(GPS) L1 and L2 civil codes for signal acquisition - CiteSeerX

www.ietdl.org Published in IET Radar, Sonar and Navigation Received on 19th August 2009 Revised on 16th July 2010 doi: 10.1049/iet-rsn.2009.0207

ISSN 1751-8784

Cross-correlation performance assessment of global positioning system (GPS) L1 and L2 civil codes for signal acquisition S.U. Qaisar A.G. Dempster School of Surveying & Spatial Information Systems, University of New South Wales, Sydney 2052 NSW Australia E-mail: [email protected]

Abstract: Owing to imminent availability of global positioning system (GPS) L2C full constellation, low-cost dual-frequency GPS L1/L2C receivers are likely to appear on the market in the near future. The L1 C/A, L2 CM and L2 CL are the code choices available to combat the ‘near – far’ problem in such a receiver. The published average cross-correlation protection figures of these codes (C/A: 22 dB, CM: 28 dB and CL: 45 dB) are not sufficient to determine the right code choice for different acquisition scenarios. The aim of this study is to evaluate the robustness of each code to the near – far problem and develop recommendations for code/frequency selection in a given acquisition scenario. For comparison of L2C and C/A codes, multiple C/A periods are to be considered, in order to be consistent with the signal observation interval. It is shown that the cross-correlation performance of multiple C/A periods is strongly dependent on the relative Doppler offset between local and interfering signals, and consequently it is much superior to that of the single C/A period. It is concluded that the C/A code is more robust to the near – far problem in the assisted acquisition scenarios including warm start, hot start, assistedGPS and reacquisition, whereas L2 CM is the best code choice for the cold startup.

1

Introduction

The central focus of the global positioning system (GPS) modernisation program is the addition of new navigation signals. L2C is the first modernised GPS civilian signal to become available over the full constellation by the year 2016. It has an advanced signal structure designed to meet the demands of new and more challenging application environments. The main purpose of having longer spreading codes in the L2C signal was to achieve extra protection against the strong cross-correlation in the event of ‘near–far’ problem. The other inherent advantages of longer codes are more diffuse line spectrum and the reduced vulnerability to continuous wave (CW) interference. This additional protection was desired because the legacy coarse acquisition (C/A) code could not offer more than approximately 22 dB of cross-correlation protection. The L2 CM (moderate) and CL (long) codes extend this figure to 28 and 45 dB, respectively [1]. To achieve this cross-correlation performance, however, requires the coherent signal observation period to be 20 ms (for CM code) and 1.5 s (for CL code) as opposed to 1 ms for the C/A code. This translates to increased acquisition effort, which naturally leads to the consideration of 20 C/A epochs as an alternative to the CM code and 1500 C/A epochs to replace the CL code. The thought becomes more relevant in the context of dual-frequency GPS L1/L2C receivers where all the three (C/A, CM and CL) codes are available to combat the near– far problem. This paper provides a cross-correlation IET Radar Sonar Navig., 2011, Vol. 5, Iss. 3, pp. 195 –203 doi: 10.1049/iet-rsn.2009.0207

performance comparison of the L2C codes with the C/A code in order to recognise the appropriate code choice to overcome the near–far problem in dual-frequency GPS L1/ L2C receivers, specifically in the ‘cold-start’ and ‘assistedstart’ modes. In the case of multiple code epochs, the relative carrier Doppler offset between the local and interfering satellite signals has a significant role as it modulates the periodic product of the local and interfering satellite codes. As a result, some of the cross-correlation noise is averaged out when an accumulation across a coherent integration period several times the fundamental code period is performed. Consequently, the cross-correlation performance of multiple epochs of a shorter code (C/A code in this case) becomes better than an equivalent single code period (a CM code period here). The contents of the paper are organized as follows. The cross-correlation problem is first described. It is followed by the study of effects of observation interval on the cross-correlation performance. The impact of relative Doppler offset on periodic cross-correlations is then evaluated. Acquisition strategies based on the relative strengths of the C/A and CM codes identified in the analysis are recommended. The concerns of navigation data transitions and non-coherent integration are also addressed. Finally, some concluding remarks are given.

