TELE 9753 Advanced Wireless Communications
Tutorial 4 - Receive Diversity
Question 1
Consider a BPSK modulation that achieves a bit error rate of Pb = 10−3 on the AWGN channel. Find the outage probability of this BPSK modulation for the Rayleigh fading channel with selection combining (SC) diversity for M = 1 (no diversity), M = 2 and M = 3, where M denotes the number of receive antennas. Assume equal branch SNRs with γ = 15 dB.
Homework 4
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 or submit it via Teams.
Question 1
Consider a QPSK modulation that achieves a bit error rate of Pb = 10−3 on the AWGN channel. Find the outage probability of this QPSK modulation for the Rayleigh fading channel with selection combining (SC) diversity for M = 1 (no diversity), M = 2 and M = 3. Assume unequal branch SNRs with γ1 = 10 dB, γ2 = 15 dB, and γ1 = 20 dB.
Hint: Determine the bit error probability formula and evaluate the Q-function using Q-function table or mathematic softwares (e.g., Matlab or Mathematica). Please be aware that this question assumes unequal branch SNRs, where M = 1 contains γ1
, but M = 2 contains both γ1
and γ2
.
Question 2
Assume that four branch diversity is used, where each branch receives an independent Rayleigh fading signal. If the average SNR is 20 dB on each branch, determine the probability that the SNR will drop below 10 dB. Compare this with the case of a single receiver without diversity. Consider SC first, then MRC.