We study the effect of asymmetric doping concentrations on the electron mobility µ in GaAs/InGaAs-based single quantum well (SQW) as well as double quantum well (DQW) pseudomorphic high electron mobility transistor (pHEMT) structures. Unequal doping in the substrate and surface barriers (nd1 and nd2) causes asymmetric distributions of subband wave functions, 0 and 1, which influence the subband scattering rate matrix elements (SSRME), thereby affecting the subband mobility µn. For narrow well widths (ww), in SQW structures, mostly a single subband is occupied. We show that an increase in nd2, keeping nd1 fixed, enhances µ nonlinearly. The interface roughness (ir-) scattering mostly dominates µ in thin wells (ww<70 Å), while generally, µ is determined by ionized impurity (ii-) scattering and to some extent by alloy disorder (ad-) scattering. The influence of ir-scattering enhances, while ad-scattering diminishes, by reducing nd2. For DQW, a double subband is occupied. In a symmetric DQW structure at resonance, nd1=nd2, 0 and1 equally extend into both the wells. For a minor variation, say nd1>nd2, 0 mostly lies in one well while 1 is in the other well. In the case of nd1<nd2, the distribution reverts. The substantial changes in 0 and1 influence the intra- and inter-SSRME differently through intersubband effects, leading to nonlinear µn as a function of nd2. Taking nd1+nd2= 3× 1018 cm-3, we show that for ww1=ww2= 80Å, a shallow dip in µ occurs at nd1=nd2= 1.5× 1018 cm-3. Whereas, for ww1= 60 Å and ww2= 100Å, the dip in µ occurs near the corresponding resonance, nd1=2.3× 1018 cm-3 and nd2= 0.7× 1018 cm-3. Our results of nonlinear µ can be utilized for performance analysis of pHEMT.