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5G Radio access network disaggregation and softwarization pose challenges in terms of computational performance to the processing units. At the physical layer level, the baseband processing computational effort is typically offloaded to specialized hardware accelerators. However, the trend toward software-defined radio-access networks demands flexible, programmable architectures. In this paper, we explore the software design, parallelization and optimization of the key kernels of the lower physical layer (PHY) for physical uplink shared channel (PUSCH) reception on MemPool and TeraPool, two manycore systems having respectively 256 and 1024 small and efficient RISC-V cores with a large shared L1 data memory. PUSCH processing is demanding and strictly time-constrained, it represents a challenge for the baseband processors, and it is also common to most of the uplink channels. Our analysis thus generalizes to the entire lower PHY of the uplink receiver at gNodeB (gNB). Based on the evaluation of the computational effort (in multiply-accumulate operations) required by the PUSCH algorithmic stages, we focus on the parallel implementation of the dominant kernels, namely fast Fourier transform, matrix-matrix multiplication, and matrix decomposition kernels for the solution of linear systems. Our optimized parallel kernels achieve respectively on MemPool and TeraPool speedups of 211, 225, 158, and 762, 880, 722, at high utilization (0.81, 0.89, 0.71, and 0.74, 0.88, 0.71), comparable a single-core serial execution, moving a step closer toward a full-software PUSCH implementation.