Transmit/receive pulse-shaping design in BFDM systems over time-frequency dispersive AWGN channel

In this paper, we propose an optimal biorthogonal pulses design for a biorthogonal frequency division multiplexing (BFDM) systems operating on a time-frequency dispersive additive white Gaussian noise (AWGN) channel. The proposed transmit and receive pulse shapes which are expressed as a linear combination of the most localized Hermite waveforms and are therefore well time-frequency localized. We propose a method for designing biorthogonal pulse shapes that maximize the signal-to-interference-and-noise ratio (SINR). We demonstrate that the SINR of the BFDM systems operating over dispersive channels with additive white Gaussian noise converges to the value of signal-to-noise ratio (SNR).