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Digital Comm - 4

The property that distinguishes digital radio systems from conventiona...
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Electronics Engineering (CR 061)

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LESSON CONTENT

Digital transmission systems transport information in digital form and, therefore, require a physical facility between the transmitter and receiver, such as a metallic wire pair, a coaxial cable, or an optical fiber cable. In digital radio systems, the carrier facility could be a physical cable, or it could be free space.

Digital modulation is the transmittal of digitally modulated analog signals (carriers) between two or more points in a communications system. Digital modulation is sometimes called digital radio because digitally modulated signals can be propagated through Earth’s atmosphere and used in wireless communications systems.

The property that distinguishes digital radio systems from conventional analog modulation communications systems is the nature of the modulating signal. Both analog and digital modulation systems use analog carriers to transport the information through the system. However, with analog modulation systems, the information signal is also analog, whereas with digital modulation, the information signal is digital, which could be computer generated data or digitally encoded analog signals.

Digital modulation is ideally suited to a multitude of communications applications, including both cable and wireless systems. Applications include the following: (1) relatively low-speed voice-band data communications modems, such as those found in most personal computers; (2) high-speed data transmission systems, such as broadband digital subscriber lines (DSL); (3) digital microwave and satellite communications systems; and (4) cellular telephone Personal Communications Systems (PCS).

Digital Modulation include ASK, FSK, PSK, and QAM. If the information signal is digital and the amplitude (V) of the carrier is varied proportional to the information signal, a digitally modulated signal called amplitude shift keying (ASK) is produced. If the frequency (f) is varied proportional to the information signal, frequency shift keying (FSK) is produced, and if the phase of the carrier (θ) is varied proportional to the information signal, phase shift keying (PSK) is produced. If both the amplitude and the phase are varied proportional to the information signal, quadrature amplitude modulation (QAM) results.

𝐀(𝐀 ) = 𝐀𝐀𝐀𝐀(𝐀 (𝐀.𝐀𝐀 + 𝐀) (1)

Figure 1 shows a simplified block diagram for a digital modulation system. In the transmitter, the precoder performs level conversion and then encodes the incoming data into groups of bits that modulate an analog carrier. The modulated carrier is shaped (filtered), amplified, and then transmitted through the transmission medium to the receiver. The transmission medium can be a metallic cable, optical fiber cable, Earth’s atmosphere, or a combination of two or more types of transmission systems. In the receiver, the incoming signals are filtered, amplified, and then applied to the demodulator and decoder circuits, which extracts the original source information from the modulated carrier. The clock and carrier recovery circuits recover the analog carrier and digital timing (clock) signals from the incoming modulated wave since they are necessary to perform the demodulation process.

Figure 1. Simplified block diagram of a digital radio system

  1. Information Capacity, Bits, Bit Rate, Baud, and M-ary Encoding

  2. Information Capacity, Bits, and Bit Rate

Information theory is a highly theoretical study of the efficient use of bandwidth to propagate information through electronic communications systems. Information theory can be used to determine the information capacity of a data communications system. Information capacity is a measure of how much information can be propagated through a communications system and is a function of bandwidth and transmission time.

Information capacity represents the number of independent symbols that can be carried through a system in a given unit of time. The most basic digital symbol used to represent information is the binary digit, or bit. Therefore, it is often convenient to express the information capacity of a system as a bit rate. Bit rate is simply the number of bits transmitted during one second and is expressed in bits per second (bps). In 1928, R. Hartley of Bell Telephone Laboratories developed a useful relationship among bandwidth, transmission time, and information capacity. Simply stated, Hartley’s law is

𝐀 𝐀𝐀𝐀 (2)

where: I = information capacity (bits per second) B = bandwidth (hertz) t = transmission time (seconds)

It can be seen from equation above that information capacity is a linear function of bandwidth and transmission time and is directly proportional to both. If either the bandwidth or the transmission time changes, a directly proportional change occurs in the information capacity.

