The upcoming 5G generation is driven the expected huge growth in user bit rates and overall system throughput. This means a substantial spectral efficiency increase, which must be achieved while maintaining or even improving the power efficiency. To overcome the necessity of using inefficient linear HPA in typical communication systems, this paper addresses the use of the LINC technique for power amplification, since it employs grossly NL HPA that are simpler and much more energy efficient than the linear ones. However, this technique's efficiency is harshly damaged for signals with a large PAPR, as for systems employing high order spectral efficient modulations and/or close to Nyquist bandwidth limiting pulse-shaping, due mainly to the LINC signal separation and power combining procedures. However, given that any M-ary constellation can be split as a sum of several OQPSK signals, a new MM method is proposed for OQPSK signals with bandwidth close to Nyquist, that limit both maximum and minimum envelope excursions of the signal without spreading its spectrum. This method is also shown to improve the transmitter's resilience to small gain and phase imbalances between the LINC's amplifiers. The proposed scheme can play a critical role on the upcoming 5G, since arranging several units of the proposed transmitter in an array/parallel configuration has the potential to simultaneously achieve the required high power and spectral efficiency.