Orthogonal frequency-division multiplexing (OFDM) has been selected as a baseline waveform for long-term evolution (LTE) and fifth-generation new radio (5G NR). Fast-convolution (FC)-based frequency-domain signal processing has been recently considered as an effective tool for transmitter and receiver side subband filtering of OFDM-based waveforms. However, for the original continuous FC-based model, the filtering can, in general, be configured in time-direction only with the granularity of half subframe, corresponding to 7, 14, or 28 symbols with 15kHz, 30kHz, or 60kHz subcarrier spacing, respectively. In this paper, we present a symbol-synchronous FC-processing scheme flexibly allowing filter re-configuration with the time resolution equal to one OFDM symbol while supporting tight carrier-wise filtering for 5G NR in mixed-numerology scenarios with adjustable subcarrier spacings, center frequencies, and subband bandwidths, as well as providing co-existence with LTE. Proposed approach segments each stream of time-domain OFDM symbols into overlapping processing blocks of fixed size. Symbol synchronous processing is achieved by dynamically adjusting the overlap between the processing blocks while aligning the payload part of the processing blocks with the boundaries of the OFDM symbols. The proposed scheme is demonstrated to support the envisioned use cases of 5G NR and provide a flexible starting point for sixth generation (6G) development.

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 or avoid 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, leading to significantly reduced implementation complexity in various transmission scenarios. A very extensive set of numerical results is also provided, in terms of the radio-link performance and associated processing complexity.

In cyclic-prefix orthogonal frequency-division multiplexing (CP-OFDM)-based radio access, the coexistence of different technologies without precise time-frequency synchronization is limited due to high out-of-band (OOB) emissions. Therefore, the spectrum enhancement techniques play a key role in relaxing the synchronization and power control requirements. This allows a higher degree of opportunistic spectrum use with minimized interference. In addition, all the transmitting devices have to fulfill specific transmitted signal quality requirements, including the maximum OOB radiated signal power. With the orthogonal frequency-division multiplexing (OFDM)-based radio access, some additional signal processing for improved spectrum containment is commonly needed to achieve these requirements. The filtering and time-domain windowing are two fundamentally different approaches for spectrum enhancement. The filtered OFDM (F-OFDM) provides better spectrum localization than the time-windowing schemes [such as windowed overlap-add (WOLA)], with the cost of higher complexity. This article introduces low-complexity solutions for spectrally enhanced narrowband OFDM transmitters based on the use of lookup tables (LUTs). The proposed LUT approach, requiring only memory units and a low number of additions, allows to avoid all computationally expensive operations in online transmitter processing, as it builds the transmitted signal by summing the stored partial waveforms optimized offline. In certain cases, completely multiplication- and summation-free designs are possible. The transmitters of narrowband Internet of Things (NB-IoT) devices are natural applications for the proposed LUT approach, as they require additional digital baseband signal processing to reach the emission requirements. It is shown that the proposed LUT schemes can provide significant savings in real-time computations of NB-IoT devices, while fulfilling the 3GPP requirements.

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.

This paper investigates the application of fast-convolution (FC) filtering schemes for flexible and effective waveform generation and processing in the fifth generation (5G) systems. FC-based filtering is presented as a generic multimode waveform processing engine while, following the progress of 5G new radio standardization in the Third-Generation Partnership Project, the main focus is on efficient generation and processing of subband-filtered cyclic prefix orthogonal frequency-division multiplexing (CP-OFDM) signals. First, a matrix model for analyzing FC filter processing responses is presented and used for designing optimized multiplexing of filtered groups of CP-OFDM physical resource blocks (PRBs) in a spectrally well-localized manner, i.e., with narrow guardbands. Subband filtering is able to suppress interference leakage between adjacent subbands, thus supporting independent waveform parametrization and different numerologies for different groups of PRBs, as well as asynchronous multiuser operation in uplink. These are central ingredients in the 5G waveform developments, particularly at sub-6-GHz bands. The FC filter optimization criterion is passband error vector magnitude minimization subject to a given subband band-limitation constraint. Optimized designs with different guardband widths, PRB group sizes, and essential design parameters are compared in terms of interference levels and implementation complexity. Finally, extensive coded 5G radio link simulation results are presented to compare the proposed approach with other subband-filtered CP-OFDM schemes and time-domain windowing methods, considering cases with different numerologies or asynchronous transmissions in adjacent subbands. Also the feasibility of using independent transmitter and receiver processing for CP-OFDM spectrum control is demonstrated

