Faster GPS via the Sparse Fourier Transform. Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk

Transcription

1 Faster GPS via the Sparse Fourier Transform Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk

2 GPS Is Widely Used Faster GPS benefits many applications

3 How Do We Improve GPS? Need to Improve GPS Synchronization

4 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 100s of millions of multiplications [Team, Kaplan]

5 Goal Faster Synchronization Algorithm Reduce number of operations Reduction in power consumption and delay

6 Rest of this Talk GPS Primer Our GPS Synchronization Algorithm Empirical Results

7 How Does GPS Work? Compute the distance to the GPS satellites d 2 d 1 distance = propagation delay d 3 speed of light

8 How to Compute the Propagation Delay? CDMA code Satellite Transmits CDMA code

9 How to Compute the Propagation Delay? CDMA code delay Code arrives shifted by propagation delay

10 How to Compute the Propagation Delay? CDMA code delay Receiver knows the code and when the satellite starts transmitting

11 How to Compute the Propagation Delay? delay Correlation Spike Spike determines the delay

12 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:

13 Rest of this Talk GPS Primer Our GPS Synchronization Algorithm Empirical Results

14 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

15 How can we make GPS synchronization faster than FFT Based synchronization?

16 FFT Based GPS Synchronization Received Signal FFT Signal in Freq. IFFT FFT of Code Output

17 FFT Based GPS Synchronization Received Signal FFT Signal in Freq. IFFT FFT Stage FFT of Code IFFT Stage Output Each stage takes need to reduce complexity of both stages

18 FFT Based GPS Synchronization Received Signal FFT Signal in Freq. IFFT FFT Stage FFT of Code IFFT Stage Output Sparse Sparse IFFT

19 QuickSync A Sparse IFFT algorithm for GPS Exactly One Spike Simpler algorithm Extends to the FFT stage

20 QuickSync s Sparse IFFT 1 Bucketize Divide output into a few buckets 2 Estimate Estimate the largest coefficient in the largest bucket

21 How to Bucketize Efficiently? IFFT input samples output samples IFFT Subsamples Buckets

22 How to Estimate Efficiently? Keep largest bucket; ignore all the rest Out of the samples in the large bucket, which one is the spike? Largest bucket The spike is the sample that has the maximum correlation Buckets

23 QuickSync s Sparse IFFT is number of samples buckets samples per buckets Bucketization: Estimation:

24 QuickSync Synchronization Input FFT Signal in Freq. IFFT FFT Stage FFT of Code Output Sparse IFFT

25 QuickSync Synchronization Input FFT Signal in Freq. IFFT FFT Stage FFT of Code Output Sparse IFFT Output is not sparse Cannot Use Sparse FFT

26 QuickSync Synchronization Input FFT Signal in Freq. IFFT FFT Stage FFT of Code Output Sparse IFFT Input to next stage

27 QuickSync Synchronization Input FFT FFT Stage Signal in Freq. Subsampled FFT FFT of Code IFFT Output Sparse IFFT Need only few samples of FFT output IFFT samples its input

28 QuickSync Synchronization Input FFT Signal in Freq. Subsampled FFT FFT of Code IFFT Output Sparse IFFT FFT and IFFT are dual of each other

29 QuickSync Synchronization Input FFT Signal in Freq. Subsampled FFT FFT of Code IFFT Output Sparse IFFT Bucketization FFT Subsampling IFFT Bucketization

30 QuickSync Synchronization Input Subsampled FFT Sparse IFFT Correct delay Subsampled FFT of Code

31 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.

32 Rest of this Talk GPS Primer Our GPS Synchronization Algorithm Empirical Results

33 Setup SciGe GN3S Sampler USRP Software radios Traces are collected both US and Europe Different locations: urban suburban Different weather conditions: cloudy clear

34 Compared Schemes QuickSync Synchronization FFT Based Synchronization

35 Metrics

36 Multiplication Gain

37 Multiplication Gain 2.1x

38 Multiplication Gain 2.1x QuickSync provides an average gain of 2.1x

39 FLOPS Gain

40 FLOPS Gain QuickSync provides an average gain of 2.2

41 Related Work 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

42 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