This paper analyzes faster-than-Nyquist (FTN) signaling within a consistent framework based on a fixed time-bandwidth product (TBP), resolving potential ambiguities present in finite blocklength analysis. A key feature of FTN is its ability to increase the number of transmitted symbols in a given time and frequency resource, which can lower the rate penalties inherent in short packet communications. We derive tight bounds on the maximum channel coding rate (MCCR) and demonstrate that FTN’s rate gains over Nyquist signaling can be higher in the finite TBP regime than in the asymptotic case. Performance is benchmarked against the theoretical optimum of transmitting prolate spheroidal wave functions, showing that a well-designed FTN system can closely approach this limit. We present practical design criteria, including the optimal time-acceleration factor for maximizing signaling dimensions, an optimized pulse shape that meets strict out-of-band constraints, and a turbo-equalization-based coding scheme that performs near the derived MCCR bounds. These findings establish FTN as a practical and near-optimal technique for enhancing the rate and reliability of latency-constrained communications.

The channel capacity of multicarrier faster-than-Nyquist signaling is investigated. We develop a suitable discrete-time channel model and derive an explicit and interpretable channel capacity formula for the multicarrier faster-than-Nyquist signaling under frequency-selective channels. Fundamental capacity benefits of non-orthogonal information packing over time and frequency are discussed.

We study optimal delivery strategies of one common and K independent messages from a source to multiple users in wireless environments. In particular, two-layered superposition of broadcast/multicast and unicast signals is considered in a downlink multiuser OFDMA system. In the literature and industry, the two-layer superposition is often considered as a pragmatic approach to make a compromise between the simple but suboptimal orthogonal multiplexing (OM) and the optimal but complex fully-layered non-orthogonal multiplexing. In this work, we show that only two-layers are necessary to achieve the maximum sum-rate when the common message has higher priority than the K individual unicast messages, and OM cannot be sum-rate optimal in general. We develop an algorithm that finds the optimal power allocation over the two-layers and across the OFDMA radio resources in static channels and a class of fading channels. Two main use-cases are considered: i) Multicast and unicast multiplexing when K users with uplink capabilities request both common and independent messages, and ii) broadcast and unicast multiplexin when the common message targets receive-only devices and K users with uplink capabilities additionally request independent messages. Finally, we develop a transceiver design for broadcast/multicast and unicast superposition transmission based on LTE-A-Pro physical layer and show with numerical evaluations in mobile environments with multipath propagation that the capacity improvements can be translated into significant practical performance gains compared to the orthogonal schemes in the 3GPP specifications. The impact of real channel estimation is also analyzed and it is shown that significant gains in terms of spectral efficiency or increased coverage area are still available even in the presence of estimation errors and imperfect interference cancellation for the two-layered superposition system.

This paper presents a new framework for designing decentralized rank-1 pre-coders in MIMO interference channel. The proposed pre-coders aim to separate the received signal points corresponding to different bits into distinct clusters at every receiver. This is accomplished by minimizing the overlaps between conditional probability density functions (PDFs) given the sent bits, which is shown to be equivalent to maximizing the weighted Euclidean distance between the signal points. This formulation is shown to be synonymous to minimizing an upper bound to the probability of error or maximizing the approximated Bhattacharya distances of the conditional PDFs. When full channel state information (CSI) is given at all transmitters and receivers, our design is shown to offer significant performance gain over a wide range of SNR when compared to other pre-coder designs in the literature. We also extend our pre-coder design to the case when transmitters only have partial CSI in an arbitrary form. When the partial CSI is given in the form of quantized levels of channel coefficients, our design is shown to retain considerable performance gain as we partition the channel coefficients with finer resolutions.

Faster-than-Nyquist (FTN) signaling has recently emerged as a potential technology for the next generation mobile, long-haul optical, and satellite broadcasting. The fundamental features of the FTN signaling including the number of signaling dimensions, the theoretical capacity limits, and the optimal power allocation can be inferred from the structure of the discrete-time FTN channel matrices. In particular, their eigenvalues are closely related to a function of frequency known as folded-spectrum. This work studies key properties of the FTN channel matrices and the folded-spectrum, and elucidate precise relationships between the two. We then apply the presented properties to provide key insights in to FTN signaling including how many signaling dimensions FTN has access to, qualities of those dimensions, and how fast should the symbol rate be for the FTN signaling.

We consider the concept of faster-than-Nyquist rate (FTN) broadcasting, which nonorthogonally multiplexes more than one user message in the continuous-time domain for transmission over broadcast channels. Two FTN broadcasting approaches, namely, sub-FTN and full-FTN, are considered for broadcasting of K independent messages over K-user continuous time Gaussian broadcast channel. The derived achievable rate regions of the two approaches are shown to be, in general, greater than the capacity region of the optimally coded Nyquist-rate broadcasting using a same modulating pulse. The full-FTN broadcasting provides larger degrees of freedom (capacity pre-log factor) to each user of the broadcast channel while the sub-FTN improves signal-to-interference-plus-noise-ratios of the individual link. The amount of capacity gains in high SNR regime is linearly proportional to excess bandwidth in the modulating pulse used and dependent on FTN signaling rates, channel SNRs, and number of users in the broadcast channel. The simulated sub-FTN and full-FTN broadcast transceivers outperform coded Nyquist-rate systems both in BER performances and in capacity.

The faster-than-Nyquist (FTN) signaling has been of interest in the research literature due to recent advances in pre-coding and equalization techniques allowing practical removal of the intersymbol interference (ISI). Since the structure of ISI is deterministic in the FTN signaling, a data pre-coding at the transmitter to combat ISI is of practical importance. It is shown, however, that such pre-coding in FTN can significantly broaden the transmission spectrum and alter the shape of the power spectral density. In this paper, we analyze the power spectral density of convolutionally pre-coded FTN signals on linear time-invariant channels. We also identify sufficient conditions on the pre-coding coefficients for preventing the spectrum broadening. Simulation results with several pulse shapes are provided which agree with the analysis. The analysis and the simulation show that for many practically used pulses the pre-coded FTN suffers from the spectrum broadening. This suggests that pre-coding in the FTN signaling must be handled with care.

We consider differential MIMO architecture based on Cayley transform (Hassibi and Hochwald, 2002) when the channel state information is available neither at the transmitter nor the receiver. Within this framework, a low complexity iterative receiver is proposed based on a linearly complex space matched filtering signal detection, iterative probabilistic data association (PDA) and turbo equalization. Simulation results on Rayleigh faded MIMO channels illustrate good performances of the designed receiver.