2

Near –far problem

Signal acquisition is the first stage of digital signal processing in a GPS receiver. It is a two-dimensional search where the 195

& The Institution of Engineering and Technology 2011

www.ietdl.org receiver has to find estimates of carrier Doppler and code delay of the desired satellite from the received signal. The signal acquisition becomes more challenging as the desired signal, relative to an interfering signal, becomes weaker (e.g. an indoor signal attenuated by a roof compared with one not that attenuated by a window). The detection threshold is gradually dropped to accommodate weaker signals. Trouble starts when energies from unwanted satellites, usually remaining well below the detection threshold, might now exceed it and consequently the receiver might lock on to the wrong signal. These energies of unwanted satellites, collected in the acquisition process, are known as self-interference, cross-correlation or multiaccess interference (MAI). This phenomenon where strong cross-correlation can prevent the acquisition of a desired weak signal is also known as ‘near – far’ problem [2]. Such effects will be observed when the desired signal is either attenuated by an obstruction, has a lower elevation or offers a good geometry for the position fix while one or more other in-view satellites/pseudolites provide strong signals to the receiver. Indoor environments, urban canyons and pseudolite installations are often likely to cause such situations for a GPS receiver. Fig. 1 illustrates the crosscorrelation impact on signal acquisition using an L1 C/A signal example. The conventional approach to deal with this problem is to mitigate the cross-correlation and then acquire the desired signal. Successive interference cancellation (SIC) is one such technique where known strong components are gradually removed from the received signal in order to detect the weak component [3]. Other approaches of crosscorrelation mitigation are discussed in [2, 4 – 7]. However, if possible, best approach for dealing with the near – far problem is to have a larger cross-correlation margin in the signal design.

2.1

The L2C signal is composed of two ranging codes, namely L2 CM and L2 CL. The L2 CM code is 20 ms long and contains 10 230 chips, whereas the L2 CL code has a period of 1.5 s, containing 767 250 chips. The CM code is modulo-2 added to data (i.e. it modulates the data) and the resultant sequence of chips is time-multiplexed with CL code on a chip-by-chip basis. The individual CM and CL codes are clocked at 511.5 kHz, whereas the composite L2C code has a frequency of 1.023 MHz. Code boundaries of CM and CL are aligned and each CL period contains exactly 75 CM periods. This time multiplexed L2C sequence modulates the L2 (1227.6 MHz) carrier [8]. The original L2 CNAV data rate is 25 bits/s but a half rate convolutional encoder is employed to transmit the data at 50 symbols/s (the same symbol rate as for L1 C/A code). Consequently, each data symbol matches the CM period of 20 ms. Fig. 2 illustrates the L2C code structure over a CL code period. 2.2

Both desired autocorrelation spikes (PRN-1) and interfering spikes (PRN-7) exceeding the threshold; Simulation parameters: C/A code, T ¼ 1 ms, fs ¼ 5.7143 MHz

Cross-correlation performance

A cumulative probability distribution of the cross-correlation values provides a comprehensive measure of the crosscorrelation performance. Fig. 3 compares the crosscorrelation performance of the C/A, CM and CL codes as measured by the cumulative probability. The figure plots the cross-correlation result of pseudo-noise random number (PRN)-1 and PRN-7 chip sequences in each case. The horizontal axis of the figure indicates the cross-correlation protection as measured with reference to the autocorrelation (AC) peak. Of interest here is the top region of these curves, that is, say above 90% probability, which represents the range of highest cross-correlations for each case. In other words, it is this region where the cross-correlations ‘start’ to become a problem. A curve towards the left indicates better cross-correlation performance. In fact, the highest point of these curves represents the worst crosscorrelation value for the corresponding codes pair. This assessment approach is also used in [9, 10]. It is obvious from Fig. 3 that the CL code has the best cross-correlation performance followed by the CM and C/A codes, respectively. A similar relative cross-correlation performance will be observed for any other pair of PRN codes [11]. 2.3

Fig. 1 Illustration of a near–far scenario

L2C code structure

Code observation period

The average cross-correlation performance is directly proportional to the length of code and often the fundamental code period is selected for the cross-correlation performance assessment. The cross-correlation performances of C/A, CM and CL codes discussed above are all based on their respective code periods. The relative

Fig. 2 L2C code structure containing same CM but different CL (20 ms) segments in the CL period 196 & The Institution of Engineering and Technology 2011

IET Radar Sonar Navig., 2011, Vol. 5, Iss. 3, pp. 195 –203 doi: 10.1049/iet-rsn.2009.0207

www.ietdl.org stage can be modelled as r(t) =

2Pk dk (t)ck (t − tk ) cos[2p( fIF + fD,k )t + wk ] +

N −1

2Pj dj (t)cj (t − tj ) cos[2p( fIF + fD,j )t + wj ]

j=1 j=k

(1)

Fig. 3 Cross-correlation performance comparison of C/A, CM and CL chip sequences over the corresponding full code periods

performance improvement of L2C codes, shown in Fig. 3, is entirely due to extended code periods along with the implied increased observation intervals. An observation interval refers to the time period over which the two codes are correlated for a given relative code delay. Hence for a fair comparison, the codes must be observed over the same period. This means, for example, in a comparison with the CM code, the C/A code should be observed over 20 code epochs. Interestingly, the cross-correlation performance of 20 C/A epochs will remain the same as that for one epoch unless the relative carrier Doppler offset, experienced in the receiver, is considered. Thus the cross-correlation protection figures based on only code sequences do not reflect realistic values. For example, when a full Doppler range (typically equal to +5 kHz for a static receiver) is considered, the average worst crosscorrelation of C/A code drops to 21.6 dB [9].

