A Reduced Search Space Maximum Likelihood Delay Estimator for Mitigating Multipath Effects in Satellite-based Positioning

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1 A Reduced Search Space Maximum Likelihood Delay Estimator for Mitigating Multipath Effects in Satellite-based Positioning Mohammad Zahidul H. Bhuiyan, Elena Simona Lohan, and Markku Renfors Department of Communications Engineering, Tampere University of Technology P.O. Box 553, FIN-33101, Finland BIOGRAPHY Mohammad Zahidul Hasan Bhuiyan received his M.S. degree in Information Technology from Tampere University of Technology, Finland in He visited the Position, Location And Navigation (PLAN) group at the Geomatics Engineering Department in University of Calgary, Canada from January 07 to October He is currently doing his PhD at the department of Communications Engineering in Tampere University of Technology, Finland. He has been working in the same department as a Researcher since March His research interests include multipath mitigation and software receiver design for satellite-based positioning applications. Elena Simona Lohan obtained the M.Sc. degree in Electrical Engineering from the Politehnica 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, Simona Lohan 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. She was also involved with the EU FP6 project GREAT. Markku Renfors was born in Suoniemi, Finland, on January 21, He received the Diploma Engineer, Licentiate of Technology, and Doctor of Technology degrees from the Tampere University of Technology (TUT), Tampere, Finland, 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 Institute of Communications Engineering at TUT. His main research areas are multicarrier systems and signal processing algorithms for flexible radio receivers and transmitters. ABSTRACT Multipath is one of the dominant error sources in global navigation satellite systems, such as the Global Positioning System or the future European satellite navigation system, Galileo. The reception of multipath may create a bias into the time delay estimate of the delay lock loop of a conventional navigation receiver, which eventually leads to an error in the receiver's position estimate. In order to mitigate the impact of multipath on navigation receivers, the multipath problem has been approached from several directions, including the development of novel signal processing techniques. In this paper, we propose a maximum likelihood based algorithm, namely the Reduced Search Space Maximum Likelihood (RSSML) delay estimator, which is capable of mitigating the multipath effects in moderate-to-high carrier-to-noise-ratios. The proposed RSSML attempts to compensate the multipath error contribution by estimating the multipath parameters along with the line-of-sight signal. The multipath performance of other state-ofthe-art delay tracking methods previously studied for Binary Phase Shift Keying (BPSK) and Sine Binary Offset Carrier (SinBOC) modulated signals, is also analyzed here, together with the new Multiplexed BOC (MBOC) modulation. Simulations are carried out in closely space multipath scenarios for two-path Rayleigh fading channel model. The simulation results show that the RSSML achieves the best multipath mitigation performance in root-mean-square-error sense for all three different modulated signals (i.e., BPSK, SinBOC(1,1) and MBOC), compared with four other multipath delay estimation techniques, namely the Narrow Correlator, the High Resolution Correlator, the Teager-Kaiser estimator and the Peak Tracking estimator.

