Outage and error probabilities of QPSK with diversity reception in Rayleigh fading and log-normal shadowing channel

Mobile and portable radio communication links are modeled as an additive white Gaussian noise channel subject to Rayleigh fading and log-normal shadowing. Diversity reception with K-port macroscopic selection and L-branch microscopic maximal-ratio combining is considered. The following analytical expressions are derived: (1) outage probability based on error rate as outage and; (2) average error probability. By evaluating the derived expressions for various values of K and L, numerical results of quaternary phase-shift-keying (QPSK) modulation are obtained for four cases: (a) without diversity reception; (b) microdiversity combining; (c) macrodiversity selection; and (d) simultaneous use of macrodiversity selection and microdiversity combining