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The conventional fully-digital implementation of massive-MIMO systems is not efficient due to the large required number of radio-frequency (RF) chains. To address this issue, hybrid analog/digital (A/D) beamforming was proposed and to date remains a topic of ongoing research. In this paper, we explore the hybrid A/D structure as a general framework for signal processing in massive and ultra-massive-MIMO systems. To exploit the full potential of the analog domain, we first focus on the analog signal processing (ASP) network. We investigate a mathematical representation suitable for any arbitrarily connected feed-forward ASP network comprised of the common RF hardware elements in the context of hybrid A/D systems, i.e., phase-shifter and power-divider/combiner. A novel ASP structure is then proposed which is not bound to the unit modulus constraint, thereby facilitating the hybrid A/D systems design. We then study MIMO transmitter and receiver designs to exploit the full potential of digital processing as well. It is shown that replacing the linear transformation in the digital domain with a generic mapping can improve the system performance. In some cases, the performance of optimal fully-digital MIMO systems can be achieved without extra calculations compared to sub-optimal hybrid A/D techniques. An optimization model based on the proposed structure is presented that can be used for hybrid A/D system design. Specifically, precoding and combining designs under different conditions are discussed as examples. Finally, simulation results are presented which illustrate the superiority of the proposed architecture to the conventional hybrid designs for massive-MIMO systems. INDEX TERMS Hybrid beamforming, hybrid analog and digital signal processing, ultra massive MIMO, massive MIMO, precoding, combining, beamforming.