Faster-than-Nyquist System Research Articles

Faster-Than-Nyquist Transmission With Frame-by-Frame Decision-Directed Successive Interference Cancellation

Faster-than-Nyquist (FTN) signaling can improve spectral efficiency and enable high-speed transmission for next-generation communication systems. One of the most significant challenges in FTN transmission is how to remove the inter-symbol interference (ISI). In this paper, we propose a novel decision-directed successive interference cancellation (DDSIC) based on frequency-domain minimum-mean-square-error (MMSE) equalization for practical FTN systems. To reduce the computational complexity, the detection process is performed frame-by-frame in the frequency domain. In addition, we derive the theoretical bit error rate (BER) expression for each iteration in DDSIC as well as the BER lower bound for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary quadrature amplitude modulated FTN systems. The simulation results verify the theoretical analyses and demonstrate that our proposed method enables lower complexity and better performance compared with state-of-the-art methods.

Spatially-Coupled Faster-Than-Nyquist Signaling: A Joint Solution to Detection and Code Design

In this paper, we investigate two important issues of faster-than-Nyquist (FTN) signaling, namely, reduced-complexity detection and code design. Different from previous works, we consider these two issues jointly by designing a scheme that increases the minimum squared Euclidean distance of FTN signaling via repetition coding at a cost of an increased complexity. Furthermore, to reduce the rate loss of the repetition, we adopt the idea of spatially-coupling from coding theory to FTN signaling, and the resultant signaling scheme is therefore referred to as spatially-coupled faster-than-Nyquist (SC-FTN) signaling. The signal of SC-FTN signaling is generated in a continuous manner by interleaving and repeating the coded FTN signals and a graph-based iterative sliding-window detector is applied for signal detection. Both bounding and extrinsic information transfer chart analysis are provided to study the error-floor and convergence performances of SC-FTN signaling. These analyses unveil the intrinsic relationship between error floor, decoding threshold, and detection/decoding complexity, which provides guidelines for the designs of practical systems. Simulation results show that the promising error performance can be achieved with a simple FTN detection, where the bit error rate performance of coded SC-FTN signaling outperforms that of state-of-the-art coded FTN systems and the capacity of Nyquist signaling.

Optimal Option of n-Level Polybinary Transformation in Faster than Nyquist System According to the Time-Packing Factor

According to an in-depth analysis of the relationship among n-level polybinary transformation, the time-packing factor and the performance of the decoding algorithm, we find that the appropriate n-level polybinary transformation can improve the performance of the decoding algorithm within a certain range of the time-packing factor in the Faster than Nyquist (FTN) system. In this paper, we explain the reason that this phenomenon occurs. Based on the above analysis, we propose a modified blind phase search (BPS) algorithm to compensate for phase noise (PN) in the FTN system with an extremely small time-packing factor. As a result, the modified-BPS algorithm can cope with the PN with the linewidth × symbol rate at 1.07 × 10−5, 1.79 × 10−5, 2.86 × 10−5 and 3.57 × 10−5 under a time-packing factor of 0.55, 0.50 and 0.45, respectively. At the same time, the spectrum efficiency (SE) is improved to 3.27 bit/s/Hz, 4 bit/s/Hz and 4.88 bit/s/Hz.

A Transmission Scheme Based on Uniform Shortening LDPC Codes for Performance Improvement in Faster-Than-Nyquist Systems

Faster-than Nyquist (FTN) signaling is a research topic that has been drawing increased attention due to its capability of improving transmission speed without the need of extra bandwidth. However, the deployment of FTN signaling introduces inter-symbol interference (ISI) which severely degrade system performance. Interestingly, even without ISI equalizer, it has been recently shown that the joint application of LDPC codes with FTN signaling can exhibit rather good performance. To further improve the performance of LDPC codes over FTN systems, a transmission scheme that utilizes uniform shortening LDPC codes is proposed in this paper. It was found that their shortening counterpart can provide a coding gain at least 0.4 dB over a wide range of FTN factors compared with FTN systems that employ conventional LDPC codes. Moreover, using LDPC coded ISI-free system as the benchmark, the proposed transmission scheme can possibly provide 43&#x0025; improvement in data rate with rather small performance degradation.

Data-Driven and Model-Driven Joint Detection Algorithm for Faster-Than-Nyquist Signaling in Multipath Channels.

