Dr. Ahmed Masri Department of Communications An Najah National University 2012/2013 Communications and Signals Processing 1 Dr. Ahmed Masri

7.1 Some Preliminaries 7.2 Binary Amplitude-Shift Keying 7.3 Phase-Shift Keying 7.4 Frequency-Shift Keying Chapter 7 - Outlines 2 Dr. Ahmed Masri

Section 7.1 – Some Preliminaries 3 Dr. Ahmed Masri

 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: Section 7.1 – Some Preliminaries 4 Dr. Ahmed Masri

 We may now identify three distinct forms of digital band-pass modulation techniques: 1) 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 2) 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. Section 7.1 – Some Preliminaries 5 Dr. Ahmed Masri

3) 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. Section 7.1 – Some Preliminaries 6 Dr. Ahmed Masri

 In the analog communications literature, the sinusoidal carrier is commonly defined as in Eq. (7.1). On the other hand,  In the digital communications literature, the usual practice is to assume that the carrier c(t) has unit energy measured over one symbol (bit) duration  We recall that the carrier amplitude is given by: Where T b is the bit duration Section 7.1 – Some Preliminaries 7 Dr. Ahmed Masri

 We can rewrite c(t) as  We learned that decreasing the duration of a rectangular pulse has the effect of widening the effective band of frequencies contained in the pulse. In a corresponding fashion, decreasing the bit duration T b has the effect of increasing the transmission bandwidth requirement of a binary modulated wave. Section 7.1 – Some Preliminaries 8 Dr. Ahmed Masri

 We have learned also that the transmission bandwidth requirement of an angle-modulated wave is greater than that of the corresponding amplitude-modulated wave.  In light of that fact, we may say that the transmission bandwidth requirement of BFSK is greater than that of BASK for a given binary source.  However, the same does not hold for BPSK, as we shall see from the material presented in this chapter. This is one of many differences that distinguish digital modulation from analog modulation. Section 7.1 – Some Preliminaries 9 Dr. Ahmed Masri

BAND-PASS ASSUMPTION  The spectrum of a digitally modulated wave (BASK, BPSK and BFSK) is centered on the carrier frequency f c  Consider a linear modulation scheme for which the modulated wave is defined by where b(t) denotes an incoming binary wave.  We may use Eq. (7.3) to express the modulated wave s(t) as Section 7.1 – Some Preliminaries 10 Dr. Ahmed Masri

BAND-PASS ASSUMPTION  Under the assumption f c >>W, where W is the bandwidth of the binary wave b(t): there will be no spectral overlap in the generation of s(t)  The transmitted signal energy per bit: Section 7.1 – Some Preliminaries 11 Dr. Ahmed Masri

BAND-PASS ASSUMPTION  Using the trigonometric identity Section 7.1 – Some Preliminaries 12 Dr. Ahmed Masri

BAND-PASS ASSUMPTION  The band-pass assumption implies that |b(t)| 2 is essentially constant over one complete cycle of the sinusoidal wave cos(4 π f c t) which, in turn, means that  Accordingly, we may approximate Eq. (7.7) as Section 7.1 – Some Preliminaries 13 Dr. Ahmed Masri

BAND-PASS ASSUMPTION  In words, for linear digital modulation schemes governed by Eq. (7.5), the transmitted signal energy (on a per bit basis) is a scaled version of the energy in the incoming binary wave responsible for modulating the sinusoidal carrier. Section 7.1 – Some Preliminaries 14 Dr. Ahmed Masri

To formally describe BASK, consider a binary data stream b(t) which is of the ON–OFF signaling variety. That is, b(t) is defined by Section 7.2 – Binary Amplitude-Shift Keying 15 Dr. Ahmed Masri

Then, multiplying b(t) by the sinusoidal carrier wave of Eq. (7.3) with the phase ϕ s set equal to zero for convenience of presentation, we get the BASK wave Section 7.2 – Binary Amplitude-Shift Keying 16 Dr. Ahmed Masri

When a bit duration is occupied by symbol 1, the transmitted signal energy is E b.  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  For this formula to hold, however, the two binary symbols must be equiprobable. Section 7.2 – Binary Amplitude-Shift Keying 17 Dr. Ahmed Masri

