Chapter 3 Pulse Modulation CHAPTER 3 PULSE MODULATION

Chapter 3: Pulse Modulation CHAPTER 3 PULSE MODULATION Digital Communication Systems 2012 R. Sokullu 1/61

Chapter 3: Pulse Modulation Outline • • • 3. 7 Pulse Code Modulation 3. 8 Noise in PCM Systems 3. 9 Time Division Multiplexing 3. 10 Digital Multiplexers 3. 11 Modifications of PCM Digital Communication Systems 2012 R. Sokullu 2/61

Chapter 3: Pulse Modulation 3. 7 Pulse Code Modulation • This part deals with the most basic form of digital modulation. • It is based on the two main processes we have studied - the sampling process and the quantization process. • Definition: Pulse Code Modulation is a technique where the message signal is represented by a sequence of coded pulses. It realizes digital representation of the signal both time-wise and amplitude-wise. Digital Communication Systems 2012 R. Sokullu 3/61

Chapter 3: Pulse Modulation PCM – essentially an analog-to-digital conversion (delta modulation (DM) and differential pulse code modulation (DPCM)); – special – information contained in the instantaneous sample is represented by digital words in a serial bit stream. Transmitter – sampling – quantization (A/DC) – encoding (A/DC) Receiver – regeneration – decoding – reconstruction Digital Communication Systems 2012 R. Sokullu 4/61

Chapter 3: Pulse Modulation The basic elements of a PCM system. Figure 3. 13 Digital Communication Systems 2012 R. Sokullu 5/61

Chapter 3: Pulse Modulation PCM Transmission System Digital Communication Systems 2012 R. Sokullu 6/61

Chapter 3: Pulse Modulation Sampling • • train of narrow rectangular pulses > 2 W (sampling theorem) low-pass filter – anti-aliasing effect result = limited number of discrete values per second Digital Communication Systems 2012 R. Sokullu 7/61

Chapter 3: Pulse Modulation Quantization • uniform law (described in sec. 3. 6) • non-uniform – (voice applications); step size increases in accordance with input-output amplitude separation from origin – compressor + uniform quantizer – µ-law (m and v – normalized I/O voltages) – µ-law - |m| >>1 – logarithmic; |m| << 1 – linear Digital Communication Systems 2012 R. Sokullu 8/61

Chapter 3: Pulse Modulation Compression laws. (a) m -law. (b) A-law. Figure 3. 14 Digital Communication Systems 2012 R. Sokullu 9/61

Chapter 3: Pulse Modulation A-law Digital Communication Systems 2012 R. Sokullu 10/61

Chapter 3: Pulse Modulation Transmission side - Encoding • Aim – robust to noise, interference and channel impairments (see Table 3. 2/204) – line codes – differential codes • discrete set of values – appropriate signal • binary codes – 1 and 0 (resistant to high noise ratio) – 256 q. levels – 8 bit code word • ternary codes - 1, 0 and -1 Digital Communication Systems 2012 R. Sokullu 11/61

Chapter 3: Pulse Modulation Line codes for the electrical representations of binary data. (a) Unipolar non-return-to-zero (NRZ) signaling (on-off signalling). (b) Polar NRZ signaling. (c) Unipolar return-to-zero (RZ) signaling. (d) Bipolar RZ signaling. (e) Split-phase or Manchester code. Figure 3. 15 Digital Communication Systems 2012 R. Sokullu 12/61

Chapter 3: Pulse Modulation Bandwidth of PCM Signals What is the spectrum of a PCM data waveform – For PAM – obtained as a function of the spectrum of the input analog signal, because PAM is a linear function of the signal – PCM is non-linear function of the input analog signal – Spectrum is not directly related to the spectrum of the input analog signal Bandwidth depends on: bit rate and pulse shape used to represent the data – where n is the number of bits in the PCM word, sampling frequency. For no aliasing, . (B is the analog signal bandwidth). – Dimensionality theorem gives the bounds: Digital Communication Systems 2012 R. Sokullu 13/61

Chapter 3: Pulse Modulation Bandwidth of PCM Signals • Min bandwidth is for the case of. • Exact bandwidth depends on the type of line encoding used (unipolar NRZ, bipolar RZ etc. • Next slides provide information of bandwidth and power requirements for different line encoding schemes. • For rectangular pulses first null bandwidth is: so lower bound for PCM is Digital Communication Systems 2012 R. Sokullu . 14/61

Chapter 3: Pulse Modulation Bandwidth of PCM Signals • Finally, bandwidth for PCM signals in the case where sampling is higher than , is significantly higher than the corresponding analog signal it represents. Digital Communication Systems 2012 R. Sokullu 15/61

