Chap 2 Bandpass Signaling-Notes

8/3/2019 Chap 2 Bandpass Signaling-Notes

http://slidepdf.com/reader/full/chap-2-bandpass-signaling-notes 1/25

CHAPTER 2 – BANDPASS DIGITAL COMMUNICATION SYSTEM

Binary Modulated Bandpass Signaling

Most common binary bandpass signaling techniques, as illustrated in Fig. 5-19:

1) On-off keying (OOK) – also called amplitude shift keying (ASK). Consists of

keying (switching) a carrier sinusoid on and off with a unipolar binary signal.Morse code radio transmission is an example. One of the first modulation

techniques and precedes analog communication system.

2) Binary phase shift keying (BPSK) – consists of shifting the phase of a sinusoidal

carrier 0 or 180 with a unipolar binary signal. Equivalent to PM signaling witha digital waveform.

3)

Frequency shift keying (FSK) – consists of shifting the frequency of a sinusoidalcarrier from a mark frequency (corresponding, e.g., to send a binary 1) to a spacefrequency (corresponding to send a binary 0), according to the baseband digital

signal. Identical to modulating an FM carrier with a binary digital signal.

On-Off Keying (OOK)

OOK signal is represented by

t t m At s cc cos)()( (5-70)

where m(t ) = unipolar baseband data signal, as shown in Fig. 5-19a.

Its complex envelope is

)()( t m At g c for OOK (5-71)

The spectrum of OOK signal as shown in Fig. 5-20a shows that:a) the null-to-null BW, BT = 2 R where R = 1 / T b is the bit rate

b) absolute BW, BT = c) transmission BW, BT = 2 B where B = baseband BW since OOK is AM-

type signaling.

If raised cosine-rolloff filtering is used (to conserve BW), the absolute BW of filteredbinary signal is related to the bit rate R by Eq. (3-74), where D = R for binary digitalsignaling.



Thus, the absolute baseband BW is

Rr B 12

1, where r = rolloff factor of filter (5-73)

This gives absolute transmission BW of

Rr BT 1 (5-74)

for OOK signaling with raised cosine-rolloff filtering.

OOK Detection

OOK can be detected by using either:

1) envelope detector (noncoherent detection)2) product detector (coherent detection)

because it is a form of AM signaling.

These detectors are shown in Figs. 5-21a and 5-21b.

For optimum detection of OOK (to obtain the lowest BER when input OOK signal is

corrupted by additive white Gaussian noise (AWGN)) require product detection

with matched filter processing.

This is shown in Fig. 5-21c where waveforms at various points of the circuit for OOKsignal reception are illustrated corresponding to binary data stream 1101.

Matched filter requires a clocking signal to reset the integrator at the beginning of each bit interval and to clock the sample-and-hold circuit at the end of each bitinterval. (Clock is provided by bit synchronizer circuit).

Binary Phase Shift Keying (BPSK)

BPSK signal is represented by

)(cos)( t m Dt At s pcc (5-75a)

where m(t ) = polar baseband data signal D p = peak deviation

Let m(t ) have peak values of 1 and a rectangular pulse shape.



Showing that BPSK is also a form of AM signaling by expanding Eq. (5-75a) we get

t t m D At t m D At s c pcc pc sin)(sincos)(cos)(

Recalling that m(t ) has values of 1 and that cos ( x) and sin ( x) are even and oddfunctions of x, then BPSK signal representation reduces to

t t m D At D At s c pcc pc sin)(sincoscos)( (5-75b)

pilot carrier term data term

The level of pilot carrier term is set by the value of peak deviation, p D .

For digital angle-modulated signals, the digital modulation index, h is defined by

2h (5-76)

where 2 = maximum peak-to-peak phase deviation (radians) during the time

required to send one symbol, T s . (T s = T b for binary signaling)

The level of pilot carrier term is set by p D for m(t ) = 1.

If D p is small, the pilot carrier term has larger amplitude compared to data term;leading to very little power in the data term (which contains the source information).

To maximize signaling efficiency, the power in data term needs to be maximized.