3

where Pk is the received signal power (subscript k identifies received satellite signals and local replica signals will be identified by subscript i), dk(t) ¼ +1 denotes navigation data symbols, ck(t) is the spreading code whereas tk represents the phase or delay of the received code and f IF is the IF carrier frequency. Owing to continuous satellite motion and possible receiver dynamics, the signal frequency suffers from the Doppler effect, incorporated as fD,k and wk denotes the carrier phase. The subscript ‘j ’ identifies the interfering satellite (i.e. causing the crosscorrelation) and N represents the number of in-view satellites. The second term in (1) is responsible for introducing the cross-correlation noise in the receiver. With reference to the correlation system shown in Fig. 5, the above received satellite signal is mixed with the replicas of code and carrier and the cross-correlation noise appearing at the I and Q channels can be respectively given as ⎫ ⎧ ⎪ ⎪ ⎪ T⎪ −1 ⎬ 1 ⎨N j,i I = 2Pj dj (t)cj (t − tj ) cos[2p( fIF + fD,j )t + wj ] ⎪ T 0⎪ ⎪ ⎪ ⎭ ⎩j=1 j=k

Effect of relative doppler offset

In signal acquisition, the receiver trials a certain range (or band) of carrier Doppler frequencies to match the Doppler of the desired satellite signal. Each Doppler trial, at the same time, creates an offset with the Doppler of all of the in-view interfering (unwanted) satellites, termed here a relative Doppler offset (see Fig. 4). As already mentioned, this relative Doppler offset is essentially an offset carrier that modulates the product of the local and interfering codes and can have a strong impact on the cross-correlation performance over multiple code epochs. Considering multiple in-view satellites, the received signal at the IF

Q

j,i

× ci (t − ti ) cos[2p( fIF + fD,i )t + wi ] dt (2) ⎫ ⎧ ⎪ ⎪ ⎪ T⎪ N −1 ⎬ ⎨ 1 2Pj dj (t)cj (t − tj ) cos[2p( fIF + fD,j )t + wj ] = ⎪ T 0⎪ ⎪ ⎪ ⎭ ⎩j=1 j=k

× ci (t − ti ) sin[2p( fIF + fD,i )t + wi ] dt (3) Equations (2) and (3) can be combined as I j,i + jQ j,i =

1 T

T N −1 2Pj dj (t)cj (t − tj )ci (t − ti ) 0 j=1 j=k

× ej(2pDfj,i t+Dwj,i ) dt

Fig. 4 Graphical illustration of the relative Doppler offset concept: difference in Doppler frequencies of the local and interfering satellite signals IET Radar Sonar Navig., 2011, Vol. 5, Iss. 3, pp. 195 –203 doi: 10.1049/iet-rsn.2009.0207

(4)

Fig. 5 Reference correlation system considered for the crosscorrelation analysis 197


www.ietdl.org where Dfj,i represents the relative Doppler offset between the local and interfering satellite signals described above and Dwj,1 denotes the difference in phases of the local and interfering carrier signals. Equation (4) shows that the Doppler offset carrier, Dfj,i , modulates the product of the local and interfering codes cj (t 2 tj)ci(t 2 ti) in the correlation process. 3.1

Multiple code epochs

In the case of a signal being observed over multiple code periods, the code product cj (t 2 tj )ci(t 2 ti) becomes periodic with respect to the fundamental code period, Tp , (1 ms in the case of the C/A code). The offset carrier takes a certain phase across adjacent periods of the code product. For relative Doppler offsets equal to m kHz, where m is an integer, the offset carrier will have integer number of cycles in each period of the codes product, and consequently the offset carrier will take the same phase across each period of the codes product. Considering the case of 20 C/A code epochs, the offset carrier of 1 kHz (having exactly 1 cycle/ 1 ms of the underlying codes product) is shown in Fig. 6. In this case, the modulation from one 1 ms interval to the next remains relatively constant, and hence the accumulation across 1 ms dumps does not provide any ‘averaging’ benefit. As a result, for these relative Doppler offsets, the cross-correlation performance of multiple C/A periods is the same as that of the fundamental code period. These relative Doppler offsets of m kHz are herein termed ‘critical Doppler offsets’ (CDO) [12]. On the other hand, for non-critical relative Doppler offsets, the offset carrier will take a different phase across different 1 ms intervals as shown in Fig. 6 for the offset carrier of 500 Hz. In this example, the offset carrier has an exactly opposite phase across adjacent 1 ms intervals of the underlying codes product. In this case, the dump from one 1 ms interval to the next will have an opposite sign and consequently an accumulation across 20 dumps will lead to cancellation of virtually the entire cross-correlation. For all other values of relative Doppler offsets between the two extreme cases of 1 and 500 Hz discussed above, the crosscorrelation will have a relative behaviour. To study this effect of relative Doppler offset in more detail, a simulation was conducted where the worst cross-correlation envelope (|I j,i + JQ j,i |) of C/A code, when observed over 20 epochs, and the CM code was monitored over a relative Doppler offset range of +5 kHz, whereas the PRN-1 and PRN-7 codes used for the test were sampled at 5 MHz (a synchronous sampling to remove any effects other than the Doppler on the cross-correlation performance). Fig. 7a shows the results of this test, indicating that the worst C/A cross-correlation oscillates between approximately 22 and

