Consider a diversity reception system which employs MRC combining the SNRs of N receivers. Each of.

Consider a diversity reception system which employs MRC
combining the SNRs of N receivers. Each of the N receivers is equipped with M
antennas and employs selection combining between the M antennas. The channel is
assumed to undergo Rayleigh fading with the same mean SNR _ for each
channel.

a. Derive the cdf and the pdf of SNR at the output of a
receiver with M antennas. Hint: you may use binomial expansion.

b. Derive the MGF of the output of each receiver for an
arbitrary value of M.

c. Derive the BEP at the output of the MRC combiner for DPSK
modulation for arbitrary values of M and

Consider a diversity reception system which employs MRC
combining the SNRs of N receivers. Each of the N receivers is equipped with M
antennas and employs selection combining between the M antennas. The channel is
assumed to undergo Rayleigh fading with the same mean SNR _ for each
channel.

a. Derive the cdf and the pdf of SNR at the output of a
receiver with M antennas. Hint: you may use binomial expansion.

b. Derive the MGF of the output of each receiver for an
arbitrary value of M.

c. Derive the BEP at the output of the MRC combiner for DPSK
modulation for arbitrary values of M and N.

d. Derive the SNR at the MRC output for arbitrary values of
M and N.

e. Plot the BEP for N = M = 1, N = M = 2, M = 1, N = 4 and M
= 4, N = 1. Compare the BEP performances for _ = 10 dB.

f. Determine the diversity gain for N = M = 2 and compare
with that for M = 1, N = 4 and M = 4, N = 1 at 10_3 BEP.

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