Generation Of Ask Signals  From Eqs. (7.9) and (7.10), we readily see that a BASK signal is readily generated by using a product modulator with two inputs. One input, the ON–OFF signal of Eq. (7.9), is the modulating signal.  The sinusoidal carrier wave supplies the other input. Section 7.2 – Binary Amplitude-Shift Keying 18 Dr. Ahmed Masri

Generation Of Ask Signals Section 7.2 – Binary Amplitude-Shift Keying 19 Dr. Ahmed Masri

Detection Of Ask Signals  A property of BASK that is immediately apparent from Fig. 7.1(b), which depicts the BASK waveform corresponding to the incoming binary data stream of Fig. 7.1(a), is the nonconstancy 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 nonconstant- envelope property of the BASK signal. Section 7.2 – Binary Amplitude-Shift Keying 20 Dr. Ahmed Masri

Section 7.3 – Phase-Shift Keying 21 Dr. Ahmed Masri

(A) BINARY PHASE-SHIFT KEYING (BPSK) In the simplest form of PSK known as BPSK, the pair of signals s 1 (t) and s 2 (t) used to represent symbols 1 and 0, respectively, are defined by where 0 ≤ t ≤ T b with T b denoting the bit duration and E b denoting the transmitted signal energy per bit; Section 7.3 – Phase-Shift Keying 22 Dr. Ahmed Masri

For a representation example of BPSK: A pair of sinusoidal waves, s 1 (t) and s 2 (t), which differ only in a relative phase-shift of π radians Section 7.3 – Binary- Phase-Shift Keying 23 Dr. Ahmed Masri

BPSK differs from BASK in an important respect: The envelope of the modulated signal is maintained constant at the value, for all time t. This property, which follows directly from Eq. (7.12), has two important consequences: 1. The transmitted energy per bit, is constant; equivalently, the average transmitted power is constant. 2. Demodulation of BPSK cannot be performed using envelope detection; rather, we have to look to coherent detection as described next. Section 7.3 – Binary- Phase-Shift Keying 24 Dr. Ahmed Masri

Generation And Coherent Detection Of BPSK Signals (i) Generation: To generate the BPSK signal, we build on the fact that the BPSK signal is a special case of DSB-SC modulation. Specifically, we use a product modulator consisting of two components Section 7.3 – Binary- Phase-Shift Keying 25 Dr. Ahmed Masri

Generation  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: respectively  Product modulator, which multiplies the level-encoded binary wave c(t) by the sinusoidal carrier of amplitude to produce the BPSK signal. Section 7.3 – Binary- Phase-Shift Keying 26 Dr. Ahmed Masri

Detection  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 Section 7.3 – Binary- Phase-Shift Keying 27 Dr. Ahmed Masri

Detection  Product modulator, which is also supplied with a locally generated reference signal that is a replica of the carrier wave c(t)  Low-pass filter, designed to remove the double-frequency components of the product modulator output (i.e., the components centered on 2f c ) and pass the zero-frequency components. Section 7.3 – Binary- Phase-Shift Keying 28 Dr. Ahmed Masri

Detection  Sampler, which uniformly samples the output of the low-pass filter at t = iT b where i = 0, ±1, ±2, … ; the local clock governing the operation of the sampler is synchronized with the clock responsible for bit-timing in the transmitter.  Decision-making device, which compares the sampled value of the low-pass filter’s output to an externally supplied threshold, every T b seconds. If the threshold is exceeded, the device decides in favor of symbol 1; otherwise, it decides in favor of symbol 0. Section 7.3 – Binary- Phase-Shift Keying 29 Dr. Ahmed Masri

Detection  The BPSK receiver 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  This requirement can be achieved by using a phase-locked loop, which was described in Section 4.8.  In addition to synchrony with respect to carrier phase, the receiver also has an accurate knowledge of the interval occupied by each binary symbol. Section 7.3 – Binary- Phase-Shift Keying 30 Dr. Ahmed Masri

