Digital Communications I: Modulation and Coding Course Term 3 - 2008 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 shaping to achieve zero ISI at the sampling time Equalization to combat the filtering effect of the channel Lecture 7 2 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 Block diagram of a DCS Format Source encode Channel encode Pulse modulate Bandpass modulate Channel Digital modulation Digital demodulation Format Source decode Channel decode Lecture 7 Detect
Demod. Sample 4 Bandpass modulation Bandpass modulation: The process of converting a data signal to a sinusoidal waveform where its amplitude, phase or frequency, or a combination of them, are varied in accordance with the transmitting data. Bandpass signal: 2 Ei si (t ) gT (t ) cosc t (i 1)t i (t ) 0 t T T where gT (t ) is the baseband pulse shape with energy Eg . 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 E denotes average symbol energy givenEsby
s Lecture 7 M M E i 1 5i 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 the ML detection rule. 1 (t ) T z1 0 r (t ) N (t ) T 0 zN
z1 z N Lecture 7 z z Decision circuits (ML detector) m 6 Coherent detection Coherent detection requires carrier phase recovery at the receiver and hence, circuits to perform phase estimation. Sources 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
Coherent detection .. Circuits such as Phase-Locked-Loop (PLL) are implemented at the receiver estimation ( for carrier phase ). I branch r (t ) gT (t ) 2 Ei cosi t i (t ) n(t ) T PLL Oscillator 2 cosc t T Used by correlators 90 deg. 2 sin c t T Lecture 7 Q branch 8 Bandpass Modulation Schemes
One dimensional waveforms Amplitude Shift Keying (ASK) M-ary Pulse Amplitude Modulation (MPAM) 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 One dimensional modulation, demodulation and detection Amplitude Shift Keying (ASK) modulation: 2 Ei si (t ) cosc t T si (t ) ai 1 (t ) i 1, , M On-off keying (M=2): 0 s2 2
1 (t ) cosc t T 0 1 s1 1 (t ) E1 ai Ei Lecture 7 10 One dimensional mod., M-ary Pulse Amplitude modulation (MPAM) 2 si (t ) ai cosc t T 4-PAM: si (t ) ai 1 (t ) i 1, , M 00 01 s1 2 1 (t )
cosct T 3 Eg 11 s3 s2 Eg 0 Eg 10 s4 1 (t ) 3 Eg ai (2i 1 M ) E g Ei s i 2 E g 2i 1 M 2 ( M 2 1) Es Eg 3 Lecture 7
11 Example of bandpass modulation: Binary PAM Lecture 7 12 One dimensional mod.,...contd Coherent detection of M-PAM 1 (t ) r (t ) T 0 z1 ML detector (Compare with M-1 thresholds) Lecture 7 m 13 Two dimensional modulation, demodulation and detection (MPSK) M-ary Phase Shift Keying (M-PSK) 2 Es
2i si (t ) cos c t T M si (t ) ai1 1 (t ) ai 2 2 (t ) i 1, , M 2 1 (t ) cosc t T 2i ai1 Es cos M Es Ei s i 2 2 (t ) sin c t T 2i ai 2 Es sin M 2 Lecture 7 14 Two dimensional mod., (MPSK) BPSK (M=2) 2 (t ) 0
1 s1 8PSK (M=8) s2 Eb Eb 1 (t ) 010 s4 s3 2 (t ) 011 s2 QPSK (M=4) Es 2 (t ) 01 s2 00 s1
s5 10 1 (t ) 111 100 s6 1 (t ) 11 s000 1 110 Es s3 001 s8 101 s7 s4 Lecture 7 15 Two dimensional mod.,(MPSK)
Coherent detection of MPSK 1 (t ) T 0 r (t ) 2 (t ) z1 z1 arctan z2 T 0 Compute | i | Choose smallest z2 Lecture 7 16 m Two dimensional mod., (MQAM) M-ary Quadrature Amplitude Mod. (MQAM)2 E i si (t )
