TELE 9753 Advanced Wireless Communications
Tutorial 3 – Time Diversity and Receive Diversity
Question 1
Consider coherent detection in Rayleigh fading channels. Prove the exact error probability given by
(1)
and the asymptotic error probability, as SNR → ∞, given by
(2)
Question 2
Consider the use of the rotation code which is explained in Chapter 3.2.2 in David Tse’s book.
a) Derive an explicit expression for the exact pairwise error probability, which is given by the expectation of
b) Derive the asymptotic pairwise error probability and show it goes to zero with increasing SNR.
Home Work
Requirements
1. Write down your full name, student number, and signature.
2. Detail the steps of your analysis/calculations/solutions. A single answer without derivations or expla-nations is not acceptable.
3. Hand in a hard copy in the following class.
Question 1
Consider the simplest complex constellation QPSK which sends symbols along both the I and Q compo-nents. Specifically, the constellation is given by {a(1 + j), a(1 − j), a(−1 − j), a(−1 + j)}.
a) Derive an expression for the symbol error probability of QPSK over AWGN channel based on Q function. Compare it with the symbol error probability of 4-PAM, given by {−3b, −b, b, 3b}, over AWGN channel. Explain why the power advantage of QPSK over 4-PAM is approximately 4dB.
b) Derive the symbol error probability of QPSK and 4-PAM over Rayleigh fading channels with repetition coding over L branches of diversity. Compare their performance and explain which parameter determines their performance difference.
Hint: The characteristic function of exponential distribution might be adopted to determine the expectation of Q-function.
c) As per the rules of QPSK, draw the constellation maps of 8-PSK and 16-PSK. Present the advantages and disadvantages of 8-PSK and 16-PSK relative to QPSK.