Acquisition of Composite GNSS Signals

Transcription

1 Acquisition of Composite G ignals. Borio C. O riscoll and G. Lachapelle Position Location And avigation (PLA) Group epartment of Geomatics Engineering chulich chool of Engineering University of Calgary IO Alberta ection Meeting 7 April 008

2 Outline Composite G signals ingle code period acquisition - non-coherent channel combining - coherent channel combining with sign recovery - differentially coherent channel combining Multiple code period acquisition - without sign recovery - with sign recovery Real data analysis Conclusions of 3

3 Composite G signals Principle: two different pieces of information are required for determining the user position atellite position Pseudo-range (and carrier phase) The transmission of the two messages on a single channel can be troublesome olution: split the two messages on two different channels ata channel Pilot channel 3 of 3

4 Composite G signals: some examples Galileo: GP: all the new Galileo signals have a data/pilot structure L5 LC and LC signals From. Lo A. Chen P. Enge G. Gao. Akos J. Issler L. Ries T. Grelier and J. antepal G Album Image and pectral ignatures of the ew G ignals Inside G May/June of 3

5 QP signals Quadrature Pilot ata and pilot channels are transmitted with a 90 degree phase difference on the in-phase and quadrature branches In-phase ata ignal structure data navigation message data secondary code data primary code pilot pilot secondary code pilot primary code time 5 of 3

6 ingle Code Period Acquisition ingle channel acquisition on-coherent channel combining Coherent channel combining with sign recovery ifferentially coherent channel combining 6 of 3

7 ingle Channel Acquisition Coherent integrations quaring: phase removal r[n] Frequency generator 90 sin cos ( πf n) ( πf n) code generator τ n = 0 n = 0 ( ) ( ) ( ) ( ) ( F τ ) ecision statistic Only half of the available power is employed; It requires the lowest computational load. It works as a traditional acquisition block for BP signals. 7 of 3

8 on-coherent channel combining n = 0 ( ) ( ) cos ( πf n ) n = 0 ( ) ( ) Frequency generator 90 sin ( πf n ) code generator (data) code generator (pilot) n = 0 ( ) ( ) decision variable n = 0 ( ) ( ) A. J. V. ierendonck and J. J. pilker Jr. Proposed civil GP signal at MHz: In-phase/quadrature codes at 0.3 MHz chip rate in Proc. of IO Annual Meeting (AM) Cambridge MA June 999 pp F. Bastide O. Julien C. Macabiau and B. Roturier Analisis of L5/E5 acquisition tracking and data demodulation thresholds in Proc. of IO GP/G Portland OR ept. 00 pp of 3

9 Coherent channel combining with sign recovery Principle If the sign between data and pilot were known all the signal power could be recovered by employing the correct composite code: c c + [ n] = c [ n] = c I I [ n] + [ n] jc jc Q Q [ n] [ n] The sign between data and pilot is unknown Parameter to be estimated { } + ( F τ ) ( F ) ( F τ ) = max τ Correlation with the code + Correlation with the code - C. Yang C. Hegarty and M. Tran Acquisition of the GP L5 signal using coherent combining of I5 and Q5 in Proc. of IO G 7th International Technical Meeting Long Beach CA ept. 004 pp C. J. Hegarty Optimal and near-optimal detector for acquisition of the GP L5 signal in Proc. of IO TM ational Technical Meeting Monterey CA Jan. 006 pp of 3

10 Coherent channel combining (I) n = 0 ( ) ( ) cos ( πf n) n = 0 ( ) ( ) Input signal Frequency generator 90 sin ( πf n) code generator (data + j*pilot) code generator (data j*pilot) n = 0 ( ) ( ) m a x decision variable n = 0 ( ) ( ) 0 of 3

