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In this paper, new digital predistortion (DPD) solutions for power amplifier (PA) linearization are proposed, with particular emphasis on reduced processing complexity in future 5G and beyond wideband radio systems. The first proposed method, referred to as the spline-based Hammerstein (SPH) approach, builds on complex spline-interpolated lookup table (LUT) followed by a linear finite impulse response (FIR) filter. The second proposed method, the spline-based memory polynomial (SMP) approach, contains multiple parallel complex spline-interpolated LUTs together with an input delay line such that more versatile memory modeling can be achieved. For both structures, gradient-based learning algorithms are derived to efficiently estimate the LUT control points and other related DPD parameters. Large set of experimental results are provided, with specific focus on 5G New Radio (NR) systems, showing successful linearization of multiple PA samples as well as a 28 GHz active antenna array, incorporating channel bandwidths up to 200 MHz. Explicit performance-complexity comparisons are also reported between the SPH and SMP DPD systems and the widely-applied ordinary memory-polynomial (MP) DPD solution. The results show that the linearization capabilities of the proposed methods are very close to that of the ordinary MP DPD, particularly with the proposed SMP approach, while having substantially lower processing complexity. [ABSTRACT FROM AUTHOR]