Digital Modulation.docx

Chapter 9 Digital Modulation Digital transmission OR Digital modulation(DM) is transmittal of digital pulses b/w 2 points in comm. Sys DM called → Digital radio (DR ) DR is digitally mod. analog carriers b/w 2 pts in comm. Sys Digital comm (DC) include systems where HF analog carrier are modulated by LF digital info. signals (DR) Digital transmission systems require a physical facility b/w 𝑻𝑿 & 𝑹𝑿 (metallic wire pair, a coaxial cable, or a FO cable) In DR sys. medium is free space OR earth's atmosphere In DR sys. carrier could be physical cable OR free space Property that distinguish DR system from conventional analog modulation comm. sys is nature of modulation signal Analog / digital modulation comm. Sys use analog carrier to transport information through system

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 Analog modulation→ info signal analog  Digital modulation→ info signal digital ( computer – generated or digitally encoded)

DC include HF analog carrier modulated by LF - DR DM suited to multitude of communications (cable &wireless) Applications 1. Low speed voice band data communication (modem) 2. High speed data transmission systems broad band digital subscriber lines (DSL) 3. Digital microwave & satellite systems 4. Cellular telephone

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 Pre-coder: performs level conversion & then encodes incoming data into groups of bits that modulate analog carrier  Modulated carrier is shaped (filtered), amplified & then transmitted through transmission medium (wire/ wireless) to Rx  In Rx incoming signals are filtered, amplified & then applied to de-modulator & decoder ckt which extract original source info. From modulated carrier  Clk & carrier recovery ckts recovers analog carrier & digital timing (clk) signals from incoming modulated wave perform demodulation process

Bandwidth and Information Capacity Two limitations on system performance are noise & BW

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BW of Comm Sys is min. PB required to propagate source info through system BW Comm. Sys. sufficiently large to pass all info. frequencies Information capacity of comm.sys is measure how much source info. carried through system in given period of time. Amount of info that can propagated through a transmission system is α product of system BW & time of transmission Relationship among: 𝐁𝐖 𝟏 , 𝒕𝒓𝒂𝒏𝒔𝒎𝒊𝒔𝒔𝒊𝒐𝒏 𝒕𝒊𝒎𝒆𝟐 , 𝒊𝒏𝒇𝒐𝒓𝒎𝒂𝒕𝒊𝒐𝒏 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚𝟑 developed by Hartley of Bell Telephone Laboratories in 1928  Hartley's law is

IαBαt Where I – info. Capacity, B – BW, T – transmission time Eq. shows that information capacity is linear function α to both system BW & transmission time If either BW or transmission time changes info. capacity changes by same proportion  3 kHz-BW reqd. transmit voice-quality telephone signals  200 kHz- BW req d for FM transmission of hi-fi music  6 MHz-BW reqd. for broadcast-quality (vestigial SB)  TV signals (more info./unit time more BW reqd.) 4

M-ary Encoding M-ary is term derived from word "binary" “M” simply a digit that represents no. of conditions possible , levels or combinations for given no. of binary variables It’s advantageous to encode at level higher than binary There are more than 2 conditions possible E.g Digital signal with 4 possible conditions (voltage levels, frequencies, phase & so on) It is an M-ary system where M = 4, If M= 8 and so forth No. of bits produce given no of conditions as Where :- N - - - No. of bits M - - - No of conditions Eq. re- arranged as 𝟐𝑵 = M If N= 1 two condition , N= 2 , four condition& so on bit Rate Most basic digital symbol used to represent info. is binary digit or bit Speed of data, expressed in (bits/s or bps). Data rate “R” is function of duration of bit or bit time (TB) fig R = 1/TB Rate is also → channel capacity “C” If bit time is 10 ns, data rate equals R = 1/10 x 𝟏𝟎−𝟗 = 100 million bits/s  Usually expressed as 100 Mbits/s. 5

Fig. Data rate is indicated in bits per second (bits/s). Baud Rate The term “baud” originates from French engineer Emile Baudot, who invented the 5-bit teletype code Baud rate refers to no.of signal or symbol changes occur / sec A symbol is one of several volt., freq., or phase changes 2 symbols, one for each bit 0 or 1, represents voltage levels In this case, baud or symbol rate is same as bit rate It’s possible to have more than two symbols per transmission interval, each symbol represents multiple bits With more than 2 symbols, data is transmitted using modulation techniques  Baud like bit rate is also a rate of change

