The Hong Kong Polytechnic University

The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

File name: eie331 08pam.pdf

PULSE MODULATION: Part II Contents: • Encoding • Pulse-code modulation (PCM) • Delta modulation (DM) • Comparison of pulse-code and delta modulation systems • Time division multiplexing (TDM) • TDM: Concept of framing and synchronization • Comparison of time and frequency division multiplexing

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

References: Haykin: Sections 6.8–6.11, pp. Lecture notes

EIE331: Communication Fundamentals

378–396, Section 6.4, pp.362–364

PULSE MODULATION Some parameter of a pulse train is varied in accordance with the message signal Two families of pulse modulation are distinguished: • Analog pulse modulation: Sampling, i.e., information is transmitted only at discrete time instants • Digital pulse modulation: Sampling and quantization, i.e., information is discretized in both time and amplitude

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

Main question: Can we recover the original message signal without distortion? Sampling: Answer: YES, see sampling theorem A band-limited signal of finite energy, which has no frequency components higher than W hertz, is completely described by specifying the values of 1 the signal at instants of time separated by 2W seconds A band-limited signal g(t) of finite energy, which has no frequency components higher than W hertz, may be completely recovered from a knowledge of its samples taken at the rate of 2W samples per second Quantization: Answer: NO, a quantization error occurs Quantization error may be modeled as a quantization noise if the step size of quantization is small enough Sampling and quantization are discussed in eie331 08pam.pdf ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

ENCODING Sampler converts the analog signal into a discrete one that is discrete in time but continuous in amplitude Quantizer converts the discrete time signal into a sampled and quantized signal that is discrete in both time and amplitude Due to sampling and quantizing the analog signal is mapped to a finite discrete set of sample values or quantized samples Encoder maps the quantized samples into digital code words In a binary code, each code word consists of v bits. Note, v denotes the number of bits per sample Using code word with length of v, we may represent a total of 2v quantized sample values There are several ways of establishing a one-to-one correspondence between quantized sample values and code words, a simple solution is to express the quantized sample value as a binary number ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

Generation of pulse-code modulation (PCM): An example for simultaneous application of sampling, quantization and encoding

where • • • • • • •

ADC: Analog-to-digital converter, available as one integrated circuit LPF: Low-pass filter, S/H: Sample-and-hold circuit x(t): Analog signal to be converted fs: Sampling frequency x(kTs): Sampled signal xq (kTs): Quantized signal v: Length of code word

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

PULSE-CODE MODULATION (PCM) In pulse-code modulation (PCM), an analog message signal is represented by a sequence of coded pulses, which is accomplished by representing the signal in discrete form in both time and amplitude PCM is the most basic form of digital pulse modulation A PCM system contains three main blocks: • PCM transmitter • Transmission path • Receiver

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

PCM transmitter

T.1: Sampling To avoid aliasing, a pre-alias (low-pass) filter is used to limit the bandwidth of message signal Sampling rate must be greater than the Nyquist rate 2W T.2: Quantization To reduce quantization noise, a nonuniform quantizer is used T.3: Encoding contains two encoding processes Encoder maps quantized samples into v-length code word A line encoding converts the digital signal (codeword) into an analog waveform ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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EIE331: Communication Fundamentals

Why do we need line encoding: • Channels used to transmit information are analog channels which can transmit only analog signals • Line encoder maps digital code words into voltage levels • Simplest line encoding is on-off signaling where symbol 1 is represented by transmitting a pulse of constant amplitude for the duration of symbol, and symbol 0 is represented by switching off the pulse

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

PCM transmission path

TP.1: Regeneration Regenerative repeater performs three tasks: • Equalization means a compensation for the effects of amplitude and phase distortion produced by the channel • Timing circuitry assigns the decision time instants when the probability of making of a wrong decision is minimum • Decision making regenerates the PCM wave The most important feature of PCM systems is the ability to control the effects of distortion and noise. A PCM signal may be reconstructed from the distorted and noisy input by means of regenerative repeaters placed sufficiently close to each other along the transmission route ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

PCM receiver

R.1: Regeneration circuit Reshapes and cleans up the received noise and distorted signal. Its three tasks were discussed in the previous transparency R.2: Decoding First the code word is recovered from the data sequence and then a pulse is generated, where the amplitude of pulse is determined by the code word R.3: Reconstruction filter The cut-off frequency of low-pass reconstruction filter is equal to the message bandwidth W . It recovers the analog message signal

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

Transmission bandwidth of a PCM wave Each encoded message sample is represented by a v-digit code word. Consequently, the signaling rate becomes r = vfs

with fs ≥ 2W . The transmission bandwidth required by the PCM wave is BT ≥

1 1 r = vfs ≥ vW 2 2

Main feature of pulse-code modulation: If the regenerators are well placed then they cancel the effect of channel distortion and noise. In this case the only source of distortion and noise is the quantization error