Fig. 7 Cross-correlation behaviour of C/A and CM codes both observed over 20 ms, in response to relative Doppler offset a Over a relative Doppler offset range of +5 kHz b Over the relative Doppler offset range of 0 –1000 Hz

48 dB from one critical Doppler offset to the next. This cross-correlation behaviour is consistent with the above explanation of phase correlation across 1 ms intervals. Fig. 7b provides a closer view of these results over one cycle of cross-correlation behaviour, that is, the relative Doppler offsets from 0 to 1000 Hz. The figure indicates that the worst C/A cross-correlation basically follows a periodic ‘Sinc’ function that has its maximum located at the critical Doppler offsets (m kHz) and nulls occurring at every 1/T ¼ 50 Hz, where T is the coherent observation period equal to 20 ms here [13]. For a given Tp and T, this crosscorrelation behaviour can thus be expressed as a function of relative Doppler offset as C(Dfj,i ) = Sinc

m + Dfj,i T Tp

(5)

On the other hand, the theoretical expression for crosscorrelation at the correlator output is obtained by solving (4) as [14] (see the Appendix for derivation) I j,i + JQ j,i =

−1 +1 1 N 2Pj ejDwj,i R j,i w T j=1 w=−1 j=k

× Sinc

w + Dfj,i T Tp

(6)

where w is an integer while Rj,i w is given as Fig. 6 Offset carriers of 500 and 1000 Hz, respectively, taking exactly opposite and the same phase across 1 ms intervals of the product of the local and the interfering spreading codes 198 & The Institution of Engineering and Technology 2011

Rj,i w =

+1

Cl Cw−l ej2p(l/Tp )(Dt)

(7)

l=−1


www.ietdl.org where l is an integer and, Cl and Cw2l , respectively, represent the Fourier coefficients of the interfering and local replica codes when represented by Fourier series (given in the Appendix). It can be noticed that, as far as the overall cross-correlation behaviour is concerned, (5), based on the observation of simulation results, and the theory given by (6) are in good agreement. The CM code, on the other hand, has a consistent crosscorrelation behaviour along the entire test range of relative Doppler offsets, as shown in Fig. 7. This is because it is observed over the single code period and hence the periodic cross-correlations phenomenon does not occur. Although these results consider worst cross-correlation obtained by trialing all relative code delays for each relative Doppler offset, the same relative performance will be observed for any given relative code delay. Hence in the context of cross-correlation behaviour in response to relative Doppler offset, the relative code delay is not imperative. 3.2

Critical Doppler window

An interesting point about the results shown in Fig. 7 is that the C/A code provides better cross-correlation protection than the CM code except for certain segments of the relative Doppler offset range. Simulation results show that this critical range of relative Doppler offsets (called here a ‘critical Doppler window’, CDW) remains less than 100 Hz about the CDOs. This CDW will have a specific significance in the signal search space of a dual-frequency GPS L1/L2C receiver as discussed in the following section.

4

Signal search space

In the context of the near – far problem, locally trialed Doppler frequency and the associated relative Doppler offset are the two key signal search parameters. For each Doppler frequency trial, the receiver comes across a cross-correlation peak based on the associated relative Doppler offset. As long as a desired satellite signal is strong and the detection threshold is well above the cross-correlation peak, it does not cause any harm to the signal acquisition [15]. However, when the desired signal is weak and thus the detection threshold is set low, a cross-correlation peak exceeding the detection threshold might mislead the receiver to a false acquisition. Fig. 8 shows the status of the search space in a dual-frequency GPS L1/L2C receiver for a test scenario where the Doppler of desired L1 signal is set to ‘21500 Hz’, and hence the Doppler on L2 can be found as ‘21500 × (L2/L1) Hz’, whereas the Doppler of the

