Non-Orthogonal Frequency-Division Multiplexing Based on Eigenvalue Decomposition

This paper proposes a novel ultra-dense non-orthogonal frequency-division multiplexing (NOFDM) transmission, where subcarrier spacing is set significantly lower than that of OFDM. Eigenvalue-decomposition-aided precoding is conceived for eliminating the detrimental effects of NOFDM-specific inter-carrier interference and correlated noises. The classic capacity formula is extended to that supporting our precoded NOFDM scheme. Optimal power allocation (PA) is developed for maximizing the derived capacity of the proposed scheme. In analytical and numerical results, we demonstrate that the proposed NOFDM scheme with optimal PA outperforms the conventional NOFDM and the classic OFDM schemes.

I. Introduction

Non-orthogonal resource allocation in the frequency domain has been developed in several different contexts, such as non-orthogonal frequency-division multiplexing (NOFDM) [1],[2], generalized frequency-division multiplexing (GFDM) [3], and spectrally efficient frequency-division multiplexing (SEFDM) [4],[5], in contrast to the classic orthogonal frequency-division multiplexing (OFDM) counterpart [6]. In NOFDM, by allowing the introduction of inter-carrier interference (ICI) between non-orthogonally overlapped subcarriers, further flexible resource allocation becomes realistic. In addition to the scenario of microwave communications, NOFDM was experimentally investigated in the context of the optical fiber communications [7],[8], the visible light communications [9], and the E-band wireless transmission [10]. In [11], the precoded NOFDM scheme was presented for decoupling ICI effects between substreams, while any power allocation (PA) onto each substream is not incorporated. However, information-theoretic analysis of the explicit merits attained by NOFDM has not been well investigated. The only exception is that constituted in [12], where the potential capacity gain of NOFDM was shown without any precoding and PA.