Thus there are three basic modulation techniques: 1) AMPLITUDE SHIFT KEYING 2) FREQUENCY SHIFT KEYING 3) PHASE SHIFT KEYING

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Jonas Claude Cole
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1 CHAPTER 5 Syllabus 1) Digital modulation formats 2) Coherent binary modulation techniques 3) Coherent Quadrature modulation techniques 4) Non coherent binary modulation techniques. Digital modulation formats: Modulation is defined as the process by which characteristics of a carrier signal is varied in accordance with the message signal. In digital communication, the modulating wave consists of binary data with sinusoidal carrier. The feature that is used by modulator to distinguished one signal from the another is a step change in frequency, amplitude or phase of the carrier Thus there are three basic modulation techniques: 1) AMPLITUDE SHIFT KEYING 2) FREQUENCY SHIFT KEYING 3) PHASE SHIFT KEYING The modulation scheme is as shown in the figure We have a hybrid form of modulation for example change in both amplitude and phase of the carr 1

2 To perform demodulation at the receiver we have two types of detectors i) Coherent detectors In coherent detectors the receiver is phase locked with the transmitter, means that the receiver has exact knowledge of carrier wave s phase reference. ii) Non coherent detectors In non coherent detectors, knowledge of the carrier is not required. The complexity of the receiver is reduced with increased errors. The designers of digital communication make a choice in favor of the scheme that attains as many of the following goals as possible 1) Maximum data rate 2) Minimum probability of symbol error 3) Minimum transmitted power 4) Minimum resistance to interfering signals 5) Minimum circuit complexity Coherent binary modulation techniques 1) Binary phase shift keying In binary phase shift keying the pair of signals S 1 (t) and S 2 (t) used to represent symbol 1 and symbol 0 respectively defined as, for symbol 1 for symbol 1 Where A c = within limit Above expression can be represented by a single basic function Hence 0 for symbol 1 for symbol 0 2

3 Signal space representation The signal space representation is as shown in the figure. The message point S 1 corresponding to signal S 1 (t) is located on the axis at while message point S 2 corresponding to signal S 2 (t) is located on the axis at. The signal space consists of two regions Z 1 and Z 2. Assume symbol 0 and 1 are equi - accruable, decision in region Z 1 corresponding to symbol 1 while decision in region Z 2 corresponds to symbol 0 Decision rule: If the observation point X 1 satisfies following conditions corresponding decisions will be taken If X 1 > 0, decision will be in favor of symbol 1. If X 1 < 0, decision will be in favor of symbol 0. If X 1 = 0, decision will be in favor of arbitrary. Generation of BPSK The binary data is represented in polar NRZ format then multiplied with a carrier of unit energy i.e. to produce BPSK signal. 3

4 I.e. when symbol 1 is transmitted: When symbol 0 is transmitted: BPSK signal S(t) = { Detection of BPSK signal To detect the original binary sequences 1s and0s we apply noisy PSK wave x(t) to a correlator, it is also supplied with locally generated coherent reference signal as shown in the figure. The correlator output is compared with threshold of zero volts ie., If X 1 > 0, decision will be in favor of symbol 1. If X 1 < 0, decision will be in favor of symbol 0. Probability of symbol error in BPSK Let x(t) be the received signal i.e. { let us assume that the symbol 0 is transmitted. Then the output of the correlators is 4

5 Mean of the random variable = E [ = E [ + E [ = Variance of is [ ] [ ] Condition probability density when symbol 0 is transmitted is given by [ ( ) ] Let transmitted. Region [ ( ) ] denotes the conditional probability of deciding in favor of symbol 1 when 0 is [ ( ) ] Let ( ) 5

6 Limits When ( ) when z = W.K.T complementary error function erfc (u) hence, * and / by 2 we obtain, Hence Similarly we can find the probability of error for 2 nd kind The average probability of error is given as Let probability of transmitting symbol 0 is P(0) = 1/2 Let probability of transmitting symbol 1 is P(1) = 1/2, 6