In 1948, mathematician Claude E. Shannon (also of Bell Telephone Laboratories) published a paper in the Bell System Technical Journal relating the information capacity of a communications channel to bandwidth and signal-to-noise ratio. The higher the signal-to-noise ratio, the better the performance and the higher the information capacity. Mathematically stated, the Shannon limit for information capacity is

𝐀

𝐀 =𝐀𝐀𝐀𝐀𝐀 (𝐀 +𝐀 ) (3)

𝐀𝐀𝐀𝐀 = (7)

𝐀𝐀

where: baud = symbol rate (baud per second) ts = time of one signaling element (seconds)

A signaling element is sometimes called a symbol and could be encoded as a change in the amplitude, frequency, or phase. For example, binary signals are generally encoded and transmitted one bit at a time in the form of discrete voltage levels representing logic 1s (highs) and logic 0s (lows). A baud is also transmitted one at a time; however, a baud may represent more than one information bit. Thus, the baud of a data communications system may be considerably less than the bit rate. In binary systems (such as binary FSK and binary PSK), baud and bits per second are equal. However, in higher-level systems (such as QPSK and 8-PSK), bps is always greater than baud.

According to H. Nyquist, binary digital signals can be propagated through an ideal noiseless transmission medium at a rate equal to two times the bandwidth of the medium. The minimum theoretical bandwidth necessary to propagate a signal is called the minimum Nyquist bandwidth or sometimes the minimum Nyquist frequency. Thus, fb = 2B, where fb is the bit rate in bps and B is the ideal Nyquist bandwidth. The actual bandwidth necessary to propagate a given bit rate depends on several factors, including the type of encoding and modulation used, the types of filters used, system noise, and desired error performance. The ideal bandwidth is generally used for comparison purposes only.

The relationship between bandwidth and bit rate also applies to the opposite situation. For a given bandwidth (B), the highest theoretical bit rate is 2B. For example, a standard telephone circuit has a bandwidth of approximately 2700 Hz, which has the capacity to propagate 5400 bps through it. However, if more than two levels are used for signaling (higher-than-binary encoding), more than one bit may be transmitted at a time, and it is possible to propagate a bit rate that exceeds 2B. Using multilevel signaling, the Nyquist formulation for channel capacity is

𝐀𝐀 = 𝐀 𝐀𝐀𝐀𝐀𝐀𝐀 (8)

where: fb = channel capacity (bps) B = minimum Nyquist bandwidth (hertz) M = number of discrete signal or voltage levels

Equation 8 can be rearranged to solve the minimum bandwidth necessary to pass M-ary digitally modulated carriers

𝐀𝐀 (9)

𝐀 = ( )

𝐀𝐀𝐀𝐀𝐀

If N is substituted for 𝐀𝐀𝐀 2 𝐀, Equation 9 reduces to

𝐀𝐀 (10)

𝐀 =

𝐀 where N is the number of bits encoded into each signaling element.

If information bits are encoded (grouped) and then converted to signals with more than two levels, transmission rates in excess of 2B are possible. In addition, since baud is the encoded rate of change, it also equals the bit rate divided by the number of bits encoded into one signaling element. Thus,

𝐀𝐀 (11)

𝐀𝐀𝐀𝐀 =

𝐀

By comparing Equation 10 with Equation 11, it can be seen that with digital modulation, the baud and the ideal minimum Nyquist bandwidth have the same value and are equal to the bit rate divided by the number of bits encoded. This statement holds true for all forms of digital modulation except frequency- shift keying.

  1. Forms of Digital Modulation

  2. Amplitude-Shift Keying

Amplitude-shift keying (ASK) is the simplest form of digital modulation technique, where a binary information signal directly modulates the amplitude of an analog carrier. ASK is similar to standard amplitude modulation except there are only two output amplitudes possible. Amplitude-shift keying is sometimes called digital amplitude modulation (DAM).

𝐀𝐀𝐀𝐀 (𝐀) = [𝐀 +[ 𝐀𝐀 (𝐀)] [ 𝐀 𝐀 𝐀𝐀𝐀(𝐀𝐀 𝐀)] (12)

The equation above is a mathematical representation of amplitude-shift keying where: 𝐀𝐀𝐀𝐀( ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ( ℎ) = −ℎ 𝐀𝐀 (( (( (( (( (( (( (( (( (( (( (( (( (( (( () = ))))))))))))))(((((((((((((( )( () 𝐀 = (((((((((((((( () 2

𝐀𝐀 = ( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( , 2 𝐀𝐀) The modulating signal (((((((((((((((𝐀 [[[[[[[[[[[[[[[]) is a normalized waveform, where +1V = logic 1 and -1V = logic 0. Therefore, for a logi 1 input, (((((((((((((((𝐀 [1[1[1[1[1[1[1[1[1[1[1[1[1[1[]) = + 1

