Acquisition of BOC Modulated Signals Using Enhanced Sidelobes Cancellation Method Adina Burian, Elina Laitinen, Elena Simona Lohan, Markku Renfors Department of Communications Engineering, Tampere University of Technology, P.O. BOX 553, FIN-33101, Tampere, Finland
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BIOGRAPHY Adina Burian received an MSc degree from Tampere University of Technology (TUT) in April 2003 with major in Software Engineering. Currently she is working at Atheros Technology Finland (formerly u-Nav Microelectronics) and she is a PhD candidate at TUT, Department of Communications Engineering. Her research interests focus on acquisition and tracking algorithms for GNSS signals. Elina Laitinen got her MSc degree at Tampere University of Technology in August 2005 with major in Telecommunications and she is currently a PhD candidate at TUT, Department of Communications Engineering. Her research interests include acquisition and tracking algorithms for GNSS signals and indoor channel modeling. Elena Simona Lohan obtained the M.Sc. degree in Electrical Engineering from the Polytechnic University of Bucharest, Romania, in 1997, the D.E.A. degree in Econometrics, at Ecole Polytechnique, Paris, France, in 1998, and the Ph.D. degree in Telecommunications from Tampere University of Technology. In 2007 she was nominated as a Docent in the field of “Wireless communication techniques for personal navigation.” Since November 2003, she has been working as a Senior Researcher at TUT and she has been acting as a group leader for the mobile and satellite-based positioning activities at the Department of Communications Engineering. Her research interests include satellite positioning techniques, CDMA signal processing, and wireless channel modeling and estimation. Markku Renfors received the Diploma Engineer, Licentiate of Technology, and Doctor of Technology degrees from the Tampere University of Technology in 1978, 1981, and 1982, respectively. From 1976 to 1988, he held various research and teaching positions at TUT. From 1988 to 1991, he was a Design Manager at the Nokia Research Center and Nokia Consumer Electronics, Tampere, Finland, where he focused on video signal processing. Since 1992, he has been a Professor and Head of the Department of Communications Engineering at TUT. His main research areas are multicarrier systems and signal processing algorithms for flexible radio receivers and transmitters. Markku Renfors is a Fellow of the IEEE.
ABSTRACT The Binary Offset Carrier (BOC) modulation, proposed for future Galileo and GPS M-code signals, provides a high spectral separation from BPSK-modulated signals, such as GPS C/A code. This modulation type introduces new challenges in the delay-frequency acquisition and tracking processes, because it creates multiple peaks in the envelope of the autocorrelation function (ACF). In this paper, we analyze the performance of the Sidelobe Cancellation Method (SCM) which is used to suppress or diminish the contribution of sidelobes, when acquiring the BOC modulated signals. In order to provide a further decrease in sidelobes amplitudes and thus to enhance the performance, we use the SCM approach in conjunction with two differential correlation methods, where correlation is performed using consecutive outputs of coherent integration. The proposed methods are analyzed in the presence of multipath fading channels, considering parameters specified in the proposals for Galileo system.
I. INTRODUCTION The Galileo and GPS inter-operability is realized by a partial frequency overlap with different signal structures and/or different code sequences, for example, the GPS civil C/A-code, the military M-code and P/Y-code, and Galileo OS and Public Regulated Service (PRS) signals will be all clustered around the 1575 MHz band of the L1 frequency [1]. Thus, in order to accommodate several signals on same carrier, a new modulation type, the Binary Offset Carrier (BOC) modulation, has been proposed. Its split spectrum property allows moving the signal energy away from the band center, thus achieving a higher degree of spectral separation between the BOCmodulated signals and other GPS legacy signals, such as the C/A code [2]. Due to the multiple peaks presents in the two chip interval of the envelope of the ACF function, the delayDoppler synchronization becomes ambiguous since the receiver can declare acquisition on a false peak. Moreover, the mobile wireless channels suffer adverse effects during transmission, such as high level of noise or presence of multipath propagation, which degrade further the accuracy of delay-Doppler estimates.
