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Orthogonal frequency-division multiplexing (OFDM) has been selected as thebasis for the fifth-generation new radio (5G-NR) waveform developments.However, effective signal processing tools are needed for enhancing the OFDMspectrum in various advanced transmission scenarios. In earlier work, we haveshown that fast-convolution (FC) processing is a very flexible and efficienttool for filtered-OFDM signal generation and receiver-side subband filtering,e.g., for the mixed-numerology scenarios of the 5G-NR. FC filteringapproximates 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 processingmodels with fixed block-size and fixed overlap, the FC-processing blocks cannotbe aligned with all OFDM symbols of a transmission frame. Furthermore, 5G-NRnumerology does not allow to use transform lengths shorter than 128 becausethis would lead to non-integer cyclic prefix (CP) lengths. In this article, wepresent new FC-processing schemes which solve the mentioned limitations. Theseschemes are based on dynamically adjusting the overlap periods andextrapolating the CP samples, which make it possible to align the FC blockswith each OFDM symbol, even in case of variable CP lengths. This reducescomplexity 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 subbandallocation, greatly reducing the implementation complexity. On the receiverside, the proposed scheme makes it possible to effectively combine cascadedinverse and forward FFT units in FC-filtered OFDM processing. Transformdecomposition is used to simplify these computations. Very extensive set ofnumerical results is also provided, in terms of radio-link performance andassociated processing complexity.

Frequency-Domain Signal Processing for Spectrally-Enhanced CP-OFDM Waveforms in 5G New Radio