By letting2

90

p D radians, this corresponds to digital modulation index

h = 1.

For optimum case of h = 1, the BPSK signal becomes

t t m At s cc sin)()( (5-77)

Equation 5-77 shows that BPSK is equivalent to DSB-SC signaling with a polar

baseband data waveform.



BPSK Detection

To detect BPSK, synchronous detection must be used as illustrated in Fig. 5-22a.

Since there is no discrete carrier term in BPSK signal, a PLL can be used to extract

the carrier reference only if a low-level pilot carrier is transmitted together with

BPSK signal.

For optimum detection of BPSK, the LPF in Fig. 5-22a is replaced by an integrate-

and-dump matched filter processing that was illustrated in Fig. 5-21c, where V T is set

to 0 V for BPSK.

Differential Phase Shift Keying (DPSK)

PSK signals cannot be detected incoherently.

However, partial coherent technique can be used whereby the phase reference for thepresent signaling interval is provided by a delayed version of the signal that occurred

during the previous signaling interval.

As illustrated in Fig. 5-22b, the differential decoding is provided by the (one bit)

delay and the multiplier.

Then, if the data on the BPSK signal are differentially encoded (e.g., in Table 3-4),the decoded data sequence will be recovered at the output of the receiver.

This signaling technique consisting of transmitting differentially encoded BPSKsignal is known as DPSK.

For optimum detection of DPSK signal, the LPF of Fig. 5-22 is replaced by anintegrate-and-dump matched filter and the DPSK input signal needs to be prefiltered

by a bandpass filter that has an impulse response of

t T T t t h cbb cos / 5.0)( .

In practice, DPSK is often used instead of BPSK because DPSK receiver does notrequire a carrier synchronization circuit.



Frequency Shift Keying (FSK)

Continuous phase FSK signal is generated by feeding the data signal into a frequencymodulator, as shown in Fig. 5-23b and its signal is shown in Fig. 5-19e.

FSK signal is represented by

t

f cc d m Dt At s )(cos)(

or

t j cet gt s

)(Re)( (5-81a)

where)()(

t j

ce At g (5-81b)

t

f d m Dt )()( for FSK (5-81c)

m(t ) = baseband digital signal

Although m(t ) is discontinuous at switching time, the phase function (t ) is

continuous because (t ) is proportional to the integral of m(t ).

If serial data input waveform is binary, i.e., polar baseband signal, the resulting FSKsignal is called a binary FSK signal.

In general, the spectra of FSK signals are difficult to evaluate since the complex

envelope, g(t ), is a nonlinear function of m(t ).

Transmission Bandwidth of FSK Signal

The approximate transmission BW, BT for FSK signal is given by Carson’s rule,

BT = 2( + 1) B, where B

F which is equivalent to

BF BT 22 (5-87)

where B = BW of digital signal (e.g., square-wave) modulation waveform.

For alternating binary 1 and 0 test pattern waveform, the BW of this square-wavemodulating waveform is B = R, and using Eq. (5-87), we find that FSK transmission

BW becomes

RF BT 2 (5-88)

The result is shown in Fig. 5-26.



If a raised cosine-rolloff premodulation filter is used, the transmission BW of FSK

signal becomes

Rr F BT 12 (5-89)

For wideband FSK, where >> 1, F dominates in the above equations and we haveF BT 2 .

For narrowband FSK, the transmission BW is BT = 2 B.

FSK Detection

FSK can be detected by using (as shown in Fig. 5-28):

1) frequency (noncoherent) detector, or

2) two product detectors (coherent detection)

To obtain the lowest BER when FSK signal is corrupted by AWGN, coherentdetection with matched filter processing and a threshold device (comparator) is

required. (See Fig. 7-8.)

5-10 MULTILEVEL MODULATED BANDPASS SIGNALING

Fig. 5-29 shows multilevel signals can be generated from a serial binary input streamby using a digital-to-analog converter (DAC).

Let l = 2 bit DAC is used:

- number of levels, M = 2l = 22= 4

- the symbol rate (baud) of multilevel signal, D = R / l = R2

1where R = 1 / T b

bits/s.

