Information Theory and Reliable Communication

A new coded modulation scheme is proposed. At the transmitter, the concatenation of a distribution matcher and a systematic binary encoder performs probabilistic signal shaping and channel coding. At the receiver, the output of a bitwise demapper is fed to a binary decoder. No iterative demapping is performed. Rate adaption is achieved by adjusting the input distribution and the transmission power. The scheme is applied to bipolar amplitude-shift keying (ASK) constellations with equidistant signal points and it is directly applicable to two-dimensional quadrature amplitude modulation (QAM). The scheme is implemented by using the DVB-S2 low-density parity-check (LDPC) codes. At a frame error rate of $10^{-3}$ , the new scheme operates within less than 1.1 dB of the AWGN capacity $\frac{1}{2}\log_2(1+{\mathsf{SNR}})$ at any spectral efficiency between 1 and 5 bits/s/Hz by using only 5 modes, i.e., 4-ASK with code rate 2/3, 8-ASK with 3/4, 16-ASK and 32-ASK with 5/6, and 64-ASK with 9/10.

Bandwidth Efficient and Rate-Matched Low-Density Parity-Check Coded Modulation

A new coded modulation scheme is proposed. At the transmitter, the concatenation of a distribution matcher and a systematic binary encoder performs probabilistic signal shaping and channel coding. At the receiver, the output of a bitwise demapper is fed to a binary decoder. No iterative demapping is performed. Rate adaption is achieved by adjusting the input distribution and the transmission power. The scheme is applied to bipolar amplitude shift keying (ASK) constellations with equidistant signal points and it is directly applicable to two-dimensional quadrature amplitude modulation (QAM). The scheme is implemented by using the DVB-S2 low-density parity-check (LDPC) codes. At a frame error rate of 1e-3, the new scheme operates within less than 1 dB of the AWGN capacity 0.5log2(1+SNR) at any spectral efficiency between 1 and 5 bits/s/Hz by using only 5 modes, i.e., 4-ASK with code rate 2/3, 8-ASK with 3/4, 16-ASK and 32-ASK with 5/6 and 64-ASK with 9/10.

We review probabilistic constellation shaping (PCS), which has been a key enabler for several recent record-setting optical fiber communications experiments. PCS provides both fine-grained rate adaptability and energy efficiency (sensitivity) gains. We discuss the reasons for the fundamentally better performance of PCS over other constellation shaping techniques that also achieve rate adaptability, such as time-division hybrid modulation, and examine in detail the impact of sub-optimum shaping and forward error correction (FEC) on PCS systems. As performance metrics for systems with PCS, we compare information-theoretic measures such as mutual information (MI), generalized MI (GMI), and normalized GMI, which enable optimization and quantification of the information rate (IR) that can be achieved by PCS and FEC. We derive the optimal parameters of PCS and FEC that maximize the IR for both ideal and non-ideal PCS and FEC. To avoid plausible pitfalls in practice, we carefully revisit key assumptions that are typically made for ideal PCS and FEC systems.

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Probabilistic Constellation Shaping for Optical Fiber Communications

At present, reliable ambiguity resolution in real-time GPS precise point positioning (PPP) can only be achieved after an initial observation period of a few tens of minutes. In this study, we propose a method where the incoming triple-frequency GPS signals are exploited to enable rapid convergences to ambiguity-fixed solutions in real-time PPP. Specifically, extra-wide-lane ambiguity resolution can be first achieved almost instantaneously with the Melbourne-Wubbena combination observable on L2 and L5. Then the resultant unambiguous extra-wide-lane carrier-phase is combined with the wide-lane carrier-phase on L1 and L2 to form an ionosphere-free observable with a wavelength of about 3.4 m. Although the noise of this observable is around 100 times the raw carrier-phase noise, its wide-lane ambiguity can still be resolved very efficiently, and the resultant ambiguity-fixed observable can assist much better than pseudorange in speeding up succeeding narrow-lane ambiguity resolution. To validate this method, we use an advanced hardware simulator to generate triple-frequency signals and a high-grade receiver to collect 1-Hz data. When the carrier-phase precisions on L1, L2 and L5 are as poor as 1.5, 6.3 and 1.5 mm, respectively, wide-lane ambiguity resolution can still reach a correctness rate of over 99 % within 20 s. As a result, the correctness rate of narrow-lane ambiguity resolution achieves 99 % within 65 s, in contrast to only 64 % within 150 s in dual-frequency PPP. In addition, we also simulate a multipath-contaminated data set and introduce new ambiguities for all satellites every 120 s. We find that when multipath effects are strong, ambiguity-fixed solutions are achieved at 78 % of all epochs in triple-frequency PPP whilst almost no ambiguities are resolved in dual-frequency PPP. Therefore, we demonstrate that triple-frequency PPP has the potential to achieve ambiguity-fixed solutions within a few minutes, or even shorter if raw carrier-phase precisions are around 1 mm. In either case, we conclude that the efficiency of ambiguity resolution in triple-frequency PPP is much higher than that in dual-frequency PPP.

Triple-frequency GPS precise point positioning with rapid ambiguity resolution

Carrier phase measurements are extremely accurate but ambiguous. The reliability of integer ambiguity resolution is improving with Galileo which uses a Binary Offset Carrier (BOC) modulation, large signal bandwidths of up to 50 MHz and additional carrier frequencies.