𝐀𝐀𝐀𝐀 ((((((((((((((() = [1 + 1] [ 𝐀2 (((((((((((((((𝐀𝐀)]

𝐀𝐀𝐀𝐀 ( (( (( (( (( (( (( (( (( (( (( (( (( (( (() = (𝐀𝐀)

And for a logic 0 input, (((((((((((((((𝐀 [1[1[1[1[1[1[1[1[1[1[1[1[1[1[ ]) = − 1

𝐀𝐀𝐀𝐀 ((((((((((((((() = [1 − 1] [ 𝐀2 (((((((((((((((𝐀𝐀)]

𝐀𝐀𝐀𝐀 ((((((((((((((() = 0

Thus, the modulated wave 𝐀𝐀𝐀𝐀 ((((((((((((((( ), is either (((((((((((((((𝐀𝐀)) or 0. Hence, the carrier is either “on” or “off,” which is why amplitude-shift keying is sometimes referred to as on-off keying (OOK).

than a continuously changing analog waveform. Consequently, FSK is sometimes called binary FSK (BFSK). The general expression for FSK is

𝐀𝐀𝐀𝐀 ((𝐀) = 𝐀𝐀 𝐀𝐀𝐀{𝐀[𝐀𝐀[𝐀 𝐀 + 𝐀𝐀 (∆](𝐀 ∆𝐀]𝐀) } (13)

Where: 𝐀𝐀𝐀𝐀((((((((((((((( ) = binary FSK waveform

𝐀𝐀 = peak analog carrier amplitude (volts)

𝐀𝐀 = analog carrier center frequency (hertz)

∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆ = peak change (shift) in the analog carrier frequency (hertz)

𝐀𝐀 ((((((((((((((() = binary input (modulating) signal (volts)

From Equation 13, it can be seen that the peak shift in the carrier frequency (∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆) is proportional to the

amplitude of the binary input signal (𝐀𝐀[[[[[[[[[[[[[[[ ]), and the direction of the shift is determined by the polarity.

The modulating signal is a normalized binary waveform where a logic 1 = +1 V and a logic 0= - 1 V.

Thus, for a logic 1 input, 𝐀𝐀 ((((((((((((((() = +1 , Equation 13 can be rewritten as

𝐀𝐀𝐀𝐀 ((((((((((((((() = 𝐀 cos{ 22222222222222 [[[[[[[[[[[[[[ 2 [ 𝐀 +∆] ∆]}

For a logic 0 input, 𝐀𝐀 ((((((((((((((() = −1 , Equation 13 becomes

𝐀𝐀𝐀𝐀((((((((((((((( ) = 𝐀 cos{2[2[2[2[2[2[2[2[2[2[2[2[2[2[ 2[𝐀 −∆] ∆]}

Figure 3. FSK in the frequency domain

With binary FSK, the carrier center frequency (𝐀𝐀) is shifted (deviated) up and down in the frequency

domain by the binary input signal as shown in Figure 3. As the binary input signal changes from a logic 0 to a logic 1 and vice versa, the output frequency shifts between two frequencies: a mark, or logic 1

frequency (𝐀𝐀 ), and a space, or logic 0 frequency (𝐀𝐀). The mark and space frequencies are separated

from the carrier frequency by the peak frequency deviation (∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆) and from each other by 2( ∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆).

With FSK, frequency deviation is defined as the difference between either the mark or space frequency and the center frequency, or half the difference between the mark and space frequencies. Frequency deviation is illustrated in Figure 3 and expressed mathematically as

∆∆𝐀 =|𝐀𝐀−𝐀𝐀| (14)

𝐀

where: ∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆ = frequency deviation (hertz)

||||||||||||||| 𝐀 − 𝐀| = absolute difference between the mark and space frequencies (hertz)

Figure 4a shows in the time domain the binary input to an FSK modulator and the corresponding FSK

output. As the figure shows, when the binary input (𝐀𝐀) changes from a logic 1 to a logic 0 and vice

versa, the FSK output frequency shifts from a mark (𝐀𝐀) to a space (𝐀𝐀) frequency and vice versa. In

Figure 4a, the mark frequency is the higher frequency (𝐀𝐀 + ∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆), and the space frequency is the lower

frequency (𝐀𝐀 − ∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆), although this relationship could be just the opposite. Figure 4b shows the truth

table for a binary FSK modulator. The truth table shows the input and output possibilities for a given digital modulation scheme.

