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.

This contribution analyzes the fundamental performance limits of traditional two-step Global Navigation Satellite System (GNSS) receiver architectures, which are directly linked to the achievable time-delay estimation performance. In turn, this is related to the GNSS baseband signal resolution, i.e., bandwidth, modulation, autocorrelation function, and the receiver sampling rate. To provide a comprehensive analysis of standard point positioning techniques, we consider the different GPS and Galileo signals available, as well as the signal combinations arising in the so-called GNSS meta-signal paradigm. The goal is to determine: (i) the ultimate achievable performance of GNSS code-based positioning systems; and (ii) whether we can obtain a GNSS code-only precise positioning solution and under which conditions. In this article, we provide clear answers to such fundamental questions, leveraging on the analysis of the Cramér–Rao bound (CRB) and the corresponding Maximum Likelihood Estimator (MLE). To determine such performance limits, we assume no external ionospheric, tropospheric, orbital, clock, or multipath-induced errors. The time-delay CRB and the corresponding MLE are obtained for the GPS L1 C/A, L1C, and L5 signals; the Galileo E1 OS, E6B, E5b-I, and E5 signals; and the Galileo E5b-E6 and E5a-E6 meta-signals. The results show that AltBOC-type signals (Galileo E5 and meta-signals) can be used for code-based precise positioning, being a promising real-time alternative to carrier phase-based techniques.

This article investigates on the derivation of good log likelihood ratio (LLR) approximations under uncorrelated fading channels with partial statistical channel state information (CSI) at the receiver. While previous works focused mainly on solutions exploiting full statistical CSI over the normalized Rayleigh fading channel, in this article, a Bayesian approach based on conjugate prior analysis is proposed to derive LLR values that only uses moments of order one and two associated with the random fading coefficients. The proposed approach is shown to be a more robust method compared to the best existing approximations, since it can be performed independently of the fading channel distribution and, in most cases, at a lower complexity. Results are validated for both binary and M-ary modulations over different uncorrelated fading channels.

Nonlinear regression models play a crucial role in signal processing and multi-sensor applications. Traditionally, performance bounds for these models assume independent Gaussian observations. In practice, the Gaussian assumption fails in multi-sensor systems if some proportion of sensors are corrupted by non-Gaussian noise and outliers. In this context, we extend the Misspecified Cramér-Rao Bound (MCRB) framework to the contaminated Gaussian noise model, where observations are generated from a mixture of nominal Gaussian noise and occasional outliers. Building on previous work with Complex Elliptically Symmetric noise models, we derive analytical MCRB expressions under the mismatched Gaussian assumption and study the asymptotic behavior of the corresponding Misspecified Maximum Likelihood Estimator (MMLE). To demonstrate practical relevance, we apply the theory to joint time-delay and Doppler estimation in GPS signals under contamination. Numerical simulations confirm that the MMLE root mean squared error converges to the theoretical MCRB, which aligns with the classical Gaussian CRB.

This work provides a comparative study of the complexity and performance for a range of different types of robust estimators. The interest of this analysis is to find the preferred robust estimator that can define the system time for a swarm of satellites. The Student’s t-distribution is used as a model for the noise corrupting the measurements. The ideal performance of an unbiased estimator for a fixed number of degrees of freedom is known in the form of the Cram´er-Rao Bound (CRB). In this article, two examples of a robust Mestimator and an approximation of the Maximum Likelihood Estimator (MLE) resulting from an Expectation-Maximization algorithm are each tested with respect to the performance bounds. Each estimator is also compared with the Gaussian MLE under Gaussian noise, to identify any losses in efficiency under Gaussian conditions. The complexity of the algorithms is also studied by comparing the time until convergence in the iterative update of the robust estimators.

Global Navigation Satellite Systems rely on estimating the signal propagation delay and Doppler shift to a set of visible satellites, which in turn allows to determine the receiver position, velocity and timing. However, the presence of interfering signals degrades the estimation of such synchronization parameters, reason why robust solutions must be accounted for. One specific kind of interference are jamming, where a powerful signal is emitted in the same bandwidth as the signal of interest. One possible way to mitigate jamming is to resort to an antenna array. Doing so, spatial diversity can help to estimate the most powerful signal, allegedly the interference, and perform detection, localization and mitigation. In our solution, we propose two methods: the first one is an offline one, which uses snapshots where the interference is the most powerful to allow for precise detection and localization of the interferer. The other one is an online one, allowing to perform detection, localization and mitigation in real time of the interfering signal.