An N-branch MRC diversity receiver sums the branch SNRs after weighting them by the corresponding…

An N-branch MRC diversity receiver sums the branch SNRs
after weighting them by the corresponding complex conjugated channel gain.
Hardware implementation of a MRC receiver is often costly because of the
difficulty of estimating the channel gains. In practice, a less complex and
cheaper combining technique is preferred where the branch with the highest SNR
is selected (SC). A SC receiver checks all the diversity branches during each
channel coherence time and then uses only the signal of the diversity branch
with the highest SNR.

a. Consider that N antennas of a SC diversity receiver

An N-branch MRC diversity receiver sums the branch SNRs
after weighting them by the corresponding complex conjugated channel gain.
Hardware implementation of a MRC receiver is often costly because of the
difficulty of estimating the channel gains. In practice, a less complex and
cheaper combining technique is preferred where the branch with the highest SNR
is selected (SC). A SC receiver checks all the diversity branches during each
channel coherence time and then uses only the signal of the diversity branch
with the highest SNR.

a. Consider that N antennas of a SC diversity receiver
suffer i.i.d. Rayleigh fading. Determine a high-SNR (as _ _)
approximation to the pdf given by (12.74). Using only the pdfs for SC and MRC,
determine how many times the BEP for SC would be higher than MRC.

b. The asymptoticBEP forMRC ofNBPSK signals with equal mean
SNRs _ is given by (11.222). Starting with (12.77), determine the
asymptotic BEP for SC and the required increase in _ for SC compared to
MRC for N = 2, 3 and 4.

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