Figure 4. FSK in the time domain: (a) waveform; (b) truth table

3.2. FSK Bit Rate, Baud, and Bandwidth

In Figure 4a, it can be seen that the time of one bit (tb) is the same as the time the FSK output is a mark of space frequency (ts). Thus, the bit time equals the time of an FSK signaling element, and the bit rate equals the baud.

The baud for binary FSK can also be determined by substituting N = 1 in Equation 11:

𝐀𝐀

𝐀𝐀𝐀𝐀 = = 𝐀

1

FSK is the exception to the rule for digital modulation, as the minimum bandwidth is not determined from Equation 10. The minimum bandwidth for FSK is given as

(((((((((((((( = |( 𝐀 − 𝐀) −(((((((((((((( (𝐀 − 𝐀)|

((((((((((((((( = |(𝐀 𝐀 − 𝐀)| + 22222222222222 2 𝐀

and since ||||||||||||||| 𝐀 − 𝐀| equals 2 ∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆ , the minimum bandwidth can be approximated as

The worst-case modulation index (deviation ratio) is that which yields the widest bandwidth. The worst-case or widest bandwidth occurs when both the frequency deviation and the modulatingsignal frequency are at their maximum values. As described earlier, the peak frequency deviation in FSK is constant and always at its maximum value, and the highest fundamental frequency is equal to half the incoming bit rate. Thus,

||||||||||||||| 𝐀 −−−−−−−−−−−−−−− 𝐀|

ℎ = 𝐀2𝐀 (unitless)

2 or

𝐀 =||𝐀𝐀−−𝐀𝐀| (18)

𝐀𝐀

Figure 5. FSK modulator, tb, time of one bit = 1/fb; fm, mark frequency; fs, space frequency; T 1 , period of shortest cycle; 1/T 1 , fundamental frequency of binary square wave; fb, input bit rate (bps)

where: h = h-factor (unitless) fm = mark frequency (hertz) fs = space frequency (hertz) fb = bit rate (bits per second)

Example 3: Using a Bessel table, determine the minimum bandwidth for the same FSK signal described in Example 1 with a mark frequency of 49 kHz, a space frequency of 51 kHz, and an input bit rate of 2 kbps.

Solution: The modulation index is found by substituting into Equation 17: |49 − 51 | ℎ = = 1 2

From a Bessel table, three sets of significant sidebands are produced for a modulation index of one. Therefore, the bandwidth can be determined as follows: = 2(3 1000) = 6000 𝐀 𝐀

The bandwidth determined in Example 3 using Bessel table (Bessel table attached at the last page) is identical to the bandwidth determined in Example 2.

3.2. FSK Transmitter

Figure 6 shows a simplified binary FSK modulator, which is very similar to a conventional FM modulator and is very often a voltage-controlled oscillator (VCO). The center frequency (fc) is chosen such that it falls halfway between the mark and space frequencies. A logic 1 input shifts the VCO output to the mark frequency, and a logic 0 input shifts the VCO output to the space frequency. Consequently, as the binary input signal changes back and forth between logic 1 and logic 0 conditions, the VCO output shifts or deviates back and forth between the mark and space frequencies.

In a binary FSK modulator, Δf is the peak frequency deviation of the carrier and is equal to the difference between the carrier rest frequency and either the mark or the space frequency (or half the difference between the carrier rest frequency) and either the mark or the space frequency (or half the difference between the mark and space frequencies).A VCO-FSK modulator can be operated in the sweep mode where the peak frequency deviation is simply the product of the binary input voltage and the deviation sensitivity of the VCO. With the sweep mode of modulation, the frequency deviation is expressed mathematically as

∆∆𝐀 =𝐀𝐀()(𝐀)𝐀𝐀 (19)

Where: ∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆ = peak frequency deviation (hertz) 𝐀𝐀 ((((((((((((((() = peak binary modulating-signal voltage (volts) 𝐀𝐀 = deviation sensitivity (hertz per volt)

Figure 6. FSK modulator

With binary FSK, the amplitude of the input signal can only be one of two values, one for a logic 1 condition and one for a logic 0 condition. Therefore, the peak frequency deviation is constant and always at its maximum value. Frequency deviation is simply plus or minus the peak voltage of the binary signal times the deviation sensitivity of the VCO. Since the peak voltage is the same for a logic 1 as it is for a logic 0, the magnitude of the frequency deviation is also the same for a logic 1 as it is for a logic 0.