This paper investigates the use of effective and flexible fast-convolution (FC) implementation for two main types of filter bank multicarrier (FBMC) waveforms, FBMC/OQAM and filtered multitone (FMT). The generated waveforms are spectrally well-contained, with very small power leakage to adjacent frequencies, and are thus good candidates for opportunistic and heterogeneous spectrum use scenarios. On the receiver side, the FC filter bank (FC-FB) approach can be used for simultaneously processing multiple channels with individually tunable bandwidths, center frequencies, and timing offsets, supporting asynchronous multi-user operation. FC-FB implementations are compared with traditional polyphase designs in terms of spectral characteristics and computational complexity.

Multirate filter banks can be implemented very efficiently using fast-convolution (FC) processing. The main advantage of the FC filter banks compared with the conventional polyphase implementations is their increased flexibility, that is, the number of channels, their bandwidths, and the center frequencies can be independently selected. In this paper, an approach for optimizing the FC filter banks is proposed. First, a subband representation of the adjustable FC filter banks is derived. Then, the optimization problems are formulated with the aid of the subband model. Finally, these problems are conveniently solved with the aid of a nonlinear optimization algorithm. Two examples are included to illustrate the performance of the proposed overall scheme.

This paper introduces an efficient filter structure for implementing finite-impulse response (FIR) filters with an adjustable fractional delay. In this structure the first two subfilters are the same as in the modified Farrow structure, whereas the remaining ones are generated by properly combining these two subfilters with some additional very short filters, pure delay terms, adders, and multipliers. For significantly reducing the number of multipliers, the three-step synthesis scheme proposed by Yli-Kaakinen and Saramaki in the case of the modified Farrow structure is followed. First, the number of subfilters and their orders are determined such that the given criteria are sufficiently exceeded. Second, an initial filter is determined using a simple design scheme. This filter serves as a start-up solution for further optimization being performed using a constrained nonlinear optimization algorithm. Third, those coefficient values of the subfilters having a negligible effect on the overall system performance are fixed to be zero-valued. Both the performance and complexity of the proposed adjustable digital filters are compared with those of some existing adjustable FIR filters proposed in the literature. This comparison shows that, in the case of stringent amplitude and phase delay specifications, the number of multipliers for the proposed filters is less than 80 percent when compared with the corresponding optimized modified Farrow structure.

This paper considers designing in the minimax sense complementary low-pass/high-pass approximately linear-phase recursive filters with variable magnitude characteristics. A filter structure based on the parallel connection of a delay and a variable fractional delay all-pass filter is proposed for implementing these filters. The filter optimization is performed in two basic steps. First, an initial filter is generated using a simple design scheme. Second, this filter is used as a start-up solution for further optimization being carried out by an efficient constrained nonlinear optimization algorithm. Examples are included for illustrating the efficiency of the proposed design scheme. In addition, the performance and the complexity of the proposed variable recursive digital filters are compared with those of the other variable recursive digital filters proposed in the literature. This comparison shows that the number of multipliers for the proposed filters is less than 30 percent compared with the other existing structures

This paper describes an efficient algorithm for the design of multiplierless approximately linear-phase lattice wave digital (LWD) filters (parallel connection of two all-pass filters). The coefficient optimization is performed in two basic steps. First, a nonlinear optimization algorithm is used for determining a parameter space of the finite-precision coefficients including the feasible space where the filter meets the given amplitude and phase specifications. The second step involves finding the filter parameters in this space such that the resulting filter meets the given criteria with the simplest coefficient representation forms. The proposed algorithm guarantees that the optimum multiplierless finite-wordlength solution can be found. This is illustrated by means of an example.