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.

This article focuses on the study of time-delay and Doppler estimation under high dynamic non-Gaussian scenarios. We aim at analysing the Mean Squared Error (MSE) performance of a misspecified receiver architecture which deliberately simplifies the signal model by neglecting the acceleration parameter and assumes the noise process as complex normal distributed. Specifically, we derive the pseudo-true parameters by minimazing the Kullback-Leibler (KL) divergence between the true and assumed models and the related Misspecified Cramér-Rae Bound (MCRB) will be provided in closed form. Theoretical derivations are validated via Monte Carlo simulations showing the asymptotic efficiency of the Misspecified Maximum Likelihood Estimator (MMLE). One remarkable outcome of this study is that the lack of knowledge of the true statistical noise model does not lead to asymptotic performance degradation in the estimation of the parameters of interest.

Since time-delay estimation is a fundamental task in various engineering fields, several expressions for the CRB and MLE have been developed over the past decades. In all of these previous studies, a common assumption was that the wave transmission process introduced an unknown phase component, which made it impossible to exploit the phase component related to the delay from the carrier signal. However, there are practical scenarios where this unknown phase can be estimated and compensated for, enabling the utilization of the delay phase component from the carrier signal. In this context, we provide a comprehensive treatment of this scenario, including the derivation of the MLE and the associated CRB. This approach allows us to analyze the impact of each signal component (carrier frequency and baseband signal) on the achievable MSE of delay estimation relative to the SNR. It also reveals five distinct regions of operations, in contrast to the well-known three.

Accurately determining signal time-delay is crucial across various domains, such as localization and communication ystems. Understanding the achievable optimal estimation peformance of such technologies, especially during design phases, is essential for benchmarking purposes. One common approach is to derive bounds like the Cramer-Rao Bound (CRB), which directly reflects the minimum achievable estimation error for unbiased estimators. Different studies vary in their approach to deal with the degree of misalignment in the global phase originating from both the transmitter and the receiver in a single input, single output (SISO) link during time-delay estimation assessment. While some treat this phase term as unknown, others assume ideal calibration and compensation. As an alternative to these two opposing approaches, this study adopts a more balanced approach by considering that such a phase can be estimated with a defined uncertainty, a measure that could be mplemented in many practical applications. The primary contribution provided lies in the derivation of a closed-form CRB expression for this alternative signal model, which, as observed, exhibits an asymptotic behavior transitioning between the results observed in previous studies, influenced by the uncertainty assumed for the mentioned phase term.

Time-delay and Doppler estimation is an operation performed in a plethora of engineering applications. A common hypothesis underlying most of the existing works is that the noise of the true and assumed signal model follows a centered complex normal distribution. However, everyday practice shows that the true signal model may differ from the nominal case and should be modeled by a non Gaussian distribution. In this paper, we analyse the asymptotic performance of the time-delay and Doppler estimation for the non-nominal scenario where the true noise model follows a centered complex elliptically symmetric (CES) distribution and the receiver assumed that the noise model follows a centered complex normal distribution. It turns out that performance bound under the misspecified model is equal to the one obtained for the well specified Gaussian scenario. In order to validate the theoretical outcomes, Monte Carlo simulations have been carried out.