Chapter 3: Pulse Modulation Digital Communication Systems 2012 R. Sokullu 16/61

Chapter 3: Pulse Modulation Power spectra of line codes: Assumptions: 2. Average power is normalized to unity 1. Symbols 1 and 0 are equiprobable 3. Frequency is normalized to the bit rate 1/Tb Figure 3. 16 a (a) Unipolar NRZ signal. Disadvantages – DC component; power spectra – not 0 at 0 freq. Digital Communication Systems 2012 R. Sokullu 17/61

Chapter 3: Pulse Modulation Average power is normalized to unity Figure 3. 16 b Frequency is normalized to the bit rate 1/Tb (b) Polar NRZ signal. Disadvantages – large power near zero frequency Digital Communication Systems 2012 R. Sokullu 18/61

Chapter 3: Pulse Modulation Figure 3. 16 c (c) Unipolar RZ signal. Advantages – presence of delta function at f=0, 1/Tb- used for sync Disadvantage – 3 d. B more power polar RZ for same error probability Digital Communication Systems 2012 R. Sokullu 19/61

Chapter 3: Pulse Modulation Figure 3. 16 d (d) Bipolar RZ signal. Advantages – no DC component; bipolar AMI Digital Communication Systems 2012 R. Sokullu 20/61

Chapter 3: Pulse Modulation Figure 3. 16 e (e) Manchester-encoded signal. Advantages – no DC; insignificant low-frequency components Digital Communication Systems 2012 R. Sokullu 21/61

Chapter 3: Pulse Modulation Differential Codes • encoding based on signal transitions • reference signal (1) is necessary Figure 3. 17 Digital Communication Systems 2012 R. Sokullu 22/61

Chapter 3: Pulse Modulation Transmission Path - Regeneration • PCM advantage – control effects of noise and distortion • PCM signal – reconstructed by a series of regenerative repeaters along the transmission route • functions: – equalization – reshaping, compensates for noise and distortion – timing – circuitry to provide a periodic pulse train for determining sampling instants – decision making – comparison to a predetermined threshold Note: Occasional wrong decisions = bit errors Digital Communication Systems 2012 R. Sokullu 23/61

Chapter 3: Pulse Modulation Regeneration • Possible problems: – Noise and interference on the channel can add resulting in wrong decisions = bit errors – Spacing between pulses can deviate from originally assigned = jitter Digital Communication Systems 2012 R. Sokullu 24/61

Chapter 3: Pulse Modulation Block diagram of regenerative repeater. Figure 3. 18 Digital Communication Systems 2012 R. Sokullu 25/61

Chapter 3: Pulse Modulation Receiving side - Decoding • Receiver side functions – regeneration – regrouping into code-words – decoding • Decoding: generating a pulse the amplitude of which is the linear sum of all pulses in the code word, with each pulse being weighted by its place value (20, 21, … 2 R-1) Digital Communication Systems 2012 R. Sokullu 26/61

Chapter 3: Pulse Modulation Filtering • Final operation – after decoder low-pass reconstruction filter with bandwidth W (message bandwidth). • If transmission path is error free the recovered signal has: – no noise from channel – only distortion - quantization Digital Communication Systems 2012 R. Sokullu 27/61

Chapter 3: Pulse Modulation Outline • • • 3. 7 Pulse Code Modulation 3. 8 Noise in PCM Systems 3. 9 Time Division Multiplexing 3. 10 Digital Multiplexers 3. 11 Modifications of PCM Digital Communication Systems 2012 R. Sokullu 28/61

Chapter 3: Pulse Modulation 3. 8. Noise Considerations in PCM Systems • Two major sources: – channel noise – quantization noise – signal dependent Digital Communication Systems 2012 R. Sokullu 29/61

Chapter 3: Pulse Modulation Channel and Quantization Noise • Channel Noise – Introduces bit errors – Fidelity – average probability of symbol errors (probability that the reconstructed symbol differ from the transmitted binary symbol); in BER (equal or weighted). – Modeling - AWGN; reduce distance between repeaters; performance dependent on quantization noise • Quantization noise –presented before; design stage Digital Communication Systems 2012 R. Sokullu 30/61

Chapter 3: Pulse Modulation Error Threshold • BER due to AWGN depends on Eb/N 0 – ratio of the transmitted signal energy per bit Eb, to the noise spectral density N 0. • Table 3. 3 – different behavior below and above 11 d. B. (compare to - 60 -70 d. B for high quality speech transmission with AM). • No error accumulation – regeneration Digital Communication Systems 2012 R. Sokullu 31/61