In recent years, Faster-than-Nyquist (FTN) transmission has been regarded as one of the key technologies for future 6G due to its advantages in high spectrum efficiency. However, as a price to improve the spectrum efficiency, the FTN system introduces inter-symbol interference (ISI) at the transmitting end, whicheads to a serious deterioration in the performance of traditional receiving algorithms under high compression rates and harsh channel environments. The data-driven detection algorithm has performance advantages for the detection of high compression rate FTN signaling, but the current related work is mainly focused on the application in the Additive White Gaussian Noise (AWGN) channel. In this article, for FTN signaling in multipath channels, a data and model-driven joint detection algorithm, i.e., DMD-JD algorithm is proposed. This algorithm first uses the traditional MMSE or ZFinear equalizer to complete the channel equalization, and then processes the serious ISI introduced by FTN through the deepearning network based on CNN or LSTM, thereby effectively avoiding the problem of insufficient generalization of the deepearning algorithm in different channel scenarios. The simulation results show that in multipath channels, the performance of the proposed DMD-JD algorithm is better than that of purely model-based or data-driven algorithms; in addition, the deepearning network trained based on a single channel model can be well adapted to FTN signal detection under other channel models, thereby improving the engineering practicability of the FTN signal detection algorithm based on deepearning.

Faster-Than-Nyquist Signaling with Time-Based Receive Transformation

We propose in this paper the time-based receive transformation (TRT), which can be regarded as the time-based version of the decorrelation based receive transformation proposed in Wang (IEEE Wirel Commun Lett 3(3):305–308, 2014), to suppress the inter-block interference (IBI) in the faster-than-Nyquist (FTN) system. We show that TRT can completely eliminate the effect of IBI in the FTN system so that instead of compromising the performance, FTN with TRT can make the achievable rate reach the maximum rate of the FTN system while having acceptable delay and complexity.

Iterative Carrier Frequency Offset Estimation Scheme for Faster-Than-Nyquist Signaling Systems

As a nonorthogonal mode, faster-than-Nyquist (FTN) signaling transmission can effectively improve the spectrum efficiency of a system. However, FTN signaling inevitably causes inter-symbol interference (ISI). The ISI hinders traditional synchronization methods from operating accurately, and this makes the carrier synchronization of FTN systems more complex. To overcome this issue, we propose an iterative carrier frequency offset (CFO) estimation scheme for an FTN signaling system. The proposed CFO estimation scheme consists of two steps: i) a coarse estimation step based on discrete Fourier transform and ii) a fine estimation step based on a golden-section search algorithm. The simulation results show that the mean square error of the proposed scheme is lower than that of the conventional CFO estimation schemes and approaches the Cramer-Rao Bound, which is an optimal estimation performance bound.

Efficient frequency‐domain linear distortion equaliser in faster‐than‐Nyquist systems

Faster-than-Nyquist (FTN) signalling is regarded as a promising technology in satellite communications for the past few years, however, existing inter-symbol interference (ISI) elimination algorithms for FTN signalling cannot eliminate the linear distortion caused by the input-multiplexing and output-multiplexing filters, which are very common in satellite communications. On the strength of the fractionally-spaced equaliser (FSE), the authors propose a precoding-based frequency-domain linear distortion equaliser (PFLDE) to eliminate the above-mentioned linear distortion in FTN systems. On the one hand, by virtue of fast Fourier transform (FFT) and inverse FFT, the proposed PFLDE lends itself naturally to high-throughput parallel architectures, which are quite essential in high throughput satellite communications. On the other hand, the mean square error performance of the proposed PFLDE is superior to that of the existing time-domain FSEs. Furthermore, combining PFLDE with the existing ISI elimination algorithms for FTN signalling, the satisfactory bit error ratio performance can be obtained.

Continuous-variable quantum key distribution based on a faster-than-Nyquist scheme

In previous continuous-variable quantum key distribution (CV-QKD) systems, the transmission rate is limited by the Nyquist criterion. Since the data symbols transmit without intersymbol interference (ISI) under this limitation, how to improve the secret key rate is still a notoriously hard problem. Faster-than-Nyquist (FTN) technology has been viewed as a potential technique in future communication systems, because of its higher spectrum efficiency and faster symbol rate. In this paper, a CV-QKD system based on FTN is proposed. The transmission of an FTN system is simulated, and then we analyze the Mazo limit and the constrained capacities of the system, and finally compare the secret key rate of FTN signals and Nyquist signals. Our proposed scheme is especially beneficial for the high-speed scenario. Simulation results demonstrate that such a CV-QKD system can increase channel capacity and enhance key rate; it can also improve the safe transmission distance of CV-QKD.

