Channel modeling and analysis of PN code ranging precisionfor BOC navigation receiver

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Procedia Engineering

Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 2705 – 2710 www.elsevier.com/locate/procedia

Advanced in Control Engineering and Information Science

Channel modeling and analysis of PN code ranging precisionfor BOC navigation receiver Li Caihuaa* ,Li Pengpengb a,b

School of Electronic Science and Engineering National Univ. of Defense Technology,Changsha, China

Abstract The pseudo-code ranging precision is an important indicator of satellite navigation system. The current channel modeling and simulation of BOC signal receiver is still no general method for quantitative analysis. Based on this situation, in this paper the model of channel estimation is proposed based on ranging precision of BOC receiver, then relationship between the channel characteristics and pseudo-code ranging accuracy is derived, and the influence brought by different bandwidth of front-end signal and channel characteristics on the ranging accuracy is analyzed, finally the simulation is carried out on the software receiver. Keywords: BOC navigation receiver; pseudo-code ranging precision; channel characteristics; software receiver

1.Introduction With the development of satellite navigation systems, the measurement accuracy of current satellite navigation system for time synchronization has been requested to the sub-nanosecond order of magnitude [1]. BOC signal is a very crowded effective use of radio navigation frequency band when compared to the BPSK signal, and it has a better performance in the code tracking accuracy, multipath rejection and jamming [2]. While the BOC signal bring in promotion, broadening the signal band made more serious deterioration of channel characteristics and the impact of channel characteristics on high-precision ranging is more prominent, but most of the past research are carried out ignored the impact of channel characteristics. Ries had compared the advantages and disadvantages of different BOC signal tracking

* Corresponding author. Tel.: +86 13707315250 E-mail address: [email protected]

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.509

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algorithms[3].Fante and Julien had put forward a new BOC signal tracking algorithms, and in an ideal channel conditions tracking performance was detailed analysis[4] [5]. Adams[6] pointed out the SAW filter characteristics would affect the shape of the correlation peak on BOC receiver, but no quantitative analysis. Against this background, the relationship between pseudo-code ranging accuracy and the channel characteristics of BOC receiver is derived. Then the impact of non-ideal channel characteristics on the pseudo-code ranging accuracy is analyzed. And finally with simulate the channel characteristics using Butterworth filter, simulation is carried out on the software receiver. 2 The estimation model of BOC receiver 2.1The model of accuracy estimation BOC receiver time delay estimation accuracy equivalent model is shown in Figure 2. Where s(t) is the BOC signal from the antenna, w (t) is the thermal noise from the antenna aperture. Amplifier, frequency inverter and filters which caused the change of channel characteristics is equivalent to a low-pass filter hL(t) after a move in the spectrum. The solution of the mediation, including the satellite signal can be equivalent to a matched filter. yS (t ) + yW (t )

x(t)

s (t )

hL (t )

hC (t )

w (t ) Figure2.The model of accuracy estimation The signal received by BOC receiver is:

x(t ) = AD (t )c (t )e j (2π f0t +θ ) + w(t )

( 4) Where, A is the signal amplitude, D(t) for the data, c (t)is the BOC modulation code for the carrier frequency is f0, θ is the carrier phase, w(t)is the Gaussian white Noise for bilateral power spectral density equal to N0 /2 . Analysis of pseudo-code accuracy can ignore the impact of data and D(t) is constant 1.The channel band-pass filter is h(t) at any frequency, assuming the center frequency isf0, and it’s Fourier transform is H(f).The equivalent low-pass filter is hL(t) with Fourier transform HL(f). So the relationship is:

