communication basics

World Institute Of Technology

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Syllabus EE-206-F COMMUNICATION SYSTEMS L T P Class Work mark: 50 3 1 0 Theory marks: 100 Total marks: 150 Duration of Exam: 3 hr NOTE: For setting up the question paper, Question No. 1 will be set up from all the four sections which will be compulsory and of short answer type. Two questions will be set from each of the four sections. The students have to attempt first common question, which is compulsory, and one question from each of the four sections. Thus students will have to attempt 5 questions out of 9 questions. SECTION-A INTRODUCTION TO COMMUNICATION SYSTEMS : The essentials of a Communication system, modes and media’s of Communication, Classification of signals and systems , Fourier Analysis of signals. Analog Communication & Digital Communication. Basic concepts of Modulation, Demodulators, Channels,Multiplexing & Demultiplexing. SECTION-B AMPLITUDE MODULATION : Amplitude modulation, Generation of AM waves, Demodulation of AM waves, DSBSC, Generation of DSBSC waves, Coherent detection of DSBSC waves, single side band modulation, generation of SSB waves, demodulation of SSB waves, vestigial sideband modulation (VSB). ANGLE MODULATION : Basic definitions: Phase modulation (PM) & frequency modulation(FM), narrow band frequency modulation, wideband frequency modulation, generation of FM waves, Demodulation of FM waves. SECTION C PULSE ANALOG MODULATION : Sampling theory, sampling and hold circuits. Time division (TDM) and frequency division (FDM) multiplexing, pulse amplitude modulation (PAM), pulse time modulation.




PULSE DIGITAL MODULATION : Coding & Decoding techniques, Elements of pulse code modulation, noise in PCM systems, Measure of information, channel capacity, channel capacity of a PCM system, differential pulse code modulation (DPCM). Delta modulation (DM) SECTION D DIGITAL MODULATION TECHNIQUES : ASK, FSK, BPSK, QPSK, M-ary PSK. PC-PC data Communication INTRODUCTION TO NOISE : External noise, internal noise, S/N ratio, noise figure. TEXT BOOKS: 1. Communication systems (4th edn.): Simon Haykins; John Wiley & sons. 2. Communication systems: Singh & Sapre; TMH. REFERENCE BOOKS: 1. Electronic Communication systems: Kennedy; TMH. 2. Communication Electronics: Frenzel; TMH. 3. Communication system: Taub & Schilling; TMH.

LECTURE NOTES OF COMMUNICATION SYSTEM

SECTION A

LECTURE1 Essentials of communication system modes and media’s of Communication -: Communication is the process of establishing connection or link between two points for information exchange. The essential components of basic communication system are:

1) Information source 2) Transmitter




3) Channel 4) Reciever

o/p

input message

1) Information Source: The message or information originates in information source.There can be various messages in form of words, group of words , codes, symbols, sound signal etc. However out of these messages only desired message is selected and conveyed.

2) Input Transducer: A transducer is a device which converts one form of energy into another . The message from information source may or may not be electrical in nature.

3) Transmitter: Modulation is a function of transmitter. In modulation message signal is super imposed upon high frequency carrier signal. In short we can say that inside the transmitter signal processing such as restriction of range of audio frequencies, amplification and modulation are achieved.

4) Channel and Noise: The term channel means medium through which message travels from transmitter and receiver .Noise is an unwanted signal which tend to interfere with required signal . Noise signal is always random.

5) Reciever: The reproduction of original signal is accomplished by process known as demodulation or detection .

6) Destination: it is the final stage which is used to convert an electrical message signal into its original form.

Information

source

I/P

transducer

transmitter channel reciever o/p

transducer

Distortion

or noise




LECTURE2 Classification of signals and system-: DEFINATION-: Signal in the present context means electrical manifestation of a physical process. Usually an essence of ‘information’ will be associated with a signal. Mathematical representation or abstraction should also be possible for a signal such that a signal and its features can be classified and analyzed. Examples of a few signals-:

(a) Electrical equivalent of speech/voice as obtained at the output of a microphone.

(b) Electrical output of a transducer used to sense the temperature of a furnace.

(c) Stream of electrical pulses (digital) generated by a computer.

(d) Electrical output of a TV camera (video signal). (e) Electrical waves received by the antenna of a radio/TV/communication receiver. (f) ECG signal.

When a signal is viewed as electrical manifestation of a process, the signal is a function of one or more independent variables. For all the examples cited above, the respective signals may commonly be considered as function of ‘time’. So, a notation like the following may be used to represent a signal:

s(a, b, c, t,..), where a, b,… are the independent variables. However, observe that a mere notation of a signal, say s(t), does not reveal all its features

and behavior and hence it may not be possible to analyze the signal effectively. Further, processing and analyses of many signals may become easy if we can associate them, in some cases even approximately, with mathematical functions that may be analyzed by well-developed mathematical tools and techniques. The approximate representations, wherever adopted, are usually justified by their ease of analysis or tractability or some other evidently rewarding reason. For example, the familiar mathematical function

s(t) = A cos(ωt +θ)




is extensively used in the study, analysis and testing of several principles of communication theory such as carrier modulation, signal sampling etc. However, one can very well contest the fact that

s(t) = A cos(ωt +θ) hardly implies a physical process because of the following reasons:

(i) No range of‘t’ is specified and hence, mathematically the range may be from -∞ to +∞. This implies that the innocent looking function s(t) should exist over the infinite range of ‘t’, which is not true for any physical source if ‘t’ represents time. So, some range for ‘t’ should be specified.

(ii) S (t), over a specified range of‘t’, is a known signal in the sense that, over the range of ‘t’, if we know the value of s(t) at say t = t0, and the values of A, ω and θ we know the value of s(t) at any other time instant ‘t’. We say the signal s(t) is deterministic. In a sense, such a mathematical function does not carry information.

While point (i) implies the need for rigorous and precise expression for a signal, point (ii) underlines the usage of theories of mathematics for signals deterministic or non-deterministic (random).

To illustrate this second point further, let us consider the description of s(t) = A cos ωt, where ‘t’ indicates time and ω = 2πf implies angular frequency: (a) Note that s(t) = A cos ωt , -∞ < t < ∞ is a periodic function and hence can be expressed by its exponential (complex) Fourier series. However, this signal has infinite energy E, E= ∫s2 (t) dt Hence, theoretically, can not be expressed by Fourier Transformation.

(b) Let us now consider the following modified expression for s(t) which may be a closer representation of a physical signal:

s(t) = A cos ωt , 0≤ t < ∞ = A.u (t). Cos ωt where u (t) is the unit step function, u(t) = 0, t < 0 and u(t) = 1, t ≥ 0

If we further put an upper limit to ‘t’, say, s(t) = A cos ωt , t1≤ t ≤ t2, such a signal can be easily generated by a physical source, but the frequency spectrum of s(t) will now be different compared to the earlier forms. For simplicity in notation, depiction and understanding, we will, at times, follow mathematical models for describing and understanding physical signals and processes. We will, though, remember that such mathematical descriptions, while being elegant,




may show up some deviation from the actual behavior of a physical process. Henceforth, we will mean the mathematical description itself as the signal, unless explicitly stated otherwise.

Now, we briefly introduce the major classes of signals that are of frequent interest in the study of digital communications. There are several ways of classifying a signal and a few types are named below.

TYPES OF SIGNAL-:

Energy signal: If, for a signal s(t)=

i.e. the energy of the signal is finite, the signal is called an energy signal. However, the same signal may have large power. The voltage generated by lightning (which is of short duration) is a close example of physical equivalent of a signal with finite energy but very large power.

