Time Localization and Capacity of Faster-Than-Nyquist Signaling

In this paper, we consider communication over the bandwidth limited analog white Gaussian noise channel using non-orthogonal pulses. In particular, we consider non-orthogonal transmission by signaling samples at a rate higher than the Nyquist rate. Using the faster-than-Nyquist (FTN) framework, Mazo showed that one may transmit symbols carried by sinc pulses at a higher rate than that dictated by Nyquist without loosing bit error rate. However, as we will show in this paper, such pulses are not necessarily well localized in time. In fact, assuming that signals in the FTN framework are well localized in time, one can construct a signaling scheme that violates the Shannon capacity bound. We also show directly that FTN signals are in general not well localized in time. Therefore, the results of Mazo do not imply that one can transmit more data per time unit without degrading performance in terms of error probability. We also consider FTN signaling in the case of pulses that are different from the sinc pulses. We show that one can use a precoding scheme of low complexity to remove the inter-symbol interference. This leads to the possibility of increasing the number of transmitted samples per time unit and compensate for spectral inefficiency due to signaling at the Nyquist rate of the non sinc pulses. We demonstrate the power of the precoding scheme by simulations

Optical Time-Frequency Packing: Principles, Design, Implementation, and Experimental Demonstration

Time-frequency packing (TFP) transmission provides the highest achievable spectral efficiency with a constrained symbol alphabet and detector complexity. In this work, the application of the TFP technique to fiber-optic systems is investigated and experimentally demonstrated. The main theoretical aspects, design guidelines, and implementation issues are discussed, focusing on those aspects which are peculiar to TFP systems. In particular, adaptive compensation of propagation impairments, matched filtering, and maximum a posteriori probability detection are obtained by a combination of a butterfly equalizer and four 8-state parallel Bahl-Cocke-Jelinek-Raviv (BCJR) detectors. A novel algorithm that ensures adaptive equalization, channel estimation, and a proper distribution of tasks between the equalizer and BCJR detectors is proposed. A set of irregular low-density parity-check codes with different rates is designed to operate at low error rates and approach the spectral efficiency limit achievable by TFP at different signal-to-noise ratios. An experimental demonstration of the designed system is finally provided with five dual-polarization QPSK-modulated optical carriers, densely packed in a 100 GHz bandwidth, employing a recirculating loop to test the performance of the system at different transmission distances.Comment: This paper has been accepted for publication in the IEEE/OSA Journal of Lightwave Technolog

Improving the Spectral Efficiency of Nonlinear Satellite Systems through Time-Frequency Packing and Advanced Processing

We consider realistic satellite communications systems for broadband and broadcasting applications, based on frequency-division-multiplexed linear modulations, where spectral efficiency is one of the main figures of merit. For these systems, we investigate their ultimate performance limits by using a framework to compute the spectral efficiency when suboptimal receivers are adopted and evaluating the performance improvements that can be obtained through the adoption of the time-frequency packing technique. Our analysis reveals that introducing controlled interference can significantly increase the efficiency of these systems. Moreover, if a receiver which is able to account for the interference and the nonlinear impairments is adopted, rather than a classical predistorter at the transmitter coupled with a simpler receiver, the benefits in terms of spectral efficiency can be even larger. Finally, we consider practical coded schemes and show the potential advantages of the optimized signaling formats when combined with iterative detection/decoding.Comment: 8 pages, 8 figure

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

Constrained capacities for faster-than-Nyquist signaling

This paper deals with capacity computations of faster-than-Nyquist (FTN) signaling. It shows that the capacity of FTN is higher than the orthogonal pulse linear modulation capacity for all pulse shapes except the sinc. FTN signals can in fact achieve the ultimate capacity for the signal power spectral density (PSD). The paper lower and upper bounds the FTN capacity under the constraint of finite input alphabet. It is often higher than the capacity for comparable orthogonal pulse systems; sometimes it is superior to all forms of orthogonal signaling with the same PSD

Automatic Trellis Generation for Demodulation of Faster Than Nyquist Signals

Mobile communication has become one of the most important and fast developing technology in the past couple of decades. Future of telecommunication raises a high demand for higher data rate and system capacity. There are plenty of researches taking place across the world to provide a better service. One such research is Faster than Nyquist signaling and it has grabbed the attention of many researchers in the recent past. In digital communication implemented using Nyquist pulses, the pulse rate is upper-bounded by twice the channel bandwidth. Signaling above this rate results in the loss of pulse orthogonality and introduces ISI. However, under certain conditions, it is possible to lose orthogonality and still maintain the same error probability, as Nyquist signaling. This allows time-compression of the transmitted symbols, resulting in a larger data rate than predicted by classic information theory results. The ISI caused by FTN signaling has a trellis structure and the transmitted symbols can be decoded using the Viterbi or BCJR algorithms. In this thesis, we introduce an algorithm that can automatically generate the trellis for any pulse shape, constellation and time-compression factor. we have simulated the FTN system, processed and decoded by the Viterbi decoder using the trellis generated by the proposed algorithm for BPSK and PAM 4 constellations with raised cosine pulses. The simulation results are promising and encourage more research in this direction. We have discussed possible directions this research can be pursued in future work. Overall, the results would indicate that the FTN technology has a significant potential for the next generation wireless communication

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

Successive interference cancellation in multistream faster-than-Nyquist Signaling

In earlier work we have extended Mazo's concept of faster-than-Nyquist signaling to pulse trains that modulate adjacent subcarriers, a method we called two dimensional Mazo signaling. The signal processing is similar to orthogonal frequency division multiplex (OFDM) transmission. Despite pulses that are faster than the Nyquist limit and subcarriers that significantly overlap, the transmission achieves the isolated pulse error performance. In this paper we review the method and test a receiver based on successive interference cancellation. It virtually achieves the matched filter bound

Reduced complexity optimal detection of binary faster-than-Nyquist signaling

In this paper, we investigate the detection problem of binary faster-than-Nyquist (FTN) signaling and propose a novel sequence estimation technique that exploits its special structure. In particular, the proposed sequence estimation technique is based on sphere decoding (SD) and exploits the following two characteristics about the FTN detection problem: 1) the correlation between the noise samples after the receiver matched filter, and 2) the structure of the intersymbol interference (ISI) matrix. Simulation results show that the proposed SD-based sequence estimation (SDSE) achieves the optimal performance of the maximum likelihood sequence estimation (MLSE) at reduced computational complexity. This paper demonstrates that FTN signaling has the great potential of increasing the data rate and spectral efficiency substantially, when compared to Nyquist signaling, for the same bit-error-rate (BER) and signal-to-noise ratio (SNR)