# By using the results of the Problem 14.8, show that the outage probability with fixed channel gain,.

By using the results of the Problem 14.8, show that the
outage probability with fixed channel gain, multiple antennas at source and
destination and relay selection, may be expressed analytically as follows:

where _1 and _2 are central chi-square distributed
with means _1 and _2 and degrees of freedom n and m, respectively.
Compare the outage probability given above with (11) in [18].

Problem 14.8

The pdf and cdf of a random variable with central chi-square
distribution are given below (see (F.115)):

By using the results of the Problem 14.8, show that the
outage probability with fixed channel gain, multiple antennas at source and
destination and relay selection, may be expressed analytically as follows:

where _1 and _2 are central chi-square distributed
with means _1 and _2 and degrees of freedom n and m, respectively.
Compare the outage probability given above with (11) in [18].

Problem 14.8

The pdf and cdf of a random variable with central chi-square
distribution are given below (see (F.115)):

Show that Kth power of the cdf, which corresponds to the
selection of one of the K relays with the highest equivalent SNR with the
chi-square pdf, may be expressed as follows

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