Time-Frequency Localization optimization of PR FMT: Case of an overlapping factor equal to 2

Abstract

In this paper, we analyze the perfect reconstruction property of Filtered MultiTone (FMT) systems with overlapping factor equal to 2. If small overlapping factors are not common for FMT systems that originally targeted nearly perfect subchannels isolation, we show that they can provide pretty good results when the optimization is carried out with the Time-Frequency Localization (TFL) criterion. Furthermore, it appears that the TFL criterion can ease the treatment of the PR equations. In this respect, our study exhibits nearly optimal TFL results and also leads to a simple and interesting closed form expression for the PR FMT prototype filter coefficients. Numerical results and illustrations are also provided showing the good behavior of our proposed design method in terms of TFL performance and computational complexity.dual RRC (dRRC) [3], this waveform is nearly optimal when considering the Time-Frequency Localization (TFL) criterion.Since the mid-nineties and a famous publication about Coded OFDM systems [4], the TFL criterion is considered as a highly relevant objective function for the design of multicarrier (MC) systems for transmission over time and frequency dispersive channels. Furthermore, as it naturally leads to compact waveforms in time and frequency, for a given transmission performance, the resulting computational complexity is relatively low. In [3], we provided Optimal TFL (OTFL) windows with duration limited, as also the case for WOLA-OFDM, to one CP-OFDM symbol, i.e. an overlapping factor equal to 1. Such a short time window can be also considered as the prototype filter for Filtered MultiTone (FMT) systems satisfying the Perfect Reconstruction (PR) property. With this PR FMT scheme, differently from the original FMT system [5], there is no overlapping in time but in frequency. So this MC system also received other names as, for instance, Weighted Cyclic Prefix (WCP)-OFDM in [6] or Pulse-Shaped OFDM in [7]. Here, for simplicity, we keep the FMT denomination for all these types of MC systems in which waveform overlapping may occur in time and/or in frequency. As recalled in [7], even if the shortest windows are preferred for the enhanced mobile broadband (eMBB) service, given the large extent of other envisioned services in 5G, the requirements may vary accordingly and waveform constraints too. For instance, massive Machine Type Communication (mMTC) does not necessarily require short packet transmission and then longer waveforms are of interest if they can bring some improvements. In this sense, in this paper, we propose a new FMT system with a prototype filter the length of which has a duration equal to two MC symbols,i.e. an overlapping factor equal to 2.Denoting by M its number of subcarriers and N its expansion/decimation factor, that means we focus on the design of a prototype filter with length L = 2N . We also constrain this FMT system to fulfill the PR property. As the Spectral Efficiency (SE) is a key parameter for transmission systems, this has resulted sometimes before to only consider...