In this paper, the design and analysis of a new bandwidth-efficient signalling method over the bandlimited intensity-modulated direct-detection (IM/DD) channel is proposed. The channel can be modeled as a bandlimited channel with nonnegative input and additive white Gaussian noise. Due to the nonnegativity constraint, the methods previously proposed for conventional bandlimited channels cannot be applied here. We propose a method to transmit without intersymbol interference in a narrower bandwidth compared to previous works, by combining Nyquist pulses with a constant bias. In fact, we can transmit with a bandwidth equal to that of coherent transmission. A trade-off between the required average optical power and the bandwidth is investigated. At low bandwidths, the most power-efficient transmission is obtained by either the parametric linear pulse or the so-called 'better than Nyquist' pulse, depending on the exact bandwidth.
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