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 Baud refer to rate of change of a signal on transmission medium after encoding & modulation occurred  Baud is a unit of transmission rate , modulation rate , symbol rate or symbols per second  Baud is reciprocal of time of one o/p signaling element 𝟏 baud = 𝒕 𝒔

where baud - - - symbol rate /sec 𝒕𝒔 - - - time of one signaling element  Signaling element called symbol & encode as change in amplitude , frequency or phase E.g : binary signals are encoded & transmitted one bit at time in form of discrete volt levels logic 1(high) & logic 0 (low) Baud is transmitted one at time & more than one info. bit In binary systems ( FSK & PSK ) baud & bps are equal In higher systems (QPSK & 8-PSK) bps always < than baud For a given BW “B” the highest theoretical bit rate is 2B In multilevel signaling, Nyquist formulation for ch. capacity 𝒇𝒃 = 2B 𝒍𝒐𝒈𝟐 M

Where

𝒇𝒃 = channel capacity (bps) B = min. Nyquist BW (hertz) M = no. of discrete signals or voltage levels 7

Above formula re-arranged to solve for minimum BW necessary to pass M-ary digitally modulated carrier as follow 𝒇

B = (𝒍𝒐𝒈𝒃 𝑴) 𝟐

If N is substituted for 𝒍𝒐𝒈𝟐 M eq. reduce to 𝒇

B = 𝑵𝒃 “ N” is no. of bits encoded into each signaling element  Bit rate – refers to rate of change of digital information which is usually binary  Baud – refers to rate of change of a signal on a transmission medium after encoding and modulation have occurred. Amplitude Shift Keying (ASK) Simplest DM technique → ASK, Where binary info. signal directly modulates ampl of analog carrier ASK similar to standard AM except 2 o/p’s amplitudes ASK also called digital amplitude modulation (DAM) Mathematically 𝑨

𝑽𝒂𝒔𝒌 (t) = [ 1 + 𝑽𝒎 (t) ][ 𝟐 cos ( 𝝎𝒄 t) ] Where 𝑽𝒂𝒔𝒌 (t) = ASK wave 𝑽𝒎 (t) = digital information modulation signal (volts) 8

A/2 = un-modulated carrier amplitude (volts) 𝝎𝒄 = analog carrier radian frequency (radian /second , 2𝝅𝒇𝒄 t) In above modulating signal 𝑽𝒎 (t) a normalized binary WF where +1V = logic 1 & -1V = logic 0  For a logic 1 input, 𝑽𝒎 (t) = +1V, & reduces to 𝑨

𝑽𝒂𝒔𝒌 (t) = [ 1 + 𝟏 ][ cos ( 𝝎𝒄 t) ] => Acos ( 𝝎𝒄 t) 𝟐

 For logic 0 input,𝑽𝒎 (t) = -1V, & reduces to 𝑨

𝑽𝒂𝒔𝒌 (t) = [ 1 - 𝟏 ][ 𝟐 cos ( 𝝎𝒄 t) ] = 0 so the modulated wave 𝑽𝒂𝒔𝒌 (t) is either Acos ( 𝝎𝒄 t) or 0, means carrier is either “ON” or “OFF”.  ASK is sometimes referred as on-off keying (OOK)

Fig shows input & output WFs of ASK modulator For every i/p binary data stream , one change in ASK WF one bit (𝒕𝒃 ) = one analog signaling (𝒕𝒔 ) Frequency Shift Keying (FSK) 9

