Perfect Reconstruction Conditions and Design of Oversampled DFT-Modulated Transmultiplexers

Abstract

This paper presents a theoretical analysis of oversampled complex modulated transmultiplexers. The perfect reconstruction (PR) conditions are established in the polyphase domain for a pair of biorthogonal prototype filters. A decomposition theorem is proposed that allows it to split the initial system of PR equations, that can be huge, into small independent subsystems of equations. In the orthogonal case, it is shown that these subsystems can be solved thanks to an appropriate angular parametrization. This parametrization is efficiently exploited afterwards, using the compact representation we recently introduced for critically decimated modulated filter banks. Two design criteria, the out-of-band energy minimization and the time-frequency localization maximization, are examined. It is shown, with various design examples, that this approach allows the design of oversampled modulated transmultiplexers, or filter banks with a thousand carriers, or subbands, for rational oversampling ratios corresponding to low redundancies. Some simulation results, obtained for a transmission over a flat fading channel, also show that, compared to the conventional OFDM, these designs may reduce the mean square error.

Multi-carrier modulation analysis and WCP-COQAM proposal

“…Therefore, the waveform design only needs to satisfy a one-dimensional Nyquist condition, e.g., square root raised cosine (SRRC), leaving more room for the signal spectrum improvement as well as the waveform flexibility. The first proposal in this direction dates back from 1971 [8] and it was later known under different acronyms, such as fraction-spaced multi-carrier modulation [9], over-sampled OFDM [10], over-sampled DFT [11], and more recently, it is often denoted as FMT [12]. Aside from the above-mentioned advantages, both FBMC/OQAM and FMT have some weak points.…”

On zero-forcing equalization for short-filtered multicarrier faster-than-Nyquist signaling

“…It is also interesting to mention that causality of the system has not been taken into account in the previous relations for the sake of brevity and without loss of generality in terms of system performance. However, the reader concerned by the topic might refer to [15].…”

Cyclic block filtered multitone modulation

“…In such a case, the implementation complexity may increase significantly. Therefore, the efficient FMT implementation as well as the design of good pulses is an important aspect [6][7][8][9][10].…”