Quadrature Phase Shift Keying (QPSK) and M-ary Phase Shift Keying (MPSK)

A PAM transmitter with an M = 4 level digital modulation, M -ary phase shift keying(MPSK) is generated at transmitter output.

Assume rectangular shaped data pulses, a plot of permitted values of complex

envelope, )()(t j

ce At g , contains 4 points, one value of g (a complex number in

general) for each of the 4 multilevel values, corresponding to the 4 phases that is

permitted to have.



A plot of 2 possible sets of g(t ) is shown in Fig. 5-30.

Suppose, permitted multilevel values at DAC are -3, -1, +1 and +3 V; then, in Fig. 5-30a, these multilevel values correspond to PSK phases 0, 90, 180 and 270

respectively.

In Fig. 5-30b, those levels correspond to carrier phases of 45, 135, 225 and 315respectively.

The two signal constellations are the same except for a shift in the carrier phasereference.

This example of M-ary PSK where M = 4 is called quadrature phase shift keyed(QPSK) signaling.

MPSK Generation

MPSK can be generated by using two quadrature carriers modulated by the x and ycomponents of the complex envelope (instead of using a phase modulator); in that

case,

)()()( )( t jyt xe At gt j

c (5-91)

where the permitted values of x and y are

ici A x cos (5-92)

ici A y sin (5-93)

for permitted phase anglesi

, i = 1, 2, …, M , of MPSK signal.

The above situation is illustrated in Fig. 5-31, where signal processing elementsimplements Eqs. (5-92) and (5-93).

Fig. 5-30 gives the relationship between permitted phase anglesi

and the ii y x ,

components for 2 QPSK signal constellations.

Quadrature Amplitude Modulation (QAM)

Quadrature carrier signaling, as shown in Fig. 5-31, is called quadrature amplitudemodulation (QAM).



In general, QAM signal constellations are not restricted to having permitted signaling

points only on a circle (of radius Ac, as for MPSK).

The general QAM signal is

t t yt t xt s cc sin)(cos)()( (5-94)

Where)()()()()( t j

et Rt jyt xt g (5-95)

A popular 16-symbol ( M = 16 levels) QAM constellation is shown in Fig. 5-32 where

the relationship between ii R , and ii y x , can be readily be evaluated for each of

16 signal values permitted.

QAM Generation

This 16-symbol QAM signal can be generated by using two ( l /2 = 2) bit digital-to-analog converters and quadrature balanced modulators as shown in Fig. 5-31b.

The waveforms of I and Q components are represented by

n

n D

nt h xt x 1)( (5-96)

And

n

n D

n

t h yt y 1)( (5-97)

where D = R / l and ( xn, yn) denotes one of the permitted ( xi, yi) values during thesymbol time that is centred on t = nT s = n / Ds. (It takes T s to send each symbol.)

h1(t ) = pulse shape that is used for each symbol.

In some applications, the timing between the x(t ) and y(t ) components is offset by

T s / 2 = 1 / (2 D) s.

Then, x(t ) is described by Eq. (5-96), and the offset is described by

n

n D D

nt h yt y

2

1)( 1 (5-98)



OQPSK and /4 QPSK

Offset quadrature phase shift keying (OQPSK) is M = 4 PSK in which the allowed

data transition times for the I and Q components are offset by a2

1symbol (i.e., by 1

bit) interval.

The technique is described by Eqs. (5-96) and (5-98) where the offset is 1 / (2 D).

This offset provides an advantage when nonrectangular (i.e., filtered) data pulses areused, because the offset greatly reduces the AM on the OQPSK signal compared with

AM on the corresponding QPSK signal.

The AM is reduced because a maximum phase transition of only 900occurs for

OQPSK signaling (as opposed to 1800for QPSK), since the I and Q data cannot

change simultaneously because the data are offset.

A /4 quadrature phase shift keying ( /4 QPSK) signal is generated by alternating

between two QPSK constellations that are rotated by /4 = 450with respect to each

other.