Power signal: A power signal, on the contrary, will have a finite power but may have finite or infinite energy. Mathematically,

Note: While electrical signals, derived from physical processes are mostly energy signals, several mathematical functions, usually deterministic, represent power signals. Deterministic and random signals: If a signal s(t), described at t = t1 is sufficient for determining the signal at t = t2 at which the signal also exists, then s(t) represents a deterministic signal.

Example: s(t) = A cos ωt , T1≤ t ≤ T2 There are many signals that can best be described in terms of a probability and one may

not determine the signal exactly. Example: (from real process) Noise voltage/current generated by a resistor. Such signals are labeled as non-deterministic or random signals. Continuous time signal: Assuming the independent variable ‘t’ to represent time, if s(t) is

defined for all possible values of t between its interval of definition (or existence), T1≤ t ≤ T2. Then the signal s(t) is a continuous time signal.




If a signal s(t) is defined only for certain values of t over an interval T1≤ t ≤ T2, it is a discrete-time signal. A set of sample values represent a discrete time signal. Continuous time signal: Assuming the independent variable ‘t’ to represent time, if s(t) is defined for all possible values of t between its interval of definition (or existence), T1≤ t ≤ T2. Then the signal s(t) is a continuous time signal.

If a signal s(t) is defined only for certain values of t over an interval T1≤ t ≤ T2, it is a discrete-time signal. A set of sample values represent a discrete time signal.

Periodic signal: If s(t) = s(t + T), for entire range of t over which the signal s(t) is

defined and T is a constant, s(t) is said to be periodic or repetitive. ‘T’ indicates the period of the signal and 1T is its frequency of repetition.

Example: s(t) = A cos ωt , - ∞ ≤ t ≤ ∞ , where T = 2π/ω. Analog signal: If the magnitudes of a real signal s(t) over its range of definition, T1≤ t ≤

T2, are real numbers (there are infinite such values) within a finite range, say, Smin ≤ S(t) ≤ Smax, the signal is analog.

A digital signal s(t), on the contrary, can assume only any of a finite number of values. Usually, a digital signal implies a discrete-time, discrete-amplitude signal. LECTURE 3-: FOURIER ANALYSIS OF SIGNAL-:

Fourier analysis takes a signal and represents it either as a series of cosines (real part)

and sines (imaginary part) or as a cosine with phase (modulus and phase form). As an illustration we will look at Fourier analysing the sum of the two sine waves shown below. The resultant summed signal is shown in the third graph.




If we now carry out a Fourier Analysis of the combined signal then we obtain the following result.

. The amplitude shown is exactly half of the original constituent sine waves. This is to make so called half range analysis compatible with full range analyses.This is because Fourier analysis uses cosines and sines. It is cosines, not the sines, which are the basic reference. Signal Duration Effects If we have data taken over a longer period then the frequency spacing will be narrower. In many cases this will assist the problem but if there is no exact match the same phenomenonwill arise. Fourier nalysis tells us the amplitude and phase of that set of cosines which have the same duration as the original signal. A Fourier analysis shows the (half) amplitudes and phases of the constituent cosine waves that exist for the whole duration of that part of the signal that has been analysed then so does the Fourier transformed signal. Fourier analysis by itself does nothing to remove or minimise the effects of noise. Thus simple Fourier analysis is not suitable for random data, but it is for signals such as transients and complicated or simple periodic signals such as those generated by an engine running at a constant speed.




Mathematically, We will not go into all the mathematical niceties except to see that a Fourier series could be written in the forms below. In real and imaginary terms we have

The above forms are a slightly unusual way of expressing the Fourier expansion. For instance θ is in degrees. More significantly the product n k f t is shown explicitly.

However the point of using n k f t explicitly above is to indicate that nothing in the Fourier expansion inhibits the choice of actual frequency at which we evaluate the Fourier coefficients. Fourier Representation of continuous time signals Any periodic signal f(t) can be represented with a set of complex exponentials as shown below.

The exponential terms are orthogonal to each other because

the energy of these signals is unity since

Representing a signal in terms of its exponential Fourier series

components is called Fourier Analysis.




The weights of the exponentials are calculated as Extending this representation to aperiodic signals: Extending this representation to aperiodic signals: When T −→ ∞ and ω 0 −→ 0, the sum becomes an integral and ω 0 becomes continuous. The resulting represention is termed as the Fourier Transform (F(ω)) and is given by

The signal f(t) can recovered from F(ω) as

Some Important Functions Delta function is a very important signal in signal analysis. It is defined as




The Diac delta function is also called the Impulse function. This function can be represented as the limiting function of a number of sampling functions: 1. Gaussian Pulse

2. Triangular Pulse

3. Exponential Pulse

4. Sampling Function




5. Sampling Square function

The unit step function is another important function signal processing. It is defined by

The Fourier transform of the unit step can be found only in the limit.




LECTURE 4-:

Concepts of Modulation, Demodulators-:

Communication is the process of establishing connection or link between two points for information exchange. The essential components of basic communication system are:

1)Information source 2) Transmitter 3) Channel 4)Reciever

o/p

input message msg

1) Information Source: The message or information originates in information source.There can be various messages in form of words, group of words , codes, symbols, sound signal etc. However out of these messages only desired message is selected and conveyed. 2) input Transducer: A transducer is a device which converts one form of energy into another . The message from information source may or may not be electrical in nature. 3) Transmitter: Modulation is a function of transmitter. In modulation message signal is super imposed upon high frequency carrier signal. In short we can say that inside the transmitter signal processing such as restriction of range of audio frequencies, amplification and modulation are achieved.

Analog Communication & Digital Communication. Basic

Information

source

I/P

transducer

transmitter channel reciever o/p

transducer

Distortion

or noise




4) Channel and Noise: The term channel means medium through which message travels from transmitter and receiver .Noise is an unwanted signal which tend to interfere with required signal . Noise signal is always random. 5) Reciever: The reproduction of original signal is accomplished by process known as demodulation or detection .

6)Destination: it is the final stage which is used to convert an electrical message signal into its original form. DIGITAL COMMUNICATION-:

Block Schematic Description of a Digital Communication System In the simplest form, a transmission-reception system is a three-block system, consisting of a) a transmitter, b) a transmission medium c) a receiver. If we think of a combination of the transmission device and reception device in the form of a transceiver and if (as is usually the case) the transmission medium allows signal both ways, we are in a position to think of a both-way (bi-directional). In a simple form, again consists of three different entities, viz. a transmitter, a communication channel and a receiver. A digital communication system has several distinguishing features when compared with an analog communication system. Both analog (such as voice signal) and digital signals (such as data generated by computers) can be communicated over a digital transmission system. A key feature of a digital communication system is that a sense of information with appropriate unit of measure, is associated with such signals.The overall purpose of the digital communication system is to collect information from the source and carry out necessary electronic signal processing such that the information can be delivered to the end user (information sink) with acceptable quality.




It is possible to expand our basic three-entity description of a digital communication

system in multiple ways. For example, Fig. shows a somewhat elaborate block diagram explicitly

showing the important processes of ‘modulation-demodulation source coding-decoding and channel

encoding-decoding

To elaborate this potentially useful style of representation, let us note that we have hardly discussed

about the third entity of our model, viz. the ‘channel’. One can define several types of channel. For

example, the channel in Fig should more appropriately be called as a modulation channel with an

understanding that the actual transmission medium (called physical channel), any electromagnetic (or

other wise) transmission reception operations, amplifiers at the transmission and reception ends and

any other necessary signal processing units are combined together to form this ‘modulation channel.