⎧ H ( f ) ( f > 0) H L ( f − f0 ) = ⎨ ( f < 0) ⎩ 0

( 5) Order HL(f) = A(f) exp[jφ(f)], where A (f) and φ (f) are the frequency response and phase frequency response of filter.Considering the filter of ideal channel, that within a given channel bandwidth frequency response remains constant and the phase characteristics is linear, the absolute zero value ofthe filter itself can be summed to signal propagation delay, then the ideal channel filter meets A(f) = 1, φ(f) = 0. Assuming BOC receiver is a linear system and there is no Doppler shift of carrier frequency f0 and carrier phase θ is estimated correctly, then the signal estimation model can be simplified as shown below, that is equivalent to the equivalent correlation function RC(t) of BOC signals through a low pass filter hL(t)

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Li CaihuaLiand Li Pengpeng / Procedia Engineering (2011) 2705 – 2710 Caihua et al / Procedia Engineering 00 15 (2011) 000–000

yS (t )

hL (t )

RC (t )

Figure3. Simplified model of signal estimation Output signal ys(t) in frequency domain is shown as follows: ∞ ys (t ) = AT ∫−∞ G ( f ) ⋅ H L ( f ) ⋅ e j 2π ft df

( 6) Where G(f) is power spectral density for the BOC signal, T is integration cumulative time of the correlator. Simplified model of noise estimation is equivalent to that the noise passes through the equivalent lowpass filter after a matched filter firstly. The autocorrelation function of noise yw(t) in frequency domain can be expressed as: 2

∞

Ryw (t) = 2N0T ⋅ ∫−∞ G( f ) ⋅ HL ( f ) ⋅ e j 2π ft df

( 7)

2.2 Impact of channel characteristics on the accuracy of delay estimation To analyze the impact of channel characteristics on accuracy of time delay estimation, we use early and late non-coherent code estimator which is the widely used. The structure of early and late non-coherent code estimator is shown below

∫

T

0

(⋅)dt

y E (ε ) 2

2

yE(ε) − yL(ε) e

∫

− j⋅θˆ

T

0

(⋅)dt

y L (ε )

γ (ε )

εˆ

c(t + τˆ + D / 2)

c(t + τˆ − D / 2)

Figure 4 Implementation structure of early and late non-coherent code estimator Estimation accuracy is determined by the phase detector gain Kd, the noise variance σr2 and loop bandwidth of the equivalent side Bn σ ε2 = σ r2 ⋅ 2 Bn / K d 2 ( 8) The detection amount γ (ε) of phase detector is: 2

γ (ε ) = yE (ε ) − yL (ε )

2

(9) Where: yE(ε)=x(τ0+ε+D/2)+υE, yL(ε)=x(τ0+ε-D/2)+υL, υE and υL are components of the noise, D is the spacing of early late code As known by section 2.2 the equivalent model is:

y (τ ) = AT ⋅ ∫−bb G ( f ) ⋅ A( f ) ⋅ e jφ ( f ) e j 2π f τ df Noise variance σr2 is expressed as:

σ r2 = E{{γ (0) − E[γ (0)]}2 }

(10)

(11) Reference to the variable features of Gaussian random and the derivation process of paper[9], σr2 is simplified as:

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σ r2 = 8σ 4 − 8( ρσ 2 ) 2 + 4σ 2 ⋅ [Y12 ( f ) + Y22 ( f )] − 8( ρσ 2 ) ⋅ Y1 ( f ) ⋅ Y2 ( f ) Phase detector gain Kd can be expressed as:

Kd =

∂[γ (ε )] ∂ε ε =0

= 8π ∫−bb X1 ( f )cos(π fD)df ∫−bb f ⋅ X1 ( f )sin(π fD)df −8π ⋅ ∫−bb X2 ( f ) ⋅ sin(π fD)df ∫−bb f ⋅ X2 ( f ) ⋅ cos(π fD)df

Then accuracy is estimated as:

σε2 =

(12)

(13)

