ETI 2413 Digital Communication Principles - 2

ETI 2413 Digital Communication Principles

Lecture 2 By

Isaac Warutumo


2 Isaac Warutumo January 19, 2015

DIGITAL BAND-PASS MODULATION TECHNIQUES

In baseband data transmission, an incoming serial data stream is represented in the form of a discrete pulse-amplitude modulated wave that can be transmitted over a low-pass channel (e.g., a coaxial cable).

In applications where there is need to transmit the data stream over a band-pass channel, such as wireless and satellite channels, we usually use a modulation strategy configured around a sinusoidal carrier whose amplitude, phase, or frequency is varied in accordance with the information-bearing data stream.

In this lecture, we will look at digital modulation techniques that deal with band-pass data transmission.



We will look at some important digital band-pass modulation techniques used in practice. In particular, we describe three basic modulation schemes: namely, amplitude-shift keying, phase-shift keying, and frequency-shift keying, followed by some of their variants.

Given a binary source that emits symbols 0 and 1, the modulation process involves switching or keying the amplitude, phase, or frequency of a sinusoidal carrier wave between a pair of possible values in accordance with symbols 0 and 1.

Consider the sinusoidal carrier

c c cc(t)=A cos(2 f t+ ) (1)

Where Ac is the carrier amplitude, fc is the carrier frequency, and c

is the carrier phase. Given these three parameters of the carrier



c(t), we may now identify three distinct forms of binary modulation: o Binary amplitude shift-keying (BASK), in which the

carrier frequency and carrier phase are both maintained constant, while the carrier amplitude is keyed between the two possible values used to represent symbols 0 and 1.

o Binary phase-shift keying (BPSK), in which the carrier amplitude and carrier frequency are both maintained constant, while the carrier phase is keyed between the two possible values (e.g., 0 and 180) used to represent symbols 0 and 1.

o Binary frequency-shift keying (BFSK), in which the carrier amplitude and carrier phase are both maintained constant, while the carrier frequency is keyed between the two possible values used to represent symbols 0 and 1.

In light of these definitions, we see that BASK, BPSK, and BFSK are special cases of amplitude modulation, phase modulation, and frequency modulation, respectively.

BASK, BPSK, and BFSK share a common feature: all three of them are examples of a band-pass process.

In the analog communications, the sinusoidal carrier is commonly defined as in equation(1).

On the other hand, in the digital communications literature, the usual practice is to assume that the carrier has unit energy measured over one symbol (bit) duration. Specifically, we may define the carrier amplitude as

2

c

b

AT

(2)

Where Tb is the bit duration



Using the terminology of Eq.(2), we may thus express the carrier c(t) in the equivalent form

(3)

BINARY AMPLITUDE-SHIFT KEYING

Binary amplitude-shift keying (BASK) is one of the earliest forms of digital modulation used in radio telegraphy at the beginning of the twentieth century.

To formally describe BASK, consider a binary data stream which is of the ONOFF signaling variety. That is defined by

, 1

( )0, 0

bE forbinary symbolb tfor binary symbol

(4)



c c

2c(t)= cos(2 f t+ )

bT (5)

Then, multiplying by the sinusoidal carrier c(t) with the phase set equal to zero for convenience of presentation, we get the BASK wave

( ) ( ) ( )s t b t c t (6)

2cos(2 ), 1

( )

0, 0

bc

b

Ef t for symbol

s t T

for symbol

(7)

The carrier frequency fc may have an arbitrary value, consistent with transmitting the modulated signal anywhere in the electromagnetic radio spectrum, so long as it satisfies the bond-pass assumption (that the carrier frequency is large compared with the



bandwidth of the incoming binary data stream that acts as the modulating signal).

When bit duration is occupied by symbol 1, the transmitted signal energy is Eb. When the bit duration is occupied by symbol 0, the transmitted signal energy is zero. On this basis, we may express the average transmitted signal energy as

2

bav

EE (8)

Generation of BASK Signals From Equations (4)and(7), we see that a BASK signal is readily

generated by using a product modulator with two inputs. One input, the ONOFF signal of Equation (4) is the modulating signal.



The sinusoidal carrier wave c c

2c(t)= cos(2 f t+ )

bT supplies the

other input.



Figure 1: The three basic forms of signaling binary information. (a) Binary data stream. (b) Amplitude-shift keying. (c) Phase-shift keying. (d) Frequency-shift

keying with continuous phase.



