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We compare the maximum achievable rates in single-carrier (SC) and orthogonal frequency-division multiplexing (OFDM) modulation schemes, under the practical assumptions of independent identically distributed finite alphabet inputs and linear intersymbol interference with additive Gaussian noise. We show that the Shamai-Laroia approximation serves as a bridge between the two rates: while it is well known that this approximation is often a lower bound on the SC achievable rate, it is revealed to also essentially upper bound the OFDM achievable rate. We apply information-estimation relations in order to rigorously establish this result for both general input distributions and to sharpen it for commonly used pulse-amplitude modulation (PAM) and quadratic-amplitude modulation constellations. To this end, novel bounds on minimum mean-square error estimation of PAM inputs to a scalar Gaussian channel are derived, which may be of general interest. Our results show that, under reasonable assumptions, optimal SC schemes may offer spectral efficiency significantly superior to that of OFDM, motivating further research of such systems.

Comparison of the Achievable Rates in OFDM and Single Carrier Modulation with I.I.D. Inputs