Fig. 8 Simulation results showing the status of signal search space in dual-frequency GPS L1/L2C receiver in the absence of near– far problem Desired L1 (CA) and L2 (CM) peaks are well above the corresponding crosscorrelation peaks IET Radar Sonar Navig., 2011, Vol. 5, Iss. 3, pp. 195 –203 doi: 10.1049/iet-rsn.2009.0207

Fig. 9 Simulation results showing the status of search space in GPS L1/L2C receivers in the event of near–far problem Desired L1 (CA) and L2 (CM) have a similar level as the corresponding cross-correlation peaks. Narrow search range illustrates the expected scenarios in assisted acquisition

interfering satellite is 800 Hz and a Doppler search range of 5000 Hz starting from 22800 to 2200 Hz is selected. Fig. 8 shows the locations of the desired L1 and L2 AC peaks as well as those of the associated worst cross-correlation threats. Different slopes of the AC functions meeting at the zero local Doppler are in accordance with the relationship between the L1 and L2 frequencies [16]. It can be seen that in this case of strong desired signals, the desired acquisition peaks can be easily distinguished from those of the crosscorrelation. Note that for the purpose of cross-correlation performance measurement (in the test scenario), the correlation values of both the desired and the interfering satellites for the L1 signal are independent of those of the L2C signal and the 1.5 dB relative power difference between the L1 and L2C signals is therefore not considered here. The simulations consider correlation of PRN-1 and PRN-7 codes sampled at 5.714 MHz (such as used in Zarlink chip sets). Fig. 9 shows the result of another test where the levels of desired signal peaks are similar to those of the cross-correlation interference while everything else remains the same as in the previous scenario described above. Hence in this case the cross-correlations are likely to cause a false acquisition. This result indicates that an L1 signal search will always experience a CDW over any Doppler search range of larger than 900 Hz. As discussed above, in this window the L1 cross-correlation level is higher than that of the CM code. Hence if a Doppler search range is larger than 900 Hz, such as in the receiver coldstart, the CM is a better code to deal with the near –far problem in a dual-frequency GPS L1/L2C receiver. However, for Doppler search ranges smaller than 900 Hz, such as in a receiver warm-start, assisted (A) GPS and reacquisition scenarios, C/A can be a more effective code to combat cross-correlation interference because of its periodicity in the coherent signal observation interval, in dual-frequency GPS L1/L2C receivers, provided the search range does not experience a CDW. This is because in such scenarios, the receiver has a priori knowledge of the satellite locations through a previous known position, a valid almanac or an assistance provided by a remote A-GPS server. Compared to the full search range, as illustrated in Fig. 8, a narrower (less than 900 Hz, including the effect of the minor oscillator or previous position inaccuracies) Doppler search range is much less likely to experience the CDW. This is quite important because the near – far problem occurs mostly in restricted view (e.g. indoor) applications, where A-GPS will be used. In other words, although L2C has a global cross-correlation advantage, L1 C/A is superior in the cases where cross-correlation is most likely to be a problem. 199


www.ietdl.org 4.1

Likelihood of CDW

In order to estimate the likelihood of a dual-frequency GPS L1/L2C receiver experiencing a CDW when searching over a Doppler range of 900 Hz, the following experiments were conducted. Five test locations, evenly dispersed across the globe, were selected for experiments, as shown in Fig. 10. Table 1 gives the locations of test sites in earth-centred earth-fixed (ECEF) coordinates. For each test location, the Doppler of all visible satellites above 108 elevation was recorded every 10 min over the course of 24 h, using the almanac data. For each visible satellite, for a search range of 900 Hz (stepping at 2/3T ¼ 33.33 Hz), starting from the correct Doppler, the relative Doppler offset with all other visible satellites was computed. Fig. 10 plots the distribution of these relative Doppler offsets for each location, indicating low incidences of the CDW. Table 2 reports the percentage of relative carrier Doppler falling in the CDW, for each test location. These results indicate that the overall likelihood of experiencing a CDW in a search range of 900 Hz is 4 – 5%. In other words, for 95 –96% of the time the C/A code would perform better than the CM code, suggesting C/A to be a more robust code to resist the cross-correlation interference in the assisted acquisition mode. The likelihood of experiencing a CDW decreases further for search ranges narrower than 900 Hz.