Detection of BASK Signals A property of BASK that is immediately apparent from Figure 1(b),

which depicts the BASK waveform corresponding to the incoming binary data stream of Figure 1(a), is the non-constancy of the envelope of the modulated wave. Accordingly, insofar as detection of the BASK wave is concerned, the simplest way is to use an envelope detector, exploiting the non-constant envelope property of the BASK signal.

BINARY PHASE-SHIFT KEYING (BPSK)

In the simplest form of phase-shift keying known as binary phase-shift keying (BPSK), the pair of signals s1(t) and s2(t) used to represent symbols 1 and 0, respectively, are defined by



c

c c

2cos(2 f t), for symbol0( 1)

( )2 2

cos(2 f t+ ) cos(2 f t),for symbol 1( 2)

b

b

i

b b

b b

Ei

Ts t

E Ei

T T

(9)

Where 0 bt T , with Tb denoting the bit duration and Eb denoting

the transmitted signal energy per bit; see the waveform of Figure 1(c) for a representation example of BPSK.

A pair of sinusoidal waves, S1(t) and S2(t) which differ only in a relative phase-shift of radians as defined in equation (9), are referred to as antipodal signals.



BPSK differs from BASK in an important respect; the envelope of the modulated signal s(t) is maintained constant at the value

2 bb

ET

for all time t. This property, which follows directly from

equation (9), has two important consequences:

o The transmitted energy per bit, is constant; equivalently, the average transmitted power is constant.

o Demodulation of BPSK cannot be performed using envelope detection; rather, we have to look to coherent detection as described next.

Generation of BPSK Signals We use a product modulator consisting of two components (see

Figure 2(a)):



o Non-return-to-zero level encoder, whereby the input binary data sequence is encoded in polar form with symbols 1 and 0

represented by the constant-amplitude levels: bE and bE ,

respectively o Product modulator, which multiplies the level-encoded binary

wave by the sinusoidal carrier c(t) of amplitude 2bT

to

produce the BPSK signal.

The timing pulses used to generate the level-encoded binary wave and the sinusoidal carrier wave are usually, but not necessarily, extracted from a common master clock.



Figure 2: (a) BPSK modulator. (b) Coherent detector for BPSK; for the sampler,

integer i 0, 1, 2, .



Detection of BPSK Signals To detect the original binary sequence of 1s and 0s, the BPSK signal

x(t) at the channel output is applied to a receiver that consists of four sections, as depicted in Figure 2(b): o Product modulator, which is also supplied with a locally

generated reference signal that is a replica of the carrier wave c(t)

o Low-pass filter, designed to remove the double-frequency components of the product modulator output (i.e., the components centered on 2fc) and pass the zero-frequency components.



o Sampler, which uniformly samples the output of the low-pass

filter at bt iT where 0, 1, 2,...i ; the local clock

governing the operation of the sampler is synchronized with the clock responsible for bit-timing in the transmitter.

o Decision-making device, which compares the sampled value of the low-pass filters output to an externally supplied threshold, every seconds. If the threshold is exceeded, the device decides in favor of symbol 1; otherwise, it decides in favor of symbol 0.

The BPSK receiver described in Figure 2 is said to be coherent in the sense that the sinusoidal reference signal applied to the product modulator in the demodulator is synchronous in phase (and, of course, frequency) with the carrier wave used in the modulator.



In addition to synchrony with respect to carrier phase, the receiver also has an accurate knowledge of the interval occupied by each binary symbol.

Exercises

1. The binary sequence 11100101 is applied to an ASK modulator. The bit duration is microsecond and the sinusoidal carrier wave used to represent symbol 1 has a frequency equal to 7 MHz.

a. Find the transmission bandwidth of the transmitted signal. b. Plot the waveform of the transmitted ASK signal. c. Assume that the line encoder and the carrier-wave oscillator are

controlled by a common clock. 2. Repeat Problem 1 above, assuming that the line encoder and the carrier-wave

generator operate independently of each other. Comment on your results.



3. (a) Repeat Problem 1above for the case when the binary sequence 11100101 is applied to a PSK modulator, assuming that the line encoder and sinusoidal carrier-wave oscillator are operated from a common clock. (b) Repeat your calculations, assuming that the line encoder and carrier-wave oscillator operate independently.

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ETI 2413 Digital Communication Principles - 2