Chapter 3: Pulse Modulation Outline • • • 3. 7 Pulse Code Modulation 3. 8 Noise in PCM Systems 3. 9 Time Division Multiplexing 3. 10 Digital Multiplexers 3. 11 Modifications of PCM Digital Communication Systems 2012 R. Sokullu 32/61

Chapter 3: Pulse Modulation 3. 9. Time Division Multiplexing Figure 3. 19 Digital Communication Systems 2012 R. Sokullu 33/61

Chapter 3: Pulse Modulation Concept • 1. Restricting each input by low-pass anti-aliasing filter • 2. Commutator – takes sample from each input message (f > 2 W); interleave samples in a frame Ts; • 3. Pulse modulator – transformation for transmission over common channel • 4. Pulse demodulator • 5. Decommutator – synchronized with the commutator Digital Communication Systems 2012 R. Sokullu 34/61

Chapter 3: Pulse Modulation Synchronization • TDM - Easy to add and drop sources • Pulses duration considerations – time interval limited by the sampling rate (reciprocal) – more users – shorter pulses – difficult to generate; highly influenced by impairments – upper limit of number of independent sources • Transmitter-receiver clock sync – very important – two local clocks – separate code element or pulse at the end of a frame – orderly procedure for detecting sync pulses – searching procedure Digital Communication Systems 2012 R. Sokullu 35/61

Chapter 3: Pulse Modulation Example: The T 1 System • 24 voice channels; separate pairs of wires; regeneration every 2 km; basic to the North American Digital Switching Hierarchy • Voice signal (300 – 3100 Hz) – low pass filter (cutoff frequency 3. 1 k. Hz) – Nyquist sampling rate = 6. 2 k. Hz – actual sampling rate 8 k. Hz • Companding - µ-law; µ = 255; 15 piece linear segment for approximating the logarithmic characteristic; 1 a, 2 a, 3 a … segments above x, 1 b, 2 b, 3 b, …below x; 14 segments, each segment contains 16 uniform decision levels • for segment 0 – quantizer inputs are: ± 1, ± 3, …± 31 and the outputs are 0, ± 1, …. ± 15; for segment 1 a and 1 b the decision level quantizer inputs are: ± 31, ± 35, …± 95 and the outputs are ± 16, ± 17, …± 31 and so on for the other linear segments (up to 7 a and 7 b). • Finally we have equally spacing on the y axis corresponding to non-equally spaced inputs on the x axis (different step for different segment); • Total representation levels: 31 + 14 X 16 = 255 for the 15 segment companding characteristic; Digital Communication Systems 2012 R. Sokullu 36/61

Chapter 3: Pulse Modulation • Each of the 24 voice channels uses binary code with 8 -bit word. – first bit – 1 (positive voice input), 0 (negative voice input) – bits 2 – 4 – identify particular segment – last 4 bits – actual representation level (16 levels) • Frames – for 8 k. Hz, each frame occupies a period of 125 µs – contains 24 X 8 =192 bit words; 1 bit for sync = 193 bits – bit duration = 0. 647 µs (125µs/193 bits); transmission rate 1. 544 Mb/s • Signaling – every 6 th frame, last bit; signaling rate for each channel - 8 k. Hz/6 = 1. 333 kb/s Digital Communication Systems 2012 R. Sokullu 37/61

Chapter 3: Pulse Modulation Outline • • • 3. 7 Pulse Code Modulation 3. 8 Noise in PCM Systems 3. 9 Time Division Multiplexing 3. 10 Digital Multiplexers 3. 11 Modifications of PCM Digital Communication Systems 2012 R. Sokullu 38/61

Chapter 3: Pulse Modulation 3. 10. Digital Multiplexers Same concept (TDM) used for multiplexing digital signals of different rates. Conceptual diagram of multiplexing-demultiplexing. Figure 3. 20 Digital Communication Systems 2012 R. Sokullu 39/61

Chapter 3: Pulse Modulation • Multiplexing is accomplished by bit-by-bit interleaving; selector switch – sequentially scanning incoming line; at the receiving side – separation into low speed components. • Types of multiplexers: – relatively low data bit rate user streams are TD multiplexed over the public switched telephone network. – data transmission service by telecommunication carriers; part of the national digital TDM hierarchy. Digital Communication Systems 2012 R. Sokullu 40/61

