frequency
: Number of samples in the code State of the art GPS synchronization
algorithm:
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Rest of this Talk
GPS Primer
Our GPS Synchronization Algorithm
Empirical Results
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QuickSync
• Faster GPS synchronization algorithm
• Complexity:
– for any SNR
– when noise is bounded by
• Empirical Results: – Evaluated on real GPS signals – Improves performance by 2.2x
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How can we make GPS synchronization faster than FFT‐Based synchronization?
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FFT‐Based GPS Synchronization
Received Signal FFT Signal
in Freq.
FFT of Code
IFFTOutput
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FFT‐Based GPS Synchronization
Received Signal FFT Signal
in Freq.
FFT of Code
IFFT
FFT Stage IFFT Stage
Output
Each stage takes
need to reduce complexity of both stages
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FFT‐Based GPS Synchronization
Received Signal FFT Signal
in Freq.
FFT of Code
IFFT
FFT Stage IFFT Stage
OutputOutput
SparseSparse IFFT
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QuickSyncA Sparse IFFT algorithm for GPS
• Exactly One Spike Simpler algorithm
• Extends to the FFT‐stage
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1‐ Bucketize
∑
2‐ Estimate
QuickSync’s Sparse IFFT
Divide output into a few buckets
Estimate the largest coefficient in the largest bucket
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How to Bucketize Efficiently?
IFFTIFFT
IFFTIFFT
output samplesinput samples
Subsamples Buckets
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• Keep largest bucket; ignore all the rest
• Out of the samples in the large bucket, which one is the spike?
How to Estimate Efficiently?
Largest bucket
The spike is the sample that has the maximum correlation
Buckets
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Estimation:
QuickSync’s Sparse IFFT
• is number of samples• buckets samples per buckets
Bucketization:
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QuickSync Synchronization
Input FFT Signal in Freq.
FFT of Code
IFFT
FFT Stage Sparse IFFT
Output
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QuickSync Synchronization
Input FFT Signal in Freq.
FFT of Code
IFFT
FFT Stage Sparse IFFT
Output
Output is not sparseCannot Use Sparse FFT
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QuickSync Synchronization
Input FFT Signal in Freq.
FFT of Code
IFFT
FFT Stage Sparse IFFT
Output
Input to next stage
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QuickSync Synchronization
Input FFT Signal in Freq.
FFT of Code
IFFT
FFT Stage Sparse IFFT
Output
Subsampled FFT
IFFT samples its input
Need only few samples of FFT output
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QuickSync Synchronization
Input FFT Signal in Freq.
FFT of Code
IFFT
Sparse IFFT
Output
Subsampled FFT
FFT and IFFT are dual of each other
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QuickSync Synchronization
Input FFT Signal in Freq.
FFT of Code
IFFT
Sparse IFFT
Output
Subsampled FFT
Subsampling IFFT BucketizationFFTBucketization
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QuickSync Synchronization
Input Subsampled
FFTSubsampled FFT of Code
Sparse IFFT
Correct delay
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Theorem:
For any SNR QuickSync achieves the same accuracy as
FFT‐Based synchronization and has a complexity of
where is the number of samples in the code
When noise is bounded by , QuickSync has
complexity.
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Rest of this Talk
GPS Primer
Our GPS Synchronization Algorithm
Empirical Results
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• Traces are collected both US and Europe
• Different locations: urban – suburban
• Different weather conditions: cloudy – clear
Setup
SciGe GN3S Sampler USRP Software radios
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• QuickSync Synchronization
• FFT‐Based Synchronization
Compared Schemes
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•
•
Metrics
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Multiplication Gain
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2.1x
Multiplication Gain
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2.1x
QuickSync provides an average gain of 2.1x
Multiplication Gain
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FLOPS Gain
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QuickSync provides an average gain of 2.2 ×
FLOPS Gain
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• Past work on GPS [NC91, SA08, RZL11]– QuickSync presents the faster algorithm
• Sparse FFT Algorithms [Man02, GMS05, HKIP12a, HKIP12b]
– QuickSync’s bucketization leverages duality reduces the complexity of both stages in GPS
Related Work
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Conclusion
• Fastest GPS synchronization algorithm
– for any SNR
– for moderately low SNR
• Empirical results show an average 2x gain
• Can we do better?– / for constant noise