ENN522 Advanced Communication Systems
 Semester 1, 2016 Problem
Solving Task Multiple
Antennas
and
Space-time
Communications
 Consider a 2𝑥𝑥2 MIMO system with channel gain matrix 𝐻𝐻 given by 𝐻𝐻 = �0 0..3 4 0 1..8 5� Assume that 𝐻𝐻 is known at both transmitter and receiver and that there is a total transmit power of 𝑃𝑃 = 12 𝑚𝑚𝑚𝑚 across the two transmit antennas, AWGN with 𝑁𝑁0 = 10−9 𝑚𝑚/𝐻𝐻𝐻𝐻 at each receive antenna, and bandwidth 𝐵𝐵 = 1𝑀𝑀𝐻𝐻𝐻𝐻. Write a MATLAB script that can, a) Find the SVD for 𝐻𝐻. (20 marks) b) Find the capacity of this channel. (20 marks) c) Assume that transmit precoding and receiver shaping have been used to transform this channel into two parallel independent channels with a total power constraint 𝑃𝑃. Use MATLAB to find the maximum data rate that can be transmitted over this parallel set assuming MQAM modulation on each channel, with optimal power allocation across the channels subject to power constraint 𝑃𝑃. Assume a target BER of 10−3 on each channel and that the BER is bounded 𝑃𝑃 𝑏𝑏 ≤ 0.2𝑒𝑒− 1.5𝛾𝛾 𝑀𝑀 −1 . (20 marks) d) Suppose now that the antennas at the transmitter and receiver are all used for diversity (with optimal weighting at the transmitter and receiver) to maximize the SNR of the combiner output. Using MATLAB, find the SNR of the combiner output as well as the BER of a BPSK modulated signal transmitted over this diversity system. Compare the data rate and BER of this BPSK signalling with diversity (assuming 𝐵𝐵 = 1/𝑇𝑇𝑏𝑏) to the rate and BER from part c. (20 marks) e) Discuss the diversity‐multiplexing trade‐offs between the systems in parts c and d. (20 marks) Submission Requirements 1. This is an individual assignment; please ensure the submitted work is your own as each assignment will be tested for academic integrity. 2. The assignment report is to be submitted electronically through QUT Blackboard (due 31st May 2016). 3. The written report should provide responses to all required tasks, as well as the MATLAB scripts used to produce your results. 4. The electronic files submitted must be in a pdf file format. This ensures that your document formatting is preserved. 5. Do not zip or archive your submissions. 6. It is permissible to submit your assignment to Blackboard multiple times. 7. However, only the latest submission will be marked. 8. It is the student's responsibility to check that files submitted to Blackboard have not been corrupted in the process. All uploaded files can be reviewed post submission.