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.

In this paper, we deal with channel estimation for orthogonal frequency-division multiplexing (OFDM) systems. The channels are assumed to be time-varying (TV) and approximated by a basis expansion model (BEM). Due to the time-variation, the resulting channel matrix in the frequency domain is no longer diagonal, but approximately banded. Based on this observation, we propose novel channel estimators to combat both the noise and the out-of-band interference. In addition, the effect of a receiver window on channel estimation is also studied. Our claims are supported by simulation results, which are obtained considering Jakes' channels with fairly high Doppler spreads

We present a block minimum mean-squared error (MMSE) equalizer for orthogonal frequency-division multiplexing (OFDM) systems over time-varying multipath channels. The equalization algorithm exploits the band structure of the frequency-domain channel matrix by means of a band LDL/sup H/ factorization. The complexity of the proposed algorithm is linear in the number of subcarriers and turns out to be smaller with respect to a serial MMSE equalizer characterized by a similar performance.

We introduce an analytical approach to evaluate the error probability of orthogonal frequency-division-multiplexing (OFDM) systems subject to carrier frequency offset (CFO) in frequency-selective channels, characterized by Rayleigh or Rician fading. By properly exploiting the Gaussian approximation of the intercarrier interference (ICI), we show that the bit-error rate (BER) for an uncoded OFDM system with quadrature amplitude modulation (QAM) can be expressed by the sum of a few integrals, whose number depends on the constellation size. Each integral can be evaluated numerically, or, in Rayleigh fading, by using a series expansion that involves generalized hypergeometric functions. Simulation results illustrate that the theoretical analysis is quite accurate, especially for Rayleigh channels, and also with nonlinear amplifiers.

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly) time-varying subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely, the least mean squares (LMS) and the recursive least squares (RLS) adaptive estimation strategies. For both methods, a detailed mean-square analysis illustrates the effect of random sampling on the adaptive reconstruction capability and the steady-state performance. Then, several probabilistic sampling strategies are proposed to design the sampling probability at each node in the graph, with the aim of optimizing the tradeoff between steady-state performance, graph sampling rate, and convergence rate of the adaptive algorithms. Finally, a distributed RLS strategy is derived and is shown to be convergent to its centralized counterpart. Numerical simulations carried out over both synthetic and real data illustrate the good performance of the proposed sampling and reconstruction strategies for (possibly distributed) adaptive learning of signals defined over graphs.