BASIC CONCEPT OF MODULATORS AND DEMODULATORS




The design of the modulator can trade resolution in time for resolution in amplitude in such a way that imprecise analog circuits can be tolerated. The use of high frequency Modulation and demodulation eliminates the need for abrupt cutoffs in the analog antialiasing filter at the input to the A/D converter, as well as in the filters that smooth the analog output of the D/A converter. A digital filter smoothes the output of the modulator, attenuating noise, interference, and high-frequency components of the signal before they can alias into the signal band when the code is re sampled at the Nyquist rate. Another digital filter interpolates the code in the decoder to a high word rate before it is demodulated to analog form. Oversampling converters make extensive use of digital signal processing taking advantage of the fact that fine-line VLSI is better suited for providing fast digital circuits than for providing precise analog circuits. Because their sampling rate usually needs to be several orders of magnitude higher than the Nyquist rate, oversampling methods are best suited for relatively low-frequency signals. Applications 1) Digital audio 2) Digital telephony 3) Instrumentation. 4) Video 5) Radar systems An important difference between conventional converters and oversampling ones Involve testing and specifying their performance. With conventional converters there is a One-to-one correspondence between input and output sample values and hence one can describe their accuracy by comparing the values of corresponding input and output samples. In contrast there is no similar correspondence in oversampling converters because they inherently include digital low-pass filters, and hence each input sample value contributes to a whole train of output samples. Consequently, it has been useful to borrow techniques from communication technology to describe the performance of oversampling converters. Thus we measure their root-mean-square (rms) noise under various conditions, the distortion they introduce into sinusoidal signals, and their frequency responses. An important task in designing an oversampling converter is therefore the calculation of rms values of modulation noise and its spectral density. Some Alternative Modulator Structures 1 .Error Feedback-: Noise-shaping quantization was first introduced using the structure shown. In this circuit, the difference between the input




Quantizer with error feedback

and the output of the quantizer is a measure of the quantization error, which is fed back and subtracted from the next input sample. The circuit is algebraically equivalent to the AI circuit in, but it has the serious practical disadvantage that inaccuracies in that the circuit can be used as a demodulator because there the processing is performed digitally. The circuit can be generalized by replacing the delay with a prediction filter. 2 Cascaded Modulators-: The performance of a modulator can be improved by taking a measure of its noise digitizing that measure in a second modulator, and combining the output of the two modulators in a way that cancels the noise of the first modulator. The output of the integrator in the first modulator is fed to the second modulator. Its output is digitally differentiated and subtracted from the output of the first modulator to provide the net output of the circuit. We have used e' to denote the quantization error in the first modulator and e that of the second one. When scaling factors are ignored, it can be shown that the net output of the circuit may be expressed in the form

where g is a measure of the accuracy of the error cancellation. It depends on a number of parameters, including the precision of component values and the low-frequency gain of the first integrator. Ideally, g is unity; then the noise of the first modulator does not contribute to the output. The remaining noise is the second difference of the quantization error.




from the second modulator: It is in the same form as the noise of a second-order AL modulator given .An ideal second-order modulator oversampling by a factor of 120. At this sampling rate the noise from the first-order modulation is given by the ordinate of point . It is at -57 dB. In practice this requirement is tightened by needs to scaling signal amplitudes in practical circuits. The need for such precision is alleviated by raising the sampling rate: Because of the difficulty in obtaining adequate precision, the noise from these cascaded circuits is often dominated by the noise from the first stage. Demodulating Signals -: This circuit a digital filter interpolates sample values of the input signal in order to raise the word rate well above the Nyquist rate. A demodulator then truncates the words and Converts them to analog form at the high sample rate. In most applications it is advantageous to raise the word rate of the signal in stages at the encoder. The output of the filter resembles a PCM encoding of the signal at 32 kHz. The next stage is a linear interpolation that inserts three new values between each adjacent pair of 32-kHz samples, raising the word rate to 128 kHz. The words enter a register from which they feed the demodulator at 1 MHz; each word repeats eight times. The demodulator rounds off the code to single-bit words, converts them to analog levels, and smoothes these with an analog filter. The single-bit quantization occurs in a feedback circuit




that shapes the spectrum of the quantization noise, moving most of the power far above the signal band. The 1 MHz demodulation rate is sufficiently high that a very simple analog filter will smooth the noise. The filtering actions that are inherent in the interpolation that raises the word rate from 8 kHz to 1 MHz smooth out sampling images of the signal, leaving only those adjacent to the new sampling rate 1 MHz and its harmonics. Figure illustrates this action: (a) Represents the spectral density of the baseband signal, (b) Is spectral density when sampled at the Nyquist rate, (c) Is the frequency response of the low-pass filter including the Sine response of the holding register, Both (d) and (e) represent the output spectrum of the Low-pass filter, (f) is the sine2 response of linear interpolation, (g) is the result of this interpolation, (h) is the frequency response of the final holding register, and (i) is the spectral density of its output. The filter requirements for attenuating sampling images of the signal at the decoder are usually less stringent than are the requirements for preventing aliasing at the encoder.




FIG shows-:Spectral densities of signals, and the frequency response of filters used for interpolating sample values: (a) spectral density of the signal; (b) spectral density of the sampled signal; (c) low pass filter characteristic; (d, e) spectral density of the filter output on different frequency scales (f) frequency response of linear interpolation (g) spectral density of the interpolated signal; (h) frequency response of the holding register (i) spectral density of the held signal.




LECTURE-5

CHANNEL MULTIPLEXING & DEMULTIPLEXING

Detailed explaination later in lecture 17




LECTURE-6

REVISION & ASSIGNMENT Q1) Give three examples of types of signals that a source may generate.

Q2) Explain basic block diagram of analog communication & digital communication.

Q3) Classify signals into various categories.

Q4) Explain Fourier analysis of signal.




LECTURE7-: Amplitude Modulation, Generation of AM waves&Demodulation of AM -:

Modulation is a process that causes a shift in the range of frequencies in a signal.Signals that occupy the same range of frequencies can be separated. Modulation helps in noise immunity, attenuation - depends on the physical medium. Figure shows the different kinds of analog modulation schemes that are available

Amplitude Modulation- It is the process where, the amplitude of the carrier is varied proportional to that of the message signal.Amplitude Modulation with carrier. Let m(t) be the base-band signal, m(t)-----(M(ω)) and c(t)be the carrier, c(t) = Ac cos( ωct). fc is chosen such that fc >> W, where W is the maximum frequency component of m(t). The amplitude modulated signal is given by




Amplitude modulation

Figure shows the spectrum of the Amplitude Modulated signal.




Ka is constant called amplitude sensitivity. K am(t) < 1 and it indicates percentage modulation. Modulation in AM: A product modulator is used for Generating the modulated signal as shown in Figure

Modulation using product modulator

Demodulation in AM: An envelope detector is used to get the demodulated signal as shown in fig.

Demodulation using Envelope detector

The voltage Vm(t) across the resistor R gives the message




signal m(t).




LECTURE-8 Double Side Band - Suppressed Carrier ( DSB-SC) Modulation In AM modulation, transmission of carrier consumes lot of Power. Since, only the side bands contain the information About the message, carrier is suppressed. This results in a DSB-SC wave. A DSB-SC wave s(t) is given by

Modulation in DSB-SC: Here also product modulator is used as Shown in Figure, but the carrier is not added. Figure shows the spectrum of the DSB-SC signal.




Demodulation in DSB-SC: A coherent demodulator is used.The local oscillator present in the demodulator generates a Carrier which has same frequency and phase in a as that of the carrier in the modulated signal .




