We study quasi-spatially periodic signals (QSPSs) as a class of input signals of interest, which maintain their shapes quasi-periodically (with a phase change and a time shift) during propagation in an optical fibre. Instead of the computationally expensive nonlinear Fourier transform (NFT), the property of quasi-periodic shape invariant could be used as an alternative for decoding at the receiver. In this paper, properties of QSPSs and the signal design problem are studied, including the trade-off between various system parameters.