Faster-than-Nyquist signaling (FTNS) has already been shown to increase the communication capacity on certain channels such as additive white Gaussian noise and block flat multiple-input multiple-output (MIMO) Rayleigh fading channels. The following issues, however, remain unresolved: 1) whether FTNS enables a capacity increase in generalized MIMO Rayleigh fading channels that are selective in time, frequency, and space; and 2) how channel selectivities affect the capacity and if present, the FTN capacity gain. To address the issues, this paper firstly investigates the ergodic capacity of MIMO-FTN transmission over triply-selective fading channels. We derive a low-complexity approximate capacity formula and also show how it degenerates in other channel models, such as doubly-selective single-input single-output fading channels, which can be considered as the special cases of triply-selective fading channels. The capacity evaluation results obtained under different channel conditions show that: 1) MIMO-FTN outperforms MIMO-Nyquist in terms of capacity; 2) the FTN gains are nearly consistent, while the FTN gains obtained in the frequency-selective fading channels are slightly higher than those obtained in the flat fading channels.

The application of multiple-input multiple-output (MIMO) over orthogonal time frequency space (OTFS) modulation is envisioned to provide high-data-rate wireless transmission in high-mobility environments. However, in these communication scenarios, the multiple-dimensional interference, which can generate from space, delay and Doppler domains, challenges the channel equalization and symbol detection at the MIMO-OTFS receiver. To tackle this issue, we propose a time-space domain channel equalizer, relying on the mathematical least squares minimum residual algorithm, to remove the channel distortion on data symbols. The proposed channel equalizer adopts a recursion method to achieve symbol estimates, which can realize fast convergence by leveraging the sparsity of MIMO-OTFS channel matrix. Instead of directly remapping the equalized OTFS symbols into data bits, we develop an enhanced data detection (EDD) scheme to iteratively demodulate the superposed multi-antenna signal. The EDD can not only realize the linear-complexity interference cancellation, but also efficiently reap the spatial and multi-path diversities of MIMO-OTFS channel. The simulations show the proposed channel equalization and EDD algorithms enable the MIMO-OTFS receiver to robustly demodulate multi-stream 256-ary quadrature amplitude modulation symbols, under a maximum velocity of 550 km/h at 5.9 GHz carrier frequency.

The state-of-the-art radio-frequency (RF) devices limit the deployment of extremely high-order quadrature amplitude modulation (QAM) formats (e.g., 16384-QAM) to meet the high-capacity demand on microwave backhaul links. This paper turns to faster-than-Nyquist (FTN) transmission using lower-order constellations and lower-cost RF devices as a solution to the demand. To realize low-complexity interference cancellation, we pre-equalize the FTN-induced inter-symbol interference at the transmitter by using Tomlinson-Harashima precoding (THP), while at the receiver suppressing the phase noise (PHN) generated by the RF local oscillators with pilot symbol assisted approaches. However, the THP may distort the pilots, which degrades the performance of PHN compensation. To resolve this problem, we propose two pilot designs that are distortion-free to precisely estimate the PHN samples. Moreover, we derive a closed-form expression of the symbol detection signal-to-noise ratio (SNR), in terms of the THP-FTN waveform parameters. With the SNR expression, a waveform optimization procedure is developed to maximize the SNR and enhance the achievable FTN capacity. The proposed scheme is validated in the simulated platform of 4096-QAM microwave link. The results demonstrate that the FTN signaling achieves the system capacity equivalent to that of the 16384-QAM Nyquist signaling with an SNR gain of 5.8 dB.

