通信代写-ELE4009/ELE8078
时间:2021-08-10
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?















ELE4009/ELE8078 – Wireless Communications – Tutorial 4 Questions

2. Consider a multi-user wireless system where users intend to communicate with the BS. Users
are selected to access the channel by means of opportunistic scheduling, without consideration
for fairness, i.e., using the greedy access scheduling (GS). All channels between the users and
the BS are assumed to be independent Rayleigh faded channels, and all users and the BS are
equipped with a single antenna.

Assume that, for successful communication, the SNR of the scheduled user must be %? ≥ ,
where is the minimum required SNR, and assume that the average SNR is ? for all users.

(a) Write down an expression for the probability of successful communication with GS, in terms
of the average SNR ?, the minimum required SNR , and the number of users .

(b) Let % be the SNR for user and Pr(% ≤ ) = 0.1. What is the minimum value of to
achieve an outage probability (for the scheduled user) of 0.001?

(c) Say that the average SNR for the different users is now different, i.e., ?% ≠ ?J for ≠ , and
that some of the users have much higher average SNR than others, i.e., ?% ? ?J for some , . Do you anticipate any issues with greedy access scheduling? Explain the difference
between the GS and proportional fair scheduling (PFS) selection rules.




3. Consider a single-antenna multiuser scenario where = 10 users intend to opportunistically
communicate with the BS using M-QAM. The BS selects the user with highest SNR to access the
time-frequency resource at each transmission time interval (TTI), i.e., it employs Greedy
Scheduling (GS).

The uplink channels ?%, for = 1,… , , are i.i.d. complex Gaussian random variables, ?%~(0,1). Assume availability of perfect CSI at the BS every TTI and that the system can only
recover the data reliably if %? ≥ , where %? is the SNR of the scheduled user, and is the
threshold for successful transmission.
(a) Let the reliable throughput of the multiuser system be = log/()Pr( ).
Write down an expression for the reliable throughput (bps/Hz), given in terms of the
average SNR ?, the minimum required SNR , and the number of users .
(b) Suppose that the average SNR for every user is ? = 4 and that = 3 . When = 10
and = 2 (BPSK), determine the reliable throughput of the GS-based system, and compare
it with that of a random access (RA) system (where users are randomly selected).
















































































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