A Sensitivity Enhancement Method for Weak GPS signals

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A Sensitivity Enhancement Method for Weak GPS signals Powered By Docstoc
					                                       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,
                                          Hyun-Ja Im
                    Department of Information and communication Engineering
                              Chungnam National University, Korea
                   Tel:+82-42-821-7607, Fax: +82-42-824-6807,
                                       Tae-Kyung Sung
                           Division of Electric and Computer Engineering
                               Chungnam National University, Korea
                  Tel:+82-42-821-5660, Fax: +82-42-824-6807,


             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
            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


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.


2.1 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 ⎢⎜
                                                          ⎟ ⎥

                                                    ( ) ⎟⎥
                                            ⎢⎜ π f − f NT
                                                          ⎠ ⎦

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

              IF data      Coarse Doppler                                      Zero
               s(nTs)        Removal                         ⁞N  2

                                                        Correlator                                  X τ (k )

                                                    Frequency         > th ?

                                 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
     X τˆ , 0 (k ) =
                          ∑ xτ (m)e
                          m =0

                                              ~                   ~            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.

(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              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


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


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.


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