If, the demodulator has constant phase, the original signal is reconstructed by passing v(t) through an LPF.

lECTURE 9

SINGLE SIDE BAND MODULATION-:

In DSB-SC it is observed that there is symmetry in thebandstructure. So, even if one half is transmitted, the other half can be recovered at the received. By doing so, the bandwidth and power of transmission is reduced by half. Depending on which half of DSB-SC signal is transmitted, there are two types of SSB modulation 1. Lower Side Band (LSB) Modulation 2. Upper Side Band (USB) Modulation




Fig(1) SSB signals from orignal signal




Fig(2) Frequency analysis of SSB signals

From Figure 2 and the concept of the Hilbert Transform,

But, from complex representation of signals,




So,

Similarly,

Generation of SSB signals A SSB signal is represented by:

Fig(3) Generation of SSB signals

As shown in Figure 3, a DSB-SC modulator is used for SSB signal generation. Coherent Demodulation of SSB signals Ф SSB(t) is multiplied with cos(ωct) and passed through low pass filter to get back the orignal signal.




Figure 4: Demodulated SSB signal The demodulated signal is passed through an LPF to remove unwanted SSB terms. LECTURE-10 VESTIGIAL SIDEBAND MODULATION-: The following are the drawbacks of SSB signal generation: 1. Generation of an SSB signal is difficult. 2. Selective filtering is to be done to get the original signal back. 3. Phase shifter should be exactly tuned to 900. To overcome these drawbacks, VSB modulation is used. It can viewed as a compromise between SSB and DSB-SC. Figure 5 shows all the three modulation schemes.




Figure 5: VSB Modulation In VSB 1. One sideband is not rejected fully. 2. One sideband is transmitted fully and a small part (vestige) of the other sideband is transmitted.The transmission BW is BWv = B + v. where, v is the vestigial frequency band. The generation of VSB signal is shown in Figure 6

Figure 6: Block Diagram - Generation of VSB signal Here, Hi(ω) is a filter which shapes the other sideband.

To recover the original signal from the VSB signal, the VSB signal is multiplied with cos(ωct) and passed through an LPF such that original signal is recovered.




The Hilbert Transform The Hilbert Transform on a signal changes its phase by _900. The Hilbert transform of a signal g(t) is represented as ^g(t).

We, say g(t) and ^g(t) constitute a Hilbert Transform pair. If we observe the above equations, it is evident that Hilbert transform is nothing but the convolution of g(t) with 1.The Fourier Transform of ^g(t) is computed from signum function sgn(t).

Where,




Properties of Hilbert Transform 1. g(t) and ^g(t) have the same magnitude spectrum. 2. If ^g(t) is HT of g(t) then HT of ^g(t) is -g(t). 3. g(t) and ^g(t) are orthogonal over the entire interval -∞ to +∞.

Complex representation of signals If g(t) is a real valued signal, then its complex representation g+(t) is given by

Therefore,

g+(t) is called pre-envelope and exists only for positive frequencies. For negative frequencies g(t) is defined as follows:




Therefore,

Essentially the pre-envelope of a signal enables the suppression of one of the sidebands in signal transmission. The pre-envelope is used in the generation of the SSB-signal.




LECTURE-11,12&13 ANGLE MODULATION-: In this type of modulation, the frequency or phase of carrier is varied in proportion to the amplitude of the modulating signal.

Figure 1: An angle modulated signal If s(t) = Accos(θi(t)) is an angle modulated signal, then

1. Phase modulation:

2. Frequency Modulation

Phase Modulation If m(t) = Am cos(2πfmt) is the message signal, then the phase modulated signal is given by




Here, kp is phase sensitivity or phase modulation index. Frequency Modulation If m(t) = Am cos(2πfmt) is the message signal,then the Frequency modulated signal is give

here, k fAm/2π is called frequency deviation (∆f) and ∆f/ fmis called modulation index (β). The Frequency modulated signal is

given by

Depending on how small is β FM is either Narrowband FM(β << 1) or Wideband FM(β >> 1). Narrow-Band FM (NBFM) In NBFM β << 1, therefor s(t) reduces as follows:

Since, β is very small, the above equation reduces to




The above equation is similar to AM. Hence, for NBFM the bandwidth is same as that of AM i.e., 2 *message bandwidth(2 *B). A NBFM signal is generated shown in Figure as

Generation of NBFM signal Wide-Band FM (WBFM) A WBFM signal has theoretically infinite bandwidth. Spectrum calculation of WBFM signal is a tedious process. For, practical applications however the Bandwidth of a WBFM signal is calculated as follows: Let m(t) be band limited to Hz and sampled adequately at 2BHz. If time period T = 1/2B is too small, the signal can be approximated by sequence of pulses as shown in Figure




Approximation of message signal If tone modulation is considered, and the peak amplitude of the sinusoid is mp, the minimum and maximum frequency deviations will be ω c- K fm p and ω c+ K fm p respectively. The spread of pulses in frequency domain will be 2 π/T=4πB as shown in fig.




Bandwidth calculation of WBFM signal Therefore, total BW is 2 K fm p + 8πB and if frequency deviation is considered

The bandwidth obtained is higher than the actual value. This is due to the staircase approximation of m(t). The bandwidth needs to be readjusted. For NBFM, k f is very small an d hence ∆f is very small compared to B. This implies

But the bandwidth for NBFM is the same as that of AM which is 2B.A better bandwidth estimate is therefore:

This is also called Carson's Rule. Demodulation of FM signals-: Let Фf m(t) be an FM signal.

This signal is passed through a differentiator to get




If we observe the above equation carefully, it is both amplitude and frequency modulated. Hence, to recover the original signal back an envelope detector can be used. The envelope takes the form

FM signal - both Amplitude and Frequency Modulation The block diagram of the demodulator is shown in Figure

Demodulation of an FM signal




The analysis for Phase Modulation is identical. Analysis of bandwidth in PM

The difference between FM and PM is that the bandwidth is independent of signal bandwidth in FM while it is strongly dependent on signal bandwidth in PM. EXAMPLE OF ANGLE MODULATION-: An angle-modulated signal with carrier frequency ω c = 2π*106 is described by the equation:

1. Determine the power of the modulating signal. 2. What is ∆f? 3. What is β? 4. Determine ∆Ф the phase deviation. 5. Estimate the bandwidth of Ф EM(t)? 1. P = 122/2= 72 units 2. Frequency deviation ∆f, we need to estimate the instantaneous frequency:

The deviation of the carrier is

When the two sinusoids add in phase, the maximum value will be 7500 + 20000π




Hence, 3)

4)

The angle

The maximum angle deviation is 15, which is the phase deviation. 5)

LECTURE -14 REVISION &ASSIGNMENT-: Q1) Explain Amplitude modulation in detail. Q2) Explain SSB and its generation &demodulation. Q3) Write a short note on VSB. Q4) Explain Frequency modulation and its generation. Also explain its demodulation.




LECTURE-15 PULSE ANALOG MODULATION-: 1) Sampling Theorem and its Importance Sampling Theorem: A band limited signal can be reconstructed exactly if it is sampled at a rate at least twice the maximum frequency component in it. Figure shows a signal g(t) that is band limited.