3.2. FSK Receiver

Figure 7 shows a simple FSK demodulation circuit. The FSK input signal is applied to the inputs of both bandpass filters (BPFs) simultaneously through a power splitter. The respective filter passes only the mark or only the space frequency on to its respective envelope detector. The envelope detectors, in turn, indicate the total power in each passband, and the comparator responds to the largest of the two powers. This type of FSK detection is referred to as

Figure 9. PLL-FSK demodulator

Binary FSK has a poorer error performance than PSK or QAM and, consequently, is seldom used for high-performance digital radio systems. Its use is restricted to low-performance, low- cost, asynchronous data modems that are used for data communications over analog, voice- band telephone lines.

3.2. Continuous-Phase Frequency-Shift Keying

Continuous-phase frequency-shift keying (CP-FSK) is binary FSK except the mark and space frequencies are synchronized with the input binary bit rate. As a result, there is a precise time relationship between the two; it does not mean they are equal. With CP-FSK, the mark and space frequencies are selected such that they are separated from the center frequency by an exact multiple of one-half the bit rate (fm and fs = n[fb /2]), where n = any integer). This ensures a smooth phase transition in the analog output signal when it changes from a mark to a space frequency or vice versa.

Figure 10 shows a noncontinuous FSK waveform. It can be seen that when the input changes from a logic 1 to a logic 0 and vice versa, there is an abrupt phase discontinuity in the analog signal. When this occurs, the demodulator has trouble following the frequency shift; consequently, an error may occur.

Figure 10. Noncontinuous FSK waveform

Figure 11 shows a continuous phase FSK waveform. Notice that when the output frequency changes, it is a smooth, continuous transition. Consequently, there are no phase discontinuities. CP-FSK has a better bit-error performance than conventional binary FSK for a given signaltonoise ratio. The disadvantage of CP-FSK is that it requires synchronization circuits and is, therefore, more expensive to implement.

Figure 11. Continuous-phase MSK waveform

  1. Phase-Shift Keying

Phase-shift keying (PSK) is another form of angle-modulated, constant-amplitude digital modulation. PSK is an M-ary digital modulation scheme similar to conventional phase modulation except with PSK the input is a binary digital signal and there are a limited number of output phases possible. The input binary information is encoded into groups of bits before modulating the carrier. The number of bits in a group ranges from 1 to 12 or more. The number of output phases is defined by M as described in Equation 6 and determined by the number of bits in the group (n).

3.3. Binary Phase-Shift Keying

The simplest form of PSK is binary phase-shift keying (BPSK), where N = 1 and M = 2. Therefore, with BPSK, two phases (2 1 = 2) are possible for the carrier. One phase represents a logic 1, and the other phase represents a logic 0. As the input digital signal changes state (i., from a 1 to a 0 or from a 0 to a 1), the phase of the output carrier shifts between two angles that are separated by 180°. Hence, other names for BPSK are phase reversal keying (PRK) and biphase modulation. BPSK is a form of square-wave modulation of a continuous wave (CW) signal.

3.3.1. BPSK Transmitter

Figure 12. BPSK transmitter

Figure 13 (c) logic 0 input

If the binary input is a logic 0 (negative voltage), diodes D1 and D2 are reverse biased and off, while diodes D3 and D4 are forward biased and on (Figure 13c). As a result, the carrier voltage is developed across transformer T2 180° out of phase with the carrier voltage across T1. Consequently, the output signal is 180° out of phase with the reference oscillator.

Figure 14 shows the truth table, phasor diagram, and constellation diagram for a BPSK modulator. A constellation diagram, which is sometimes called a signal state-space diagram, is similar to a phasor diagram except that the entire phasor is not drawn. In a constellation diagram, only the relative positions of the peaks of the phasors are shown.

Figure 14. BPSK modulator: (a) truth table; (b) phasor diagram; (c) constellation diagram

3.3.1. Bandwidth considerations of BPSK

A balanced modulator is a product modulator in which the output signal is the product of the two input signals. In a BPSK modulator, the carrier input signal is multiplied by the binary data. If +1 V is assigned to a logic 1 and -1 V is assigned to a logic 0, the input carrier (sin ωct) is multiplied by either a + or -1.