In order to eliminate these ambiguities from the ACF at acquisition stage, different methods have been introduced in the literature. One technique is the “BPSKlike” or sideband method, where the BOC modulated signals can be obtained either as one or the sum of two BPSK-like modulated signals, located at positive and/or negative sub-carrier frequencies, thus removing the effect of sub-carrier modulation [3]. There are different implementations of this method, differing in the number of spectrum lobes selected, the number of filters used in sidelobes selection and in complexity of correlation part [3] [4] [5] [6]. These methods have the advantage they allow the use of a higher searching step of timeuncertainty window compared with the ambiguous situation, but due to filtering and correlation loss, they bring some degradation in the signal power. Another alternative solution is to transform the ambiguous ACF into an unambiguous one via adequate filtering of the signal, a generalized class of frequency-based unambiguous acquisition methods - the filter-bank-based approaches being proposed in [7]. A different approach, the Sidelobes Cancellation Method (SCM), introduced in [8], suppresses or diminishes the undesired contribution of sidelobes on the correlation function, while keeping the narrow width of the main peak. In contrast with other un-ambiguous tracking techniques, it has the advantage that it can be applied to any sine or cosine, odd or even BOCmodulation case and can provide a lower complexity solution. It has been prove that the SCM approach brings an improvement in performance at tracking stage, in case of multipath fading channels, with both closely-spaced and long-delayed paths [8] [9]. Recently, the differential correlation method, originally proposed in the context of CDMA wireless communications systems, has been also proved effective in the context of satellite navigation [10]. With low or medium coherence times of fading channels, this method has better resistance to noise and other temporally uncorrelated interference sources than the traditional noncoherent integration method [11]. It has been observed that the differential correlation has the potential to decrease the ACF sidelobes amplitudes, thus lowering the possibility to detect a wrong side peak. Thus, in order to provide a further enhancement in performance, we use the SCM approach in conjunction with two differential correlation methods. The first used method (denoted further by DN) is the conventional differentially noncoherent correlation, where the correlations between two consecutive outputs of coherent integration are averaged in order to obtain the differential acquisition variable [10]. The second differential correlation method (denoted by DN2) is an enhanced differential non-coherent integration method, which exploits the longer correlation times and thus improves suppressions of temporally uncorrelated interference [11]. We carry out a comprehensive comparison of the introduced methods, keeping as benchmark the traditional non-coherent (NC) integration, in the context of multipath-fading channels. This paper is organized as follows. In Section II the SCM method is presented. Section III describes the
differential correlations used to enhance the performance of SCM technique. Section IV presents the performance comparison of the introduced method, while Section V concludes the paper. II. SIDELOBE CANCELLATION METHOD The SCM approach for ambiguity cancellation was first proposed to be used at the tracking stage of BOCmodulated signals [8] [9]. This method uses an ideal reference correlation function at the receiver, which resembles the shapes of sidelobes introduced by BOC modulation. In order to remove the side peak ambiguity, this ideal reference correlation is subtracted from the ambiguous correlation, i.e., the correlation of received BOC-modulated signal with the reference PRN code. In order to reduce the number of correlation operations, an ideal subtraction function, computed only once per BOC signal, is stored at receiver. The ideal reference function to be subtracted from the received signal after code correlation is derived as bellow [9]: ( ) R
=
+(
)
+(
)
,
( 1)
(1)
) is is the BOC interval, where TB =TC/ the triangular function, centred at zero, with a width of is the sine BOC modulation order (i.e., 2TB chips, twice the ratio between subcarrier rate and chip rate) and is the second BOC modulation factor, which covers sine and cosine cases, as explained in [10]. The sine and cosine BOC ideal autocorrelation function can be written as: R
=
+(
( ) )
+(
)
,
( 1)
(2)
An unambiguous ideal ACF is obtained by subtracting the squared function which approximates the sidelobes effects (eq. 1) from the ideal ambiguous squared ( ) correlation (eq. 2). For real signals the ideal R should be replaced with the computed correlation R ( ) between the received signal and the reference BOC modulated PRN code, thus the unambiguous correlation is computed as: ( )=(
))
) ,
(3)
The weighting factor w from eq. (3) is used to perform the normalization of reference function compared to the power of R ( ), which can varies due to various channel effect, such as noise and multipath. In order to find the weighting factors, the peak magnitudes of R ( ), the correlations are sorted in increasing order
and w is computed as the ratio between the last-but-one and the highest peak. Since the subtracted pulse is based on ideal correlation function, it can be computed only once and stored at receiver.
(c) Based on , and , make an initial estimation of channel impulse response (CIR ). (d) Perform normalization of reference function and ( )= remove sidelobes by subtraction ) .
))
(e) After cancelling the strongest peak, obtain the residual ) ( )=( )) ( ) ( ) .