7 Hence we have [ ] [ ] Coherent binary FSK In binary FSK system, symbol 1 and 0 are distinguished from each other by transmitting of two sinusoidal waves that differ in frequency by a fixed amount. The binary FSK can be represented as follows BFSK signal S(t) = { Where i = 1,2 and E b is the transmitted signal energy per bit. ie., BFSK signal S(t) = { and transmitted frequency is given by Let and are orthonormal basic function as defined below Therefore S(t) may be written as { 7

8 Signal space representation Coherent binary FSK system is characterized by having signal space ie., two dimensional (ie., N = 2) with two message points as shown in the figure If x(t) is the received signal given symbol 1 is transmitted x(t) equal S 1 (t) +w(t) where w(t) is the white Gaussian noise which has a 0 mean and power spectral density N 0 /2 on the other hand if symbol 0 is transmitted then x(t) = S 2 (t) + w(t) Applying decision rule, we can see the observation space is divided into two decision regions labeled as Z 1 and Z 2. The receiver decides in favor of symbol 1 if observation point x falls inside Z 1 else 0 if it falls in region Z 2 Generation of BFSK To generate BFSK signal the input binary sequence is represented by on off form with symbol 1 represented by amplitude and with symbol 0 by zero volts. By using inverter in the lower channel we make sure that when symbol 1 is at the input, the oscillator frequency f 1 in the upper channel is on while the oscillator frequency in the lower is off and vice versa when symbol 0 is transmitted also note phase of FSK remain constant, hence FSK is also known as continuous phase FSK 8

9 Detection of BFSK In order to detect the original binary sequence given the noisy received wave x(t), we may use the receiver as shown in the figure. It consists of two correlators with common input and reference signal. The correlators outputs are subtracted one from the other with difference L, compared with the threshold of 0 volts, to get the demodulated binary sequence. Probability of symbol error in BFSK Let x(t) be the received signal i.e. { let us assume that the symbol 0 is transmitted. Then the received signal is The output of top correlator Mean of the random variable = E [ = 9

10 Variance of is The output of bottom correlator Mean of the random variable = Variance of is Let us find the mean and variance of random variable l = = is also given Var[L] = var [ = Condition probability density when symbol 0 is transmitted is given by [ ( ) ] [ ( ) ] Let denotes the conditional probability of deciding in favor of symbol 1 when 0 is transmitted. Region 10

11 [ ( ) ] Let ( ) Limits When ( ) when z = W.K.T complementary error function erfc (u) hence, * and / by 2 we obtain, Hence Similarly we can find the probability of error for 2 nd kind 11

12 The average probability of error is given as Let probability of transmitting symbol 0 is P(0) = 1/2 Let probability of transmitting symbol 1 is P(1) = 1/2, Hence we have [ ] [ ] Coherent Quadrature modulation technique The important goals of digital communication are: i) Very low probability of error. ii) Efficient utilization of channel bandwidth. Here Quadrature carrier multiplexing system is a bandwidth conserving scheme, which produces a modulated wave described as follows: Where Quadriphase shift keying In Quadrature phase shift keying, two successive bits in the data sequence are grouped together. This reduces the bit rate and hence reducing the bandwidth of the channel. In particular, in quadriphase shift keying the phase of the carrier takes on one the four values S(t) = { Where i = 1,2,3,4 based on this representation 12

13 Each possible value of phase corresponds to a unique pair of bits called dibit. Hence we choose the foregoing set of phase values to represent the gray encoded set of dibits 10, 00,01and 11. { There are only two orthonormal basic functions and, contained in expansion of hence There are four message points and the associated signal vector [ ] [ ] Signal space diagram A QPSK signal is characterized by having a two dimensional signal constellation and four message points (i.e. M=4) as shown in the figure 13

14 The signal space characterization of QPSK is given by Input Bit Phase of QPSK signal Coordinates of message points 10 π/ π/4 01 5π/4 11 7π/4 Generation of QPSK The input binary sequence represented in polar form, with symbol 1 and 0 represented by + and - volts respectively. The binary wave is divided by means of a Demultiplexer into two separate binary waves consisting of odd and even number of input bits and. The two binary waves and are used to modulate a pair of Quadrature carriers or orthonormal basic function and. The result is a pair of BPSK, finally BPSK are added up to form QPSK QPSK receiver 14

