The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed squared η-μvariates, applicable to the output statistics of maximal ratio combining (MRC) receiver operating over η-μfading channels that includes the Hoyt and the Nakagami-m models as special cases, is presented in closed-form in terms of the Fox's H-bar function. Further analysis, particularly on the bit error rate via PDF-based approach, is also represented in closed form in terms of the extended Fox's H-bar function (H-hat). The proposed new analytical results complement previous results and are illustrated by extensive numerical and Monte Carlo simulation results.