Figure 1. Example of SCM for a SinBOC(1,1) modulated signal; upper plot: ambiguous correlation function and subtracted pulse, lower plot: the obtained unambiguous signal.
As an example, Figure 1 shows for a SinBOC(1,1) modulated signal, the shapes of the ideal ambiguous correlation function, the subtracted function and the unambiguous correlation. It can be observed that SCM removes the side peaks within the ±1 chips interval, which can be false detected. If the subtraction is done at the correct estimated delay, there is no decrease in the signal power, as for other unambiguous acquisition methods. On the other hand, the step of sweeping across the time-uncertainty window in the acquisition process should be at most half of the width of main lobe in order for SCM method to make an accurate detection. Thus the narrow width of the main lobe (which depends on the BOC modulation order) translates in larger number of timing hypotheses, thus an increasing in the Mean Acquisition Time (MAT). However, this method can be prove to be useful when receiver hardware constraints require the usage of same search step at both acquisition and tracking stages. Eq. (3) is valid for single path channel, and, when applied to multipath situations, the subtraction pulse should be aligned to the line-of-sight (LOS) path. Therefore some initial estimate of LOS delay is necessary. The SCM applied with path estimation and cancellation, is explained in the following steps: ( ) between the (a) Compute the correlation received signal and reference BOC-modulated PRN code and find the maximum peak (peak 1) at | ( )|, its delay , amplitude and phase .
(b)
Compute
the ideal reference , centred at .
function
(f) Find the maximum peak (peak 2) of the residual ) ( ) and corresponding delay , function amplitude and phase . Re-estimate the maximum global peak, after subtracting contribution of both peaks 1 and 2 from the unambiguous correlation ) ( )=( )) ( ) ( ( ) ) .
(g) Repeat steps from (c) to (f) until all peaks above a threshold value are estimated.
III. DIFFERENTIAL NON-COHERENT CORRELATION METHODS Traditionally non-coherent combining of results of successive coherent integrations is used to increase the integration time in order to improve the sensitivity of the receiver. Compared to coherent averaging, the noncoherent envelope detection results in a loss of SNR often referred as squaring loss). As an alternative to noncoherent processing, different differential correlation methods have been introduced in literature. In the differential approach the decision statistics is the product of uncorrelated samples, thus these methods offer an improved suppression of temporally uncorrelated interferers and pseudo-random noise. Here only noncoherent differential correlations are considered due to the fact that differential coherent correlation has been proved to be more sensitive to residual Doppler errors [12]. For the conventional NC integration the acquisition variable is given as: =
1
|
| ,
(4)
The differentially non-coherent correlation (DN) test statistics is given as: =
1
1
,
(5)
where yk, k= 1, ..., M, are the outputs of the coherent integration and M is the differential integration length. In order to have a fair comparison between the NC and DN methods it is assumed that NNC = M.
Figure 2. Envelopes of ideal correlation functions obtained with non-coherent, SCM and SCM DN2 methods, for a SinBOC(10,5) modulated signal.
Since temporal correlation may occur in relatively long intervals, if prior differential processing the coherent integration time is small enough, long time differential correlations can be exploited. This approach improves suppression of temporally uncorrelated interference. An enhanced DN method which takes advantage of above property is introduced in [12]. The acquisition variable of this DN2 method is given by: =
1
2
(
) ,
(6)
After computing the correlation between the received signal and the PRN code, the signal is coherently integrated over Nc integration time, then either noncoherent integration (NC) or differential correlation (DN or DN2) is applied, depending on the used method. For a further decrease in side-peaks amplitudes, after noncoherent or differential accumulations, the SCM technique is applied, as explained in the previous section. In Fig. 2 the shapes of ideal correlations functions are illustrated, in case of a signal with no multipath and with a strong signal power. As shown here, the combination of DN2 and SCM algorithms can decrease even further the sidelobes ambiguities, compared to SCM method. The conventional non-coherent integration, without sidelobes removal, is denoted by NC. IV. PERFORMANCE COMPARISON This section presents the simulation results of the proposed algorithms. The SCM methods (SCM, SCM DN and SCM DN2) are compared with the conventional non-coherent integration (NC) in multipath fading channels. The coherent integration length is denoted by Nc and the conventional and differential integration lengths, denoted by Nnc, respectively M. The used BOC-modulations are SinBOC(1,1) (chosen as common baseline for Galileo Open Service structure) and CosBOC(10,5), proposed for Galileo Public Regulated Service.