⎧⎪8σ4 −8(ρσ2 )2 +4σ2[Y12 ( f ) +Y22 ( f )]⎫⎪ Bn ⎨ ⎬ 2 ⎩⎪−8(ρσ )Y1( f )Y2 ( f ) ⎭⎪ ⎧⎪[∫−bb X1( f )cos(π fD)df ∫−bb fX1( f )sin(π fD)df ⎫⎪ 4π ⎨ b ⎬ b ⎪⎩−∫−b X2 ( f )sin(π fD)df ∫−b fX2 ( f )cos(π fD)df ]⎪⎭

(14)

The expression of PN code tracking accuracy on non-coherent estimator is much complicated, so we consider the ideal channel conditions which means A(f) = 1, φ(f) = 0, that the expression of accuracy can be simply to:

⎛ ⎞ b ' 2 b 2 ⎜ ⋅ B G ( f )sin ( π fD ) df [∫−b G( f )cos (π fD)df ] ⎟ ∫−b n ⎟ σε2 = ⋅ ⎜1 + Cs b b 2 Cs 2 ⎜ 2 ⎟ 4π [∫ f ⋅ G( f )sin(π fD)df ] ⎜ T [∫−b G( f )cos(π fD)df ] ⎟ N0 −b N0 ⎝ ⎠

(15)

Where: CS/N0 is ratio of the carrier to noise, and it meets CS/N0 = A2 / (2N0) The expression(21) is the precision estimation formula of non-coherent estimator in case of ideal channel filter, which is the same to that described in thesis[10]. It shows the correctness of the proposed model. With a given front-end signal bandwidth, the lower bound of code tracking accuracy (ie, Cramer-Rao lower bound) has nothing to do with the interval of the correlator, and its expression is [12]: 2 σ LB =

BL

4π 2

C b 2 ⋅ ∫ f G ( f ) ⋅ df N 0 −b

(16)

The simulation results indicate: z For the ideal channel conditions, the BOC receiver within a certain interval of the early late code, code tracking accuracy can be approximately close to the Cramer-Rao lower bound. But to some intervals of early late code, code tracking accuracy increases dramatically. Therefore, to code tracking device early late codes must be chosen away from this interval region. z 2) For ideal channel conditions, the pseudo-code tracking accuracy will change slightly when the signal bandwidth gets narrower, but will be relatively insensitive with the changes of the code interval in estimator. For non-ideal channel conditions, the pseudo-code tracking accuracy is extraordinarily sensitive with changes of the code interval in estimator, it means that it’s change of the channel characteristics that narrow the choice of code interval in estimator.

Li CaihuaLiand Li Pengpeng / Procedia Engineering 15 (2011) 2705 – 2710 Caihua et al / Procedia Engineering 00 (2011) 000–000

z

Changes of channel characteristics will lead to a serious deterioration in pseudo-code ranging accuracy. When the interval of estimator d=0.1Tc, after simulate in channel characteristics, the accuracy is 2 to 3 times worse. And when d=0.2Tc, accuracy deteriorated 2 ~ 10 times. The error of estimated accuracy at this time could be significant if using the traditional formula.

2.3 Simulation on software receiver In this paper, we take Galileo's E6-P signal Sin-BOC (10,5) as an example to simulate on software receiver and to compare differences between the theoretical calculation and simulation on software receiver. Firstly Matlab simulator generate Sin-BOC (10,5) modulated signal, and then signal through Butterwoth filter to act the channel characteristics. After Butterwoth filter it begins acquisition and tracking through the softwarereceiver, the final results of position resolution are carried out. Software receiver simulation process is show below.

Figure 5 Block diagram of numerical simulation software receiver Software receiver parameter is set as: CS / N0 is 40dBHz, sampling rate is 81.84MHz, code loop equivalent bandwidth Bn = 2Hz, correlator spacing d = 0.15. 1dB bandwidth of Butterwoth filter W1dB = 30 MHz, stop-band WS = 35 MHz, stop-band rejection is 30dB. Theoretical calculations and simulation results are shown below.