11 Coherent channel combining (II) Coherent channel combining (II) 4 exp ) ( = n P fa σ β β = d P Q exp ) ( σ β σ λ σ β β False alarm and detection probability: False alarm and detection probability: of 3 = s s s n n n d f f C f P Q exp Q 4 exp ) ( β β σ σ σ β Probability of false alarm for the ideal case of coherent integration Probability of detection for the ideal case of coherent integration

12 ifferentially coherent channel combining (I) n = 0 ( ) cos ( πf n) n = 0 ( ) Input signal Frequency generator 90 sin ( πf n) code generator (pilot) code generator (data) n = 0 ( ) j *complex conjugate {} Im decision variable n = 0 ( ) j J. A. A. Rodriguez T. Pany and B. Eissfeller A theoretical analysis of acquisition algorithms for indoor positioning in In Proc. of the nd EA Workshop on atellite avigation User Equipment Technologies (AVITEC) oordwijk The etherlands ec of 3

13 ifferentially coherent channel combining (II) ecision variable: { } d p ( F τ ) = Im ( F τ ) ( F τ ) d d ( F τ ) = ( F τ ) j ( F τ ) d I + Q p p ( F τ ) = ( F τ ) j ( F τ ) p I + Q False alarm and detection probability: P d β + λ P fa ( β ) β λ β exp σ n = β β ( β ) = exp exp Q + Q σ n σ n σ n σ n σ n σ n λ λ λ C 4 M.. imon Probability istributions Involving Gaussian Random Variables: A Handbook for Engineers and cientists st ed. The International eries in Engineering and Computer cience. pringer May of 3

14 ROC results Parameter Value Parameter Value ampling frequency 40.9 MHz B IF = f s / 0.46 MHz Intermediate frequency 0.3 MHz Code Length 030 chips Pre-detection integration time ms ample/chip 4 4 of 3

15 Multiple Code Period Acquisition on-coherent combining emi-coherent combining Without sign recovery ifferentially Coherent combining Exhaustive sign search econdary code partial correlation With sign recovery 5 of 3

16 ignal Acquisition without ign recovery Front-end ingle period acquisition k =0 ( ) ingle code periods Multi-period acquisition Input signal ( Fτ ) ( Fτ ) ( F ) ( F τ ) 3 τ ingle period decision variables = k = 0 ( F τ ) ( F τ ) k Final decision variable 6 of 3

17 on-coherent combining on-coherent combining ingle Channel ingle Channel ata and Pilot ata and Pilot ( ) ( ) ( ) ( ) + = = = = 0 0 τ τ τ τ x k Q x k I i k i F F F F 7 of 3 ( ) ( ) ( ) ( ) ( ) = = 0 τ τ τ τ τ p k Q p k I d k Q d k I i F F F F F In both cases the decision variable is χ square distributed with and 4 degrees of freedom respectively The false alarm (central χ square) and detection probabilities (non-central χ square) are known from the literature

18 emi-coherent combining ecision variable: = k = k = 0 k = 0 { } + ( ) ( ) ( ) F τ F τ max F τ ( F τ ) k k False alarm probability: et of constants that can be easily determined by means of an iterative algorithm P fa i β ( ) n β β exp a b exp = 4σ i= n= 0 4σ n n n! i i 4σ n The decision threshold can be determined by using a ewton-raphson algorithm. The starting point of the algorithm can be determined by using a Gaussian approximation for the false alarm probability. P fa β 6σ ( ) erfc n β for >> 4 0σ n C. Yang C. Hegarty and M. Tran Acquisition of the GP L5 signal using coherent combining of I5 and Q5 in Proc. of IO G 7th International Technical Meeting Long Beach CA ept. 004 pp of 3

19 ifferentially Coherent combining ecision variable: False alarm probability: = k k τ k = 0 { } d p ( F τ ) Im ( F τ ) ( F ) P fa ( β ) β β =0 σ n = exp σ n i= 0 ome remarks All these techniques remove the bit dependence by means of a non-linear operation (squaring absolute value ); The size of the oppler bin doesn t have to be reduced since the coherent integration time is constant and is equal to ms; The non-coherent (dual channel) the semi-coherent and the differentially coherent combining require similar computational loads. i 9 of 3

