Fifth-generation (5G) cellular communications promise to deliver the gigabit experience to mobile users, with a capacity increase of up to three orders of magnitude with respect to current long-term evolution (LTE) systems. There is widespread agreement that such an ambitious goal will be realized through a combination of innovative techniques involving different network layers. At the physical layer, the orthogonal frequency division multiplexing (OFDM) modulation format, along with its multiple-access strategy orthogonal frequency division multiple access (OFDMA), is not taken for granted, and several alternatives promising larger values of spectral efficiency are being considered. This article provides a review of some modulation formats suited for 5G, enriched by a comparative analysis of their performance in a cellular environment, and by a discussion on their interactions with specific 5G ingredients. The interaction with a massive multiple-input, multiple-output (MIMO) system is also discussed by employing real channel measurements.

We present two new iterative decoding algorithms for channels affected by strong phase noise and compare them with the best existing algorithms proposed in the literature. The proposed algorithms are obtained as an application of the sum-product algorithm to the factor graph representing the joint a posteriori probability mass function of the information bits given the channel output. In order to overcome the problems due to the presence in the factor graph of continuous random variables, we apply the method of canonical distributions . Several choices of canonical distributions have been considered in the literature. Well-known approaches consist of discretizing continuous variables or treating them as jointly Gaussian, thus obtaining a Kalman estimator. Our first new approach, based on the Fourier series expansion of the phase probability density function, yields better complexity/performance tradeoff with respect to the usual discretized-phase method. Our second new approach, based on the Tikhonov canonical distribution, yields near-optimal performance at very low complexity and is shown to be much more robust than the Kalman method to the placement of pilot symbols in the coded frame. We present numerical results for binary LDPC codes and LDPC-coded modulation, with particular reference to some phase-noise models and coded-modulation formats standardized in the next-generation satellite Digital Video Broadcasting (DVB-S2). These results show that our algorithms achieve near-coherent performance at very low complexity without requiring any change to the existing DVB-S2 standard.

Many recent works in the literature declare that Orthogonal Time-Frequency-Space (OTFS) modulation is a promising candidate technology for high mobility communication scenarios. However, a truly fair comparison with its direct concurrent and widely used Orthogonal Frequency-Division Multiplexing (OFDM) modulation has not yet been provided. In this paper, we present such a fair comparison between the two digital modulation formats in terms of achievable communication rate. In this context, we explicitly address the problem of channel estimation by considering, for each modulation, a pilot scheme and the associated channel estimation algorithm specifically adapted to sparse channels in the Doppler-delay domain, targeting the optimization of the pilot overhead to maximize the overall achievable rate. In our achievable rate analysis we consider also the presence of a guard interval or cyclic prefix. The results are supported by numerical simulations, for different time-frequency selective channels including multiple scattering components and under non-perfect channel state information resulting from the considered pilot schemes. This work does not claim to establish in a fully definitive way which is the best modulation format, since such choice depends on many other features which are outside the scope of this work (e.g., legacy, intellectual property, ease and know-how for implementation, and many other criteria). Nevertheless, we provide the foundations to properly compare multi-carrier communication systems in terms of their information theoretic achievable rate potential, within meaningful and sensible assumptions on the channel models and on the receiver complexity (both in terms of channel estimation and in terms of soft-output symbol detection).

We investigate the spectral efficiency, achievable by a low-complexity symbol-by-symbol receiver, when linear modulations based on the superposition of uniformly time- and frequency-shifted replicas of a base pulse are employed. Although orthogonal signaling with Gaussian inputs achieves capacity on the additive white Gaussian noise channel, we show that, when finite-order constellations are employed, by giving up the orthogonality condition (thus accepting interference among adjacent signals) we can considerably improve the performance, even when a symbol-by-symbol receiver is used. We also optimize the spacing between adjacent signals to maximize the achievable spectral efficiency. Moreover, we propose a more involved transmission scheme, consisting of the superposition of two independent signals with suitable power allocation and a two-stage receiver, showing that it allows a further increase of the spectral efficiency. Finally, we show that a more involved equalization algorithm, based on soft interference cancellation, allows to achieve an excellent bit-error-rate performance, even when error-correcting codes designed for the Gaussian-noise limited channel are employed, and thus does not require a complete redesign of the coding scheme.

The problem of noncooperative resource allocation in multicell uplink orthogonal frequency division multiple access (OFDMA) systems is considered in this paper. Noncooperative games for subcarrier allocation and transmit power control are considered, aiming at maximizing the users' SINRs and, most notably, the users' energy efficiency, measured in bit/Joule and representing the number of error-free delivered bits for each Joule of energy used for transmission. The theory of potential games is used to come up with several noncooperative games admitting Nash equilibrium points. Since the proposed resource allocation games exhibit a computational complexity that may be in some cases prohibitive, approximate, reduced-complexity, implementations are also considered. For comparison purposes, some considerations on social-optimum solutions are also discussed. Numerical results confirm that the proposed resource allocation schemes are effective in increasing the network energy efficiency (as compared to rate-maximizing schemes), thus permitting to optimize the use of the energy stored in the battery. Moreover, the proposed approximate implementations exhibit a performance very close to that of the exact procedures.