FSK ia simple, low performance type of DM FSK is form of constant ampl angle –modulation similar to FM, except modulating signal is binary signal varies b/w 2 discrete voltage levels rather continuously changing analog WF FSK called → BFSK (binary FSK) General expression for FSK is 𝒗𝒇𝒔𝒌 (t) = 𝑽𝒄 cos {2𝝅[𝒇𝒄 + 𝒗𝒎 (t) ∆f]t} Where 𝑽𝒇𝒔𝒌 (t) = binary FSK waveform 𝑽𝒄 = peak analog carrier amplitude (volts) 𝒇𝒄 = analog carrier center frequency (hertz) ∆f =peak change shift in the analog carrier frequency (hertz) 𝑽𝒎 (t) = binary i/p modulating signal (volts) The above eq. the peak shift in carrier frequency (∆f ) is ∝ to amplitude of binary i/p signal (𝑽𝒎 [t]) & direction of shift is determined by polarity Modulating signal is normalized binary WF where logic “ 1 ” = + 1V & logic “ 0 “ For logic i/p 𝑽𝒎 (t) = +1 𝑽𝒇𝒔𝒌 (t) = 𝑽𝒄 cos 2𝝅[𝒇𝒄 + ∆f ) t ] For logic i/p 𝑽𝒎 (t) = -1 10

𝑽𝒇𝒔𝒌 (t) = 𝑽𝒄 cos 2𝝅[𝒇𝒄 - ∆f ) t ] With binary FSK carrier center freq. (𝒇𝒄 ) shifted(deviated) up & down in freq. domain by binary i/p signal as shown in fig Binary i/p signal changes from logic 0 → logic 1 & vice versa o/p freq shifts b/w 2 frequencies mark & space , logic 1 freq (𝒇𝒎 ) & logic 0 freq (𝒇𝒔 ) Mark & space frequencies are separated from 𝒇𝒄 by peak freq. deviation (∆f ) & from each other by 2∆f With binary FSK, 𝒇𝒄 is shifted(deviated) up & down in freq. domain by binary i/p signal as shown in fig

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Frequency deviation in fig expressed mathematically as |𝒇 −𝒇 |

∆f = 𝒎𝟐 𝒔 |𝒇𝒎 − 𝒇𝒔 | - - - absolute diff b/w mark & space frequencies Fig (a) shows time domain, binary i/p to FSK modulator & FSK o/p. Fig (b) shows truth table for binary FSK modulator

FSK Bit Rate, Baud and Bandwidth Baud for binary FSK determined by substituting N= 1 𝒇 B = 𝑵𝒃 = 𝒇𝒃 Minimum BW for FSK is given as B = |(𝒇𝒔 − 𝒇𝒃 ) − (𝒇𝒎 − 𝒇𝒃 )| = |𝒇𝒔 − 𝒇𝒎 | + 2𝒇𝒃 Since |𝒇𝒔 − 𝒇𝒎 | equals 2∆𝒇𝒔 , minimum BW can approximated B = 2(∆f + 𝒇𝒃 ) B - - - minimum Nyquist BW ∆f - - - frequency deviation |𝒇𝒔 − 𝒇𝒎 | 12

𝒇𝒃 - - - input bit rate(bps)

FSK Transmitter Binary- FSK modulator similar to FM modulator & called VCO 𝒇𝒄 falls half way b/w mark& space frequencies Logic 1 shift 𝑽𝑪𝑶𝒐/𝒑 to mark & 0 shift𝑽𝑪𝑶𝒐/𝒑 to space freq. 𝑽𝑪𝑶𝒐/𝒑 shifts/deviate back & forth b/w mark & space freqs VCO-FSK modulator operated in sweep mode. With sweep mode freq. deviation is ∆f = 𝑽𝒎 (t) 𝒌𝒍 Where ∆f - - -peak freq. deviation (hertz) 𝑽𝒎 (t) - - - peak binary modulating signal voltage(volts) 𝒌𝒍 - - -deviation sensitivity (hertz/ volt)

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Non Coherent FSK Receiver FSK i/p signal is simultaneously applied to i/p of both BPF through power splitter Respective filters passes only mark or space freq. to respective detector envelop

This type of FSK detection called non coherent detection b/c 14

(no freq , involved in demod process that is synchronized either in phase , freq. or both with incoming FSK signal ) Coherent FSK Rx

Incoming FSK signal is multiplied by a recovered carrier signal has same freq. & phase as𝑻𝑿 reference Two transmitted frequencies (mark & space) are not continuous Coherent FSK detection rarely used Continuous Phase Frequency Shift Keying When 𝒇𝒐 changes it is a smooth , continuous transition and there is no phase discontinuities (CP-FSK) has better bit-error performance than conventional FSK for a given S/N ratio