Beyond DVB-S2X: Faster-Than-Nyquist Signaling With Linear Precoding

Faster-than-Nyquist (FTN) signaling with linear precoding is investigated as a potential technique to transcend digital video broadcasting-satellite-second generation extension (DVB-S2X). Combining cyclic prefix (CP), cyclic suffix (CS) and discrete Fourier transform (DFT) with existing linear precoding algorithms, such as G-to-minus-half (GTMH) precoding (GTMHP), the CPS-GTMH-DFTP algorithm is proposed to eliminate inter-symbol interference (ISI) for FTN signaling. By comparison with most existing algorithms, our proposed CPS-GTMH-DFTP algorithm requires much lower implementation complexity. Specifically, only two multipliers and the corresponding fast Fourier transform (FFT)/inverse fast Fourier transform (IFFT) operations are required with the proposed CPS-GTMH-DFTP algorithm, which makes our proposed algorithm more suitable for practical implementation. Furthermore, the CPS-GTMH-DFTP algorithm has better bit error rate (BER) performance than most existing precoding algorithms. Simulation results show that even when the time acceleration parameter and roll-off factor equal to 0.75 and 0.35 respectively, our proposed CPS-GTMH-DFTP algorithm can still approach the BER performance of the ISI-free Nyquist signaling for all the modulation types adopted in DVB-S2X. More precisely, with 256-amplitude phase shift keying (APSK), the BER performance degradation is almost 0.03 and 0.01 dB in uncoded and coded FTN systems respectively. As far as we know, with regard to low complexity ISI elimination algorithms for FTN signaling, this is the first time to achieve such excellent performance with a time acceleration parameter 0.75 and a practical roll-off factor 0.35.

Iterative-Detection-Aided Tomlinson-Harashima Precoding for Faster-Than-Nyquist Signaling

Faster-than-Nyquist(FTN) is a promising technique due to higher spectral efficiency, but at a cost of introducing the inter-symbol interference (ISI) which usually requires the computationally demanding detection algorithms. In order to reduce the detection complexity at the receiver, in this paper, a novel Tomlinson-Harashima precoding (THP) scheme is proposed for FTN system. In the conventional THP (CTHP) scheme, the ISI introduced by time-packing can only be diminished from several preceding information symbols, which results in large residual ISI and an unattractive bit-error-rate (BER) performance. Moreover, due to the suboptimal receiver - a simple modulo operation which ignores the correlation between received symbols, CTHP faces obvious capacity loss and is ineffective to execute interference cancellation for FTNS. In this paper, residual ISI of FTNS in CTHP is formulated in detail and modeled mathematically. Further more, an improved THP method with an optimized receiver based on the soft interference cancelation (SIC) algorithm and iterative turbo process is proposed to combat residual ISI for FTNS. Computational complexity analysis and numerical simulation results show that the proposed scheme not only has inexpensive computational cost but also greatly outperforms CTHP and other cited schemes. Moreover, for moderate time-packing, it can approach the ISI-free BER performance boundary and is also competitive to the MAP equalization technique.

MLSE Equalizer With Channel Shortening for Faster-Than-Nyquist Signaling

Faster-than-Nyquist (FTN) signaling by introducing controlled inter-symbol interference (ISI) has been viewed as a potential technique in future communication systems due to its higher spectrum efficiency. In order to achieve the high transmission rate, the effective receivers have to been designed to suppress the ISI and extract the transmit signals. Therefore, we propose a channel shortening-based maximum-likelihood sequence estimation (MLSE) scheme. In this scheme, the length of the shortening channel can be optimized for the different time-squeezing factor, which determines the transmission rate and ISI in FTN systems, to achieve a good tradeoff between the detection performance and the implementation complexity. The simulation analysis results show that the proposed MLSE equalizer with optimized channel shortening can achieve a good tradeoff between the performance and the complexity.

Training sequences design for channel estimation in FTN system using discrete Fourier transform techniques

This study addresses the training sequence design problem for multipath channel estimation in faster-than-Nyquist (FTN) system. The authors process the estimation in the frequency domain and give the search criterion which is only the function of the power spectrum of the training sequence. The optimal sequence according to this criterion is found by using search strategy described in detail in this study and the performance of it is tested by Monte Carlo simulation.

Adaptive detection method of FTN signalling at constant Nyquist sampling rate

Faster-than-Nyquist (FTN) signalling, as a candidate technology of fifth generation, can transmit more data with the same bandwidth. In the adaptive transmission system based on FTN signalling (FNS), the transmitter changes the packing ratios to adapt to the wireless channels. The scheme that combines the adaptive coding and modulation with the FNS has higher spectral efficiency. However, the symbol rate changing with the packing ratio challenges the receiver of adaptive transmission system based on FNS. Moreover, the decoding complexity based on viterbi algorithm (VA) is increasing exponentially when the packing ratios of FNS decrease. In this study, the authors proposed an adaptive detection method to detect FTN signal at constant sampling rate. The proposed method adopted an linear minimum mean square error (LMMSE) equaliser to solve the mismatch of the symbol rate and the sampling rate. Their simulation results show that the adaptive detection method of FNS can approach the optimal bit error rate performance of the coded FTN system. At the same time, the proposed method can avoid the complexity induced by the variable sampling rate in the adaptive transmission system based on FNS.

