On information theoretic aspects of single- and multi-carrier communications

Abstract

In this paper, we investigate the relation between the quadrature amplitude modulation (QAM) input information rates (IRs) of multi-carrier (MC) and single carrier (SC) systems transmitted over inter-symbol interference (ISI) channels with additive white Gaussian noise (AWGN). In particular, considering uniform power spectrum transmission, we conjecture that, for a given channel impulse response, the IR corresponding to an SC input distribution is higher than that corresponding to an MC input distribution. We give an intuitive justification of our conjecture and confirm it, by means of numerical results, considering two sets of randomly generated channels.

Comparison of OFDM and Ideal SC-DFE Achievable Rates and Performances Without Channel Knowledge at the Transmitter

“…To the best of the authors knowledge, such limitation has been only observed in [10] and [18], and, in parallel, without knowledge of these previous publications, by the authors in [7]. The problem is that [18] misses a detailed explanation and, in [7], [10], although they provide compelling evidence, they do not provide conclusive proofs on the achievable rate comparison.…”

“…However, these papers also show an interesting trend in that the performance gap between such communications schemes becomes smaller and tends to vanish as the modulation order increases and/or the coding rates are kept low. Some numerical examples for specific channels and only for 16-QAM, but without providing any generalization for any channel through an analytical approach, are given in [10] to corroborate such conjecture. In [7], the cutoff rate [11], which is a less tight bound on the achievable rate, is used to analytically compare ideal SC-DFE and OFDM, but is limited for any three tap channel and just for QPSK modulation.…”

“…Particularly, in comparison with the latter, we use the same approach to compare both systems, i.e., we employ the Jensen's inequality [12] analytical tool, but in place of the cutoff rate, we use Shannon's mutual information in this paper. This allows us to achieve a more rigorous and general conclusion applicable to the conjecture presented by [7], [10] is valid for any given channel but only for 4-and 16-QAM schemes. For higher-order modulations, there are some particular cases where the OFDM scheme can present some marginal rate advantage over the ideal SC-DFE system.…”

“…One way to overcome this achievable rate limitation of OFDM is to use a larger cardinality, i.e., a larger M for the same average SNR value so that the best subcarriers can provide a higher rate to compensate the attenuated ones (cf., [7], [10]). However, the question that arises is how the OFDM scheme compares to the ideal SC-DFE.…”

“…We focus our attention in this paper on the ideal SC-DFE scheme, which has no error propagation, since it can achieve the channel capacity under the constraint of a uniform power spectrum at the transmission and Gaussian signaling [7], [9]. In the case of M-ary quadrature amplitude modulation (QAM), this is no longer true and it cannot be said that it is the optimal receiver, despite it outperforms OFDM in the scenarios simulated in [1], [7], [10]. However, these papers also show an interesting trend in that the performance gap between such communications schemes becomes smaller and tends to vanish as the modulation order increases and/or the coding rates are kept low.…”