Detection  The bandwidth of the low-pass filter in the coherent BPSK receiver has to be equal to or greater than the reciprocal of the bit duration T b  (1/T b ) Section 7.3 – Binary- Phase-Shift Keying 31 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  An important goal of digital communication is the efficient utilization of channel bandwidth  QPSK is a bandwidth-conserving modulation, which builds on the same idea as that of quadrature-carrier multiplexing that was discussed before  In QPSK, as with BPSK, information carried by the transmitted signal is contained in the phase of a sinusoidal carrier  In particular, the phase of the sinusoidal carrier takes on one of four equally spaced values Section 7.3 – Binary- Phase-Shift Keying 32 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  The four equally spaced values, such as  For this set of values, we define the transmitted signal as where i = 1, 2, 3, 4 and E is the transmitted signal energy per symbol and T is the symbol duration Section 7.3 – Binary- Phase-Shift Keying 33 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  Each one of the four equally spaced phase values corresponds to a unique pair of bits called a dibit.  For example, we may choose the foregoing set of phase values to represent the Gray encoded set of dibits: 10, 00, 01, and 11. In this form of encoding, we see that only a single bit is changed from one dibit to the next.  Note that the symbol duration (i.e., the duration of each dibit) is twice the bit duration Section 7.3 – Binary- Phase-Shift Keying 34 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  Using a well-known trigonometric identity, we may recast the transmitted signal in the interval 0 ≤ t ≤ T in the expanded form Section 7.3 – Binary- Phase-Shift Keying 35 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  we can make some important observations: 1. In reality, the QPSK signal consists of the sum of two BPSK signals. 2. One BPSK signal, represented by the first term Which defines the product of modulating binary wave by the sinusoidal carrier which has unit energy over the symbol duration T. Section 7.3 – Binary- Phase-Shift Keying 36 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  We also recognize that 3. The other BPSK signal, represented by the second term defines the product of modulating a different binary wave by the sinusoidal carrier which also has unit energy per symbol Section 7.3 – Binary- Phase-Shift Keying 37 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  This time, we recognize that 4. The two sinusoidal carrier waves identified under points 2 and 3 are in phase quadrature with respect to each other Section 7.3 – Binary- Phase-Shift Keying 38 Dr. Ahmed Masri

(B) QUADRIPHASE-SHIFT KEYING  Relationship Between Index i And Identity of Corresponding Dibit, and Other Related Matters Section 7.3 – Binary- Phase-Shift Keying 39 Dr. Ahmed Masri

Generation: Section 7.3 – Binary- Phase-Shift Keying 40 Dr. Ahmed Masri

Generation :  To generate the QPSK signal, the incoming binary data stream is first converted into polar form by a non-return-to-zero level encoder; the encoder output is denoted by b(t).  Symbols 1 and 0 are thereby represented by where the resulting binary wave is next divided by means of a demultiplexer (consisting of a serial- to-parallel converter) into two separate binary waves consisting of the odd- and even numbered input bits of b(t) Section 7.3 – Binary- Phase-Shift Keying 41 Dr. Ahmed Masri

Detection: Section 7.3 – Binary- Phase-Shift Keying 42 Dr. Ahmed Masri

Section 7.4 – Binary- Frequency-Shift Keying 43 Dr. Ahmed Masri

 In Binary frequency-shift keying (BFSK), symbols 0 and 1 are distinguished from each other by transmitting one of two sinusoidal waves that differ in frequency by a fixed amount  When the frequencies f 1 and f 2 are chosen in such a way that they differ from each other by an amount equal to 1/T b,the BFSK signal is referred to as Sunde’s BFSK after its originator Section 7.4 – Binary- Frequency-Shift Keying 44 Dr. Ahmed Masri

 In the following figure, we plot the waveform of Sunde’s BFSK produced by the input binary sequence for a bit duration T b = 1.  Part (a) of the figure displays the waveform of the input sequence, and part (b) displays the corresponding waveform Section 7.4 – Binary- Frequency-Shift Keying 45 Dr. Ahmed Masri

. Section 7.4 – Binary- Frequency-Shift Keying 46 Dr. Ahmed Masri

(i) BASK, BPSK, and BFSK are the digital counterparts of amplitude modulation, phase modulation, and frequency modulation, respectively; this point further reinforces previous observations. (ii) Both BASK and BPSK exhibit discontinuity. In contrast, it is possible to configure BFSK in such a way that phase continuity is maintained across the entire input binary data stream Section 7.5 – Summary of Three Binary Signaling Schemes 47 Dr. Ahmed Masri

. Section 7.5 – Summary of Three Binary Signaling Schemes 48 Dr. Ahmed Masri