2 INTRODUCTION Multipath errors are mostly due to reflected GNSS signals from surfaces (such as buildings, metal surfaces etc.) near the receiver, resulting in one or more secondary propagation paths. These secondary path signals, which are superimposed on the desired direct path signal, always have a longer propagation time and can significantly distort the amplitude and phase of the direct path signal. In the past years, lots of work has been done in order to improve the multipath rejection performance of the receivers. In order to reduce multipath error, several approaches have been used. Among them, the use of special multipath limiting antennas (i.e., choke ring or multi-beam antennas), the post-processing techniques to reduce carrier multipath, the carrier smoothing to reduce code multipath, and the code tracking algorithms based on receiver internal correlation technique (i.e., narrow Early-Minus-Late (Dierendonck et al, 1992) or High Resolution Correlator (McGraw and Braasch, 1999) are the most prominent approaches. In this paper, our focus is limited to the correlation based multipath mitigation techniques. The most known correlation-based code tracking algorithm is the traditional Early-Minus-Late (EML), which is composed of 1 chip spacing between early and late correlator pair. The traditional EML has limited multipath mitigation capability, and therefore, several enhanced EML-based techniques have been introduced, especially to mitigate closely spaced multipath. One class of these enhanced EML techniques is based on the idea of narrowing the spacing between the early and late correlators, i.e., narrow EML (neml), provided that sufficient frontend bandwidth is assured (Dierendonck et al, 1992). Another enhanced version of this type of structure is the High Resolution Correlator (HRC), which uses a higher number of correlators (i.e., 5 complex correlators) for better coping with medium-to-long delay multipath (Hurskainen et al, 2008; McGraw and Braasch, 1999) in good Carrier-to-Noise-Ratio (CNR). Alternatively, several feed-forward techniques have been introduced in the literature in past few years (Bhuiyan et al, 2008; Lohan et al, 2006a). While improving the delay estimation accuracy, these techniques require a higher number of correlators than the traditional Delay Lock Loop (DLL), and they are sensitive to the noise-dependent threshold choice. Among the feed-forward techniques, two most competitive ones, previously proposed by the authors, are selected herein for performance comparison. These are Peak Tracking, based on 2 nd order Differentiation (PT(Diff2)), and Teager-Kaiser (TK) based delay estimation, the details of which can be found in (Bhuiyan et al, 2008). This paper introduces a novel code tracking algorithm, the Reduced Search Space Maximum Likelihood (RSSML) delay estimator, which attempts to compensate the multipath error contribution by estimating the multipath parameters along with the Line-Of-Sight (LOS) signal. Simulation results in fading multipath environment are included in order to compare the performance of the proposed algorithm with the various conventional DLLs and other developed feed-forward algorithms (which are briefly reviewed here). The performance of these tracking algorithms is analyzed for the newly proposed Multiplexed Binary Offset Carrier (MBOC) modulation along with the existing Binary Phase Shift Keying (BPSK) and Sine Binary Offset Carrier (SinBOC) modulations. This paper begins with a brief overview of MBOC modulation, followed by a description about the implemented closed loop model and the existing code tracking algorithms. Then, the novel RSSML delay estimator is presented followed by a description on the implementation issues. Next, the simulation results for the closed loop model are shown. Finally, some general conclusions are drawn based on the simulation results. OVERVIEW OF MBOC MODULATION The GIOVE-B, the second Galileo satellite, launched on April 27, 2008 started transmitting the Galileo L1 signal using a specific optimized wave-form, MBOC that will be inter-operable with the L1C signal to be used in future Block III GPS satellites, in accordance with the July 2007 agreement between the European Union and the United States (Simsky et al, 2008). The MBOC modulation enables receivers to obtain significantly better multipath mitigation performance than BPSK and SinBOC(1,1) modulations. The multipath improvement of MBOC modulation over SinBOC(1,1) is shown in (Simsky et al, 2008) with the transmitted GIOVE-B signal. The MBOC(6,1,1/11) power spectral density is a mixture of SinBOC(1,1) and SinBOC(6,1) spectra. The MBOC(6,1,1/11) spectrum can be generated by a number of different time waveforms that allows flexibility in implementation. The Time-Multiplexed BOC (TMBOC) implementation interlaces SinBOC(6,1) and SinBOC(1,1) spreading symbols in a regular pattern, whereas Composite BOC (CBOC) uses multilevel spreading symbols formed from the weighted sum (or difference) of SinBOC(1,1) and SinBOC(6,1) spreading symbols, interplexed to form a constant modulus composite signal (Hein et al, 2006). Following the BOC model and derivations of (Lohan et al, 2006b), the composite CBOC signal which is used here can be written as: )= () () () () = (1) ± (1) (1)

