New results on maximal ratio combining in Nakagami-m fading channels

Novel expressions for the symbol error probability (SEP) of maximal ratio combining (MRC) diversity detection are derived. The case of independent and identically distributed Nakagami-m fading channels is considered. It is shown that expressions for the SEPs of MRC diversity operating in Nakagami-m fading channels can be obtained by both replacing the diversity order, L, with mL and replacing the average signal-to-noise ratio (SNR) per bit, γ̅ with γ̅/m in expressions for the SEPs of MRC diversity in Rayleigh fading channels. An identity which states that the bit error probability (BEP) of L-branch soft-decision MRC detection equals that of (2L - 1)-branch hard-decision detection with majority logic combining, both in independent Rayleigh fading channels and with equal branch SNRs, is recalled. The identity is used to derive new expressions for the SEP of MRC diversity in Nakagami-m fading channels. It is also shown that outage probability and average level-crossing rate for MRC reception in Nakagami-m fading channels can be obtained from corresponding outage probability and average level-crossing rate for MRC reception in Rayleigh fading channels. The relationships established will find application both in deriving solutions to unsolved problems and, where past solutions exist, in finding simpler solutions.