Figure 6 Theoretical calculations and simulation results under different CS / N0 From the Figure6 above, we can see that the calculated value is compared with the simulation on software receiver so to illustrate the accuracy of the model. This model can be extended to analysis of the BOC receiver accuracy under any channel characteristics 2.4 Conclusion The impact of channel characteristics on ranging accuracy on BOC receiver is quantitatively analyzed in case of any channel characteristics in this paper, and theoretical calculation and simulation software

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Li Caihua andetLial/ Pengpeng Engineering (2011) 2705 – 2710 Li Caihua Procedia/ Procedia Engineering 00 (2011)15 000–000

accuracy significantly. So when design the BOC receiver, it is necessary to take the signal bandwidth, channel characteristics and the interval of estimator into consider. For non-ideal channel conditions, pseudo-code tracking accuracy is very sensitive to changes of the early and late code’s interval, so it has to ensure that channel characteristics of BOC receiver should be close to the ideal channel condition when engineering applications. This model can be extended to analysis of ranging accuracy on the BOC receiver under different tracking algorithms, also it works in jamming and multipath conditions Acknowledgements These and the Reference headings are in bold but have no numbers. Text below continues as normal. receiver are in good agreement. Simulation results show that: channel characteristics affects code tracking References [1] Zhu Xiang-wei. The study of key techniques in satellite navigation system time synchronization [D]. [Ph.D thesis] National University of Defense Technology, 2007 [2]J.W. Betz. Binary Offset Carrier Modulations for Radionavigation[J].Navigation, Journal of the Institute of Navigation. 2002. 48: 227-246 [3]L. Ries, L. Lestarquit.et. A Software Simulation Tool for GNSS2 BOC Signals Analysis[A]. Proceedings of U.S. Institute of Navigation GPS Conference. Portland, OR. 2002. 2225-2239 [4]R. Fante. Unambiguous Tracker for GPS Binary-Offset-Carrier Signals. MITRE Technical Report MTR02B0000055, December 2002.. [5]Julien,O.Macabiau,C,Lachapelle,G.,Cannon,M. E, and Mongr´edien, C. A new unambiguous BOC(n,n) signal tracking technique.In Proceedings of the European Navigation Conference GNSS 2004 Conference,Rotterdam,The Netherlands,session “Signal,”2004,12 pages, CD-ROM. [6]Damon Adams, The Effects of SAW GROUP Delay Ripple on GPS and Glonass signal. NovAtel Inc, Calgary Alberta, 2003.Damon Adams, The Effects of SAW GROUP Delay Ripple on GPS and Glonass signal. NovAtel Inc, Calgary Alberta, 2003. [7]P.W. Ward. A Design Technique to Remove the Correlation Ambiguity in Binary Offset Carrier(BOC) Spread Spectrum Signals [A]. Proceedings of U.S. Institute of Navigation NTM Conference. San Diego, CA. 2004. 886-896 [8]Rebeyrol, L. Lestarquit et. BOC Power Spectrum Densities[A]. Proceedings of U.S. Institute of Navigation NTM Conference. San Diego, CA. 2005. 769-778. [9]Xu Xiao-yong. Study on high-precision modeling, analysis and optimization design for satellite navigation receiver [D]. [Ph.D thesis]. National University of Defense Technology, 2008. [10]K. R. Kolodziejski and J.W.Betz, Effect of Non-White Gaussian Interference on GPS Code Tracking Accuracy, The MITRE Corporation Technical Report MTR99B21R1, June 1999. [11]Julien,O.Macabiau,C,Lachapelle,G.,Cannon,M. E, and Mongr´edien, C. A new unambiguous BOC(n,n) signal tracking technique.In Proceedings of the European Navigation Conference GNSS 2004 Conference, Rotterdam, The Netherlands,session “Signal,” 2004, 12 pages, CD-ROM. [12]Fortin, Guay and Landry.Development of a universal GNSS tracking channel.The 22nd International Meeting of the Satellite Division of The Institute of Navigation,Savannah, GA, September 22-25, 2009