Chapter 3: DIFFERENTIAL ENCODING Differential Encoding Eye Patterns Regenerative Receiver Bit Synchronizer Binary to Mary Conversion Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University Eeng360 1
Differential Coding System Differential encoding removes the problem of Unintentional Signal Inversion. Polarity of the differentially encoded signal may be inverted without affecting the decoded signal. Modulo-2 addition Exclusive OR I 1 I 2 Out 0 0 0 0 1 1 1 0 1 1 1 0 e = d e d = e e n n n 1 n n n 1 Represents Modulo-2 adder (XOR) Eeng360 2
Encoding e Input sequence d n 1 1 0 1 0 0 1 Encoded sequence e n 1 0 1 1 0 0 0 1 Reference digit Decoding (with correct channel polarity) Receiver sequence 1 0 1 1 0 0 0 1 (Correct polarity) n Example of Differential Coding = dn en 1 e n d n = en en 1 Decoded sequence 1 1 0 1 0 0 1 ~ d n ~ ~ Decoding (with inverted channel polarity) Received sequence 0 1 0 0 1 1 1 0 (Inverted polarity) e n d n Decoded sequence 1 1 0 1 0 0 1 Decoded sequence is same whether there is inversion or not. EEE 360 3
Eye patterns The effects of channel filtering and channel noise can be seen by observing the received line code on an oscilloscope. Received Line Code Information from Eye Pattern Timing error Eye opening Sensitivity Slope of the open eye Noise Margin height of the eye opening Eeng360 4
Regenerative Repeater Regenerate a noise-free digital signal. Amplify and clean-up the signal periodically Increases the amplitude Produces a sample value Produces a high level o/p if sample value>v T Minimize the effect of channel noise & ISI Generates a clocking signal Eeng360 5
Synchronization Synchronization signals are clock-type signals necessary within a receiver for detection of data from the corrupted input signal. Digital communications need at least 3 types of synchronization signals. Bit Synchronization (Bit Synch.): To distinguish bit intervals. Frame Synchronization (Frame Synch.): To distinguish groups of bits. Carrier Synchronization: For bandpass signals with coherent detection. Sync signals are derived from Corrupted input signal. From a separate channel that transmits sync signals. Eeng360 6
Bit Synchronizer for NRZ Signals Derive the synch signal from the corrupted received signal. Used for unipolar NRZ signals. Synchronizer complexity depends on the line code used. Synchronizarion of RZ signals is easier since PSD has delta at f=r=1/t b. Bit synchronizer for NRZ signals is given below. Eeng360 7
Square-law Bit Synchronizer for NRZ Signals Square Law Device converts polar NRZ signal to unipolar RZ format. Unipolar RZ signals have delta in the PSD at f=r=1/t b. This frequency component can be obtained by filtering. Filtered sinusoidal is converted to clock pulses using a comparator. Eeng360 8
Binary-to-multilevel polar NRZ Signal Conversion Binary to multilevel conversion is used to reduce the bandwidth required by the binary signaling. Multiple bits (l number of bits) are converted into words having SYMBOL durations T s =lt b where the Symbol Rate or the BAUD Rate D=1/T s =1/lT b. The symbols are converted to a L level (L=2 l ) multilevel signal using a l-bit DAC. Note that now the Baud rate is reduced by l times the Bit rate R (D=R/l). Thus the bandwidth required is reduced by l times. T s : Symbol Duration L: Number of M ary levels T b : Bit Duration l: Bits per Symbol L=2l D=1/Ts=1/lT b =R/l B null =R/l Eeng360 9
Power Spectra for Multilevel Polar NRZ Signals (c) L = 8 = 2 3 Level Polar NRZ Waveform Out Eeng360 10
Spectral Efficiency The Spectral efficiency of a digital signal is given by, where R is the data rate and B is the bandwidth required. R ( Bit s) η = B Hz If limited BW is desired, then use a signaling technique that has high spectral efficiency. Maximum spectral efficiency (which is limited by channel noise) is given by the Shannon s Channel Capacity formula: C = = log 1+ B max 2 Spectral efficiency for multilevel signaling is η η = l S N ( bit s) Hz Eeng360 11
PSD of a multilevel polar NRZ waveform R ( k ) = I i = 1 ( a a n n + k ) i P i For k = R 0 8 ( 0) = ( ) i= 1 2 i a n P = 21 ( k) 0. For k 0, R = i 1 where P i = for all of 8 the eight possible values. Then the P ( ) PSD ( f ) 2 for w2 = + T s ω ( ) is 2 t F f ( 21 0) 3. For the rectangular pulse width 3T P multilevelnrz ( f ) sin lπft = K lπftb The null bandwidth is where the pulse width is Ts = Tb PSD for a multilevel polar NRZ signal: b 2 B b : where k is a constant null R = l P s (f) Multilevel signaling is used to reduce the BW of a digital signal = F(f) T s 2 k = R( k) e j2πkft s Eeng360 12