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

DELTA MODULATION (DM) The physical signals have a low-pass characteristic. function is similar to a sinc(Cτ ) =

Their autocorrelation

sin(πCτ ) πCτ

function, where C is a constant. It means that the correlation between two adjacent sample increases by shortening the time that separates the two adjacent samples In delta modulation (DM), the incoming signal is oversampled (i.e., the sampling rate is much higher than the Nyquist rate) in order to purposely increase the correlation between the adjacent samples of incoming signal Oversampling means a higher sampling rate (and wider transmission bandwidth), but it permits the use of a simple quantizing strategy for constructing the encoded digital signal The delta modulator directly generates a binary sequence, there is no need for encoder and parallel-to-serial converter ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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EIE331: Communication Fundamentals

Delta modulation: A staircase approximation to the message signal In basic form, delta modulation provides a staircase approximation to the message signal. The difference between the analog input m(t) and the staircase approximation mq (t) is quantized into only two levels ±∆ depending on the sign of the difference

The DM wave is a binary sequence as shown in the bottom part of the figure ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

Encoding performed by the delta modulator Delta modulator includes a DM demodulator that generates a staircase approximation mq (t) of the analog message signal m(t) by an accumulator As shown in the figure, if the staircase approximation mq (t) falls below the message signal m(t) at any sampling time instant then the DM modulator emits a bit 1 which means that the value of mq (t) has to be increased by ∆ If mq (t) lies above m(t) then the DM modulator emits a bit 0 which means that the value of staircase approximation mq (t) has to be reduced by ∆

DM wave is the binary sequence that shows if the actual value of message signal m(t) is above or below the previous reconstructed signal value mq (t) ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

Quantization errors in delta modulation

Slope overload distortion If the step size ∆ is too small then the staircase approximation mq (t) cannot follow the fast variations in the input waveform m(t) Granular noise If the step size ∆ is too large then the staircase approximation oscillates around the relatively flat segments of input waveform. Granular noise is analogous to quantization noise in a PCM system ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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COMPARISON SYSTEMS

OF

EIE331: Communication Fundamentals

PULSE-CODE

AND

DELTA

MODULATION

Pulse code modulation Quantization noise depends on the step size, i.e., on the resolution of quantizer. There is an efficient exchange of increase transmission bandwidth for improved signal-to-noise ratio (SNR), obeying an exponential law PCM requires a relatively complex system, but today it is available as a very-large-scale integrated (VLSI) circuit Delta modulation Actual signal value is reconstructed from the previous one. This behavior leads to the drawback of delta modulation in that the transmission disturbances caused by noise, for example, result in an accumulative error in the demodulated signal Due to oversampling, an increased transmission bandwidth is required Delta modulation requires a simple circuitry ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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EIE331: Communication Fundamentals

TIME-DIVISION MULTIPLEXING

Since only samples of a message signal are transmitted, the channel is occupied only for a short time slot in pulse modulation systems. Consequently, samples of N message signals may be transmitted over the same channel Message signals 1, 2, . . . , N are separated in the time domain Note, the multiplexed signal is the input to the pulse modulator ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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EIE331: Communication Fundamentals

TDM: CONCEPT OF FRAMING AND SYNCHRONIZATION Consider a multiplexed PAM wave generated by the commutator. The time interval TF containing one sample from each message signal is called a frame

Synchronization must be established and maintained between the commutator and decommutator. Generally, an extra pulse (called marker) or a special sequence of pulses are transmitted at the beginning of each frame to help the clock recovery circuit to establish the synchronization ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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COMPARISON OF MULTIPLEXING

EIE331: Communication Fundamentals

TIME

AND

FREQUENCY

DIVISION

Time division multiplexing: Individual TDM channels are assigned to distinct time slots but jumbled together in the frequency domain. Channels are separated in the time domain Frequency division multiplexing: Individual FDM channels are assigned to distinct frequency regions but jumbled together in the time domain. Channels are separated in the frequency domain Comparison of TDM and FDM: Many of the TDM advantages are technology driven. The digital circuits are much cheaper and easier to implement In FDM, imperfect bandpass filtering and nonlinear cross-modulation cause cross talk. TDM is not sensitive to these problems ´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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The Hong Kong Polytechnic University

EIE331: Communication Fundamentals

However, TDM is sensitive to transmission bandwidth and delay distortion Multiplexing of digital signals is much more easier in TDM Depending on the type of fading, TDM may or may not be advantageous when the transmission channel subject to fading. Rapid wideband fading might strike only occasional pulses in a given TDM channel, while all FDM channels would be affected. But slow narrow-band fading wipes out all TDM channels, whereas it might hurt only one FDM channel

Always remember: In engineering there is no general medicine and free meal!

´ — Dept. of Electronic and Information Engineering G´ eza KOLUMBAN

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