Chapter 3: Pulse Modulation North American Digital TDM Hierarchy • First level multiplexers – 24 64 kb/s streams (primary rate) into a DS 1 (digital signal 1) stream of 1. 544 Mb/s carried on the T 1 system. • Second level multiplexers – 4 DS 1 streams into a DS 2 stream at 6. 312 Mb/s • Third level multiplexers – 7 DS 2 streams into a DS 3 stream at 44. 736 Mb/s • Fourth level multiplexers – 6 DS 3 into a DS 4 stream at 274. 176 Mb/s • Fifth level multiplexers – 2 DS 4 streams into a DS 5 at 560. 160 Mb/s Digital Communication Systems 2012 R. Sokullu 41/61

Chapter 3: Pulse Modulation Important Note: • Digital transmission facilities ONLY carry bit streams without interpreting what the bits themselves mean. • The two sides have common understanding of how to interpret the bits: voice, data, framing format, signaling format etc. Digital Communication Systems 2012 R. Sokullu 42/61

Chapter 3: Pulse Modulation Problems: • 1. Digital signals cannot be directly interleaved into a format that allows for their separation automatically. Common clock or perfect synchronizations is needed. • The multiplexed signal must include some form of framing so the individual streams can be identified at the source. • The multiplexer should be able to handle small variations in bit rates – bit stuffing. Digital Communication Systems 2012 R. Sokullu 43/61

Chapter 3: Pulse Modulation Bit stuffing • To make the outgoing rate of the multiplexer a little bit higher than the sum of the max expected input rates. • Each input is fed into an elastic store at the multiplexer (reading can be done at different rate). • Identify stuffed bits – example AT&T M 12 Multiplexer. Digital Communication Systems 2012 R. Sokullu 44/61

Chapter 3: Pulse Modulation Example: signal format of the AT&T M 12 Multiplexer • Designed to combine 4 DS 1 into one DS 2 bit stream • Each frame contains total of 24 control bits, separated by sequences of 48 data bits • 4 frames, transmitted one after the other • 12 bits from each input bit-by-bit interleaved, 48 bits • Four types of control bits – F, M and C inserted by multiplexer – total of 24 control bits Digital Communication Systems 2012 R. Sokullu 45/61

Chapter 3: Pulse Modulation Signal format of AT&T M 12 multiplexer Figure 3. 21 Digital Communication Systems 2012 R. Sokullu 46/61

Chapter 3: Pulse Modulation Control bits • F – 2 per subframe; main framing pulses (0101) • M – 1 pr subframe; secondary framing, identifying the subframes (0111) • C – 3 per subframe; stuffing indicators; indexes denote input channel; – first subframe has 3 C bits, indicating stuffing in first DS 1 stream; value 1 of all three indicates stuffed bits; value 0 – no stuffed bits; majority logic decoding – if there is stuffing position of stuffing is – first bit after F 1 Digital Communication Systems 2012 R. Sokullu 47/61

Chapter 3: Pulse Modulation Receiver • 1. Searches for main framing sequence – 0101 in F bits • 2. Establishes the identity of the four DS 1 streams and position of M and C bits • 3. From the position of the M bits the correct position of the C bits is verified • 4. Streams properly demultiplexed and destuffed. • Safeguards: – Double checking F and M bits for framing. – Single error correction capability built into the C-control bits ensures that the 4 DS 1 streams are properly destuffed Digital Communication Systems 2012 R. Sokullu 48/61

Chapter 3: Pulse Modulation Outline • • • 3. 7 Pulse Code Modulation 3. 8 Noise in PCM Systems 3. 9 Time Division Multiplexing 3. 10 Digital Multiplexers 3. 11 Modifications of PCM Digital Communication Systems 2012 R. Sokullu 49/61

Chapter 3: Pulse Modulation 3. 11. Virtues, Limitations and Modifications of PCM • • Advantages: 1. Robustness to channel noise and interference. 2. Signal regeneration possibilities along the path. 3. Efficient trade-off between increased bandwidth and improved SNR (exponential law) • 4. Integration of different base-band signals. • 5. Comparative easy of add and drop sources. • 6. Secure communication (special modulation, encryption). Digital Communication Systems 2012 R. Sokullu 50/61

Chapter 3: Pulse Modulation • Disadvantages: • 1. Increases complexity - VLSI technology • 2. Increased bandwidth – satellites and fiber optic cables; data compression techniques; Digital Communication Systems 2012 R. Sokullu 51/61

Chapter 3: Pulse Modulation Home reading assignment • Conditions for optimality of Scalar Quantizers –Haykin, p. 198 – 201. • Provide one A 4 page summary on what you have read. To be uploaded on the site. Digital Communication Systems 2012 R. Sokullu 52/61