5

Overall performance comparison

In order to assess the overall cross-correlation performance of the C/A and CM codes for the assisted acquisition mode in dual-frequency GPS L1/L2C receivers, including the occurrences of critical Doppler offsets, the following simulation experiment was performed. The PRN-1 was set as the local satellite code and the cases of one, two, three and four interfering satellites were considered one by one. Considering the case of one interferer, the local code was correlated with each of the five interfering satellite codes, given by the first row of Table 3. For correlation of each pair of local and interfering codes, five different values of relative Doppler offsets, given by the first column of Table 4, were trialed one by one. This resulted in 25 crosscorrelation results and the mean of these 25 results was used to plot the cross-correlation performance curve of the C/A and CM codes for the one interferer case. The PRN of interfering satellites were chosen to be unique on an

Table 1

ECEF coordinates of test sites

Location

X

Y

Z

Sydney Paris Singapore Brasilia Toronto

24 644 468.695 4 229 481.535 21 434 445.575 3 603 134.231 885 646.252

2 549 957.976 161 741.023 6 213 266.401 25 145 808.97 24 556 254.98

23 538 921.13 4 755 371.006 134 890.627 21 100 248.547 4 359 896.076

Table 2

Percentage of relative Doppler offsets observed for each test location Location

Critical Doppler offsets (%)


4.3 5 5.2 4.8 5.1

arbitrary basis. In order to generate realistic values of relative carrier Doppler, the following procedure was adopted. For each test location, the distributions of expected relative Doppler offsets (Fig. 11) were turned into cumulative distributions (Fig. 12) and the values of relative Doppler offsets were then obtained by reading off the horizontal axis of cumulative probability curves for uniformly distributed points along vertical axis. This entire procedure was repeated for the two, three and four interferers cases, where additional sets of unique satellites and relative carrier Dopplers are provided by the rows and columns of Tables 3 and 4, respectively. Fig. 13 plots the Table 3

Satellite PRN selected for experiments Satellite PRN

Sydney 2 5 19 3

Paris

Singapore

Brasilia

Toronto

4 11 12 10

7 8 18 27

9 6 16 21

23 28 24 31

Fig. 10 Test sites selected for computation of relative Doppler offset distribution 200



www.ietdl.org Table 4

Relative Doppler offsets obtained for the experiments

Location Sydney Paris Singapore Brasilia Toronto

Relative Doppler offset, kHz 0.6553 0.7748 0.6386 0.6657 0.8194

1.3483 1.6629 1.3333 1.3136 1.7120

2.2140 2.5852 2.1174 2.0825 2.4872

3.4207 3.6552 2.8915 2.9204 3.6565

Fig. 13 Overall cross-correlation performance comparison of C/A and CM, both observed over 20 ms, codes in the assisted acquisition scenario

Fig. 11 Distribution of relative Doppler offsets computed for each test location a b c d e


results of these experiments for an overall cross-correlation performance comparison of the C/A and CM codes in the assisted acquisition mode in the presence of one, two, three and four interfering satellites, indicating that the C/A code is consistently performing better than the CM code by 11– 14 dB above the 90% probability (the region of interest). It can also be observed from these results that the crosscorrelation performance of both codes is degraded as more and more interferers are introduced in the system. Also, the relative performance improvement offered by the C/A code decreases with more interferers.

Fig. 12 Cumulative probability of relative Doppler offsets for the test locations a b c d e



The above analysis also suggests a more sophisticated strategy for dealing with the near – far problem in a dualfrequency GPS L1/L2C receiver in the assisted acquisition mode. In this strategy, the expected relative Doppler offset can be computed first based on the a priori knowledge of satellite locations and the receiver can then decide on employing the C/A or CM code, depending on whether the expected relative Doppler offsets fall in the critical window or not. In the case of an expected critical Doppler offset, the receiver can employ the CM code for signal acquisition, or the C/A code otherwise.

6

Navigation data transitions

The data bit length in both L1 and L2C signals is 20 ms. Although the actual data rate in L2C signal is 25 bps, a half-rate convolutional encoder is employed to transmit the data at 50 symbols/s. Although we know in CM where the boundaries are with respect to the code, the probability of having a data bit transition in L1 and L2C signals is still exactly the same. In the case of 20 C/A epochs considered here, the transitions can occur at any of the 20 C/A code boundaries. As discussed earlier, in the case of CDOs (m kHz), the values of 1 ms dumps are approximately the same. A data transition in this case will cause a sign reversal for some of the 1 ms dumps depending on the location of data bit transition. Consequently, accumulation across 20 dumps will remove some of the cross-correlation noise. For example, considering the 1 kHz relative Doppler offset example, a data bit transition in the middle, that is, at the 10th millisecond boundary, will virtually remove the entire cross-correlation. Hence the data transitions will be an advantage at CDOs for cross-correlation. Considering the example of relative Doppler offset equal to 500 Hz, the bit transition at the 10th millisecond, for example, will not affect the cross-correlation performance as the values of any two successive 1 ms dumps will still remain the same. In order to evaluate the performance of the C/A and CM codes in the presence of a data bit transition, the following simulation was performed. A relative Doppler offset range of 0 – 1000 Hz was selected, and for each relative Doppler offset a data bit transition was introduced from the first to 19th millisecond boundaries (one by one) of the interfering code. Fig. 14 presents the results of this test. It can be observed from the results that the overall C/A crosscorrelation performance is degraded by about 9 dB in the worst case; however, it still remains much better than the 201


