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



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.



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



The basic elements of a PCM system.

Figure 3.13


PCM Transmission System




Sampling

• train of narrow rectangular pulses

• > 2W (sampling theorem)

• low-pass filter – anti-aliasing effect

• result = limited number of discrete values per second



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

)48.3()1log(

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Compression laws. (a) -law. (b) A-law.

Figure 3.14



A-law

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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



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


Bandwidth of PCM SignalsWhat 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:


sR nf sf2sf B

1 1

2 2PCM sB R nf


Bandwidth of PCM Signals• Min bandwidth is for the case of .• Exact bandwidth depends on the type of line

encoding used (unipolar NRZ, polar 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 .


1 1

2 2 sR nf (sin ) /x x

PCM sB R nf PCMB nB


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.


sf



(a) Unipolar NRZ signal. Disadvantages – DC component; power spectra – not 0 at 0 freq.

Figure 3.16a

3. Frequency is normalized to the bit rate 1/Tb

2. Average power is normalized to unity

1. Symbols 1 and 0 are equiprobable

Power spectra of line codes:

Assumptions:



(b) Polar NRZ signal. Disadvantages – large power near zero frequency

Figure 3.16bFrequency is normalized

to the bit rate 1/Tb

Average power is normalized to unity



(c) Unipolar RZ signal. Advantages – presence of delta function at f=0, 1/Tb- used for syncDisadvantage – 3dB more power polar RZ for same error probability

Figure 3.16c



(d) Bipolar RZ signal. Advantages – no DC component; bipolar AMI

Figure 3.16d



(e) Manchester-encoded signal. Advantages – no DC; insignificant low-frequency components

Figure 3.16e



Differential Codes

• encoding based on signal transitions

• reference signal (1) is necessary

Figure 3.17



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 thresholdNote: Occasional wrong decisions = bit errors



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



Block diagram of regenerative repeater.

Figure 3.18



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,…2R-1)



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



Outline








3.8. Noise Considerations in PCM Systems

• Two major sources:– channel noise– quantization noise – signal dependent



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



Error Threshold

• BER due to AWGN depends on Eb/N0 – ratio of the transmitted signal energy per bit Eb, to the noise spectral density N0.

• Table 3.3 – different behavior below and above 11 dB. (compare to - 60-70 dB for high quality speech transmission with AM).

• No error accumulation – regeneration



Outline








3.9. Time Division Multiplexing

Figure 3.19



Concept• 1. Restricting each input by low-pass anti-aliasing

filter• 2. Commutator – takes sample from each input

message (f > 2W); interleave samples in a frame Ts;

• 3. Pulse modulator – transformation for transmission over common channel

• 4. Pulse demodulator • 5. Decommutator – synchronized with the

commutator



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



Example: The T1 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 kHz)

– Nyquist sampling rate = 6.2 kHz – actual sampling rate 8 kHz• Companding - µ-law; µ = 255; 15 piece linear segment for approximating

the logarithmic characteristic; 1a, 2a, 3a … segments above x, 1b, 2b, 3b,…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 1a and 1b 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 7a and 7b).

• 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 + 14X16 = 255 for the 15 segment companding characteristic;



• 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 kHz, 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/193bits); transmission rate 1.544 Mb/s

• Signaling – every 6th frame, last bit; signaling rate for each channel - 8 kHz/6 = 1.333 kb/s



Outline








3.10. Digital Multiplexers

Same concept (TDM) used for multiplexing digital signals of different rates.Conceptual diagram of multiplexing-demultiplexing.

Figure 3.20



• 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.



North American Digital TDM Hierarchy• First level multiplexers – 24 64 kb/s streams (primary

rate) into a DS1 (digital signal 1) stream of 1.544 Mb/s carried on the T1 system.

• Second level multiplexers – 4 DS1 streams into a DS2 stream at 6.312 Mb/s

• Third level multiplexers – 7 DS2 streams into a DS3 stream at 44.736 Mb/s

• Fourth level multiplexers – 6 DS3 into a DS4 stream at 274.176 Mb/s

• Fifth level multiplexers – 2 DS4 streams into a DS5 at 560.160 Mb/s



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.



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.



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 M12 Multiplexer.



Example: signal format of the AT&T M12 Multiplexer

• Designed to combine 4 DS1 into one DS2 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



Signal format of AT&T M12 multiplexer

Figure 3.21



Control bits• F – 2 per subframe; main framing pulses (01010101)• 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 DS1

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 F1



Receiver• 1. Searches for main framing sequence – 01010101 in

F bits• 2. Establishes the identity of the four DS1 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 DS1 streams are properly destuffed



Outline








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).



• Disadvantages:

• 1. Increases complexity - VLSI technology

• 2. Increased bandwidth – satellites and fiber optic cables; data compression techniques;



Home reading assignment

• Conditions for optimality of Scalar Quantizers –Haykin, p.198 – 201.

• Provide one A4 page summary on what you have read. To be uploaded on the site.

chapter 3 pulse modulation

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