  Orthogonal frequency-division multiplexing (OFDM) has been selected as the
basis for the fifth-generation new radio (5G-NR) waveform developments.
However, effective signal processing tools are needed for enhancing the OFDM
spectrum in various advanced transmission scenarios. In earlier work, we have
shown that fast-convolution (FC) processing is a very flexible and efficient
tool for filtered-OFDM signal generation and receiver-side subband filtering,
e.g., for the mixed-numerology scenarios of the 5G-NR. FC filtering
approximates linear convolution through effective fast Fourier transform
(FFT)-based circular convolutions using partly overlapping processing blocks.
However, with the continuous overlap-and-save and overlap-and-add processing
models with fixed block-size and fixed overlap, the FC-processing blocks cannot
be aligned with all OFDM symbols of a transmission frame. Furthermore, 5G-NR
numerology does not allow to use transform lengths shorter than 128 because
this would lead to non-integer cyclic prefix (CP) lengths. In this article, we
present new FC-processing schemes which solve the mentioned limitations. These
schemes are based on dynamically adjusting the overlap periods and
extrapolating the CP samples, which make it possible to align the FC blocks
with each OFDM symbol, even in case of variable CP lengths. This reduces
complexity and latency, e.g., in mini-slot transmissions and, as an example,
allows to use 16-point transforms in case of a 12-subcarrier-wide subband
allocation, greatly reducing the implementation complexity. On the receiver
side, the proposed scheme makes it possible to effectively combine cascaded
inverse and forward FFT units in FC-filtered OFDM processing. Transform
decomposition is used to simplify these computations. Very extensive set of
numerical results is also provided, in terms of radio-link performance and
associated processing complexity.
