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).