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.

/pdf/probabilistic-constellation-shaping-for-optical-fiber-zv2jhsi78g.pdf

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

Precise Point Positioning (PPP) provides accurate absolute position information without the direct need of measurements from a reference station at the user The current challenge of GPS L1/L2-based PPP is its long convergence time of more than 20 minutes being caused by the need to estimate atmospheric parameters, and the relatively large code noise and multipath errors There are two options to reduce the convergence time of PPP: First, the Galileo wideband signals on E5 and E6 have a much lower code noise than current GPS L1 and L2 pseudoranges Second, the satellite positions and satellite-related biases can be determined much faster and more accurately with optical inter-satellite links supporting ranging, time-transfer and intra-system communication In this paper, we consider both options A joint estimation of the receiver position, receiver clock offset, tropospheric zenith delay, ionospheric slant delays and carrier phase ambiguities is performed with a Kalman filter Orbital errors and pseudo range multipath are also taken into account The float carrier phase ambiguity estimates are mapped to integers using the famous Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) method The simulation results show that an ambiguity fixing and, thereby, a highly-accurate PPP solution, can be achieved consistently within a few epochs This is a quite substantial benefit and could make PPP attractive for numerous applications

Precise Point Positioning for Next-Generation GNSS

Real-Time Kinematic (RTK) positioning with Global Navigation Satellite Systems (GNSS) enables centimeter-level positioning accuracies. However, the small wavelength of the GNSS carrier signals often prevents a reliable ambiguity resolution. This paper proposes a cascaded RTK positioning with multifrequency linear combinations. The combinations are characterized by a large wavelength, which enables a robust ambiguity resolution even in the presence of uncorrected geometric and ionospheric biases at the price of a slightly increased noise level.

/pdf/cascaded-real-time-kinematic-positioning-with-multi-477mbrutha.pdf

Cascaded Real-Time Kinematic Positioning with Multi-Frequency Linear Combinations

Precise point positioning requires precise knowledge of satellite phase biases, satellite position and satellite clock corrections. In this paper, a method for the estimation of these parameters with a global network of multi-frequency reference stations is presented. It includes a clustering of the reference stations. First, individual satellite phase biases, position and clock corrections are derived for each cluster. Subsequently, the solutions of each cluster are combined. We exploit the integer property of the carrier phase ambiguities and perform an integer decorrelation and fixing within each cluster and also in the multi-cluster combination. The performance of the proposed method is analyzed with Galileo measurements on both E1 and E5a of the IGS stations. We defined 16 clusters and obtained satellite phase biases with an accuracy of better than 2 cm.

/pdf/satellite-phase-bias-estimation-with-global-networks-and-1jysiqib6f.pdf

Satellite Phase Bias Estimation with Global Networks and High-Dimensional Integer Ambiguity Fixing

Almanacs are satellite position and clock data of reduced precision, which are transmitted by navigation satellites to fasten signal acquisition. Currently, each satellite is transmitting the almanacs of all satellites independent of the receiver-satellite geometry. This means that the transmission of the complete almanacs takes 12 minutes for GPS. This paper suggests an optimized almanac transmission scheme, which takes the receiver-satellite geometry into account and thereby reduces the number of almanac transmissions for each satellite. The optimization of the subsets of satellites and of the order of transmissions within each subset reduces the number of almanac transmissions from 27 to 8 for Galileo. Moreover, the optimization of the almanacs also enables an approximately two times faster signal acquisition.

Reduction and optimization of almanac transmission for GNSS satellites

The steering of timescales involves a wide range of different algorithms which each deals with different timescale aspects. For instance producing highly accurate time and frequency offset estimations for different prediction intervals or computing reasonable steering values which on the one hand hold time and frequency nearby zero and on the other hand few affect Allan Deviation. In the following, two different steering algorithms are shortly introduced: the method of the National Physical Laboratory of Israel (INPL) [1] and the Least Quadratic Gaussian Control approach [2]. In contrast to the INPL method which corresponds to a parameterized ad-hoc solution of the timescale steering problem, the LQG Control approach which uses Kalman filtered measurements and the solution of the regulator problem as steering implementation is a considerable more complex method. To come up with the answer to the question if the indeep approach of the LQC method is justified the performance of both steering techniques is tested in the situation of a simulated steering against the public frequency standard of the Physikalische Technische Bundesanstalt (PTB).

/pdf/steering-of-the-reference-timescale-for-german-galileo-test-1vnr8flrg1.pdf

Patrick Henkel

Papers

Precise Point Positioning for Next-Generation GNSS

Cascaded Real-Time Kinematic Positioning with Multi-Frequency Linear Combinations

Satellite Phase Bias Estimation with Global Networks and High-Dimensional Integer Ambiguity Fixing

Reduction and optimization of almanac transmission for GNSS satellites

Steering of the Reference Timescale for German Galileo Test Environment