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EE 3220: Digital Communication

EE 3220: Digital Communication. Lec-8: Error performance of bandpass modulation. Dr. Hassan Yousif Ahmed Department of Electrical Engineering College of Engineering at Wadi Aldwasser Slman bin Abdulaziz University. Last time we talked about:. Some bandpass modulation schemes

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EE 3220: Digital Communication

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  1. EE 3220: Digital Communication Lec-8: Error performance of bandpass modulation Dr. Hassan Yousif Ahmed Department of Electrical Engineering College of Engineering at Wadi Aldwasser Slman bin Abdulaziz University Dr Hassan Yousif

  2. 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 Dr Hassan Yousif

  3. “011” “010” “001” “0000” “0001” “0011” “0010” “000” 3 “110” “1000” “1001” “1011” “1010” 1 “111” “100” -3 -1 1 3 “101” -1 “1100” “1101” “1111” “1110” “00” “01” -3 “0100” “0101” “0111” “0110” “11” “10” Example of two dim. modulation 16QAM 8PSK QPSK Dr Hassan Yousif

  4. 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? Dr Hassan Yousif

  5. 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. Dr Hassan Yousif

  6. Error probability … • The matched filters output (observation vector= ) is the detector input and the decision variable is a function of , i.e. • 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. Dr Hassan Yousif

  7. Error probability … • AWGN channel model: • The signal vector is deterministic. • The elements of the noise vector are i.i.d 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 Dr Hassan Yousif

  8. “0” “1” “0” “1” Error probability … • BPSK and BFSK with coherent detection: BPSK BFSK Dr Hassan Yousif

  9. + - Error probability … Decision variable: Difference of envelopes • Non-coherent detection of BFSK Decision rule: Dr Hassan Yousif

  10. Rician pdf Error probability – cont’d • Non-coherent detection of BFSK … • Similarly, non-coherent detection of DBPSK Rayleigh pdf Dr Hassan Yousif

  11. “00” “01” “11” “10” 0 ML detector (Compare with M-1 thresholds)‏ Error probability …. • Coherent detection of M-PAM • Decision variable: 4-PAM Dr Hassan Yousif

  12. Gaussian pdf with zero mean and variance Error probability …. • Coherent detection of M-PAM …. • Error happens if the noise, , exceeds in amplitude one-half of the distance between adjacent symbols. For symbols on the border, error can happen only in one direction. Hence: Dr Hassan Yousif

  13. “0000” “0001” “0011” “0010” “1000” “1001” “1011” “1010” “1100” “1101” “1111” “1110” ML detector “0100” “0101” “0111” “0110” Parallel-to-serial converter ML detector Error probability … • Coherent detection of M-QAM 16-QAM Dr Hassan Yousif

  14. Average probability of symbol error for Error probability … • Coherent detection of M-QAM … • M-QAM can be viewed as the combination of two modulations on I and Q branches, respectively. • No error occurs if no error is detected on either the I or the Q branch. • Considering the symmetry of the signal space and the orthogonality of the I and Q branches: Dr Hassan Yousif

  15. “011” “010” “001” “000” “110” “111” “100” “101” Compute Choose smallest Error probability … • Coherent detection of MPSK 8-PSK Decision variable Dr Hassan Yousif

  16. Error probability … • Coherent detection of MPSK … • The detector compares the phase of observation vector to M-1 thresholds. • Due to the circular symmetry of the signal space, we have: where • It can be shown that or Dr Hassan Yousif

  17. Error probability … • Coherent detection of M-FSK ML detector: Choose the largest element in the observed vector Dr Hassan Yousif

  18. Error probability … • Coherent detection of M-FSK … • The dimension of the signal space is M. An upper bound for the average symbol error probability can be obtained by using the union bound. Hence: or, equivalently Dr Hassan Yousif

  19. Bit error probability versus symbol error probability • Number of bits per symbol • For orthogonal M-ary signaling (M-FSK)‏ • For M-PSK, M-PAM and M-QAM Dr Hassan Yousif

  20. Probability of symbol error for binary modulation • Note! • “The same average symbol energy for different sizes of signal space” Dr Hassan Yousif

  21. Probability of symbol error for M-PSK • Note! • “The same average symbol energy for different sizes of signal space” Dr Hassan Yousif

  22. Probability of symbol error for M-FSK • Note! • “The same average symbol energy for different sizes of signal space” Dr Hassan Yousif

  23. Probability of symbol error for M-PAM • Note! • “The same average symbol energy for different sizes of signal space” Dr Hassan Yousif

  24. Probability of symbol error for M-QAM • Note! • “The same average symbol energy for different sizes of signal space” Dr Hassan Yousif

  25. Example of samples of matched filter output for some bandpass modulation schemes Dr Hassan Yousif

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