基于拉曼努金和的非均匀多载波调制系统

针对高速移动通信，多普勒效应和多径效应导致信道非均匀，提出一种基于拉曼努金和的频谱可调的非均匀调制多载波系统.首先，根据拉曼努金和的正交性和周期性，推导了拉曼努金傅里叶正反变换的完全重建条件，进而建立基于拉曼努金和的多载波调制系统（RFMT，Ramanujan Fourier Multi-Tone system）.由于拉曼努金和的非均匀频谱分布性质及频率共振性质，RFMT在不同载波通道的误比特率不同，可实现对数据的不均等保护.在非均匀信道下RFMT具有优于OFDM的抗多径能力，仿真验证了RFMT的抗多径有效性.在使用迫零均衡算法时，10-5误比特率下，根据信道情况设计的非均匀多载波系统RFMT对E_b/N₀的要求可以比OFDM低4 dB. 

Novel non-uniform multi-tone system based on Ramanujan sums

In the high speed mobile communication systems, the channel is usually a random or jitter of uniform frequency channel because of the fluctuations in speed of moving vehicles and multi-path effect. This fact leads to a study of non-uniform spectrum system. A novel non-uniform multi-tone system based on Ramanujan sums was proposed. First it was proved that the transform pair based on Ramanujan sums can be perfectly reconstructed at some circumstance. Then an efficient realization structure to build a multi-tone system named as Ramanujan Fourier multi-tone system (RFMT) was proposed and simulated in additive white Gaussian noise (AWGN) and multi-path channels. With the help of non-uniform spectrum and diversity character, RFMT can protect different data in different sub-carriers and achieve a 4 dB lower E_b/N₀ than orthogonal frequency division multiplexing (OFDM) in 3-path channel using zero-forcing equalization with bit error rate (BER) 10^-5.