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ELE4009/ELE8078 – Wireless Communications – Tutorial 4 Questions
1. Consider a wireless multiuser system where the base station (BS) serves users. The
transmitter (BS) and the users are all equipped with a single antenna. The received signal at user is given by % = '? ?% % + %,
where % is the transmitted symbol for user with E{% }=0 and E{|%|/}=1, ? denotes the
average signal-to-noise ratio (SNR), ?% are independent and identically distributed (i.i.d.)
complex Gaussian for all , i.e., ?%~(0,1), and % is the background noise, %~(0,1).
Assume that both the BS and all users have perfect channel state information.
The BS performs opportunistic scheduling by serving the user with highest SNR at each given
time (i.e., greedy access or ‘best user’ scheduling).
(a) Write down expressions for the instantaneous SNR of the scheduled user and for the
corresponding capacity (in bits/s/Hz) of the system with ‘best user’ scheduling.
(b) Write down an expression for the CDF of the SNR of the scheduled user. Note: Remember
that if 8, … , : are independent random variables, the joint probability Pr(8 ≤ , /, ≤,? , : ≤ ) = ∏ Pr(% ≤ ):%A8 .
(c) An outage event occurs if the SNR of the scheduled user falls below 10 dB. Assuming there
are = 5 users and that the average SNR per user is ? = 10 dB, compute the outage
probability.
(d) Denote by E (bits/s/Hz) the minimum desired data rate. An outage is now defined as the
event that the capacity falls below E= 2 bits/s/Hz. Determine the probability of capacity
outage for the multiuser diversity system when there are = 10 users and ? = 10 dB.
What if the number of users increases to = 20?