Figure 3. Exemplification of SCM algorithms for a SinBOC(1,1)-modulated signal sent through a 2-path Rayleigh fading channel
The search over time-frequency space was performed in a hybrid fashion, with a maximum frequency uncertainty range of 9 kHz. The Carrier-to-Noise ratio (CNR) is given in decibel[ ]= Hertz (dB-Hz) and is defined as 10 , where Eb is the bit or symbol energy and
BW is the signal bandwidth after despreading (here BW = 1 kHz). The test statistic is formed via the ratio of the first two local maxima in the time-frequency mesh [12] and the detection threshold is a variable computed according to the current CNR and integration times, in order to meet a constant probability of false alarm Pfa. For the performed simulations the Pfa = 10-2. The detection probability Pd is the probability to have the decision variable for at least one path higher than the decision threshold, provided that we are in the correct bin and the error is not exceeding one chip. The introduced algorithms were tested under the assumption of a multipath channel, with either fixed Rayleigh distribution of all paths or with Rician distribution for the first path and Rayleigh distribution for the next paths. The successive channel paths have uniformly random and xmax distribution spacing between 1/ chips, where Ns is the oversampling factor. For all presented simulations the step time bin is assumed to be . sufficiently small, i.e. t = 1/
Fig. 3 exemplifies the obtained correlations shapes, for a 2-path Rayleigh fading channel with an equal power distribution profile. It can be observed that the SCM correlation, as well as SCM method enhanced by differential correlations (SCM DN and SCM DN2) diminishes the threat of the side-peak situated at 145th sample, which can be detected instead the correct one, situated at the 139th sample. Figures 4 and 5 present the obtained simulations results, for a SinBOC(1,1) modulated signal, in terms of probability of detection, respectively in terms of mean acquisition time. The simulated channel has fixed Rayleigh distribution, with 2-paths with average power Rayleigh delay profile (PDP) of 0 and -2 dB.
Figure 4. Performance in terms of detection probability, for a SinBOC(1,1) modulation case, Rayleigh channel with 2 paths.
Figure 5. Performance in terms of mean acquisition time SinBOC(1,1) modulation case, Rayleigh channel with 2 paths.
Figure 6. Performance in terms of detection probability, for a SinBOC(1,1) modulation case, Rician channel with 2 paths.
Figure 7. Performance in terms of detection probability, for a CosBOC(10,5) modulation case, Rayleigh channel with 3 paths.
The mobile speed is v = 3 km/h, NC = 10 ms, Nnc = M = 10 and xmax= 0.5 chips. As can be seen from both figures, the performance of SCM methods exceeds that of NC approach. The SCM DN and DN2 techniques, which both have similar performance, also bring an enhancement in simulation results, compared to SCM method. Figure 6 shows the simulations results, for a SinBOC(1,1) modulated signal, in terms of probability of detection, for a channel with 2-paths equal average powers, with Rician distribution for the first path and Rayleigh distribution for the next path. The maximum separation between successive paths is xmax = 1 chip. In this case also the best results are provided by the SCM enhanced by DN and DN2 methods. The simulations results for a CosBOC(10,5) modulated signals are presented in Figures 7 and 8, for Rayleigh channel with average PDP of -1, 0 and -2 dB, Nc = 10 ms, Nnc = M =20 and xmax = 1 chip. Also here all SCM techniques outperform the NC method, with SCM DN and DN2 having similar performances.
Figure 8. Performance in terms of mean acquisition time, for a CosBOC(10,5) modulation case, Rayleigh channel with 3 paths.
V. CONCLUSIONS In this paper we investigated the potential of Sidelobe Cancellation method to suppress the contribution of sidepeaks ambiguities of BOC-modulated signal at acquisition stage. The SCM method, introduced previously to enhance the tracking performance, has been proved to be beneficial also at acquisition stage, if the search step of time uncertainty is sufficiently small. We have tested the SCM method in conjunction with two differential correlation techniques, which enhances further the performance when comparing to the traditional non-coherent processing. The results were checked via simulations in case of multipath fading channels for BOC-modulated signals, modelled according to Galileo proposals.
ACKNOWLEDGEMENTS This work was carried out in the “Future GNSS Applications and Techniques” (FUGAT) project, funded by the Finnish Funding Agency for Technology and Innovation (Tekes). This work has also been partially supported by the Academy of Finland.
REFERENCES
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