Spectrum of band limited signal g(t) The maximum frequency component of g (t) is fm

To recover the signal g (t) exactly from its samples it has to be sampled at a rate fs= 2fm. The minimum required sampling rate fs = 2fm is called Nyquist rate. Proof: Let g(t) be a band limited signal whose bandwidth is fm and (ω=2πfm)




Original signal g(t) Spectrum G(ω)

Let gS(t) be the sampled signal. Its Fourier Transform GS(ω) is given by




If ωS = 2ωm, i.e., T = 1/2fm. Therefore, Gs (ω) is given by




To recover the original signal G (ω): 1. Filter with a Gate function, H 2ωm (ω) of width 2ω m

2. Scale it by T.

Recovery of signal by filtering with a filter of width 2ωm

Aliasing Aliasing is a phenomenon where the high frequency components of the sampled signal interfere with each other. because of inadequate sampling ωs< 2fm




. Aliasing due to inadequate sampling Aliasing leads to distortion in recovered signal. This is the reason why sampling frequency should be at least twice the bandwidth of the signal. Oversampling-: In practice signal are oversampled, where fs is significantly higher than Nyquist rate to avoid aliasing.




Oversampled signal-avoids aliasing.




LECTURE-16 SAMPLE AND HOLD CIRCUIT- Sample-and-hold (S/H) is an important analog building block with many applications, Including analog-to-digital converters (ADCs) and switched-capacitor filters. The Function of the S/H circuit is to sample an analog input signal and hold this value over a Certain length of time for subsequent processing. Taking advantages of the excellent properties of MOS capacitors and switches, traditional switched capacitor techniques can be used to realize different S/H circuits. The simplest S/H circuit in MOS technology is shown in Figure 1, where Vin is the inputsignal, M1 is an MOS transistor operating as the sampling switch, Ch is the hold capacitor, ck is the clock signal, and Vout is the resulting sample-and-hold output signal.

Figure 1: Simplest sample-and-hold circuit in MOS technology. As depicted by Figure 1, in the simplest sense, a S/H circuit can be achieved using only one MOS transistor and one capacitor. The operation of this circuit is very straightforward. Whenever ck is high, the MOS switch is on, which in turn allows Vout to track Vin. On the other hand, when ck is low, the MOS switch is off. During this time, Ch will keep Vout equal to the value of Vin at the instance when clk goes low.




LECTURE-17

and frequency division (FDM) multiplexing

Time division (TDM)




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.

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

FDM:- Frequency-division multiplexing (FDM) is a form of signal multiplexing which involves assigning non-overlapping frequency ranges to different signals or to each "user" of a medium. FDM is derived from AM techniques in which the signals occupy the same physical ‘line’ but in different frequency bands. Each signal occupies its own specific band of




frequencies all the time, i.e. the messages share the channel bandwidth. FDM – messages occupy narrow bandwidth – all the time.

• FDM is widely used in radio and television systems (e.g. broadcast radio and TV) and was widely used in multichannel telephony (now being superseded by digital techniques and TDM).

• The multichannel telephone system illustrates some important aspects and is considered below. For speech, a bandwidth of ≈ 3kHz is satisfactory.

• The physical line, e.g. a co-axial cable will have a bandwidth compared to speech as shown next

In order to use bandwidth more effectively, SSB is used i.e

3kHz

GHz

freq

From AM we have noted:

m(t)

cos( )ωct

DSBSC

carrier

fc

freq

freq

B

m(t)

DSBSC

m(t)

cos( )ωct

carrier

fc

freq

SSBFilter

SSBSC




We have also noted that the message signal m(t) is usually band limited

The Band Limiting Filter (BLF) is usually a band pass filter with a pass band 300Hz to

3400Hz for speech. This is to allow guard bands between adjacent channels.

For telephony, the physical line is divided (notionally) into 4kHz bands or channels, i.e.

the channel spacing is 4kHz. Thus we now have:

Note, the BLF does not have an ideal cut-off – the guard bands allow for filter ‘roll off’

m(t)

cos( )ωct

SSBFilter

SSBSCBandLimitingFilter

Speech

300Hz – 3400Hz

1 0 k H z3 0 0 H z 3 4 0 0 H z 3 0 0 H z 3 4 0 0 H z

f f f

S p e e c h m ( t ) C o n v e n t io n

f

BandlimitedSpeech

Guard Bands

4kHz




in order to reduce adjacent channel crosstalk. Consider now a single channel SSB system

The spectra will be

Consider now a system with 3 channels

m(t)BLF

SSBFilter

fc

DSBSC SSBSC

300Hz 3400Hz

m(t)

DSBSC

freq

freq

freq

fc

fc




Each carrier frequency, fc1, fc2 and fc3 are separated by the channel spacing

frequency, in this case 4 kHz, i.e. fc2 = fc1 + 4kHz, fc3 = fc2 + 4kHz. The spectrum of the FDM signal, M(t) will be:

Note that the baseband signals m1(t), m2(t), m3(t) have been multiplexed into adjacent

channels, the channel spacing is 4kHz. Note also that the SSB filters are set to select

f

f

f

ΣΣΣΣ

B L F

B L F

B L F

S S BF i l t e r

S S BF i l t e r

S S BF i l t e r

f c 1

f c 2

f c 3

f1

f2

f3

F D MS ig n a l

M ( t )

B a n d l im ite d

m 1( t )

m 2( t )

m 3( t )

F D M T r a n s m i t te ro r E n c o d e r

fc1 fc2 fc3

4kHz 4kHz 4kHz

freq

M(t)

Shaded areas are toshow guard bands.

f1 f2 f3




the USB, tuned to f1, f2 and f3 respectively.

The diagram below illustrates the FDM principle for 12 channels (similar to 3 channels)

to a form a basic group.

i.e. 12 telephone channels are multiplexed in the frequency band 12kHz → 60 kHz in

4kHz channels ≡ basic group. LECTURE-18&19 Pulse amplitude modulation (PAM), pulse time modulation

SSBFilter

SSBFilter

SSBFilter

LPF

LPF

LPF

M(t)FDMSignal

f1

f2

f3

fc1

fc2

fc3

m1(t)

m2(t)

m3(t)

BandLimited

Back tobaseband

m1(t)

m2(t)

m3(t)

m12(t)

Multiplexer

12kHz 60kHz

freq




Introduction The purpose of the modulator is to convert discrete amplitude serial symbols (bits in a binary system) ak

to analogue output pulses which are sent over the channel.

The demodulator reverses this process

Introduction

Possible approaches include – Pulse width modulation (PWM) – Pulse position modulation (PPM) – Pulse amplitude modulation (PAM)

We will only be considering PAM in these lectures

PAM is a general signalling technique whereby pulse amplitude is used to convey the messageFor example, the PAM pulses could be the sampled amplitude values of an analoguesignal. We are interested in digital PAM, where the pulse amplitudes are constrained to chosen from a specific alphabet at the transmitter

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PAM

In binary PAM, each symbol i.e., M-ary system, symbols may take Each transmitted pulse is given by

Where hT(t) is the time domain pulse shape

To generate the PAM output signal, we may choose to represent the input to the transmit filter hT(t) as a train of weighted impulse functions

Consequently, the filter output

∑∞

−∞=

−=k

ks kTtatx )()( δ



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In binary PAM, each symbol ak takes only two values, say {A1 and ary system, symbols may take M values {A1, A2 ,... AM}.Signalling period,

Each transmitted pulse is given by

is the time domain pulse shape

To generate the PAM output signal, we may choose to represent the input to the transmit as a train of weighted impulse functions

Consequently, the filter output x(t) is a train of pulses, each with the required shape

)( kTtha Tk −

∑∞

−∞=

−=k

ks kTtatx )()( δ

tx )(

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and A2}.In a multilevel, Signalling period, T

