Frequency Domain Multi-Carrier Modulation Based on Prolate Spheroidal Wave Functions

Abstract

A novel frequency domain multi-carrier modulation (MCM-FD) scheme is proposed based on prolate spheroidal wave functions (PSWFs) for reducing the high complexity in the conventional time domain PSWFs multi-carrier modulation (MCM-PSWFs-TD) schemes. By constructing the relationship between discrete representation and exponential function representation of MCM-PSWFs-TD signals, it can be observed that the orthogonality and parity symmetry of the waveforms of PSWFs in the frequency domain are the same as that in the time domain. Thus, the PSWFs signal can be divided into two groups based on their parity symmetry, while these two groups of PSWFs signals can be processed simultaneously. Based on this concept, signal waveforms with only half spectrum range are invoked in the process of information loading and signal detection for reducing the number of sampling points participated in the signal operation. Compared to the MCM-PSWFs-TD scheme, the proposed MCM-PSWFs-FD scheme is capable of significantly reducing the computational complexity without severely degrading the system performance, such as spectral efficiency (SE), bit error rate performance, signal energy concentration and peak-to-average power ratio (PAPR). Furthermore, the cyclic-prefix orthogonal frequency division multiplexing (CP-OFDM), OFDM with weighted overlap and add (WOLA-OFDM), filter OFDM (F-OFDM), universal filtered multi-carrier (UFMC), as well as the filter bank multi-carrier with offset quadrature amplitude modulation (FBMC-OQAM) are also demonstrated as benchmarks. Simulation results are provided for illustrating that the proposed MCM-PSWFs-FD scheme is capable of striking a favorable tradeoff between the computational complexity and the system performance (i.e. SE, out-of-band energy leakage, adjacent frequency band interference, and PAPR), while the signal waveform design of the MCM-PSWFs-FD scheme is also more concise and flexible than the benchmarks.

Keywords

• Prolate spheroidal wave functions
• multi-carrier modulation
• waveform design
• time-frequency resource allocation
• spectral efficiency