tailieunhanh - Digital Communication I: Modulation and Coding Course-Lecture 8

Some bandpass modulation schemes MPAM, MPSK, MFSK, MQAM How to perform coherent and noncoherent to calculate the average probability of symbol error for different modulation schemes that we studied? How to compare different modulation schemes based on their error performances? | Digital Communications I: Modulation and Coding Course Term 3 - 2008 Catharina Logothetis Lecture 8 Lecture 8 Last time we talked about: Some bandpass modulation schemes M-PAM, M-PSK, M-FSK, M-QAM How to perform coherent and non-coherent detection Lecture 8 Example of two dim. modulation “00” “11” “10” “01” QPSK “110” “000” “001” “011” “010” “101” “111” “100” 8PSK “0000” “0001” “0011” “0010” 1 3 -1 -3 “1000” “1001” “1011” “1010” “1100” “1101” “1111” “1110” “0100” “0101” “0111” “0110” 1 3 -1 -3 16QAM Lecture 8 Today, we are going to talk about: How to calculate the average probability of symbol error for different modulation schemes that we studied? How to compare different modulation schemes based on their error performances? Lecture 8 Error probability of bandpass modulation Before evaluating the error probability, it is important to remember that: The type of modulation and detection ( coherent or non-coherent) determines the structure of the decision circuits and hence the decision | Digital Communications I: Modulation and Coding Course Term 3 - 2008 Catharina Logothetis Lecture 8 Lecture 8 Last time we talked about: Some bandpass modulation schemes M-PAM, M-PSK, M-FSK, M-QAM How to perform coherent and non-coherent detection Lecture 8 Example of two dim. modulation “00” “11” “10” “01” QPSK “110” “000” “001” “011” “010” “101” “111” “100” 8PSK “0000” “0001” “0011” “0010” 1 3 -1 -3 “1000” “1001” “1011” “1010” “1100” “1101” “1111” “1110” “0100” “0101” “0111” “0110” 1 3 -1 -3 16QAM Lecture 8 Today, we are going to talk about: How to calculate the average probability of symbol error for different modulation schemes that we studied? How to compare different modulation schemes based on their error performances? Lecture 8 Error probability of bandpass modulation Before evaluating the error probability, it is important to remember that: The type of modulation and detection ( coherent or non-coherent) determines the structure of the decision circuits and hence the decision variable, denoted by z. The decision variable, z, is compared with M-1 thresholds, corresponding to M decision regions for detection purposes. Decision Circuits Compare z with threshold. Lecture 8 The matched filters output (observation vector= ) is the detector input and the decision variable is a function of , . For MPAM, MQAM and MFSK with coherent detection For MPSK with coherent detection For non-coherent detection (M-FSK and DPSK), We know that for calculating the average probability of symbol error, we need to determine Hence, we need to know the statistics of z, which depends on the modulation scheme and the detection type. Error probability Lecture 8 Error probability AWGN channel model: The signal vector is deterministic. The elements of the noise vector are Gaussian random variables with zero-mean and variance . The noise vector's pdf is The elements of the observed vector are independent Gaussian random variables. Its pdf is Lecture 8 Error probability BPSK