Consequently, the output signal is either +1 sin ωct or -1 sin ωct; the first represents a signal that is in phase with the reference oscillator, the latter a signal that is 180° out of phase with the reference oscillator. Each time the input logic condition changes, the output phase changes. Consequently, for BPSK, the output rate of change (baud) is equal to the input rate of change (bps), and the widest output bandwidth occurs when the input binary data are an alternating 1/0 sequence. The fundamental frequency (fa) of an alternative 1/0 bit sequence is equal to one-half of the bit rate (fb/2). Mathematically, the output of a BPSK modulator is proportional to

𝐀𝐀𝐀𝐀 𝐀𝐀𝐀𝐀𝐀𝐀 =[𝐀𝐀𝐀(𝐀[(𝐀𝐀 𝐀 𝐀 ]𝐀) ][𝐀𝐀𝐀(𝐀 𝐀𝐀𝐀 𝐀 𝐀)] (20)

where: 𝐀𝐀 = maximum fundamental frequency of binary input (hertz) 𝐀𝐀 = reference carrier frequency (hertz)

Solving for the trig identity for the product of two sine functions,

2(2(2(2(2(2(2(2(2(2(2(2(2(2( cos[ 2( 𝐀 − 𝐀 )))))))))))))))] − 2(2(2(2(2(2(2(2(2(2(2(2(2(2(cos[ 2(𝐀 + 𝐀 )))))))))))))))]

Thus, the minimum double-sided Nyquist bandwidth (B) is

and because 𝐀𝐀 = 𝐀2𝐀 , where 𝐀𝐀 =input bit rate,

222222222222222 𝐀

𝐀 = = 𝐀

2

where B is the minimum double-sided Nyquist bandwidth.

In the output phase-versus-time relationship for a BPSK waveform, a logic 1 input produces an analog output signal with a 0° phase angle, and a logic 0 input produces an analog output signal with a 180° phase angle (see Figure 15). As the binary input shifts between a logic 1 and a logic 0 condition and vice versa, the phase of the BPSK waveform shifts between 0° and 180°, respectively. For simplicity, only one cycle of the analog carrier is shown in each signaling element, although there may be anywhere between a fraction of a cycle to several thousand cycles, depending on the relationship between the input bit rate and the analog carrier frequency. It can also be seen that the

= 75 0 − 65 0 = 10𝐀𝐀𝐀

and the = 𝐀 𝐀 or 10 megabaud 3.3.1. BPSK Receiver

Figure 16. Block diagram of a BPSK receiver

In the block diagram of a BPSK receiver shown in Figure 16, the input signal may be +sin ωct or -sin ωct. The coherent carrier recovery circuit detects and regenerates a carrier signal that is both frequency and phase coherent with the original transmit carrier. The balanced modulator is a product detector; the output is the product of the two inputs (the BPSK signal and the recovered carrier). The low-pass filter (LPF) separates the recovered binary data from the complex demodulated signal.

Mathematically, the demodulation process is as follows.

For a BPSK input signal of +++++++++++++++ 𝐀 (((((((((((((((1) , the output of the balanced modulator is

𝐀𝐀𝐀𝐀𝐀𝐀 =(𝐀𝐀𝐀𝐀𝐀 𝐀 (𝐀𝐀𝐀𝐀) 𝐀 𝐀) = 𝐀𝐀𝐀𝐀𝐀𝐀𝐀 (21)

or

leaving 𝐀𝐀𝐀𝐀𝐀𝐀 = + =

The output of the balanced modulator contains a negative voltage (-[1/2]V) and a cosine wave at twice the carrier frequency (2ωc). Again, the LPF blocks the second harmonic of the carrier and passes only the negative constant component. A negative voltage represents a demodulated logic 0.

3.3. Quaternary Phase-Shift Keying

Quaternary phase shift keying (QPSK), or quadrature PSK is another form of angle-modulated, constant-amplitude digital modulation. QPSK is an M-ary encoding scheme where N = 2 and M = 4 (hence, the name “quaternary” meaning “4”). Because there are four output phases for a single carrier frequency, there must be four different input conditions. which requires more than a single input bit to determine the output condition. With two bits, there are four possible

conditions: 00, 01, 10, and 11. Therefore, with QPSK, the binary input data are combined into groups of two bits, called dibits. In the modulator, each dibit code generates one of the four possible output phases (+45°, +135°,- 45°, and - 135°). Therefore, for each two-bit dibit clocked into the modulator, a single output change occurs, and the rate of change at the output (baud) is equal to one-half the input bit rate (i., two input bits produce one output phase change).

