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International Global Navigation Satellite Systems Society IGNSS Symposium 2009 Holiday Inn Surfers Paradise, Qld, Australia 1 – 3 December, 2009 A Sensitivity Enhancement Method for Weak GPS signals Ji-Hee Park Department of Information and communication Engineering Chungnam National University/Korea Tel:+82-42-821-7607, Fax: +82-42-824-6807, applearoma@naver.com Hyun-Ja Im Department of Information and communication Engineering Chungnam National University, Korea Tel:+82-42-821-7607, Fax: +82-42-824-6807, rrrr7@cnu.ac.kr Tae-Kyung Sung Division of Electric and Computer Engineering Chungnam National University, Korea Tel:+82-42-821-5660, Fax: +82-42-824-6807, tksaint@cnu.ac.kr ABSTRACT In order to acquire weak GPS signals, long integration techniques for sensitivity enhancement are commonly used in AGPS receivers. In coherent integration, integration loss is determined by frequency residual, whereas by SNR in non-coherent integration. To minimize the integration loss, coherent/non-coherent hybrid scheme should be employed. After the SNR is improved by coherent integration, non- coherent integration is subsequently done in the hybrid method. As the coherent integration time increases in the hybrid method, the integration gain becomes larger if the frequency error is sufficiently small. This paper presents a hybrid integration method using frequency residual estimation to maximize integration gain. FFT is used in the frequency residual estimation, and the optimal size of FFT is proposed for L1 C/A GPS signals. Experimental results show that the frequency estimation error is less than 4.3Hz with signal power of -150dBm. KEYWORDS: Assist-GPS, sensitivity enhancement, FFT, residual frequency, coherent/non-coherent integration 1. INTRODUCTION Weak-signal situations such as indoor GPS usually require the utilization of both coherent and non- coherent integration. In the hybrid integration, coherent integration results are summed up after squaring operation during the non-coherent integration. The non-coherent integration loss increases as SNR (Signal to Noise Ratio) after the coherent integration becomes smaller. For weak signals, the coherent integration interval needs to be enlarged to improve the SNR at the integrator output. The coherent integration interval is limited by frequency residual. Thus, frequency residual should be compensated before coherent integration in order to maximize the coherent integration gain. Recently, frequency residual estimation method using FFT was proposed to estimate frequency residual efficiently. However, factors influencing on its performance were not analysed and they were not evaluated quantitatively in the previous studies. This paper presents performance analysis of A-GPS receiver using frequency residual estimator. Structure of the frequency residual estimator is explained first and SNR of FFT output is derived. Next, the resolution error according to FFT size is analysed and SNR of the estimator output is examined. Finally, distributions of frequency residual estimation errors according to SNR of the received signals are compared by field experiments. 2. THE FREQUENCY RESIDUAL ESTIMATOR 2.1 Frequency Residual Estimator Structure In the coherent integration, periodic PN sequences are accumulated for a specified interval. If frequency residual doesn’t exist, the integration gain becomes 10log(N)[dB] by coherent integration of N times. Because frequency residual usually exists in real world, however, the coherent integration loss may take place that is given by ( ( ) )⎞ ⎤ ⎡⎛ sin π f − f NT Coherent loss = 10 ⋅ log10 ⎢⎜ ˆ ⎟ ⎥ 2 ⎣⎝ ( ) ⎟⎥ ⎢⎜ π f − f NT ˆ ⎠ ⎦ (1) where T and N denote the PN sequence period and the number of the coherent integration respectively. f − fˆ means frequency residual. From Eq. (1), the frequency residual should be reduced as N becomes large if a certain integration loss would be maintained. Hence, it is found that frequency residual