This paper investigates the application of fastconvolution (FC) filtering schemes for flexible and effective waveform generation and processing in 5th generation (5G) systems. FC based filtering is presented as a generic multimode waveform processing engine while, following the progress of 5G new radio (NR) standardization in 3rd Generation Partnership Project (3GPP), the main focus is on efficient generation and processing of subband-filtered cyclic prefix orthogonal frequencydivision 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 welllocalized 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.

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A very efficient technique to drastically reduce the number of multipliers and adders in implementing linear-phase finite-impulse response (FIR) digital filters in applications demanding a narrow transition band is to use the frequency-response masking (FRM) approach originally introduced by Lim. The arithmetic complexity can be even further reduced using a common filter part for constructing the masking filters originally proposed by Lim and Lian. A drawback in the above-mentioned original FRM synthesis techniques is that the subfilters in the overall implementations are separately designed. In order to further reduce the arithmetic complexity in these two FRM approaches, the following two-step optimization technique is proposed for simultaneously optimizing the subfilters. At the first step, a good suboptimal solution is found by using a simple iterative algorithm. At the second step, this solution is then used as a start-up solution for further optimization being carried out by using an efficient unconstrained nonlinear optimization algorithm. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized filter are less than 80% compared with those of the FRM filter obtained using the original FRM design schemes in the case where the masking filters are separately implemented. If a common filter part is used for realizing the masking filters, then an additional reduction of more than 10% is achieved compared with the optimized design with separately implemented masking filters.

This paper describes an efficient algorithm for designing lattice wave digital (LWD) filters (parallel connections of two all-pass filters) with short-coefficient wordlength. The coefficient optimization is performed using the following three steps. First, an initial infinite-precision filter is designed such that it exceeds the given criteria in order to provide some tolerance for coefficient quantization. Second, a nonlinear optimization algorithm is used for determining a parameter space of the infinite-precision coefficients including the feasible space where the filter meets the given criteria. The third step involves finding the filter parameters in this space so that the resulting filter meets the given criteria with the simplest coefficient representation forms. The proposed algorithm guarantees that the optimum finite-precision solution can be found for both the fixed-point binary and multiplierless coefficient representation forms. In addition, this algorithm is applicable for producing the desired finite-precision solutions for both conventional and approximately linear-phase LWD filters. Comparisons with some other existing quantization schemes show that the proposed algorithm gives the best finite-precision solutions in all examples taken from the literature.Index Terms-Recursive digital filters, coefficient quantization, finite precision, multiplierless implementations, lattice wave digital (LWD) filters, optimization, parallel connection of all-pass filters, approximately linear-phase recursive filters, very large-scale integration (VLSI) implementations.

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A very efficient technique to drastically reduce the number of multipliers and adders in narrow transition-band linear-phase finite-impulse response digital filters is to use the one-stage or multistage frequency-response masking (FRM) approach, which has been originally introduced by Lim and further improved by Lim and Lian. In these original synthesis techniques, the subfilters in the overall implementation are separately designed. As shown earlier by the authors of this contribution together with Johansson, the arithmetic complexity in one-stage FRM filter designs can be considerably reduced by using the following two-step technique for simultaneously optimizing all the subfilters. First, a suboptimal solution is found by using a simple design scheme. Second, this solution is used as a start-up solution for further optimization, which is carried out with the aid of an efficient nonlinear optimization algorithm. This paper exploits this approach to synthesizing multistage FRM filters. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized multistage FRM filters are approximately 70 percent compared with those of the filters synthesized using the original multistage FRM filter design schemes. Additional examples are included in order to show the benefits provided by the proposed synthesis scheme over other recently published design techniques, in terms of an improved performance of Some parts of this paper were presented at 158 Circuits Syst Signal Process (2011) 30: 157-183 the resulting solution, a higher accuracy of the solution, and a faster speed required to arrive at the best solution.