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Disadvantage Required synchronization ckt& more expensive to implement Phase Shift Keying Another form of angle modulated constant amplitude - DM PSK is M-ary – DM similar to PM except with PSK i/p is binary digital signal & limited no. of o/p phases I/p binary info is encoded into groups of bits before modulating carrier No. of bits in group ranges from 1 to 12 or more No. of o/p phase is defined by “ M “& no of bits in group “ N “ Binary Phase Shift Keying Simplest form of PSK is BPSK where N= 1 & M= 2 With B-PSK two phases ( 𝟐𝟏 = 2 ) are possible for carrier , one phase represents a logic 1 and other phase represent logic 0 16

I/p digital signal changes state from 1 → 0 or from 0 → 1 phase of o/p carrier shifts b/w two angles separated by 180º Other names for BPSK are phase reversal keying (PRK) & biphase modulation  B-PSK is form of sq. wave modulation of continuous wave (CW) signal

BPSK Transmitter

Simplified block diagram of a BPSK 𝑻𝑿

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BM act as phase reversing switch , depending on logic condition of digital i/p the carrier is transferred to o/p either in phase or 180º out of phase with reference carrier oscillator  Remaining working self study by students

Constellation diagram Fig shows truth table, phase diagram & constellation diagram for a BPSK modulator Constellation diagram also called signal state space diagram similar to phasor diagram except that entire phasors is not drawn In constellation diagram only relative positions of peaks of phasors are shown

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Fig shows o/p phase vs time relationship for BPSK WF

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Logic “1” i/p produce an analog o/p signal with 180º phase angle Binary i/p shifts b/w logic 1 & logic 0 & vice versa , phase of BPSK WF shifts b/w 0º & 180º respectively BPSK Receiver ( Block diag of BPSK Rx )

I/p signal may be + sin𝝎𝒄 tOR - sin𝝎𝒄 t 20

Coherent carrier recovery ckt detects & generates carrier signal that is both frequency or phase coherent with original transmit carrier Balanced modulator :- Product detector O/p is product of two i/p’s (BPSK signal & recovered carrier) LPF separates binary data from complex de-modulated signal Quaternary PSK QPSK OR quadrature PSK is another form of angle

modulated constant amplitude digital modulation With QPSK 4 o/p phases for single carrier frequency 4 o/p phases are ( 00, 01, 10, 11 ) Modulator reqd more than single i/p bit to determine o/p With Q-PSK binary i/p data are combined into group of 2 bits called dibits In modulator each dibits code generates one of 4 possible o/p phase (+ 45º, + 135º , - 45º , - 135º ) For each 2-bit di-bit clked into modulator a single o/p change occurs & rate of change at o/p (baud) is =

𝟏 𝟐

i/p bit rate

 ( 2 i/p bits = 1 o/p phase change) QPSK transmitter

(Blk diag of QPSK modulator ) 21

2 bits (di-bit) clocked into bit splitter Both bits serially i/p simultaneously parallel o/p (SIPO). Channel “ I “ in phase with ref Oscillator & Channel “ Q “ is 90º out of phase w.r.t “ Channel “ I “ with quadrature with reference carrier Dibit split into “ I “ & “ Q “ channel, operation is same as in BPSK modulator

QPSK has 4 possible o/p phasors with same amplitude Angular separation b/w any 2 adjacent phasor in QPSK is 90º Its signal undergo almost ±45º shift in phase during transition. Fig for o/p phase vs time relationship for QPSK modulator 22

QPSK Receiver Block diagram of QPSK 𝑹𝑿 shown in fig The power splitter directs i/p QPSK signal “ I ” & “ Q ” product detector & car. recovery circuit Car. recovery ckt reproduce original transmit car. osciltr signal

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The recovered car. must be freq. & phase coherent with transmit ref. car. QPSK demodulated in signal “ I ” & “ Q ” product detector which generates original “ I ” & “ Q ” data bits O/p of detector fed to ckt from “ I ” & “ Q ” data ch. to single binary o/p data stream Incoming QPSK may be any 1 of 4 o/p phase as shown in fig

