Wavefrom Design in Doubly Dispersive Channel

This paper proposes a method of waveform design in doubly dispersive channel, which has ability of resisting time and frequency interference. The signal experiences dispersion both in time and frequency as it passes through the channel. Quality of communication is affected seriously by time-frequency interference. Weighted Fractional Fourier Transform (WFRFT) is used as time-frequency mathematical tool to solve the problem. When WFRFT is used to describe doubly dispersive channel and generate channel matrix, complex conjugate transposed row vectors of 4-WFRFT weighted matrix are eigenvectors of channel matrix, and channel response in weighted domain is corresponding eigenvalue. Taking advantage of that feature, a method of waveform design is proposed in BPSK and QPSK respectively. Though the signal designed by one complex conjugate transposed row vector of 4-WFRFT weighted matrix has ability of resisting time-frequency interference, small duty cycle and big peak-to-average power ratio (PAPR) is not negligible. To overcome these shortcomings, add several complex conjugate transposed row vectors of 4-WFRFT weighted matrix to be a signal, which enhance the ability of anti-interference. Meanwhile, waveform design happens in the transmitter simplifies the receiver where equalization is not necessary.