estimation is essential to increase the coherent integration gain. Frequency residual estimation using FFT is commonly used because of its efficient computation. To estimate frequency residual of GPS L1 C/A signal containing data bit of 20 ms, the frequency residual estimator may be constituted as shown in Figure 1. Using the Doppler aiding, Doppler frequency by satellite motion is roughly compensated and the power of 1ms PN sequence is concentrated using correlators. If the fine time acquisition is possible, 20 correlator outputs within one data bit can be used to estimate the frequency residual. In order to improve frequency resolution, zero padding technique is commonly employed. To eliminate the influence of data bit, magnitude of FFT outputs using 20 correlator outputs are accumulated for a certain period of time to improve the total SNR. Consequently, the estimate output can be successfully obtained. Aiding data 1ms Correlator ⁞M IF data Coarse Doppler Zero s(nTs) Removal ⁞N 2 padding FFT 1ms Correlator X τ (k ) ˆ,0 Residual Non-coherent Frequency > th ? integration Estimation Figure 1. Structure of frequency residual estimator The received signal can be written as s ( nTs ) = A ⋅ D ⋅ c (( n + τ ) ⋅ Ts ) ⋅ e j 2π ( f IF + f D ) nTs + w( nTs ) , (2) (n = p + qN1 + qN 2 , 0 ≤ p ≤ N1 − 1 , 0 ≤ q ≤ N 2 − 1 , 0 ≤ r ≤ N 3 − 1) where A and D denote signal amplitude and data bit respectively. c(⋅) is C/A code and τ is C/A code phase. fIF and fD are IF frequency and Doppler respectively, and Ts=1/fs. N1 is the number of sample point for 1ms, N2 is the number of the coherent integration, N3 is the number of the non-coherent integration, and n is sample point. For GPS L1 C/A signal, N2=20. w(⋅) is assumed as an AWGN(Additive White Gaussian Noise) with zero mean and variance σ w 2 . Size of FFT is determined by the number of input data and consequently, frequency resolution is determined by the number of input data. When the frequency resolution is coarse, the integration loss would increase. Because frequency resolution for GPS L1 C/A signal is not satisfactory, zero padding technique is used to improve the frequency resolution. The output of FFT after zero padding can be expressed as M −1 − j 2π km 1 X τˆ , 0 (k ) = N2 ∑ xτ (m)e m =0 ˆ M ~ ~ k = A ⋅ D ⋅ Corr (τ − τˆ) ⋅ Φ ( f DTs , N1 ) ⋅ Φ (( f D − f s ) ⋅ N1Ts , N 2 ) + w f (k ) N1 M (3) ( k = 0,...M − 1, τˆ = 0...N1 − 1) ~ where M is FFT size, f D is frequency residual, and xτˆ (m) is the signal after the zero padding. Corr (⋅) denotes auto correlation function and Φ (⋅) is periodic sinc or Dirichlet function. w f (⋅) is a complex AWGN with zero mean and variance σ w /( N 1 N 2 ) . From Eq. 2 (3), the SNR of X τˆ ,0 (k ) is written as ~ ~ A2 ⋅ D 2 ⋅ Corr (τ − τˆ) 2 ⋅ Φ ( f DTs , N1 ) 2 ⋅ Φ (( f D N1Ts − k / M ), N 2 ) 2 SNRXτˆ = 10 ⋅ log10 ( ) σ w2 (4) + 10 ⋅ log10 ( N1 N 2 ) The frequency residual can be estimated by finding the peak of FFT output that is larger than a threshold. If the peak does not exceed the threshold, SNR of X τˆ ,0 (k ) can be improved by non-coherent integration in the frequency domain. The SNR of the final frequency residual estimator is given by SNRYτˆ = SNR Xτˆ + 10 ⋅ log10 ( N 3 ) ⎛ π − 1 snrXτˆ 1 1 1 1 ⎞ ⎜ ⋅ (e 4 ⋅ [(1 + snrXτˆ ) I 0 ( snrXτˆ ) + snrXτˆ I1 ( snrXτˆ )] − 1) 2 ⎟ (5) −⎜ 2 2 4 2 4 ⎟ ⎜ π − 1 snrXτˆ 1 1 1 1 ⎟ ⎜ snrXτˆ + 2 − ⋅ (e 4 ⋅ [(1 + snrXτˆ ) I 0 ( snrXτˆ ) + snrXτˆ I1 ( snrXτˆ )]) ⎟ 2 ⎝ 2 2 4 2 4 ⎠ dB where snrXτˆ = 10 SNR X τˆ / 10 . In Eq. (5), the second term in the right side is a non-coherent integration gain in the frequency domain and the third term is a non-coherent loss induced by SNRXτˆ . It is found that the non-coherent integration loss is increased exponentially as the SNR of FFT output becomes smaller. In order to minimize the integration loss, therefore, the SNR of FFT output in Eq. (4) should become large by improving the frequency resolution in FFT processing if other factors are fixed. 