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Bootstrapping with Multi-frequency Mixed Code Carrier Linear Combinations and Partial Integer Decorrelation in the Presence of Biases

The key to high precision parameter estimation in global navigation satellite system (GNSS) applications is to properly deal with the integer valued carrier-phase ambiguities. The class of integer estimators fixes all ambiguities to integer values. This can also decrease the precision of the estimates of the non-ambiguity parameters, if the fixing is incorrect. The best integer-equivariant (BIE) estimator is optimal in the sense of minimizing the mean-squared error (MSE) of both the ambiguities and the real valued parameters, regardless of the precision of the float solution. However, the BIE estimator comprises a search in the integer space of ambiguities, whose complexity grows exponentially with the number of ambiguities. This search is not feasible for large-scale network solutions. To overcome this problem, a sequential BIE (SBIE) algorithm is proposed, which shows close to optimal performance with only linearly increasing complexity. Numerical simulations are used to verify the performance of the SBIE algorithm.

Sequential Best Integer-Equivariant Estimation for GNSS

The availability of in situ snow water equivalent (SWE), snowmelt and run-off measurements is still very limited especially in remote areas as the density of operational stations and field observations is often scarce and usually costly, labour-intense and/or risky. With remote sensing products, spatially distributed information on snow is potentially available, but often lacks the required spatial or temporal requirements for hydrological applications. For the assurance of a high spatial and temporal resolution, however, it is often necessary to combine several methods like Earth Observation (EO), modelling and in situ approaches. Such a combination was targeted within the business applications demonstration project SnowSense (2015–2018), co-funded by the European Space Agency (ESA), where we designed, developed and demonstrated an operational snow hydrological service. During the run-time of the project, the entire service was demonstrated for the island of Newfoundland, Canada. The SnowSense service, developed during the demonstration project, is based on three pillars, including (i) newly developed in situ snow monitoring stations based on signals of the Global Navigation Satellite System (GNSS); (ii) EO snow cover products on the snow cover extent and on information whether the snow is dry or wet; and (iii) an integrated physically based hydrological model. The key element of the service is the novel GNSS based in situ sensor, using two static low-cost antennas with one being mounted on the ground and the other one above the snow cover. This sensor setup enables retrieving the snow parameters SWE and liquid water content (LWC) in the snowpack in parallel, using GNSS carrier phase measurements and signal strength information. With the combined approach of the SnowSense service, it is possible to provide spatially distributed SWE to assess run-off and to provide relevant information for hydropower plant management in a high spatial and temporal resolution. This is particularly needed for so far non, or only sparsely equipped catchments in remote areas. We present the results and validation of (i) the GNSS in situ sensor setup for SWE and LWC measurements at the well-equipped study site Foret Montmorency near Quebec, Canada and (ii) the entire combined in situ, EO and modelling SnowSense service resulting in assimilated SWE maps and run-off information for two different large catchments in Newfoundland, Canada.

Advances in Snow Hydrology Using a Combined Approach of GNSS In Situ Stations, Hydrological Modelling and Earth Observation—A Case Study in Canada

A key prerequisite for Precise Point Positioning (PPP) with Global Navigation Satellite Systems (GNSS) is the precise knowledge of satellite phase and code biases. This paper proposes a method, that is based on a very general measurement model with an individual phase and code bias for each receiver, satellite and frequency. We compute a recursive least-squares float solution with a Kalman filter, and a subsequent ambiguity fixed solution using Teunissen's Best Integer Equivariant (BIE) estimator. The latter one minimizes the mean squared error (MSE) and, thus, outperforms the well-known Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method. Simulation results show the achievable performance of the BIE estimator in comparison to the LAMBDA method.

Best Integer Equivariant estimation for Precise Point Positioning

Carrier phase measurements are extremely accurate but ambiguous. The reliability of the resolution of this ambiguity is often not sufficient due to the the small carrier wavelength of 19 cm and multipath. There are two options for improving the reliability of integer least-squares estimation: (1) multi-frequencywidelane combinations that increase the wavelength to several meters, and (2) constraints on the length and orientation of the baseline which reduce the size of the search space. This paper focuses on the second aspect, and provides a soft constrained integer least-squares estimator, i.e. a method that uses a priori information on the length and orientation of the baseline to improve the ambiguity resolution and also ensures a sufficient robustness with respect to uncertainties in the a priori information. This opens up new opportunities for applications such as freight stabilization on cranes and helicopters or attitude determination of aircrafts. In all these applications, the length and orientation are constrained but not fixed.This paper suggests two approaches for soft constrained integer least-squares estimation: The first one includes a priori information on the length of the baseline and its orientation (attitude) in the form of Gaussian distributions.The second one includes the a priori information by inequality constraints on the length and orientation. This information could come from physical constraints (e.g. gravity) or other sensors. Both approaches are solved iteratively with the Newton method. The benefit of the a priori information depends on its variance or on the tightness of the inequality constraints. This paper shows that the new methods reduce the probability of wrong fixing with respect to unconstrained integer least squares estimation by more than one order of magnitude even if the a priori information on the length is biased by 1m. The proposed method is evaluated with both simulated and real measurements from PolaRx3G receivers of Septentrio.

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Patrick Henkel

Papers

Bootstrapping with Multi-frequency Mixed Code Carrier Linear Combinations and Partial Integer Decorrelation in the Presence of Biases

Sequential Best Integer-Equivariant Estimation for GNSS

Advances in Snow Hydrology Using a Combined Approach of GNSS In Situ Stations, Hydrological Modelling and Earth Observation—A Case Study in Canada

Best Integer Equivariant estimation for Precise Point Positioning

Integer Ambiguity Resolution with Tight and Soft Baseline Constraints for Freight Stabilization at Helicopters and Cranes