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Modulation and coding course- lecture 7

Another source of error due to filtering effect of the system: -Inter-symbol interference (ISI) -The techniques to reduce ISI -Pulse shaping to have zero ISI at the sampling time -Equalization to combat the filtering effect of the channel Digital Communications I: Modulation and Coding Course Period 3 - 2007 Catharina Logothetis Lecture 7 Last time we talked about: Another source of error due to filtering effect of the system: Inter-symbol interference (ISI) The techniques to reduce ISI Pulse sh

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  1. Digital Communications I: Modulation and Coding Course Period 3 - 2007 Catharina Logothetis Lecture 7
  2. Last time we talked about: Another source of error due to filtering effect of the system: Inter-symbol interference (ISI) The techniques to reduce ISI Pulse shaping to have zero ISI at the sampling time Equalization to combat the filtering effect of the channel Lecture 7 2
  3. Today, we are going to talk about: Some bandpass modulation schemes used in DCS for transmitting information over channel M-PAM, M-PSK, M-FSK, M-QAM How to detect the transmitted information at the receiver Coherent detection Non-coherent detection Lecture 7 3
  4. Block diagram of a DCS Source Channel Pulse Bandpass Format encode encode modulate modulate Digital modulation Channel Digital demodulation Source Channel Demod. Format Detect decode decode Sample Lecture 7 4
  5. Bandpass modulation Bandpass modulation: The process of converting data signal to a sinusoidal waveform where its amplitude, phase or frequency, or a combination of them, is varied in accordance with the transmitting data. Bandpass signal: cos(ωc t + (i − 1)Δωt + φi (t ) ) 0 ≤ t ≤ T 2 Ei si (t ) = gT (t ) T wheregT (t ) is the baseband pulse shape with energy E g . We assume here (otherwise will be stated): gT (t ) is a rectangular pulse shape with unit energy. Gray coding is used for mapping bits to symbols. 1 ∑ M Es denotes average symbol energy given by Es = i =1 Ei M Lecture 7 5
  6. Demodulation and detection Demodulation: The receiver signal is converted to baseband, filtered and sampled. Detection: Sampled values are used for detection using a decision rule such as ML detection rule. ψ 1 (t ) T z1 ∫ 0 ⎡ z1 ⎤ ⎢M⎥ r (t ) Decision z =z circuits ˆ m ψ N (t ) ⎢ ⎥ (ML detector) T ⎢zN ⎥ ⎣ ⎦ ∫ 0 zN Lecture 7 6
  7. Coherent detections Coherent detection requires carrier phase recovery at the receiver and hence, circuits to perform phase estimation. Source of carrier-phase mismatch at the receiver: Propagation delay causes carrier-phase offset in the received signal. The oscillators at the receiver which generate the carrier signal, are not usually phased locked to the transmitted carrier. Lecture 7 7
  8. Coherent detection .. Circuits such as Phase-Locked-Loop (PLL) are implemented at the receiver for carrier phase estimation ( α ≈ α ). ˆ I branch cos(ωi t + φi (t ) + α ) + n(t ) cos(ωc t + α ) 2 Ei 2 r (t ) = gT (t ) ˆ T T PLL Used by Oscillator 90 deg. correlators sin (ωc t + α ) 2 ˆ T Q branch Lecture 7 8