2.2 Performance of the Frequency Residual Estimator Resolution of frequency residual estimate can be reduced by making FFT size large. With the same number of input data, FFT size can be enlarged using the zero padding technique. In case that the 20 correlation outputs are used together with the zero padding technique, frequency resolution and resolution loss according to FFT size are shown in Table 1. It is known that the loss induced by data bit synchronization error in fine time acquisition is less than 0.5dB. In Table 1, when FFT size is larger than 64, resolution loss becomes less than 0.5dB. Considering the fact that a loss induced by the zero padding is about two times larger than the resolution loss, it is desirable to select the size of FFT as 128 or larger. FFT size 20 32 64 128 256 512 Resolution (Hz) 25 15.6 7.8 3.9 2 1 Resolution loss (dB) 3.92 1.44 0.35 0.09 0.02 0.01 Table 1. Frequency resolution and resolution loss according to FFT size Figure 2 shows the SNR of the frequency residual estimator with 128 FFT versus received signal strength when N3=50. Two cases are compared, i.e., ideal case and the case when frequency resolution is 4Hz. As the received signal power becomes weaker, resolution loss becomes larger. It is also found that the frequency residual estimator with 128 FFT will be successfully operated if the received signal power is larger than -150dBm. Figure 2. Received signal power vs SNR of the frequency residual estimator 3. EXPERIMENT RESULTS Performance of A-GPS receiver using frequency residual estimator is analysed by field experiments. IF signals are obtained using NordNav-R25 receiver and they are stored in PC to analyse the performance of long integration. Table 2 shows technical specification of NordNav-R25. Sampling Frequency IF frequency Code resolution 16.3676MHZ 4.1304MHz 1/16 chip Table 2. NordNav-R25 Specification First, frequency estimation errors for FFT size of 64, 128, 256, and 512 are analysed as the received signal power decreases as shown in Figure 3. As expected, for signals having power greater than -149 dBm, frequency estimation error is less than 4Hz in 128 FFT. Figure 3. Frequency estimation error vs received signal power Next, distribution of frequency estimation error is analysed for 128 FFT. Two cases are compared, i.e., strong signal (-134dBm) and weak signal (-150dBm). Figure 4 shows the estimation error distribution of two cases for 100 trials respectively. For strong signal, standard deviation is just 1.7Hz, while it is 4.3Hz for weak signal. (a) Strong signal (@-134dBm) (b) Weak signal (@-150dBm) Figure 4. Frequency estimation error distribution 4. CONCLUSIONS This paper presents the performance evaluation of the frequency residual estimator in weak signal environment. First, frequency estimation error was analysed according to FFT size. To guarantee frequency error loss less than 0.5dB with signal power greater than -150dBm, it is revealed that 128 FFT is required for GPS L1 C/A signal. Next, minimal signal power for frequency residual estimation is analysed. When the frequency residual is estimated by FFT with 1s IF data, frequency residual of signals whose power is greater than -150dBm is successfully estimated. REFERENCES Diggelen FV (2009) A-GPS : Assisted GPS, GNSS, and SBAS. Artech House Sih GC, Zou Q (2003) Position Location with Low Tolerance Oscillator. U.S. patent No. 6665593, Washinton, DC:US. Patent and Trademark Office. Persson B (2002) A Segmented Matched Filter for CDMA Code Synchronization in Systems with Doppler Frequency Offset. IEEE MILCOM 2002 Proceeding Vol. 2 Mathis H, Flammant P, Thiel A (2003) An analytic way to optimize the detector of a pose-correlation FFT acquisition algorithm. ION GPS/GNSS 2003:9-12 Cassian S, Daniel M, Heinz M (2007) The squaring-Loss Paradox, ION GNSS 20th International Technical Meeing of the Satellite Division:25-28

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A Sensitivity Enhancement Method for Weak GPS signals

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