cosc t i T si (t ) ai1 1 (t ) ai 2 2 (t ) i 1, , M 1 (t ) 2 2 cosc t 2 (t ) sin c t T T where ai1 and ai 2 are PAM symbols and Es 2( M 1) 3 ( M 1, M 1) ( M 3, M 1) ( M 1, M 1) ( M 1 , M 3 ) ( M 3 , M 3
) ( M 1 , M 3 ) ai1 , ai 2 ( M 1, M 1) ( M 3, M 1) ( M 1, M 1) Lecture 7 17 Two dimensional mod., (MQAM) 16-QAM 0000 s1 1000 s5 2 (t ) 0001 0011 s2 1001
-1 s9 s10 1 1101 s13 s14 0100 0101 s3 s4 1011 1010 s6 -3 1100 3 0010 s7 s8 1 3
s s s s 1 (t ) 12 11 -1 1111 1110 16 15 -3 0111 0110 Lecture 7 18 Two dimensional mod., (MQAM) Coherent detection of M-QAM 1 (t ) T z1 ML detector (Compare with M 1 thresholds) 0 r (t )
Parallel-to-serial converter 2 (t ) T 0 z2 ML detector (Compare with M 1 thresholds) Lecture 7 19 m Multi-dimensional modulation, demodulation & detection M-ary Frequency Shift keying (MFSK) 2 Es 2 Es si (t ) cosi t cosc t (i 1)t T T 1 f 2 2T 3 (t ) M
si (t ) aij j (t ) i 1, , M s3 j 1 2 i (t ) cosi t T Es Ei s i Es i j aij ij 0 s2 2 s1 Lecture 7 Es 1 (t ) 2 (t ) Es Es 20 Multi-dimensional mod.,(MFSK) 1 (t ) T
z1 0 r (t ) M (t ) T 0 zM z1 z M Lecture 7 ML detector: z z Choose the largest element in the observed vector m 21 Non-coherent detection Non-coherent detection: No need for a reference in phase with
the received carrier Less complexity compared to coherent detection at the price of higher error rate. Lecture 7 22 Non-coherent detection Differential coherent detection Differential encoding of the message The symbol phase changes if the current bit is different from the previous bit. si (t ) 2E cos0t i (t ) , 0 t T , i 1,...,M T k (nT ) k ((n 1)T ) i (nT ) Symbol index: k 0 1 2 3 4 5 6 7 1 1 0 1 0 1 1 Data bits: mk Diff. encoded bits 1 1 1 0 0 1 1 1 0 0 Symbol phase: k Lecture 7 i s2
0 s1 23 1 (t ) Non-coherent detection Coherent detection for diff encoded mod. assumes slow variation in carrier-phase mismatch during two symbol intervals. correlates the received signal with basis functions uses the phase difference between the current received vector and previously estimated symbol 2E r (t ) cos0t i (t ) n(t ), 0 t T T i (nT ) j ((n 1)T ) i (nT ) j ((n 1)T ) i (nT ) 2 (t ) (a2 , b2 ) Lecture 7 i (a1 , b1 ) 24 1 (t ) Non-coherent detection Optimum differentially coherent detector
1 (t ) T r (t ) m Decision 0 Delay T Sub-optimum differentially coherent detector T r (t ) 0 Decision m Delay T Performance degradation about 3 dB by using sub-optimal detector Lecture 7 25 Non-coherent detection
Energy detection Non-coherent detection for orthogonal signals (e.g. M-FSK) Carrier-phase offset causes partial correlation between I and Q branches for each candidate signal. The received energy corresponding to each candidate signal is used for detection. Lecture 7 26 Non-coherent detection Non-coherent detection of BFSK 2 / T cos(1t ) T z11 2 0 2 z11 z12
2 2 / T sin(1t ) T r (t ) z12 0 2 + z (T ) 2 / T cos( 2t ) T z 21 - 2 Decision stage: if z (T ) 0, m 1 if z (T ) 0, m 0 0 2
z 21 z 22 2 / T sin(2t ) T 0 z 22 2 2 Lecture 7 27 m
