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This paper addresses the problem of controlling the envelope's power peak of single carrier modulated signals, band limited by root-raised cosine (RRC) pulse shaping filters, in order to reduce power amplifier back-off for very small aperture terminals ground stations. Magnitude modulation (MM) is presented as a very efficient solution to the peak-to-average power ratio problem. This paper gives a detailed description of the MM concept and its recent evolutions. It starts by extending the look-up-table (LUT) based approach of the MM concept to M-ary constellations with M ≤ 16. The constellation and RRC symmetries are explored, allowing considerable reduction on LUT computation complexity and storage requirements. An effective multistage polyphase (MPMM) approach for the MM concept is then proposed. As opposed to traditional LUT-MM solutions, MM coefficients are computed in real-time by a low complexity multirate filter system. The back-off from high-power amplifier saturation is almost eliminated (reduction is greater than 95%) with just a 2-stage MPMM system even for very demanding roll-off cases (e.g., α = 0.1). Also, the MPMM is independent of modulation in use, allowing its easy application to constellations with M > 16.