3 Above, when the two right-hand terms are added, additive CBOC or CBOC(+) is formed; when the two terms are subtracted, we have the inverse CBOC or CBOC(-) implementation. Alternatively, CBOC(+/-) implementation can be used, when odd chips are CBOC(+) modulated and even chips are CBOC(-) modulated (Hein et al, 2006). In eqn. 1, =2is the BOC modulation order for SinBOC(1,1) signal, = 12 is the BOC modulation order for SinBOC(6,1) signal, the term () represents that SinBOC(1,1) signal is passed through a hold block in order to match the higher rate of SinBOC(6,1); and and are amplitude weighting delay of the LOS signal, the correlator spacing, and the number of correlators. In case of EML tracking loop, the corresponding early-late spacing is equal to 2. The received signal is correlated with each replica in the correlator bank, and the output of the correlator bank is a vector of samples in the correlation envelope. Therefore, we obtain the correlation values for the range of chips from the prompt correlator, where is the number of correlators and is the correlator spacing between successive correlators. factors, for example, = = and = 1 11 = and () is the pseudorandom code as defined in eqn. 2: () = ( ) (2) where is the th code symbol, is the code symbol energy, is the spreading factor or number of chips per code symbol ( = 1023), is the th chip corresponding to the th symbol, is the chip rate, and is a rectangular pulse of support and unit amplitude. In eqn. 1, the first term comes from the SinBOC(1,1) modulated code (held at rate 12 in order to match the rate of the second term), and the second term comes from a SinBOC(6,1) modulated code. In the simulation, we prefer a CBOC(-) implementation among all the MBOC variants as an example case, and also because, this is the modulation chosen for Galileo E1C signal (ESA 2008). Fig. 1: Block diagram for multi-correlator based DLL implementation The various code tracking algorithms (named as Discriminator block in Fig. 1) utilize the correlation values as input, and generate the estimated LOS delay as output, which is then smoothed by a loop filter. In accordance with (Kaplan and Hegarty, 2006), the implemented code loop filter is a 1 st order filter, whose function can be written as: (+1)() () (3) where is calculated based on loop filter bandwidth. A DLL loop bandwidth of 1 Hz is used, assuming that carrier aiding is always available (McGraw and Braasch, 1999). MULTI-CORRELATOR BASED STRUCTURE Compared with the conventional EML tracking loop, where only 3 correlators are used (i.e. Early, Prompt and Late), here, in the multi-correlator based structure, we generate a bank of correlators (e.g., in this implementation, we use 81 correlators with 0.05 chips spacing between successive correlators) as presented in Fig. 1. This large number of correlators is needed in order to include the feed-forward techniques in the comparison, because feed-forward techniques make use of these correlators for estimating the channel properties while taking decision about the code delay (Bhuiyan et al, 2008). Some of these correlators can be kept inactive or unused, for example when EML and HRC tracking loops are used. After the necessary front-end processing, and after the carrier has wipedoff, the received post-processed signal was passed through a bank of correlators. As shown in Fig. 1, the NCO and PRN generator block produces a bank of early and late versions of replica codes based on the CODE TRACKING ALGORITHMS USED AS A BENCHMARK A comprehensive set of code tracking algorithms are analyzed for multipath performance analysis including the newly proposed RSSML. Among them, neml and HRC are the conventional delay tracking algorithms. The narrow correlator or neml is the first approach to reduce the influence of code multipath that uses a chip spacing of 0.05 or 0.1 chips (less than 1 chip) depending on the available front-end bandwidth (Dierendonck et al, 1992). HRC uses a higher number of correlators (i.e. 5 complex correlators) for better coping with medium-to-long delay multipath (Hurskainen et al, 2008; McGraw and Braasch, 1999). The remaining set of algorithms is based on feedforward concept. Among them, PT(Diff2) and TK are studied and analyzed in (Bhuiyan et al, 2008). Both of these algorithms utilize the adaptive threshold computed from the estimated noise variance of the