  9. Bandpass Modulation Schemes One dimensional waveforms Amplitude Shift Keying (ASK) M-ary Pulse Amplitude Modulation (M-PAM) Two dimensional waveforms M-ary Phase Shift Keying (M-PSK) M-ary Quadrature Amplitude Modulation (M-QAM) Multidimensional waveforms M-ary Frequency Shift Keying (M-FSK) Lecture 7 9
  10. One dimensional modulation, demodulation and detection Amplitude Shift Keying (ASK) modulation: cos(ωc t + φ ) 2 Ei si (t ) = T On-off keying (M=2): si (t ) = aiψ 1 (t ) i = 1, K , M “0” “1” s2 s1 cos(ωc t + φ ) 2 ψ 1 (t ) ψ 1 (t ) = 0 E1 T ai = Ei Lecture 7 10
  11. One dimensional mod.,… M-ary Pulse Amplitude modulation (M-PAM) cos(ωc t ) 2 si (t ) = ai T 4-PAM: si (t ) = aiψ 1 (t ) i = 1, K, M “00” “01” “11” “10” s1 s2 s3 s4 cos(ωc t ) 2 ψ 1 (t ) ψ 1 (t ) = − 3 Eg − Eg Eg 3 Eg T 0 ai = (2i − 1 − M ) E g Ei = s i = E g (2i − 1 − M ) 2 2 ( M 2 − 1) Es = Eg 3 Lecture 7 11
  12. Example of bandpass modulation: Binary PAM Lecture 7 12
  13. One dimensional mod.,...–cont’d Coherent detection of M-PAM ψ 1 (t ) T z1 ∫ ML detector r (t ) (Compare with M-1 thresholds) ˆ m 0 Lecture 7 13
  14. Two dimensional modulation, demodulation and detection (M-PSK) M-ary Phase Shift Keying (M-PSK) 2 Es ⎛ 2πi ⎞ si (t ) = cos⎜ ωc t + ⎟ T ⎝ M ⎠ si (t ) = ai1ψ 1 (t ) + ai 2ψ 2 (t ) i = 1, K , M cos(ωc t ) sin (ωc t ) 2 2 ψ 1 (t ) = ψ 2 (t ) = − T T ⎛ 2πi ⎞ ⎛ 2πi ⎞ ai1 = Es cos⎜ ⎟ ai 2 = Es sin ⎜ ⎟ ⎝M ⎠ ⎝M ⎠ Es = Ei = s i 2 Lecture 7 14
  15. Two dimensional mod.,… (MPSK) BPSK (M=2) ψ 2 (t ) “0” “1” 8PSK (M=8) s1 s2 ψ 2 (t ) − Eb Eb ψ 1 (t ) s3 “011” “010” “001” s4 s2 QPSK (M=4) Es “000” ψ 2 (t ) “110” s1 “01” “00” s5 ψ 1 (t ) s2 s1 “111” “100” Es s6 s8 ψ 1 (t ) “101” s7 s3 “11” “10” s4 Lecture 7 15
  16. Two dimensional mod.,…(MPSK) Coherent detection of MPSK ψ 1 (t ) T z1 ∫ z1 φ 0 ˆ r (t ) ˆ m arctan Compute Choose ψ 2 (t ) z2 | φi − φ | ˆ smallest T ∫ 0 z2 Lecture 7 16
  17. Two dimensional mod.,… (M-QAM) M-ary Quadrature Amplitude Mod. (M-QAM) cos(ωc t + ϕi ) 2 Ei si (t ) = T si (t ) = ai1ψ 1 (t ) + ai 2ψ 2 (t ) i = 1, K , M cos(ωc t ) ψ 2 (t ) = sin (ωc t ) 2 2 ψ 1 (t ) = T T 2( M − 1) where ai1 and ai 2 are PAM symbols and E s = 3 ⎡ (− M + 1, M − 1) (− M + 3, M − 1) L ( M − 1, M − 1) ⎤ ⎢ ⎥ (− M + 1, M − 3) (− M + 3, M − 3) L ( M − 1, M − 3) ⎥ (ai1 , ai 2 ) = ⎢ ⎢ ⎥ M M M M ⎢ ⎥ ⎢ ⎣ (− M + 1,− M + 1) (− M + 3,− M + 1) L ( M − 1,− M + 1)⎥ ⎦ Lecture 7 17
  18. Two dimensional mod.,… (M-QAM) 16-QAM ψ 2 (t ) “0000” “0001” “0011” “0010” s1 s2 3 s3 s4 “1000” “1001” “1011” “1010” s5 s6 s7 s8 1 -3 -1 1 3 ψ 1 (t ) s9 s10 -1 s 11 12s “1100” “1101” “1111” “1110” s13 s14 -3 s 15 s 16 “0100” “0101” “0111” “0110” Lecture 7 18
  19. Two dimensional mod.,… (M-QAM) Coherent detection of M-QAM ψ 1 (t ) T z1 ∫ ML detector (Compare with M − 1 thresholds) 0 r (t ) Parallel-to-serial ˆ m converter ψ 2 (t ) T z2 ∫ ML detector (Compare with M − 1 thresholds) 0 Lecture 7 19
  20. Multi-dimentional modulation, demodulation & detection M-ary Frequency Shift keying (M-FSK) cos(ωi t ) = cos(ωc t + (i − 1)Δωt ) 2 Es 2 Es si (t ) = T T Δω 1 Δf = = 2π 2T ψ 3 (t ) M si (t ) = ∑ aijψ j (t ) i = 1, K, M s3 j =1 Es ⎧ Es i = j cos(ωi t ) 2 ψ i (t ) = aij = ⎨ s2 T ⎩0 i≠ j ψ 2 (t ) Es Es = Ei = s i 2 s1 Es ψ 1 (t ) Lecture 7 20
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