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For de-modulation QPSK signal will be − sin 𝝎𝒄 t + cos 𝝎𝒄 t Receive QPSK signal (− sin 𝝎𝒄 t + cos 𝝎𝒄 t ) is one of the i/p to “ I ’’ product detector & other i/p is recovered carrier (sin 𝝎𝒄 t) O/p of “ I ’’ product detector id I=⏟ (− 𝐬𝐢𝐧 𝝎𝒄 𝐭 + 𝐜𝐨𝐬 𝝎𝒄 𝐭 ) ⏟ (𝐬𝐢𝐧 𝝎𝒄 𝐭) 𝑸𝑷𝑺𝑲 𝒊𝒏𝒑𝒖𝒕 𝒔𝒊𝒈𝒏𝒂𝒍

𝒄𝒂𝒓𝒓𝒊𝒆𝒓

= (− 𝐬𝐢𝐧 𝝎𝒄 𝐭)( 𝐬𝐢𝐧 𝝎𝒄 𝐭) + (𝐜𝐨𝐬 𝝎𝒄 𝐭)( 𝐬𝐢𝐧 𝝎𝒄 𝐭) = − 𝒔𝒊𝒏𝟐 𝝎𝒄 t + (𝐜𝐨𝐬 𝝎𝒄 𝐭)( 𝐬𝐢𝐧 𝝎𝒄 𝐭)

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𝟏

𝟏

𝟏

= − 𝟐(1- cos2𝝎𝒄 t) + 𝟐 sin (𝝎𝒄 + 𝝎𝒄 )t + 𝟐 sin (𝝎𝒄 - 𝝎𝒄 )t 𝟏

𝟏

𝟏

𝟏

I = − 𝟐 + 𝟐 cos2𝝎𝒄 t + 𝟐 sin2𝝎𝒄 t + 𝟐 sin 0 𝟏

= − 𝟐 V( logic 0 ) Again receive QPSK signal (− sin 𝝎𝒄 t + cos 𝝎𝒄 t ) is one of the i/p to “ Q ’’ product detector. The other i/p is carrier shifted 𝟗𝟎𝟎 in phase (𝐜𝐨𝐬 𝝎𝒄 𝐭).The o/p of “ Q ’’ product detector is Q = (− ⏟ 𝐬𝐢𝐧 𝝎𝒄 𝐭 + 𝐜𝐨𝐬 𝝎𝒄 𝐭 ) (𝐜𝐨𝐬 ⏟ 𝝎𝒄 𝐭) 𝑸𝑷𝑺𝑲 𝒊𝒏𝒑𝒖𝒕 𝒔𝒊𝒈𝒏𝒂𝒍

𝒄𝒂𝒓𝒓𝒊𝒆𝒓

= 𝒄𝒐𝒔𝟐 𝝎𝒄 t - (𝐬𝐢𝐧 𝝎𝒄 𝐭)( 𝐜𝐨𝐬 𝝎𝒄 𝐭) 𝟏

𝟏

𝟏

= 𝟐(1 + cos2𝝎𝒄 t) - 𝟐 sin (𝝎𝒄 + 𝝎𝒄 )t - 𝟐 sin (𝝎𝒄 - 𝝎𝒄 )t Q= =

𝟏 𝟐

𝟏

𝟏

𝟏

𝟏

+ cos2𝝎𝒄 t - 𝟐 sin2𝝎𝒄 t - 𝟐 sin 0 𝟐 𝟐 V( logic 1 )

The demodulated “ I ” & “ Q ” bits (0 & 1) respectively correspond to constellation diagram & truth table for QPSK modulator 8-PSK Transmitter With 8-PSK, 3 bits encoded, forming tri-bits with 8 o/p phases, where n= 3 & M= 8

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Where “ I ” ------- Phase Ch. “ Q ” ------- Quadrature Ch. “ C ” ------- Control Ch. Incoming serial bit enters splitter, converted to 3 channels Bit rate is

𝒇𝒃⁄ 𝟑

Bits in “I” & “ Q ” enters “ I ” ch 2 to 4 level converter & bits in “ Q ” & “ C ” channels enter “ Q ” channel 2 to 4 level converter 27

2 to 4 level converters are parallel - input DACs “I ” & “ Q ” determines polarity of o/p analog signal (logic 1= +V & logic 0 = -V) ̅ bit determines magnitude Where “ C ” or 𝑪 (logic 1 = 1.307 V & logic 0 = 0.541 V) 2 magnitude , 2 polarities & 4 different o/p conditions