The 2 constellations shown in Fig. 5-30 are used alternately as follows:

Given a point on one of the signal constellations that corresponds to 2 bits of input

data, 2 new bits are read to determine the next point that is selected from the otherconstellation.

That is, the 2 new input bits cause a phase shift of ±450

or ±1350

depending on theirvalue.

For example, an 11 could correspond to a phase shift of 045 , a 10 to045 , a 01 to 0135 and a 00 to 0135 .

This is also called /4 differential quadrature phase shift keying ( /4 DQPSK) since ituses a form of differential encoding.

/4 DQPSK Detection

The data on the /4 QPSK signal can be detected by using 3 methods:

i) FM detector followed by a resettable integrator that integrates over a symbol (2-

bit) period. FM detector produces the derivative of the phase and the integratorevaluates the phase shift that occurs over the symbol interval.



ii) baseband IQ processing

iii) differential detection

Spectral Efficiency for MPSK, QAM, QPSK, OQPSK and /4 QPSK with Raised

Cosine Filtering

The spectrum shown in Fig. 5-33 is for rectangular symbol pulses and the spectralsidelobes are terrible.

The sidelobes can be eliminated if raised cosine filtering is used (since raised cosinefilter has an absolutely bandlimited frequency response)

To have no ISI, we select 6-dB BW of the raised cosine filter to be half the symbol(baud) rate.

The raised cosine filter has the disadvantage of introducing AM on MPSK signals.

If the overall pulse shape satisfies the raised cosine-rolloff filter characteristic, then,by Eq. (3-74), the absolute BW of the M -level modulating signal is

Dr B 12

1(5-105)

where

D = R / l r = rolloff factor of the filter

Transmission BW is related to the modulation BW by BT = 2 B, then the overallabsolute transmission BW of QAM signal with raised cosine filtered pulses is

Rl

r BT

1(5-106)

Because M = 2l , which implies that l = log2 M = (ln M ) / (ln 2), the spectral efficiency

of QAM-type signaling with raised cosine filtering is

Hz

sbit

r

M

B

R

T

/

2ln1

ln

(5-107)

This result tells us how fast we can signal for a prescribed BW.

Eq. (5-107) is used to generate Table 5-6.



To conserve BW, the number of levels M in Eq. (5-107) cannot be increased too

much, since, for a given peak envelope power (PEP), the spacing between the signalpoints in the signal constellation will decrease and noise on the received signal will

cause errors.

However, R has to be less than C , the channel capacity, if the errors are to be keptsmall.

Consequently, using Eq. (1-10), we require that

max (5-108a)

where

N

S

1log2max (5-108b)

5 -11 MINIMUM SHIFT KEYING (MSK) AND GMSK

Minimum shift keying is another BW conservation technique.

Its advantage is producing a constant amplitude and can be amplified with Class Camplifiers without distortion.

MSK is equivalent to OQPSK with sinusoidal pulse shaping [ for hi (t ) ]

Definition:

Minimum shift keying (MSK) is continuous phase FSK with a minimum modulationindex (h = 0.5) that will produce orthogonal signaling.

Proof:

Let FSK signal:

111 cos)( t At s c represent binary ‘1’ over bit interval 0 < t < T b

222 cos)( t At s c represent binary ‘0’ over bit interval 0 < t < T b

where 1 = 2 for continuous-phase condition at switching time t = 0.



For orthogonal signaling, the integral of the product of two signals over the bitinterval is zero.

Thus, we require

b b

T T

c dt t t Adt t st s0 0

22112

21 0coscos)()( (5-109a)

This reduces to

21

212121

2 sinsin

2

bc T A

+

0sinsin

2 21

212121

2

bc T A(5-109b)

The second term is negligible because21 is large, so

0

2

sin2sin 2121

h

h

(5-110)

where bb T F T 2221

and from Eq. (5-82), bFT h 2

For continuous phase case, 1 = 2 ; and Eq. (5-110) is satisfied for a minimum valueof h = 0.5, or a peak frequency deviation of

,4

1

4

1 R

T F

b

for MSK (5-111a)

For discontinuous phase FSK, 21 ; and the minimum value for orthogonality is

h = 1.0 or

,21

21 RT

F b

for discontinuous phase FSK (5-111b)

MSK signal (which is h = 0.5 continuous-phase FSK) is a form of OQPSK signalingwith sinusoidal pulse shaping.



