We investigate on binary Protograph Root-LDPC codes that can embed an interesting property, called nested property. This property refers to the ability for a coding scheme to achieve full diversity and equal coding gain for any number of received coded blocks and for any configuration of the received code blocks. One can take advantage of this property for “carousel”-type transmissions broadcasting cyclically coded information. For regular Root-LDPC codes, we show that these codes inherently have both properties over the nonergodic block fading channel and when message passing decoding is used. Then, we show that irregular Root-LDPC structures could not provide equal coding gain except if explicit design rules are enforced to ensure that the nested property is fulfilled when designing irregular Root-LDPC codes. Simulation results show that designed nested Root-LDPC codes achieve good performance and full diversity for coding rates R=1/2, R=1/3 and R=1/4.

Global Navigation Satellite System Reflectometry (GNSS-R) is a powerful way to retrieve information from a reflecting surface by exploiting GNSS as signals of opportunity. In dual antenna conventional GNSS-R architectures, the reflected signal is correlated with a clean replica to obtain the specular reflection point delay and Doppler estimates, which are further processed to obtain the GNSS-R product of interest. An important problem that may appear for low elevation satellites is signal crosstalk, that is the direct line-of-sight signal leaks into the antenna dedicated to the reflected signal. Such crosstalk may degrade the overall system performance if both signals are very close in time, similar to multipath in standard GNSS receivers, the reason why mitigation strategies must be accounted for. In this article: (i) we first provide a geometrical analysis to justify that the estimation performance is only affected for low height receivers; (ii) then, we analyze the impact of crosstalk if not taken into account, by comparing the single source conditional maximum likelihood estimator (CMLE) performance in a dual source context with the corresponding Cramér–Rao bound (CRB); (iii) we discuss dual source estimators as a possible mitigation strategy; and (iv) we investigate the performance of the so-called variance estimator, which is designed to eliminate the coherent signal part, compared to both the CRB and non-coherent dual source estimators. Simulation results are provided for representative GNSS signals to support the discussion. From this analysis, it is found that: (i) for low enough reflected-to-direct signal amplitude ratios (RDR), the crosstalk has no impact on standard single source CMLEs; (ii) for high enough signal-to-noise ratios (SNR), the dual source estimators are efficient irrespective of the RDR, then being a promising solution for any reflected signal scenario; (iii) non-coherent dual source estimators are also efficient at high SNR; and (iv) the variance estimator is efficient as long as the non-coherent part of the signal is dominant.

This article investigates new strategies to compute accurate low-complexity Log Likelihood Ratio (LLR) values based on the Bayesian formulation under uncorrelated fading channels for both antipodal and CSK modulations when no Channel State Information (CSI) is available at the receiver. These LLR values are then used as input to modern error correcting schemes used in the data decoding process of last generation GNSS signals. Theoretical analysis based on the maximum achievable rate is presented for the different methods in order to evaluate the performance degradation with respect to the optimal CSI channel. Finally, Frame Error Rate (FER) simulation results are shown, validating the appropriate performance of the proposed LLR approximation methods.

In this article, we provide closed-form approximations of log-likelihood ratio (LLR) values for direct sequence spread spectrum (DS-SS) systems over three particular scenarios, which are commonly found in the Global Navigation Satellite System (GNSS) environment. Those scenarios are the open sky with smooth variation of the signal-to-noise ratio (SNR), the additive Gaussian interference, and pulsed jamming. In most of the current communications systems, block-wise estimators are considered. However, for some applications such as GNSSs, symbol-wise estimators are available due to the low data rate. Usually, the noise variance is considered either perfectly known or available through symbol-wise estimators, leading to possible mismatched demodulation, which could induce errors in the decoding process. In this contribution, we first derive two closedform expressions for LLRs in additive white Gaussian and Laplacian noise channels, under noise uncertainty, based on conjugate priors. Then, assuming those cases where the statistical knowledge about the estimation error is characterized by a noise variance following an inverse log-normal distribution, we derive the corresponding closed-form LLR approximations. The relevance of the proposed expressions is investigated in the context of the GPS L1C signal where the clock and ephemeris data (CED) are encoded with low-density parity-check (LDPC) codes. Then, the CED is iteratively decoded based on the belief propagation (BP) algorithm. Simulation results show significant frame error rate (FER) improvement compared to classical approaches not accounting for such uncertainty.

Evaluating the time-delay, Doppler effect and carrier phase of a received signal is a challenging estimation problem that was addressed in a large variety of remote sensing applications. This problem becomes more difficult and less understood when the signal is reflected off one or multiple surfaces and interferes with itself at the receiver stage. This phenomenon might deteriorate the overall system performance, as for the multipath effect in Global Navigation Satellite Systems (GNSS), and mitigation strategies must be accounted for. In other applications such as GNSS reflectometry (GNSS-R) it may be interesting to estimate the parameters of the reflected signal to deduce the geometry and the surface characteristics. In either case, a better understanding of this estimation problem is directly brought by the corresponding lower performance bounds. In the high signal-to-noise ratio regime of the Gaussian conditional signal model, the Cramér-Rao bound (CRB) provides an accurate lower bound in the mean square error sense. In this article, we derive a new compact CRB expression for the joint time-delay and Doppler estimation in a dual source context, considering a band-limited signal and its specular reflection. These compact CRBs are expressed in terms of the baseband signal samples, making them especially easy to use whatever the baseband signal considered, therefore being valid for a variety of remote sensors. This extends existing results in the single source context and opens the door to a plethora of usages to be discussed in the article. The proposed CRB expressions are validated in two representative navigation and radar examples.