20 Acquisition with sign recovery The coherent integration time can be increased by estimating the sequence of bits that modulates the data and pilot channels. All methods that try to estimate the data and pilot bit sequences require a heavy computational load since as the integration time increases - there are more bit combinations to be tested - the size of the oppler bin has to be reduced accordingly oppler frequency Two strategies: exhaustive sign combinations search; partial secondary code correlations Code delay 0 of 3

21 ecision variable: = Exhaustive sign search [ ] d p ( F τ ) max d ( F τ ) + jd ( F τ ) { } d d k dp k k= 0 = k = 0 et of the possible sign combinations of data and pilot components The number of bit combinations grows exponentially with. of 3 d k The method estimates the bit sequence for both pilot and data channels: ˆ = arg max k= 0 k By ignoring the secondary code [ ( ) ( )] d p d F τ + jd F τ d k k p k k x00 x00 p k k x0000 x0 x00 x000 x0 possible bit combinations x000 x00 x00 x x000 x00 x0 x000 x00

22 econdary code partial correlation Only specific bit combinations are allowed by secondary codes reduced computational load; improved system performance since less candidates implies less opportunity to have a false alarm x00 x0000 x000 x000 x000 x00 x0 x00 x000 x0 x00 x x00 x00 It excludes candidates that can lead to a false alarm of 3 x00 x0

23 umber of possible bit combinations (single channel) d + ign combinations ata + Pilot channels ata channel* Exhaustive search Length of the data secondary code umber of possible bit combinations (dual channel combining) p H ( d + ) H = d Length of the pilot secondary code For increasing the coherent integration time (till to 0 ms) it is more convenient to use the data channel alone exploiting the properties of its secondary code * in order to have a fair comparison with the other two cases the integration time for the data channel alone has been doubled 3 of 3

24 ROC results Parameter Value Parameter Value ampling frequency 40.9 MHz B IF = f s / 0.46 MHz Intermediate frequency 0.3 MHz Code Length 030 chips Pre-detection integration time ms ample/chip 4 4 of 3

25 5 of 3 Real data analysis

26 Experimental etup I Front-End ata storage Live data from GIOVE-A the first Galileo experimental satellite have been collected by using the I PXI- 566 signal analyzer and used to test the acquisition algorithms proposed. Postprocessing analysis 6 of 3

27 Analysis principle Cell in the absence of signal Histogram Empirical pdf under H 0 E5a GIOVE-A Input signal elay and oppler frequency estimation ignal acquisition ( ˆ τ Fˆ ) 0 0 ignal parameters λ σ n Theoret tical pdfs Cell in the presence of signal Histogram Empirical pdf under H 7 of 3

28 8 of 3 on-coherent combining

29 9 of 3 emi-coherent combining

30 30 of 3 ifferentially coherent combining

31 Coherent vs. non-coherent = 5 Coherent combining on-coherent combining 3 of 3

32 Conclusions When the acquisition on a single code period is considered the coherent channel combining with sign recovery results the more effective acquisition strategy. For low C/ 0 the sign estimation is no more reliable and coherent and non-coherent channel combining tends to have the same performance. When considering acquisition on multiple code periods two classes of algorithms can be identified: with and without sign recovery. The pure non-coherent the semi-coherent and the differentially coherent combining belong to the first class and require a reduced computational load with respect to the other strategies since the sign combinations have not to be searched for and the oppler bin size has not to be reduced. Among these strategies the semi-coherent integration gives better performance for high C/ 0. For low C/ 0 semi-coherent and non-coherent integrations lead to similar performances. Among the second class the secondary code partial correlation outperforms all the other techniques requiring a lower computational load with respect to the exhaustive search of all the possible bit combinations. 3 of 3