Faster-than-Nyquist signaling: on linear and non-linear reduced-complexity turbo equalization

In the framework of digital video broadcasting by satellite-second generation (DVB-S2), we analyze a faster-than-Nyquist (FTN) system based on turbo equalization and low-density parity-check (LDPC) codes. Truncated maximum a posteriori and minimum mean square error equalizers provide a reduced-complexity implementation of the FTN system. On the other hand, LDPC codes allow us to demonstrate attractive performance results over an additive white Gaussian noise channel while increasing spectral efficiency beyond the Nyquist rate and keeping a complexity comparable to that of a current DVB-S2 modem.

Novel Intersymbol Interference Cancellation Scheme to Enable Parallel Computational and High-Performance Faster-Than-Nyquist Signaling

In this paper, we deal with the intersymbol interference (ISI) cancellation problem induced by the faster-than-Nyquist (FTN) signaling. In the traditional FTN signaling, the detection delay at the receiver depends on the number of states of the ISI trellis. In this case, the corresponding Viterbi algorithm or the BCJR algorithm would be far too complex and introduce a huge delay when the ISI tap set is large. In this paper, we propose a novel interference cancellation scheme to combat the ISI for the FTN communication system which enables the parallel computations. Our proposed scheme adopts a pre-coding at the transmitter and a decomposition detection at the receiver. Particularly, with the help of the parallel computations, the running time of our proposed scheme is independent of the ISI trellis, which allows the application of a more severe FTN system with a smaller time acceleration factor. Besides, based on the pre-coding scheme and the decomposition detection, an adaptive transmission strategy is developed, which can improve the performance of the proposed scheme dramatically. Finally, we compare our scheme with the offset BCJR algorithm and the offset Viterbi algorithm benchmarks. The simulation results verify that our scheme can outperform previous decoders with a better bit error rate and a much less delay.

Faster Than Nyquist Transmission With Multiple Turbo-Like Codes

The performance of turbo-like codes highly depends on their frame size and thus, the bit error rate (BER) performance of turbo-like codes can be improved by increasing the frame size. Unfortunately, increasing the frame size induces some drawbacks such as the increase of transmission and decoding latencies. On the other hand, faster than Nyquist (FTN) transmitter transmits modulated symbols at a rate higher than the Nyquist rate and thus, inter-symbol interference (ISI) is introduced. In this letter, we propose an FTN system with multiple turbo-like codes. In the proposed scheme, an information frame is divided into subframes and the subframes are encoded independently by multiple turbo-like encoders before being presented at an FTN modulator. Due to the ISI induced within the FTN modulator, the code frames generated by the multiple turbo-like encoders are combined and act as a larger code frame. Compared with conventional coded FTN schemes, the proposed scheme not only improves the BER performance but also reduces the decoding latency.

Method of timing estimation for FTN signalling with high‐order modulation

In the digital communications, due to the timing-offset existing between the transmitter and receiver, timing synchronisation is a critical problem which may have dramatic effect on the transmission performance in the faster-than-Nyquist (FTN) signalling system. For solving this problem, considering the intentionally intersymbol interference introduced by FTN, a new non-data aided timing-delay estimation scheme is proposed. Moreover, the proposed method can be also applied into the M-ary quadrature amplitude modulation. In the end, the performance of the proposed scheme for FTN system is tested and verified.

Multicarrier Faster-Than-Nyquist Transceivers: Hardware Architecture and Performance Analysis

This paper evaluates the hardware aspects of multicarrier faster-than-Nyquist (FTN) signaling transceivers. The choice of time-frequency spacing of the symbols in an FTN system for improved bandwidth efficiency is targeted towards efficient hardware implementation. This work proposes a hardware architecture for the realization of iterative decoding of FTN multicarrier modulated signals. Compatibility with existing systems has been considered for smooth switching between the faster-than-Nyquist and orthogonal signaling schemes. One such being the use of fast Fourier transforms (FFTs) for multicarrier modulation. The performance of the fixed point model is very close to that of the floating point representation. The impact of system parameters such as number of projection points, time-frequency spacing, finite wordlengths and their design tradeoffs for reduced complexity iterative decoders in FTN systems have been investigated. The FTN decoder has been designed and synthesized in both 65 nm CMOS and FPGA. From the hardware resource usage numbers it can be concluded that FTN signaling can be used to achieve higher bandwidth efficiency with acceptable complexity overhead.