Shows truth table & o/p conditions for 2 to 4 level converters ̅ bit can never on same logic states & o/ps from B/c “ C ” or 𝑪 “ I ” & “ Q ” 2 to 4 level converters can never have same magnitude although have same polarity O/p of 2 to 4 level converters is M- ary PAM signal where M=4 Example 9.7 28

For tribit input of Q= 0, 1 and C(000), determine the output phase for the 8-PSK modulator as shown fig 9.23 Sol // The i/p’s to “ I ” ch. 2-to-4 level converter are I = 0 & C = 0 from TT the o/p = -0.541V ̅ =1 again the o/p = -1.307V The i/p’s to “Q” = 0 and 𝑪 Thus 2 i/p to “Q” ch. product modulator are -0.541V and 𝐢𝐧 𝝎𝒄 . The o/p is I= (-0.541)( 𝐬𝐢𝐧 𝝎𝒄 𝒕) = -0.541 𝐬𝐢𝐧 𝝎𝒄 𝒕 The 2 i/p to “ Q ” ch. product modulator are -1.307V and 𝐜𝐨𝐬 𝝎𝒄 𝒕 The output is Q= (-1.307)( 𝐜𝐨𝐬 𝝎𝒄 𝒕) =-1.307 𝐜𝐨𝐬 𝝎𝒄 𝒕 The output of “ I ” & “ Q ” ch. product modulator=s are combined in linear summer & produce a modulated o/p Summer o/p = -0.541 𝐬𝐢𝐧 𝝎𝒄 𝒕--1.307 𝐜𝐨𝐬 𝝎𝒄 𝒕 =1.41sin(𝝎𝒄 𝒕 112.5𝟏𝟏𝟐. 𝟓𝒐 )

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8-PSK Receiver Fig shows blk .diagram of an 8-PSK 𝑹𝑿

Power splitter to i/p 8-PSK signal to the “I” & “Q” product detector & car. recovy ckt The o/p of product detector are 4- level PAM signals Quadrature Amplitude Modulation QAM is form of DM similar to PSK except digital information is contained in both amplitude & phase of transmitted carrier With QAM ampl & PSK are combined that positions of signaling elements on constellation diagram are 30

optimized to achieve greatest distance b/w elements & reducing errors occurring 8-QAM is M-Ary encoding technique where M=8 unlike 8-PSK, o/p from an 8-QAM modulator is not a constant ampl. Signal

8- QAM transmitter

Only difference b/w 8-QAM 𝑻𝑿 & 8-PSK 𝑻𝑿 is inverter b/w “C” & “ Q ” product modulator With 8-PSK i/c data divide into groups of 3 bits(tri-bits) “ I ” & “ Q ” bits determine polarity of PAM signal at o/p of 2 to 4 level converters & “ C ” Ch. determines magnitude

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“ C ” fed un-inverted to both “ I ” & “ Q ” Ch.2 to 4 level converters. Magnitude of “ I ” & “ Q ” PAM signals are always equal shown in fig b

Bandwidth Efficiency BW efficiency (called information density or spectral efficiency) is often used to compare the performance of one DM technique to another. BW efficiency is the ratio of transmission bit rate to the minimum BW reqd. for particular modulation scheme BW efficiency “𝑩𝜼 ” is normalized to 1Hz BW & indicates no. of bits that can propagated through transmission medium for each hertz of BW. Mathematically BW efficiency is 𝑩𝜼 =

𝒕𝒓𝒂𝒏𝒔𝒎𝒊𝒔𝒔𝒊𝒐𝒏 𝒃𝒊𝒕 𝒓𝒂𝒕𝒆(𝒃𝒑𝒔) 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒃𝒂𝒏𝒘𝒊𝒅𝒕𝒉 (𝑯𝒛) 32

=

𝒃𝒊𝒕𝒔/𝒔 𝒉𝒆𝒓𝒕𝒛

𝒃𝒊𝒕𝒔/𝒔

𝒃𝒊𝒕𝒔

=𝒄𝒚𝒄𝒍𝒆/𝒔 =𝒄𝒚𝒄𝒍𝒆

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