www.ietdl.org the cross-correlation peaks will retain their location in each of the 20 ms integrations. Fig. 15 compares the crosscorrelation performance of the CM and CL codes for different numbers of non-coherent integrations (K ), using a coherent integration period of 20 ms. The results shown here are based on correlation of PRN-1 and PRN-7 chip sequences. These results show that a non-coherent integration strategy using the CL code can achieve an improvement of 5 – 7 dB (for cumulative probability of 90% and above) over the CM code, for the given scenario. Hence non-coherent combinations using the CL code has a cross-correlation performance advantage over the CM code. Fig. 14 Cross-correlation performance of C/A and CM code, both observed over 20 ms in the presence of data bit transition at all possible locations

corresponding CM performance. Also, the size of the CDW is increased by about 10 Hz; however, an improved C/A performance can be seen at the CDOs for all data transition locations. Overall, it can be deduced that the superiority of the C/A code is not affected by the presence of data bit transitions.

7

Non-coherent CL combinations

As mentioned earlier, the CL code offers about 45 dB crosscorrelation protection when observed over the full code period of 1.5 s. Direct acquisition of the CL code over full period is, however, resource intensive and is therefore not recommended. Signal observation using a partial CL period on the other hand would be a compromise between saving the acquisition resources and cross-correlation performance. However, another approach for engaging the CL code for signal acquisition is the non-coherent combination of successive correlator outputs obtained by using a partial CL period. In this case, since the successive CL code segments are effectively uncorrelated, their non-coherent accumulation will provide some cross-correlation performance gain. In fact, the use of CL code requires the incoming signal to be observed for at least 1.5 s. Depending on the size of the coherent integration period, this observation interval can be divided into several noncoherent integrations. Considering a coherent integration period of 20 ms, for example, up to 75 non-coherent integrations can be made. On the other hand, any number of non-coherent integrations using the CM full period will have the same cross-correlation performance, as

Fig. 15 Cross-correlation performance of CM and CL code with non-coherent integrations, T ¼ 20 ms 202 & The Institution of Engineering and Technology 2011

8

Conclusions

Cross-correlation robustness of the C/A and CM codes to the near – far problem in dual-frequency GPS L1/L2C receivers is evaluated. Cross-correlation performance of C/A code, when observed over multiple code epochs, is shown to be strongly dependant on the relative Doppler offset between the local and interfering satellite signals. It is shown that, for Doppler search ranges larger than 900 Hz, such as occur at cold-start, a dual-frequency GPS L1/L2C receiver will experience stronger cross-correlation interference on the L1 frequency than on the L2 frequency, and hence for such scenarios the CM code should be preferred over the C/A code for signal acquisition. For Doppler search ranges smaller than 900 Hz, such as expected in the assisted GPS, warm-start and reacquisition scenarios, the C/A code is shown to be overall a more effective code than the CM code, for combating the near – far problem in dual-frequency GPS L1/L2C receivers. It is also concluded that in a dualfrequency GPS L1/L2C receive having a priori knowledge of expected satellite positions, the critical Doppler frequencies where the C/A code performs worse than the CM code can be identified beforehand, and thus for those frequencies CM code can be employed to prevent the near – far effect. Cross-correlation protection in non-coherent integration strategies using CL code is shown to be significantly more effective than with CM code due to uncorrelated successive CL code segments. The analysis shows that C/A cross-correlation will have a similar behaviour for more than 20 C/A epochs, and consequently it will offer similar cross-correlation benefits over the CL code.

