The co-design of multiple RF functions provides the means to efficiently use the resources available for transmission (i.e. time, frequency, space, and power). Digital array technology supports simultaneous control over all domains of diversity through independent generation of the waveform emitted by each antenna element. The Far-field Radiated Emission Design (FFRED) formulation considers the efficient use of all available resources by simultaneously performing multiple functions in the same frequency band via spatially separated beams. The waveforms in the FFRED problem are constrained to have attractive signal properties via reduction in peak-to-average power ratio (PAPR) to increase power efficiency. This design constraint is shown to leverage the spatial orthogonal complement to the desired transmission directions so as to not interfere with the RF functions. Here, the FFRED problem is formulated as a gradient-based optimization with reduced computational complexity relative to the previous alternating projection implementation. For a certain initialization, the optimized waveforms are shown to be near-optimal in terms of minimal energy within the orthogonal complement.