15 The QPSK receiver consists of a pair of correlators with a common input and supplied with a locally generated pair of coherent reference signal and.the correlators output x 1 and x 2 are each compared with threshold of zero volts. If x 1 > 0 a decision is made in favor of symbol 0. Similarly in case of x 2 finally the outputs are combined in a multiplexer to reproduce the original binary sequence. Probability of symbol error in QPSK Let x(t) be the received signal The samples as follows Similarly and are guassian random variable with mean and are also guassian random variable with mean When signal is transmitted, the received signal point lies in the decision region If and leading to correct decision Condition probability density function is given by ( ) [ ] ( ) [ ] 15

16 ( ) [ ( ) ] ( ) [ ( ) ] ( ) [ ( ) ] Let us assume ( ) Z 4 i.e. both x 1 and x 2 should be positive [ ( ) ] is transmitted. If the received signal x should fall in the region ( ) ( ) [ ( ) ] [ ( ) ] Let ( ) Let ( ) Limits When when When when ( ) z = ( ) z = 16

17 We have [ ] i.e. hence [ ] The average probability of symbol error In the region Z 4 : >>1, hence we can ignore second term In QPSK two bits are transmitted at a time hence E = 2E b 17

18 Non coherent binary FSK In binary FSK, the transmitted signal is defined by { Where f i is the two possible values f 1 and f 2. f 1 represents symbol 1. f 2 represents symbol 0. For non coherent detection of this frequency modulated wave, the receiver consists of a matched filter followed by envelop detector shown in figure. The resulting envelope detector outputs are sampled at t = T b and there values are compared. If l 1 > l2 the receiver decides in favor of symbol 1 If l 1 < l 2 the receiver decides in favor of symbol 0 The probability of error for non coherent FSK is given by Differential phase shift keying DPSK as the non coherent version of the PSK. It eliminates the need of reference signal at the receiver by combining two basic functions 1) Differential encoding of input binary wave. 2) Phase shift keying. 18

19 To send symbol 0 we make phase advance of 180 0, to send symbol 1 we leave the phase of current signal unchanged. The receiver is equipped with storage capability. Suppose the transmitted DPSK signal. Let S 1 (t) denote the transmitted DPSK signal for for the case when we have binary symbol 1 at transmitter input and the second part of interval via.,. The transmitter leaves the carrier phase unchanged. S 1 (t) = { Let S 2 (t) denote the transmitted DPSK signal for have binary symbol 0 at the transmitter input advances the carrier phase by the case when we. The transmission of zero S 1 (t) = { The average probability of error is given by DPSK transmitter The block diagram of DPSK transmitter is as shown in the figure. It consists of one bit delay element interconnected so as to convert input binary sequence {b k } into differentially encoded sequence {d k }. this sequence is amplitude level shifted and then used to modulate a carrier wave off frequency f c there by producing DPSK wave. The differentially encoded sequence {d k } is generated by using logical equation 19

20 DPSK receiver The block diagram of DPSK receiver is as shown in the figure. At the receiver input, the received DPSK signal plus noise is passed through a band pass filter centered at frequency f c, so as to limit the noise power. The filter output and a delayed version of it with a delay equal to one bit duration T b applied to correlators finally the correlators output is compared with decision threshold of zero volts and there by decision is made in favor of symbol 1 or symbol 0. Ex: Note: Assume the first bit of as 1 or 0 and perform XNOR operation with, here in this example the first bit of is assumed to be

EC 6501 DIGITAL COMMUNICATION UNIT - IV PART A

EC 6501 DIGITAL COMMUNICATION UNIT - IV PART A 1. Distinguish coherent vs non coherent digital modulation techniques. [N/D-16] a. Coherent detection: In this method the local carrier generated at the receiver