Computationally efficient modulation of well-localised signals for OFDM

Mitigation of inter-carrier (ICI) and inter-symbol interference (ISI) in the systems based on Orthogonal Frequency Division Multiplexing (OFDM) has been a popular research topic already for several decades. Utilisation of signal bases with ameliorated time-frequency (TF) localisation is one of the methods to increase interference robustness. However, this approach results in more complicated signal processing. In this paper we theoretically derive and formulate computationally efficient algorithms for modulation of discrete finite-dimensional signals constructed from well-localised bases. These results can be used directly for software implementation. In addition, we present the comparison of computing load for straightforward matrix multiplication, for developed algorithm and for Fast Fourier Transform (FFT) used in OFDM. This study shows that the number of operations can be significantly reduced allowing signal processing with a great number of sub-carriers and time shifts in a reasonable time.