To generate the PAM output signal, we may choose to represent the input to the transmit

is a train of pulses, each with the required shape

∑∞

−∞=

−=k

Tk kTtha )()

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Filtering of impulse train in transmit filterchoose to represent the input to the transmit filter functions

Consequently, the filter output

Hence the signal at the receiver filter output is

Where h(t) is the inverse Fourier transform of filter output. Data detection is now performed by the Data Sliceroptimum instant t=nT+td when the pulse magnitude is the greatest yields Where vn=v(nT+td) is the sampled noise and



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Filtering of impulse train in transmit filter.To generate the PAM output signal, we may choose to represent the input to the transmit filter hT(t) as a train of weighted impulse

Consequently, the filter output x(t) is a train of pulses, each with the required shape

Hence the signal at the receiver filter output is

is the inverse Fourier transform of H(w) and v(t) is the noise signal at the receive Data detection is now performed by the Data Slicer.Sampling

when the pulse magnitude is the greatest yields

is the sampled noise and td is the time delay required for optimum sampling

∑∞

−∞=

−=k

ks kTtatx )()( δ

∑∞

−∞=

−=k

Tk kTthatx )()(

)()()( tvkTthatyk

k +−= ∑∞

−∞=

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To generate the PAM output signal, we may as a train of weighted impulse

is a train of pulses, each with the required shape hT(t)

is the noise signal at the receive Sampling y(t), usually at the

is the time delay required for optimum sampling




yn is then compared with threshold(s) to determine the recovered data symbols.

LECTURE-20&21-: Elements of pulse code modulation 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

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 non uniform 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.

PCM transmission path

TP.1: Regeneration

Regenerative repeater performs three tasks:

² Equalization means a compensation for the effects of amplitude and

phase distortion produced by the channel




² Timing circuitry assigns the decision time instants when the

probability of making of a wrong decision is minimum

² 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

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

Transmission bandwidth of a PCM wave

Each encoded message sample is represented by a v-digit code word. Consequently, the signaling rate becomes

The transmission bandwidth required by the PCM wave is

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




LECTURE-22 DPCM-: The standard sampling rate for pulse code modulation (PCM) of telephone grade speech signal is fs = 8 Kilo samples per sec with a sampling interval of 125 µ sec. Samples of this band limited speech signal are usually correlated as amplitude of speech signal does not change much within 125 µ sec. A typical auto correlation function R (τ ) for speech samples at the rate 8 Kilo samples per sec is shown in Fig . R (τ = 125 µ sec) is usually between 0.79 and 0.87. This aspect of speech signal is exploited in differential pulse code modulation (DPCM) technique. A schematic diagram for the basic DPCM modulator is shown in Fig Note that a predictor block, a summing unit and a subtraction unit have been strategically added to the chain of blocks of PCM coder instead of feeding the sampler output x (kTs) directly to a linear quantizer. The error sample is given by the following expression

is a predicted value for and is supposed to be close to such that

small in magnitude is called as the ‘prediction error for the n-th sample.




Typical normalized auto-correlation coefficient for speech signal

Schematic diagram of a DPCM modulator

If we assume a final enclosed bit rate of 64kbps as of a PCM coder, we envisage smaller step size for the linear quantizer compared to the step size of an equivalent PCM quantizer. As a result, it should be possible to achieve higher SQNR for DPCM codec delivering bits at the same rate as that of a PCM code. There is another possibility of decreasing the coded bit rate compared to a PCM system if an SQNR as achievable by a PCM codec with linear equalizer is sufficient. If the predictor output can be ensured sufficiently close to then we can simply encode the quantizer output sample




v(kTs) in less than 8 bits. For example, if we choose to encode each of by 6 bits, we achieve a serial bit rate of 48 kbps, which is considerably less than 64 Kbps. This is an important feature of DPCM, when the coded speech signal will be transmitted through wireless propagation channels.

A block schematic diagram of a DPCM demodulator is shown in Fig The scheme is straightforward and it tries to esteem using a predictor unit identical to the one used in the modulator. We have already observed that is very close to within a small quantization error of . The analog speech signal is obtained by passing the sample through an appropriate low pass filter. This low pass filter should have a 3 dB cut off frequency at 3.4kHz.

Schematic diagram of a DPCM demodulator; note that the demodulator is very similar to a

portion of the modulator




LECTURE -23 Delta modulation (DM) If the sampling interval ‘Ts’ in DPCM is reduced considerably, i.e. if we sample a band limited signal at a rate much faster than the Nyquist sampling rate, the adjacent samples should have higher correlation Fig.. The sample-to-sample amplitude difference will usually be very small. So, one may even think of only 1-bit quantization of the difference signal. The principle of Delta Modulation (DM) is based on this premise. Delta modulation is also viewed as a 1-bit DPCM scheme. The 1-bit quantizer is equivalent to a two-level comparator (also called as a hard limiter). Fig. Shows the schematic arrangement for generating a delta-modulated signal.

The correlation increases when the sampling interval is reduced




Block diagram of a delta modulator

Note Some interesting features of Delta Modulation • No effective prediction unit – the prediction unit of a DPCM coder is eliminated and

replaced by a single-unit delay element.

• A 1-bit quantizer with two levels is used. The quantizer output simply indicates whether the present input sample x(kTs) is more or less compared to its accumulated approximation (ˆskTx.)

• Output (ˆskTx) of the delay unit changes in small steps.

• The accumulator unit goes on adding the quantizer output with the previous accumulated

version (ˆskTx). • u(kTs), is an approximate version of x(kTs)

• Performance of the Delta Modulation scheme is dependent on the sampling rate. Most of

the above comments are acceptable only when two consecutive input samples are very close to each other.




This diagram indicates the output levels of 1-bit quantizer. Note that if δ is the step size, the two output levels are ± s

Now, assuming zero initial condition of the accumulator, it is easy to see that

Fig shows that is essentially an accumulated version of the quantizer output for the error signal e. also gives a clue to the demodulator structure for DM. Fig. shows a scheme for demodulation. The input to the demodulator is a binary sequence and the demodulator normally starts with no prior information about the incoming sequence.




Demodulator structure for DM

Now, let us recollect from our discussion on DPCM that, u(kTs) closely represents the input signal with small quantization error

Next, from the close loop including the delay-element in the accumulation unit in the Delta modulator structure, we can write

Hence, we may express the error signal as,

That is, the error signal is the difference of two consecutive samples at the input except the quantization error (when quantization error is small). LECTURE-25 Amplitude Shift Keying (ASK) Modulation:




