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A new suboptimal selection combining (SC) scheme is proposed and is denoted by (α+ |r|)-SC, where α is the fading factor, and |r| is the received signal envelope. The (α+ |r|)-SC scheme has lower complexity than the optimal SC scheme and outperforms other existing suboptimal SC schemes such as the traditional signal-to-noise-ratio (SNR)-SC (denoted by α-SC) and |r|-SC schemes. To choose a diversity branch for signal reception, the suboptimal SNR-SC and |r|-SC schemes use SNR and |r| as their selection statistics, respectively, and the branch with the maximal selection statistic is selected. For the branch selection of (α+ |r|)-SC, basically, each diversity branch uses the linear sum of the selection statistics of α-SC and |r|-SC schemes as a new selection statistic. Unlike the optimal SC or maximal ratio combining (MRC) scheme that requires multipliers to form the selection or combining statistic, the (α+ |r|)-SC scheme only uses adders to generate the selection statistic, which makes (α+ |r |)-SC faster and more power-saving than the optimal SC or MRC. For performance comparisons, the bit error rate (BER) of binary phase-shift keying (BPSK) over independent but not necessarily identical ( i.n.d.) Rayleigh fading channels is derived. Numerical results show that the suboptimal (α+ |r|)-SC and optimal SC schemes have very close BER performance.