4 channel in order to decide on the correct code delay (Bhuiyan et al, 2008). These feed-forward algorithms first generate competitive peaks which are above the computed adaptive threshold. In PT(Diff2), the competitive peaks are then multiplied by some optimized weighting factors, which are assigned based on the peak power, the peak position and the delay difference of the peak from the previous delay estimate. Finally, PT(Diff2) selects the peak which has the maximum weight as being the best LOS candidate. In contrast to PT(Diff2), TK only considers the delay difference of the peak from the previous delay estimate while taking decision on the LOS delay (Bhuiyan et al, 2008). Apart from the above-mentioned algorithms, the authors develop a novel maximum likelihood based multipath mitigation algorithm, namely Reduced Search Space Maximum Likelihood (RSSML) delay estimator, which constitutes a separate section by its own. PROPOSED ALGORITHM: REDUCED SEARCH SPACE MAXIMUM LIKELIHOOD DELAY ESTIMATOR In the presence of multipath, the received signal at the input of a GNSS receiver can be written as: () = ( )exp[( )] () (4) where () is the spread-spectrum code, () is the white Gaussian noise, and are the amplitude, delay and phase of the th signal, respectively. In case of any GNSS signal, one of the most important parameter of interest is the LOS code delay. A conventional DLL (for example, neml) is not able to follow the LOS code delay accurately, since it does not take into consideration the bias contributed by the multipath components. The proposed RSSML attempts to compensate the multipath error contribution by estimating the multipath parameters along with the LOS signal. If () is observed for a certain time period, that is short enough to assume the parameters are constant, then the Maximum Likelihood Estimation (MLE) theory can be applied to estimate those parameters. The MLE principle states that the estimate of a certain parameter with the smallest mean square error is the estimate that maximizes the conditional probability density function of (). According to MLE, the RSSML calculates the estimated signal parameters (i.e., path delays, path amplitudes, and path phases), which minimize the mean square error of, as specified in eqn. 5. = [()()] (5) () = )exp [ ] (6) Here () is the estimate of the LOS as well as multipath signals. Eqn. 5 can be solved by setting the partial derivatives of to zero. The resulting equations for the th signal can be written as follows in accordance with (van Nee et al, 1994): {[ () ) exp ( )] exp ( )}] (7) {[ ( ) ) exp ( )] exp ( )} (8) = arg[ ( ) ( )] (9) In the above equations, ) is the down-converted correlation function, and () is the ideal reference correlation function. Generally speaking, the RSSML performs a nonlinear curve fit on the input correlation function which finds a perfect match from a set of ideal reference correlation functions with certain amplitude(s), phase(s) and delay(s) of the multipath signal. Basically, a conventional spread-spectrum receiver does the same thing, but for only one signal (i.e., the LOS signal). With the presence of multipath signal, the RSSML tries to separate the LOS component from the multipath signal(s) by estimating all the signal parameters in MLE sense, which consequently achieves the best curve fit on the received input correlation function. The number of multipath signals is generally unknown to the receiver, and therefore, has to be estimated. One possible way to estimate the number of multipath signals is to compute the mean square error for =0,1,, multipath signals, and select with which we obtain the minimum mean square error. In this implementation, is chosen such that the total number of signals does not exceed 2 (i.e., =2). In a multi-correlator based structure, the estimated LOS delay, theoretically, can be anywhere within the code-delay window range of chips, though in practice, it is quite likely to have a delay error around the previous delay estimate. The code-delay window range essentially depends on the number of correlators (i.e.,) and the spacing between the correlators (i.e.,) according to the following equation: =± 1) (10) 2 For example, if 97 correlators are used with a correlator spacing of 1/24 chips, then the resulting