3.3.2. QPSK Transmitter

Figure 17 shows a block diagram of a QPSK modulator. Two bits (a dibit) are clocked into the bit splitter. After both bits have been serially inputted, they are simultaneously parallel outputted. One bit is directed to the I channel and the other to the Q channel. The I bit modulates a carrier that is in phase with the reference oscillator (hence the name “I” for “in phase” channel), and the Q bit modulates a carrier that is 90° out of phase or in quadrature with the reference carrier (hence the name “Q” for “quadrature” channel).

It can be seen that once a dibit has been split into the I and Q channels, the operation is the same as in a BPSK modulator. Essentially, a QPSK modulator is two BPSK modulators combined in parallel. Again, for a logic 1 =+1 V and a logic 0= -1 V, two phases are possible at the output of the I balanced modulator (+sin ωct and -sin ωct), and two phases are possible at the output of the Q balanced modulator (+cos ωct and -cos ωct). When the linear summer combines the two quadrature (90° out of phase) signals, there are four possible resultant phasors given by these expressions:

  • sin ωct + cos ωct, + sin ωct - cos ωct, -sin ωct + cos ωct, and -sin ωct - cos ωct.

Figure 17. QPSK modulator

Example 5: For the QPSK modulator shown in Figure 17, construct the truth table, phasor diagram, and

constellation diagram.

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Digital Comm - 4

Course: Electronics Engineering (CR 061)

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University: Samar State University

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LESSON CONTENT
Digital transmission systems transport information in digital form and, therefore, require a physical facility
between the transmitter and receiver, such as a metallic wire pair, a coaxial cable, or an optical fiber cable.
In digital radio systems, the carrier facility could be a physical cable, or it could be free space.
Digital modulation is the transmittal of digitally modulated analog signals (carriers) between two or more
points in a communications system. Digital modulation is sometimes called digital radio because digitally
modulated signals can be propagated through Earth’s atmosphere and used in wireless communications
systems.
The property that distinguishes digital radio systems from conventional analog modulation communications
systems is the nature of the modulating signal. Both analog and digital modulation systems use analog
carriers to transport the information through the system. However, with analog modulation systems, the
information signal is also analog, whereas with digital modulation, the information signal is digital, which
could be computer generated data or digitally encoded analog signals.
Digital modulation is ideally suited to a multitude of communications applications, including both cable and
wireless systems. Applications include the following: (1) relatively low-speed voice-band data
communications modems, such as those found in most personal computers; (2) high-speed data
transmission systems, such as broadband digital subscriber lines (DSL); (3) digital microwave and satellite
communications systems; and (4) cellular telephone Personal Communications Systems (PCS).
Digital Modulation include ASK, FSK, PSK, and QAM. If the information signal is digital and the amplitude (V)
of the carrier is varied proportional to the information signal, a digitally modulated signal called amplitude shift
keying (ASK) is produced. If the frequency (f) is varied proportional to the information signal, frequency shift
keying (FSK) is produced, and if the phase of the carrier (θ) is varied proportional to the information signal,
phase shift keying (PSK) is produced. If both the amplitude and the phase are varied proportional to the
information signal, quadrature amplitude modulation (QAM) results.
) = . + )�(� ����(� �� �(� (1)
Figure 1 shows a simplified block diagram for a digital modulation system. In the transmitter, the precoder
performs level conversion and then encodes the incoming data into groups of bits that modulate an analog
carrier. The modulated carrier is shaped (filtered), amplified, and then transmitted through the transmission
medium to the receiver. The transmission medium can be a metallic cable, optical fiber cable, Earth’s
atmosphere, or a combination of two or more types of transmission systems. In the receiver, the incoming
signals are filtered, amplified, and then applied to the demodulator and decoder circuits, which extracts the
original source information from the modulated carrier. The clock and carrier recovery circuits recover the
analog carrier and digital timing (clock) signals from the incoming modulated wave since they are
necessary to perform the demodulation process.

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