Amplitude shift keying (ASK) is a simple and elementary form of digital modulation in which the amplitude of a carrier sinusoid is modified in a discrete manner depending on the value of a modulating symbol. Let a group of ‘m’ bits make one symbol. Hence one can design M = 2m different baseband signals, dm(t), 0 ≤ m ≤ M and 0 ≤ t ≤ T. When one of these symbols modulates the carrier, say, c(t) = cosωct, the modulated waveform is: sm(t) = dm(t).cosωct 5.23.1 This is a narrowband modulation scheme and we assume that a large number of carrier cycles are sent within a symbol interval, i.e. ⎟⎠⎞⎜⎝⎛cTϖπ2 is a large integer. It is obvious that the information is embedded only in the peak amplitude of the modulated signal. So, this is a kind of digital amplitude modulation technique. From another angle, one can describe this scheme of modulation as a one-dimensional modulation scheme where one basis function φ1(t) = tTcϖcos.2 , defined over 0 ≤ t ≤ T and having unit energy is used and all the baseband signals are linearly dependent. Ex. #5.23.1 Let m = 2 and d0 = 0, d1 = 1, d2 = 2 and d3 = 3. It is simple to generate such distinct and fixed levels in practice. Further, let us arbitrarily assume the following information to signal mapping: d0 ≡ (1,1), d1 ≡ (1,0), d2 ≡ (0,1) and d3 ≡ (0,0). So, we have four symbols and the modulated waveforms are: s0(t) = d0(t). tTcϖcos.2 = 0, s1 (t) = d1(t). tTcϖcos.2 = tTcϖcos.2, s2 (t) = d2(t). tTcϖcos.2 = 2. tTcϖcos.2 and s3(t) = d3(t). tTcϖcos.2 = 3. tTcϖcos.2 The signal constellation consists of four points on a straight line. The distances of the points from the origin (signifying zero energy) are 0, 1, 2 and 3 respectively. Note that in this example, no-transmission indicates that ‘d0’, i.e. the symbol (1,1) is ‘transmitted’. This is not surprising and it also should not give an impression that we are able to transmit ‘information’ without spending any energy. In fact, it is a bad practice to assign zero energy to a symbol for any good quality carrier modulation scheme because, demodulation at the receiving end and that ultimately leads to poor SER and BER. Another interesting feature to note is that the modulated symbols have different energy levels, viz. 0, 1, 4 and 9 units. This feature does not make the highest energy symbol d3 more immune to thermal noise. On the contrary, the large range of energy level, namely, from ‘0’ to ‘9’ implies that the power amplifier in the transmitter has to have a large linear range of operation – sometime a costly proposition. If the power amplifier goes into its non-linear range while amplifying s3(t), harmonics of the carrier sinusoid will be generated which will rob some power from s3(t) away and may interfere with other wireless transmissions in frequency bands adjacent to ± 2ωc, ± 3ωc, etc. The point to note is that, the Euclidean distance of s3(t) from the nearest point s2(t) in the receiver signal space decreases because of amplifier nonlinearity and it means that the receiver will confuse more between s3(t) and s2(t) while trying to detect the symbols in presence of noise.




Assuming that all the symbols are equally likely to appear at the input of the modulator, we see that the average energy per symbol (sE) is 14/4 = 3.5 unit. This is an important parameter for transmission of digital signals because it is ultimately proportional to the average transmission power. A system designer would always try to ensure low transmission power to save cost and to enhance reliability of the system. So, we see the simple example of ASK modulation of four symbols could be cited in such a way that the signal points were better placed in the constellation diagram such that sE is minimum. ♦ Now, ASK being a form of amplitude modulation, we can say that the bandwidth of the modulated signal will be the same as the bandwidth of the baseband signal. The baseband signal is a long and random sequence of pulses with discrete values. Hence, ASK modulation is not bandwidth efficient. It is implemented in practice when simplicity and low cost are principal requirements. On-off keying On-Off Keying (OOK) is a particularly simple form of ASK that represents binary data as the presence or absence of a sinusoid carrier. For example, the presence of a carrier over a bit duration Tb may represent a binary ’1’ while its absence over a bit duration Tb may represent a binary ‘0’. This form of digital transmission (OOK) has been commonly used to transmit Morse Codes over a designated radio frequency for telegraph services. As mentioned earlier, OOK is not a spectrally efficient form of digital carrier modulation scheme as the amplitude of the carrier changes abruptly when the data bit changes. So, this mode of transmission is suitable for low or moderate data rate. When the information rate is high, other bandwidth efficient phase modulation schemes are preferable.




LECTURE-26 FSK(Frequency Shift Keying) Frequency Shift Keying (FSK) modulation is a popular form of digital modulation used in low-cost applications for transmitting data at moderate or low rate over wired as well as wireless channels. In general, an M-ary FSK modulation scheme is a power efficient modulation scheme and several forms of M-ary FSK modulation are becoming popular for spread spectrum communications and other wireless applications. In this lesson, our discussion will be limited to binary frequency shift keying (BFSK). Two carrier frequencies are used for binary frequency shift keying modulation. One frequency is called the ‘mark’ frequency (f2) and the other as the space frequency ( f1). By convention, the ‘mark’ frequency indicates the higher of the two carriers used. If Tb indicates the duration of one information bit, the two time-limited signals can be expressed as :

The binary scheme uses two carriers and for special relationship between the two frequencies one can also define two orthonormal basis functions as shown below.

If T1 = 1/f1 and T2 = 1/f2 denote the time periods of th = n.T2 = Tb, where ‘m’ and ’n’ are positive integers, the two carriers are orthogonal over e carriers and if we choose m.T1 = = n.T2




= Tb, where ‘m’ and ’n’ are positive integers, the two carriers are orthogonal over the bit duration Tb. If Rb = 1/Tb denotes the data rate in bits/second, the orthogonal condition implies, f1 = m.Rb and f2 = n.Rb. Let us assume that n > m, i.e. f2 is the ‘mark’ frequency. Let the separation between the two carriers be, ∆f = f2 - f1 = (n-m).Rb.

Now, the scalar coefficients corresponding to Eq.

So, the two signal victors can be expressed as:

Please note that one can generate an FSK signal without following the above concept of orthogonal carriers and that is often easy in practice. Fig shows the possible FSK modulated waveform. Notice the waveform carefully and verify if the two carriers are orthogonal. An obvious feature of an FSK modulated signal, analogous to analog FM signal is that envelop of the modulated signal is constant. All modulation schemes which exhibit constant envelope, are preferable for high power digital transmission because, operation of the power amplifier in a non-linear region may not produce considerable harmonics.




Fig. shows the constellation diagram for binary FSK. Fig. shows a conceptual diagram for generating binary FSK modulated signal. Note that the input random binary sequence is represented by ‘1’ and ‘0’ where ‘0’ represents no voltage at the input of the multipliers. A ‘0’ input to the inverter results in a ‘1’ at its output. That is, the inverter, along with the two multipliers and the summing unit, may be thought to behave as a ‘switch’ which selects output of one of the two oscillators.

Signal constellation for binary FSK. The diagram also shows the two decision zones, Z1 and Z2.




A schematic diagram for BFSK modulation

In practice, however, this scheme will not work reliably because, the two oscillators being independent, it will be difficult to maintain the orthogonal relationship between the two carrier frequencies. Any relative phase shift among the two oscillators, which may even occur due to thermal drift, will result in deviation from the orthogonality condition. Another disadvantage of the possible relative phase shift is random discontinuity in the phase of the modulated signal during transition of information bits. A better proposition for physical implementation is to use a voltage controlled oscillator (VCO) instead of two independent oscillators and drive the VCO with an appropriate baseband modulating signal, derived from the serial bit stream. The VCO free-running frequency ( ffree ) should be chosen as:

Fig. shows the form of a coherent FSK demodulator, based on the concepts of correlation receiver as outlined in Module #4. The portion on the LHS of the dotted line shows the correlation detector while the RHS shows that the vector receiver reduces to a subtraction unit. Output of the subtraction unit is compared against a threshold of zero to decide about the corresponding transmitted bit.




Schematic diagram of a coherent BFSK demodulator

Fig. gives a scheme for non-coherent demodulation of BFSK signal using matched filters. It is often easier to follow this approach than the coherent demodulation scheme without sacrificing error performance.

General scheme for non-coherent demodulation of BFSK signal using matched filters

When the issues of performance and bandwidth are not critical and the operating frequencies are low or moderate, a low complexity realization of the demodulator is also possible. Two bandpass filters, one centered at f1 and the other centered at f2 may replace the matched filters .




