MBWC Lab
Discrete Multi-tone(LAB 5)
2021/5/13 1
MBWC Lab
Requirement
2021/5/13 2
• Generate the channel with different length (𝐡 is known)
𝐡 = [ℎ0, … , ℎ5] (delay with 5 time slots)
𝐡 = [ℎ0, … , ℎ9] (delay with 9 time slots)
• Generate 64 QPSK symbols to form a signal vector in frequency domain
• Redo the same process with 1000 realizations
• Show the QPSK symbol error rate in different SNR
MBWC Lab
Channel Delay ≤ The Length of CP (1/2)
2021/5/13 3
• The received signal (𝐇 is a circular matrix) in time domain
𝐱 = 𝐇𝐬 + 𝐰
• The signal from time domain to frequency domain (𝐐 is an FFT matrix)
𝐒 = 𝐐𝐬 𝐗 = 𝐐𝐱
• The circular matrix 𝐇 (𝚲 is a diagonal matrix)
𝐇 = 𝐐H𝚲𝐐
• The received signal in frequency domain
𝐐𝐱 = 𝐐 𝐇𝐬 + 𝐰
→ 𝐐𝐱 = 𝐐 𝐐H𝚲𝐐𝐐H𝐒 + 𝐰 = 𝐐𝐐H 𝚲 𝐐𝐐H 𝐒 + 𝐐𝐰
→ 𝐗 = 𝚲𝐒 + 𝐐𝐰
MBWC Lab
Channel Delay ≤ The Length of CP (2/2)
2021/5/13 4
• Generate 64 QPSK symbols to form a signal vector, 𝐒 ∈ 𝐂64×1, in frequencydomain
• Generate the circular matrix, 𝐇 ∈ 𝐂64×64, and derive the correspondingdiagonal matrix, 𝚲 (𝐇 = 𝐐H𝚲𝐐)
• Derive the received signal in time domain
𝐱 = 𝐇𝐬 + 𝐰 = 𝐐H𝚲𝐐𝐐H𝐒 + 𝐰
• Decode the signal vector 𝐒 ∈ 𝐂64×1(in frequency domain as follow)
𝐒 = 𝚲−1𝐐 𝐱 = 𝚲−1𝐐 𝐇𝐬 + 𝐰 = 𝚲−1𝐐 𝐐H𝚲𝐐𝐐H𝐒 + 𝐰
→ 𝐒 = 𝐒 + 𝚲−1𝐐 𝐰
MBWC Lab
Channel Delay ≥ The Length of CP
2021/5/13 5
The ISI exists here !!
MBWC Lab
The Symbol Error Rate
2021/5/13 6
Channel Delay ≤ The Length of CP Channel Delay ≥ The Length of CP