Multirate fast convolution (FC) has recently been introduced as an effective tool for communication waveform processing, especially for advanced multicarrier systems targeting at well-contained spectrum. These include filter bank based multicarrier waveforms and filtered OFDM schemes which are receiving increasing attention in the 5G radio access development. Recalling that the key idea of FC is effective implementation of high-order linear filtering through frequency-domain processing, this paper investigates possibilities to reduce the complexity of FC based waveforms. Special focus is on scenarios where a relatively small part of the bandwidth is in active use, which could be the case, e.g., in low-rate machine-type communication devices. A new variant of fast-convolution filter bank (FC-FB) is developed which uses circular convolution decomposition. The narrowband variant of decomposed structure, called D-FC-FB, achieves significantly reduced complexity, which is proportional to the active bandwidth, while maintaining filtering performance equivalent to FC-FB. Therefore, this variant is considered as a low-complexity solution for low-rate devices. D-FC-FB can be used in any multicarrier scheme that utilizes filtering at subcarrier or resource block level. This paper develops closed-form complexity expressions for the case of filter bank multi-carrier with offset-QAM subcarrier modulation (FBMC/OQAM) demonstrating significant complexity reduction in a case study.
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