Power Spectra of BFSK

Power spectrum of an FSK modulated signal depends on the choice of f1 and f2, i.e. on ‘m’ and ‘n’. When (n-m) is large, we may visualize BFSK as the sum of two OOK signals (see Fig.5.23.3) with carriers f1 and f2. However, such choice of (n-m) does not a result in bandwidth efficiency. In the following, = (m+1), i.e. f1 = m.Rb = m/Tb

Fig. 5.23.5 shows a sketch (approximate) of the power spectrum of binary FSK.we will discuss about another form of FSK, known as Minimum Shift Keying (MSK), which is operates with minimum possible separation between two frequencies f1 and f2.

Sketch of the power spectrum of binary FSK signal




LECTURE-27

BPSK, QPSK

Quaternary Phase Shift Keying (QPSK) This modulation scheme is very important for developing concepts of two-dimensional I-Q modulations as well as for its practical relevance. In a sense, QPSK is an expanded version from binary PSK where in a symbol consists of two bits and two orthonormal basis functions are used. A group of two bits is often called a ‘dibit’. So, four dibits are possible. Each symbol carries same energy. Let, E: Energy per Symbol and T: Symbol Duration = 2. Tb, where Tb: duration of 1 bit. Then, a general expression for QPSK modulated signal, without any pulse shaping

On simple trigonometric expansion, the modulated signal si (t) can also be expressed as:

The two basis functions are:

The four signal points, expressed as vectors, are:

Fig. shows the signal constellation for QPSK modulation. Note that all the four points are equidistant from the origin and hence lying on a circle. In this plain version of QPSK, a symbol transition can occur only after at least T = 2Tb sec. That is, the symbol rate Rs = 0.5Rb. This is




an important observation because one can guess that for a given binary data rate, the transmission bandwidth for QPSK is half of that needed by BPSK modulation scheme.

Signal constellation for QPSK. Note that in the above diagram θ has been considered to be zero. Any fixed non-zero initial phase of the basis functions is permissible in general.

Now, let us consider a random binary data sequence: 10111011000110… Let us designate the bits as ‘odd’ (bo) and ‘even’ (be) so that one modulation symbol consists of one odd bit and the adjacent even bit. The above sequence can be split into an odd bit sequence (1111001…) and an even bit sequence (0101010…). In practice, it can be achieved by a 1-to-2 DEMUX. Now, the modulating symbol sequence can be constructed by taking one bit each from the odd and even sequences at a time as {(10), (11), (10), (11), (00), (01), (10), …}. We started with the odd sequence. Now we can recognize the binary bit stream as a sequence of signal points which are to be transmitted: {1s, 4s, 1s, 4s, 2s, 3s, 1s, …}.




Table summarizes the features of QPSK signal constellation

Fig shows the QPSK modulated waveform for a data sequence 101110110001. For better illustration, only three carrier cycles have been shown per symbol duration.

QPSK modulated waveform

Generation of QPSK modulated signal Let us recall that the time-limited energy signals for QPSK modulation can be expressed




The QPSK modulated wave can be expressed in several ways such as:

For narrowband transmission, we can further express s(t) as:

where

is the complex low-pass equivalent representation of s(t).

One can readily observe that, for rectangular bipolar representation of information bits and without any further pulse shaping,




Block schematic diagram of a QPSK modulator

Another schematic diagram of a QPSK modulator

QPSK modulated signal can indeed be viewed as consisting of two independent BPSK modulated signals with orthogonal carriers.




The structure of a QPSK demodulator, following the concept of correlation receiver, is shown in Fig. . The received signal r(t) is an IF band pass signal, consisting of a desired modulated signal s(t) and in-band thermal noise. One can identify the I- and Q- path correlators, followed by two sampling units. The sampling units work in tandem and sample the outputs of respective integrator output every T = 2Tb second, where ‘Tb’ is the duration of an information bit in second. From our understanding of correlation receiver, we know that the sampler outputs, i.e. r1 and r2 are independent random variables with Gaussian probability distribution. Their variance is same and decided by the noise variance while their means are ±2E, following our style of representation. Note that the polarity of the sampler output indicates best estimate of the corresponding information bit. This task is accomplished by the vector receiver, which consists of two identical binary comparators as indicated in Fig. The output of the comparators are interpreted and multiplexed to generate the demodulated information

Correlation receiver structure of QPSK demodulator

Spectrum of QPSK modulated signal To determine the spectrum of QPSK modulated signal, we follow an approach similar to the one we followed for BPSK modulation in the previous lesson. We assume a long sequence of random independent bits as our information sequence. Without Nyquist filtering, the shaping function in this case can be written as:




After some straight forward manipulation, the single-sided spectrum of the equivalent complex baseband signal can be expressed as:

Here ‘E’ is the energy per symbol and ‘T’ is the symbol duration. The above expression can also be put in terms of the corresponding parameters associated with one information bit

Normalized base band bandwidth of QPSK and BPSK modulated signal




LECTURE-28

M-ary PSK

This is a family of two-dimensional phase shift keying modulation schemes. Several bandwidth efficient schemes of this family are important for practical wireless applications. As a generalization of the concept of PSK modulation, let us decide to form a modulating symbol by grouping ‘m’ consecutive binary bits together. So, the number of possible modulating symbols is, M = 2m and the symbol duration T = m. Tb. Fig. 5.25.6 shows the signal constellation for m = 3. This modulation scheme is called as ‘8-PSK’ or ‘Octal Phase Shift Keying’. The signal points, indicated by ‘*’, are equally spaced on a circle. This implies that all modulation symbols si(t), 0 ≤ i ≤ (M-1), are of same energy ‘E’. The dashed straight lines are used to denote the decision zones for the symbols for optimum decision-making at the receiver.




Signal space for 8-PSK modulation

The two basis functions are similar to what we considered for QPSK, viz.,

The signal points can be distinguished by their angular location

The time-limited energy signals si(t) for modulation can be expressed in general as




Considering M-ary PSK modulation schemes are narrowband-type, the general form of the modulated signal is

FIG shows a block schematic for an M-ary PSK modulator. The baseband processing unit receives information bit stream serially (or in parallel), forms information symbols from groups of ‘m’ consecutive bits and generates the two scalars si1 and si2 appropriately. Note that these scalars assume discrete values and can be realized in

Block schematic diagram of M-ary PSK modulator

Normalized scalars for 8-PSK modulation




Without any pulse shaping, the uI(t) and uQ(t) of Eq. are proportional to si1 and si2 respectively. Beside this baseband processing unit, the M-ary PSK modulator follows the general structure of an I/Q modulator. Fig. shows a scheme for demodulating M-ary PSK signal following the principle of correlation receiver. The in-phase and quadrature-phase correlator outputs

Structure of M-ary PSK demodulator




LECTURE-29&30

Noise Analysis

The following assumptions are made:

• Channel model

distortionless

{Additive White Gaussian Noise (AWGN)

• Receiver Model (see Figure 1)

Ideal band pass filter

Ideal demodulator




BPF (Band pass filter) - bandwidth is equal to the message Bandwidth B midband frequency is fc.

Power Spectral Density of Noise

N0/2 and is defined for both positive and negative frequency .N0 is the average power/(unit BW) at the front-end of the receiver in AM and DSB-SC.

The filtered signal available for demodulation is given by:

Input SNR:




(SNR)I =Average power of modulated signal s(t)/Average power of noise

output SNR:

(SNR)O =Average power of demodulated signal s(t)/Average power of noise

The Output SNR is measured at the receiver.

Channel SNR:

(SNR)C =Average power of modulated signal s(t)/Average power of noise in message bandwidth

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