9

References

1 Tran, M.: ‘Performance evaluations of the new GPS L5 and L2 Civil (L2C) signals’, Navigation, 2004, 51, (3), pp. 199–212 2 Madhani, P.H., Axelrad, P., Krumvieda, K., Thomas, J.: ‘Application of successive interference cancellation to the GPS pseudolite near–far problem’, IEEE Trans. Aerosp. Electr. Syst., 2003, 39, (2), pp. 481 –488 3 Moshavi, S.: ‘Multi-user detection for DS-CDMA communications’, IEEE Commun. Mag., 1996, 34, pp. 124–136 4 Glennon, E´.P., Dempster, A.G.: ‘A novel GPS cross correlation mitigation technique’. Proc. ION GNSS 18th Int. Technical Meeting of the Satellite Division, Long Beach, CA, 2005, pp. 190– 199 5 Glennon, E´.P., Dempster, A.G.: ‘Cross correlation mitigation by adaptive orthogonalization using constraints – new results’. Proc. ION GNSS 19th Int. Technical Meeting of the Satellite Division, Fort Worth, TX, 2006, pp. 1811–1820 6 Glennon, E´.P., Dempster, A.G.: ‘Apparatus and method for the mitigation of cross correlation in GPS system’. Patent Application Number: 2007005869, United States of America Patent 2007 7 Morton, Y.J., Miller, M., Tsui, J., Lin, D., Zhou, Q.: ‘GPS civil signal self-interference mitigation during weak signal acquisition’, IEEE Trans. Signal Process., 2007, 55, (12), pp. 5859– 5863 8 IS GPS 200 D: ‘Global positioning system interface specification NAVSTAR’. 7 March, 2006 IET Radar Sonar Navig., 2011, Vol. 5, Iss. 3, pp. 195 –203 doi: 10.1049/iet-rsn.2009.0207

www.ietdl.org 9 Parkinson, B.W., Spilker, J.J.: ‘Global positioning system: theory and applications’, AIAA J., 1996, 1, pp. 104–106 10 Fontana, R.D., Cheung, W., Novak, P.M.: ‘The new L2 civil signal’. Proc. ION GPS, Salt Lake City, UT, 2001, pp. 617 –631 11 Dempster, A.G.: ‘Correlators for L2C: some considerations’, Inside GNSS, October 2006, pp. 32–37 12 Qaisar, S.U., Dempster, A.G.: ‘Cross-correlation performance comparison of L1 & L2C GPS codes for weak signal acquisition’. Proc. Int. Symp. on GPS/GNSS, Tokyo, Japan, 2008 13 Kaplan, E.D., Hegarty, C.J.: ‘Understanding GPS: principles and applications’ (Artech House, 2005) 14 Balaei, A.T., Akos, D.M.: ‘Doppler collision and cross correlation interference in GPS receivers’. Proc. Int. Symp. on GPS/GNSS, Gold Coast Australia, 2009, paper 57 15 Qaisar, S.U., Dempster, A.G.: ‘Assessment of L2C replica code design for efficient signal acquisition’, IEEE Trans. Aerosp. Electr. Syst., 2009, accepted for publication 16 Qaisar, S.U.: ‘Performance analysis of Doppler aided tracking loops in modernised GPS receivers’. Proc. ION GNSS 22nd Int. Technical Meeting of the Satellite Division, Savannah, GA, 2009, pp. 209–218

10 10.1

be expressed as I j.i + jQ j,i =

0 j=1 j=k

×

+1 +1 l=−1 i′ =−1

′

Cl Ci ej2p((i +l)/Tp +Dfj,i )t

× ej2p(l/Tp )(Dt) dt

(11)

where Dt = ti − tj is the relative code delay between the local and interfering satellite codes. Putting i ′ + l ¼ w and Rj,i w as R

j,i w

=

+1

Cl Cw−l ej2p(l/Tp )(Dt)

(12)

l=−1

Appendix Derivation of the cross-correlation expression

Using Rj,i w , (11) becomes

With reference to the correlation system shown in Fig. 5, the cross-correlation at the correlator output can be expressed as I j,i + JQ j,i =

T N −1 2Pj e jDwj,i

1 T

1 T

I

j,i

+ jQ

j,i

(8)

1 T

Each of the interfering and local replica codes can be expressed as Fourier series

ci (t − ti ) =

+1

+1

Rpj,i w=−1

1 T

T

ej2p((w/Tp )+Dfj,i )t dt

0

where

× ej(2pDfj,i t+Dwj,i )

i′ =−1

jDwj,i

(13)

0 j=1 j=k

cj (t − tj ) =

2Pj e

j=1 j=k

T N −1 2Pj dj (t)cj (t − ti )ci (t − ti )

+1

=

N −1

j2p(i′ /Tp )(t−tj )

Ci′ e

Cl ej2p(l/Tp )(t−ti )

ej2p((w/Tp )+Dfj,i )t dt =

0

1 1 T p((w/Tp ) + Dfj,i ) w + Dfj,i T × sin p Tp

(14)

(9) Hence the cross-correlation at the correlator output is (10)

l=−1

where Ci ′ and Cl represent the corresponding Fourier coefficients. Using the Fourier series representation, (8) can


T

I

j,i

+ jQ

j,i

−1 +1 1 N w jDwj,i j,i 2Pj = e Rw Sinc + Dfj,i T T j=1 Tp w=−1 j=k

(15)

203