Orthogonal time frequency space (OTFS) has shown to be a promising modulation technology that achieves the robust wireless transmission in high-mobility environments. The high mobility incurred Doppler effect in OTFS system, is represented as a continuous and relatively large band in the Doppler frequency. It yields the equivalent channel responses (ECRs) in the system change significantly within one symbol block, posing a challenge to channel estimation (CE) or tracking. In order to tackle this issue, in this paper, a set of transform-domain basis functions is designed to span a low-dimensional subspace for modeling the OTFS channel. Then, the CE can be performed by estimating a few projection coefficients of ECRs in the developed subspace, with training pilots. According to the individual transmission characteristic of OTFS signal, we propose a corner-inserted pilot pattern, which targets the low pilot overhead and satisfactory CE performance. Moreover, an OTFS signal detector, leveraging the time-domain channel equalization, linear-complexity interference cancellation and delay-Doppler domain maximal ratio combining detection, is developed to retrieve the transmitted data symbols. The simulations show the precisely estimated ECRs enable the detector to ideally demodulate 256-ary quadrature amplitude modulation signaling, under a velocity of 550 km/h at 5.9 GHz carrier frequency.

Orthogonal time frequency space (OTFS) is a two-dimensional modulation scheme realized in the delay-Doppler domain, which targets the robust wireless transmissions in high-mobility environments. In such scenarios, OTFS signal suffers from multipath channel with continuous Doppler spread, which results in significant inter-symbol interference and inter-Doppler interference (IDI). In this article, we analyze the interference generation mechanism, and compare statistical distributions of the IDI in two typical cases, i.e., limited-Doppler-shift channel and continuous-Doppler-spread channel (CoDSC). Focusing on the OTFS signal transmission over the CoDSC, our study firstly indicates that the widespread IDI incurs a computational burden for the element-wise detector like the message passing in the state-of-the-art works. Addressing this challenge, we propose a block-wise OTFS receiver by exploiting the structure and characteristics of the OTFS transmission matrix. In the receiver, we deliberately design an iteration strategy among the least squares minimum residual based channel equalizer, reliability-based symbol detector and interference eliminator, which can realize fast convergence by leveraging the sparsity of channel matrix. The simulations demonstrate that, in the CoDSC, the proposed scheme achieves much less detection error, and meanwhile reduces the computational complexity by an order of magnitude, compared with the state-of-the-art OTFS receivers.

Faster-than-Nyquist signaling (FTNS) is capable of improving the spectral efficiency (SE) of communication systems. However, for conventional single-carrier FTNS (SC-FTNS) in which only symbol interval is reduced, the increase of SE is very limited due to the presence of inter-symbol interference (ISI) introduced by the FTNS. To deal with this problem, this paper proposes a new time-frequency compressed SC-FTNS (TFC-SC-FTNS) scheme that includes the conventional FTNS as a special case, to improve the SE via two dimensions simultaneously: time dimension by stacking symbols closer; frequency dimension by precoding to make the FTN signal spectrum more compact. Further, an optimization subject to a spectral mask constraint is performed on the precoder to suppress the ISI, according to a mean-square-error criterion, but the optimization problem is non-convex. A nontrivial contribution in the new scheme is that the non-convex problem is transformed into a convex one by a change of variable and an addition of admissibility constraint. Simulation results demonstrate that the proposed scheme significantly outperforms the conventional FTNS in terms of achievable SE or, equivalently, reception performance at a given SE. Further, with larger constellations applied, the gains of the TFC-FTNS increase.

Faster-than-Nyquist signaling (FTNs) is capable of improving the signaling rate of communication system, while yielding the inter-symbol interference (ISI) complicating the receiver design. However, due to the unavoidable detection performance degradation when compression factor τ drops considerably below the Mazo limit, the achievable gain is limited. In this paper, preceding the FTN modulation, a precoding based data spreading is utilized to introduce an artificial interference, which aims to support a smaller τ that corresponds to achieving a higher capacity, at the cost of detection complexity. Further, we optimize the precoder by minimizing the mean square error (MSE) of the equalizer's output. Meanwhile, the problem is transformed and reformulated as a non-convex quadratically constrained and quadratic programming with one constraint (QCQP-1), where the consensus-alternating directions method of multipliers (ADMM) algorithm is utilized to iteratively pursue the solution. Simulation results justify the proposed scheme, where the capacity of 64-, 128-, and even 256-QAM Nyquist signaling can be achieved by precoding the 16-QAM FTNs, even without SNR loss at bit error rate (BER) of 10-5.