Low-Complexity Detection of High-Order QAM Faster-than-Nyquist Signaling

Faster-than-Nyquist (FTN) signaling is a promising non-orthogonal transmission technique to considerably improve the spectral efficiency. This paper presents the first attempt in the literature to estimate the transmit data symbols of any high-order quadrature amplitude modulation (QAM) FTN signaling in polynomial time complexity. In particular, we propose a generalized approach to model the finite alphabet of any high-order QAM constellation as a high degree polynomial constraint. Then, we formulate the high-order QAM FTN signaling sequence estimation problem as a non-convex optimization problem. As an example of a high-order QAM, we consider 16-QAM FTN signaling and then transform the high degree polynomial constraint, with the help of auxiliary variables, to multiple quadratic constraints. Such transformation allows us to propose a generalized approach semidefinite relaxation (SDR)- based sequence estimation (GASDRSE) technique to efficiently provide a sub-optimal solution to the NP-hard non-convex FTN detection problem, with polynomial time complexity. For the particular case of 16-QAM FTN signaling,

Time-Frequency Packing for High Capacity Coherent Optical Links

We consider realistic long-haul optical links, with linear and nonlinear impairments, and investigate the application of time-frequency packing with low-order constellations as a possible solution to increase the spectral efficiency. A detailed comparison with available techniques from the literature will be also performed. We will see that this technique represents a feasible solution to overcome the relevant theoretical and technological issues related to this spectral efficiency increase and could be more effective than the simple adoption of high-order modulation formats.Comment: 10 pages, 9 figures. arXiv admin note: text overlap with arXiv:1406.5685 by other author

Sub-Nyquist Field Trial Using Time Frequency Packed DP-QPSK Super-Channel Within Fixed ITU-T Grid

Sub-Nyquist time frequency packing technique was demonstrated for the first time in a super channel field trial transmission over long-haul distances. The technique allows a limited spectral occupancy even with low order modulation formats. The transmission was successfully performed on a deployed Australian link between Sydney and Melbourne which included 995 km of uncompensated SMF with coexistent traffic. 40 and 100 Gb/s co-propagating channels were transmitted together with the super-channel in a 50 GHz ITU-T grid without additional penalty. The super-channel consisted of eight sub-channels with low-level modulation format, i.e. DP-QPSK, guaranteeing better OSNR robustness and reduced complexity with respect to higher order formats. At the receiver side, coherent detection was used together with iterative maximum-a-posteriori (MAP) detection and decoding. A 975 Gb/s DP-QPSK super-channel was successfully transmitted between Sydney and Melbourne within four 50GHz WSS channels (200 GHz). A maximum potential SE of 5.58 bit/s/Hz was achieved with an OSNR=15.8 dB, comparable to the OSNR of the installed 100 Gb/s channels. The system reliability was proven through long term measurements. In addition, by closing the link in a loop back configuration, a potential SE*d product of 9254 bit/s/Hz*km was achieved

Reduced Receivers for Faster-than-Nyquist Signaling and General Linear Channels

Fast and reliable data transmission together with high bandwidth efficiency are important design aspects in a modern digital communication system. Many different approaches exist but in this thesis bandwidth efficiency is obtained by increasing the data transmission rate with the faster-than-Nyquist (FTN) framework while keeping a fixed power spectral density (PSD). In FTN consecutive information carrying symbols can overlap in time and in that way introduce a controlled amount of intentional intersymbol interference (ISI). This technique was introduced already in 1975 by Mazo and has since then been extended in many directions. Since the ISI stemming from practical FTN signaling can be of significant duration, optimum detection with traditional methods is often prohibitively complex, and alternative equalization methods with acceptable complexity-performance tradeoffs are needed. The key objective of this thesis is therefore to design reduced-complexity receivers for FTN and general linear channels that achieve optimal or near-optimal performance. Although the performance of a detector can be measured by several means, this thesis is restricted to bit error rate (BER) and mutual information results. FTN signaling is applied in two ways: As a separate uncoded narrowband communication system or in a coded scenario consisting of a convolutional encoder, interleaver and the inner ISI mechanism in serial concatenation. Turbo equalization where soft information in the form of log likelihood ratios (LLRs) is exchanged between the equalizer and the decoder is a commonly used decoding technique for coded FTN signals. The first part of the thesis considers receivers and arising stability problems when working within the white noise constraint. New M-BCJR algorithms for turbo equalization are proposed and compared to reduced-trellis VA and BCJR benchmarks based on an offset label idea. By adding a third low-complexity M-BCJR recursion, LLR quality is improved for practical values of M. M here measures the reduced number of BCJR computations for each data symbol. An improvement of the minimum phase conversion that sharpens the focus of the ISI model energy is proposed. When combined with a delayed and slightly mismatched receiver, the decoding allows a smaller M without significant loss in BER. The second part analyzes the effect of the internal metric calculations on the performance of Forney- and Ungerboeck-based reduced-complexity equalizers of the M-algorithm type for both ISI and multiple-input multiple-output (MIMO) channels. Even though the final output of a full-complexity equalizer is identical for both models, the internal metric calculations are in general different. Hence, suboptimum methods need not produce the same final output. Additionally, new models working in between the two extremes are proposed and evaluated. Note that the choice of observation model does not impact the detection complexity as the underlying algorithm is unaltered. The last part of the thesis is devoted to a different complexity reducing approach. Optimal channel shortening detectors for linear channels are optimized from an information theoretical perspective. The achievable information rates of the shortened models as well as closed form expressions for all components of the optimal detector of the class are derived. The framework used in this thesis is more general than what has been previously used within the area

Next-generation long-haul optical links: Higher spectral efficiency through time-frequency packing

We consider realistic long-haul optical links, where nonlinear effects represent the main impairment, and investigate the application of time-frequency packing with low-order constellations as a the most viable solution to increase the spectral efficiency. We will see that this technique allows to overcome the relevant theoretical and technological issues related to this spectral efficiency increase and is more effective than the simple adoption of high-order modulation formats which are more sensitive to nonlinear effects