The derivation of tight estimation lower bounds is a key tool to design and assess the performance of new estimators. In this contribution, first, the authors derive a new compact Cramér–Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, the resulting CRB is particularised to the delay, Doppler, phase, and amplitude estimation for band‐limited narrowband signals, which are found in a plethora of applications, making such CRB a key tool of broad interest. This new CRB expression is particularly easy to evaluate because it only depends on the signal samples, then being straightforward to evaluate independently of the particular baseband signal considered. They exploit this CRB to properly characterise the achievable performance of satellite‐based navigation systems and the so‐called real‐time kinematics (RTK) solution. To the best of the authors’ knowledge, this is the first time these techniques are theoretically characterised from the baseband delay/phase estimation processing to position computation, in terms of the CRB and maximum‐likelihood estimation.

This work addresses the problem of integrating a new signal in the Galileo E1 band. Thus, the arising question is how the existing multiplexing methods can be efficiently used or modified to integrate a new binary signal in the Galileo E1 band with the existing Galileo E1 signals. To this end, in this study, the authors first select three efficient multiplexing methods from the state of the art (i.e. interplexing, POCET and CEMIC methods) to multiplex a new Galileo signal along with the Galileo E1 legacy signals in a constant envelope modulation. Moreover, they evaluate their performance and main advantages and drawbacks. Secondly, in order to improve both performance and flexibility/adaptability of the multiplexing method, a modified CEMIC method, called ACEMIC, is proposed. This method allows to design modulations which maximise the power efficiency with respect to a given peak-to-average-power-ratio constraint. Finally, they compare the previous multiplexing methods in terms of power signal distribution, constant envelope fluctuation and power efficiency.

Recently, the joint design of the GNSS message structure and the associated channel‐coding scheme have been investigated as a means to reduce the Time‐To‐First‐Fix (TTFF) and particularly the time to retrieve the Clock and Ephemerides Data (CED). In this context, a new method to co‐design the navigation message and the channel‐coding scheme structure is proposed in this paper. This new co‐design enables us to reduce the time to retrieve the CED while enhancing error‐correction capabilities under degraded channel conditions. In order to fulfill such requirements, some structured coding schemes are designed, which provide both maximum distance separable (MDS) and full diversity properties under a non‐ergodic channel assumption.

Global Navigation Satellite Systems (GNSS) are the main source of position, navigation, and timing (PNT) information and will be a key player in the next-generation intelligent transportation systems and safety-critical applications, but several limitations need to be overcome to meet the stringent performance requirements. One of the open issues is how to provide precise PNT solutions in harsh propagation environments. Under nominal conditions, the former is typically achieved by exploiting carrier phase information through precise positioning techniques, but these methods are very sensitive to the quality of phase observables. Another option that is gaining interest in the scientific community is the use of large bandwidth signals, which allow obtaining a better baseband resolution, and therefore more precise code-based observables. Two options may be considered: (i) high-order binary offset carrier (HO-BOC) modulations or (ii) the concept of GNSS meta-signals. In this contribution, we assess the time-delay and phase maximum likelihood (ML) estimation performance limits of such signals, together with the performance translation into the position domain, considering single point positioning (SPP) and RTK solutions, being an important missing point in the literature. A comprehensive discussion is provided on the estimators’behavior, the corresponding ML threshold regions, the impact of good and bad satellite constellation geometries, and final conclusions on the best candidates, which may lead to precise solutions under harsh conditions. It is found that if the receiver is constrained by the receiver bandwidth, the best choices are the L1-M or E6-Public Regulated Service (PRS) signals. If the receiver is able to operate at 60 MHz, it is recommended to exploit the full-bandwidth Galileo E5 signal. In terms of robustness and performance, if the receiver can operate at 135 MHz, the best choice is to use the GNSS meta-signals E5 + E6 or B2 + B3, which provide the best overall performances regardless of the positioning method used, the satellite constellation geometry, or the propagation conditions.

The derivation of tight estimation lower bounds is a key tool to design and assess the performance of new estimators. In this contribution, first, the authors derive a new compact Cramér–Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, the resulting CRB is particularised to the delay, Doppler, phase, and amplitude estimation for band-limited narrowband signals, which are found in a plethora of applications, making such CRB a key tool of broad interest. This new CRB expression is particularly easy to evaluate because it only depends on the signal samples, then being straightforward to evaluate independently of the particular baseband signal considered. They exploit this CRB to properly characterise the achievable performance of satellite-based navigation systems and the so-called real-time kinematics (RTK) solution. To the best of the authors’ knowledge, this is the first time these techniques are theoretically characterised from the baseband delay/phase estimation processing to position computation, in terms of the CRB and maximum-likelihood estimation.