The low-temperature mobility of two-dimensional electron gas (2DEG) limited scattering by ionized impurities, alloy disorder, acoustic and optical phonons, and interface roughness was calculated for novel pseudomorphic modulation-doped by donors and acceptors InGaAs/AlGaAs quantum well structures promising for high power microwave transistors. Due to the high 2DEG density in the quantum well intersubband transitions were taken into account. Scattering by the ionized donors from δ-layer located in AlGaAs barriers dominates, whereas scattering by the ionized acceptors occupying the most part of AlGaAs barriers is negligibly weak. The width of donor doping profile is a key parameter to control 2DEG mobility, thus, increasing of the profile width from 0.25 nm to 4 nm due to segregation and diffusion of donor atoms halves the mobility. We have proposed a few approaches for the weakening of Coulomb scattering and the increase in 2DEG mobility in the novel heterostructures. The predicted mobility enhancement due to δ-layer splitting into two δ-sublayers was verified experimentally.