5 code-delay window range will be ±2 chips with respect to prompt correlator. Therefore, the LOS delay estimate can be anywhere within this ±2 chips window range. For each of this LOS candidate, the ideal reference correlation functions are generated for up to paths. The ideal reference correlation functions for each LOS candidate were generated off line and saved in a look-up table in memory. In real-time, the RSSML reads the values from the look-up table and computes the Minimum Mean Square Error (MMSE) for each possible delay candidate from a reduced search space. The search space is reduced to some competitive peaks which are generated based on the computed noise thresholds, instead of considering all possible LOS delays within a predefined window range. This will further reduce the processing time required to compute the MMSE (i.e., MMSE needs to be computed only for the reduced search space). step procedure for the RSSML can be summarized below: Step 1: Noise Estimation The correlation values for early time delays (i.e., <-1 chip from the prompt correlator) are not affected by any multipath component since the multipath components are always delayed with respect to the LOS component. The noise level is estimated by taking the mean out-of-1-chip values at the early side from the prompt correlator of the normalized non-coherent correlation function as explained in Fig. 2. IMPLEMENTATION ISSUES The implementation of RSSML is discussed here for better clarification. Setting the partial derivatives of eqn. 5 to zero yields a set of nonlinear equations, as presented in eqns To overcome the difficulty of solving these equations, the RSSML generates a set of ideal reference correlation functions for each of the LOS delay samples (within a certain window range) with various multipath delays, phases and amplitudes. This means that, we generate () in eqn. 6, by varying all multipath components for each LOS delay sample (i.e., for each correlator in the correlation window range) in order to obtain a discrete set of ideal reference correlation functions. The set of multipath parameters can be specified as follows: { 1} { 1} { } (11) where, and, are the cardinalities of the sets, and, respectively. The cardinality of each set will depend on the resolution of the multipath parameters within the given range. However, the complexity will increase as the cardinality of any set increases. Finally, a set of ideal reference correlation functions are generated for all possible LOS delay samples: () = () (12) where is the total number of correlators in the correlation window range. After we generate the ideal reference correlation functions for all the correlators in the correlation window range, they are then saved in a look-up table in memory. The RSSML reads the ideal correlation values in real-time from the look-up table and computes the MMSE for each possible delay candidate from a reduced search space. The step by Fig. 2: Noise estimation in SinBOC(1,1) modulated 2 path Rayleigh channel model, path delay: [ ] chips, path power: [0-3] db, CNR: 100 db-hz Step 2: Competitive Peak Generation The competitive peaks are those peaks which are generated based on the estimated noise level in conjunction with (Bhuiyan et al, 2008). A peak threshold is computed based on the estimated noise threshold plus some weight factor as defined in (Bhuiyan et al, 2008). The weight factor is chosen in such a way that it reduces the possible risk that may arise due to the side lobes of the SinBOC(1,1) or CBOC(-) correlation. Therefore, the weight factors are different for different modulations (Bhuiyan et al, 2008). As shown in Fig. 2, in this example case, there is only one competitive peak which is above the computed peak threshold. The search space is then reduced from a large number of correlators to some delay samples (serving here as competitive peaks). Step 3: Ideal Reference Correlation Function Reading The RSSML reads the ideal reference correlation functions for each competitive peak (obtained from step 2) from the look-up table. Step 4: MMSE Computation The RSSML computes the MMSE for each competitive peak obtained from step 2. Step 5: LOS Delay Estimation The competitive peak with the lowest MMSE is chosen as the estimated LOS delay.

6 SIMULATION RESULTS Simulations are carried out in closely spaced multipath scenarios for BPSK, SinBOC(1,1) and MBOC modulated signals. The simulation profile is summarized in Table I. Rayleigh fading channel model is used in the simulation. The number of channel path is fixed to 2 with random path separation between 0.04 and 0.5 chips. The channel paths are assumed to obey a decaying Power Delay Profile (PDP), where the amplitude of the second path is exponentially decaying with respect to the amplitude of the first path and to the path separation:, where is the path separation and is a path decaying coefficient (here = 0.1 chips). The received signal was sampled at = 24, 12 and 2 for BPSK, SinBOC(1,1) and CBOC(-) modulated signals, respectively. Low is chosen intentionally for faster execution of the simulations and varies from one modulation to another in order to have the same number of samples per chip for all the three cases. TABLE I SIMULATION PROFILE DESCRIPTION Parameter Value Path Profile 2 path Rayleigh channel Path Power Decaying PDP with = 0.1 chips Path Spacing Random between 0.04 and 0.5 chips Path Phase Random between 0 and 2 Correlator Spacing, chips Number of Correlators, 97 Coherent Integration, 20 msec Non-coherent Integration, 1 block Oversampling Factor, [24, 12, 2] Initial Delay Error chips Loop Filter Bandwidth 1 Hz Loop Filter Order 1 st order Front-end Bandwidth Infinite (a) BPSK signal (b) SinBOC(1,1) signal The received signal duration is 800 milliseconds (msec) or 0.8 seconds for each particular CNR level. The tracking errors are computed after each msec (in this case, = 20 ms) interval. In the final statistics, the first 400 msec are ignored in order to remove the initial error bias that may come from the acquisition stage. We run the simulations for 100 random realizations, which give a total of = 2000 statistical points, for each CNR level. The Root- Mean-Square-Errors (RMSE) are plotted in meters, by using the relationship ; where is the speed of light, is the chip duration, and is the RMSE in chips. RMSE vs. CNR plots are shown in Fig. 3 for BPSK, SinBOC(1,1) and CBOC modulated signals. The RSSML showed the best multipath mitigation performance in RMSE sense in this two path Rayleigh fading model. Among the other algorithms, overall, PT(Diff2) and TK showed better performance than the conventional DLLs (i.e., neml). HRC showed superior performance as compared to neml only in good CNR conditions (i.e., from about 42 db-hz and onwards). (c) CBOC(-) signal Fig. 3: RMSE vs. CNR plots for 2 path Rayleigh fading channel in closed loop model The impact of second path power on the multipath error can be seen in Fig. 4. Here, the first path power was fixed to 0 db, whereas the second path power was

7 varied from [-6] db to [0] db with a step of 2 db. The simulations were run in very good CNR condition (i.e., 50 db-hz) in order to highlight the multipath behaviour of different algorithms in noise-free environment. It is evident from Fig. 4 that the RSSML showed the best overall performance, and was able to mitigate the multipath bias reasonably well. PT(Diff2) and TK were the next best algorithms, followed by HRC. CONCLUSIONS (a) BPSK signal In this paper, a novel Reduced Search Space Maximum Likelihood delay estimator is proposed and implemented in closed loop configuration in ideal infinite bandwidth case. The multipath performance of the newly proposed algorithm along with the conventional DLLs and the other feed-forward code tracking algorithms is presented in root-mean-squareerror sense. Three different modulation types are considered including the newly proposed CBOC modulation. It is shown that the RSSML, in general, achieved the best multipath mitigation performance in RMSE sense in this two path Rayleigh fading model. The multipath improvement of CBOC signal over BPSK and SinBOC(1,1) signals is evident from the simulation results for conventional DLLs, which is not so obvious for feed-forward algorithms. This can be explained by the fact that the feed-forward algorithms are generally more complex and depend on the estimated noise thresholds for delay estimation. The future work includes the adaptation of RSSML in band-limited case, which is, of course, very demanding for GNSS mass market receivers. The complexity analysis of RSSML could be another possible research direction in this context. ACKNOWLEDGEMENTS (b) SinBOC(1,1) signal This work was carried out in the project Future GNSS Applications and Techniques (FUGAT) funded by the Finnish Funding Agency for Technology and Innovation (Tekes). This work has also been supported by the Academy of Finland, which is gratefully acknowledged. REFERENCES Bhuiyan, M. Z. H. and Lohan, E. S. and Renfors, M. (2008). Code tracking algorithms for mitigating multipath effects in fading channels for satellite-based positioning, EURASIP Journal on Advances in Signal Processing, DOI: /2008/863629, Dierendonck, A. J. V. and Fenton, P. C. and Ford, T. (1992). Theory and Performance of Narrow Correlator Spacing in a GPS Receiver, Journal of The Institute of Navigation, Vol. 39, No. 3, pages (c) CBOC(-) signal Fig. 4: RMSE vs. Second Path Power plots for CNR=50 db-hz in closed loop model ESA (2008) Galileo Open Service Signal In Space Interface Control Document, Draft 1, European Space Agency, February 2008 Hein, G. W. and Avila-Rodriguez, J. A. and Wallner, S. and Pratt, A. R. and Owen, J. and Issler, J. L. and

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