Proof:

Consider FSK signal over the signaling interval (0, T b).

When Eq, (5-81) is used, the complex envelope is

t

d mF j

c

t j

c e Ae At g 02

)(

where m(t ) = 1, 0 < t < T b . Using Eq. (5-111), the complex envelope becomes

),()()()2 /(

t jyt xe At g bT t j

c 0 < t < T b

where sign = possible data during the (0, T b) interval.

Thus,

,2

1cos)(

b

cT

t At x

0 < t < T b (5-112a)

,2

1sin)(

b

cT

t At y

0 < t < T b (5-112b)

MSK signal is

t t yt t xt s cc sin)(cos)()( (5-112c)

A typical input data waveform m(t ) and the resulting x(t ) and y(t ) quadrature

modulation waveforms are shown in Fig. 5-34.

The binary data of m(t ) alternately modulate the x(t ) and y(t ) components and thepulse shape for x(t ) and y(t ) symbols (which are 2T b wide instead of T b) is a sinusoid.

Thus, MSK is equivalent to OQPSK with sinusoidal pulse shaping.

In Fig. 5-34, x(t ) and y(t ) waveforms are illustrates the so-called Type II MSK in

which the basic pulse shape is always a positive half-cosinusoid.

For Type I MSK, the pulse shape [for both x(t ) and y(t )] alternates between a positiveand negative half-cosinusoid.

Another form of MSK is Gaussian-filtered MSK (GMSK).



For GMSK, the data (rectangular-shaped pulses) are filtered by a filter having aGaussian-shaped frequency response characteristic before the data are frequency

modulated onto the carrier.

The transfer function of the Gaussian low-pass filter is

2 / 2ln / 2

)(B f

e f H (5-116)

where B = 3-dB BW of the filter.

The filter reduces the spectral sidelobes on the transmitted MSK signal.

MSK signals can be generated by using these methods (as shown in Fig. 5-36):

1) Generation of Fast Frequency shift keying (FFSK) (equivalent to Type I MSK

with differential encoding of the input data).

2) MSK Type I modulator (realization of Eq. (5-112)). It is called parallel methodof generating MSK since parallel in-phase (I) and quadrature-phase (Q) channels

are used.

4) Serial method of generating MSK.

5-12 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM)

OFDM is a technique for transmitting data in parallel by using a large number of modulated carriers with sufficient frequency spacing so that the carriers areorthogonal.

OFDM provides resistance to data errors caused by multipath channels.

Over a T -sec interval, the complex envelope for OFDM signal is

1

0

),()( N

n

nnc t At g 0 < t < T (5-117a)

where Ac = carrier amplitude

n = element of the N-element parallel data vector, w = ],...,,[ 110 N

and the orthogonal carriers are



t f j

nnet

2)( where

2

11 N n

T f

n(5-117b)

Duration of data symbol on each carrier is T seconds, and the carriers are spaced 1/T Hz apart.

This assures that the carriers are orthogonal since the n (t ) satisfy orthogonalitycondition of Eq. (2-77) over T -sec interval.

Because the carriers are orthogonal, data can be detected on each of these closely

spaced carriers without interference from other carriers.

Key advantage of OFDM is it can be generated by using FFT digital signal processingtechniques.

For example, if we suppress the frequency offset ( N – 1)/2T of Eq. (5-117b) andsubstitute Eq. (5-117b) into Eq. (5-117a), where t = kT / N , then the elements of IFFTvector as defined by Eq. (2-177) are obtained.

OFDM signal can be generated by using IFFT algorithm as shown in Fig. 5-37.

Referring to Fig. 5-37, let input serial data symbols have a duration of T s sec. each.

Data can be binary (1) to produce BPSK modulated carriers or can be multilevel

complex-valued serial data to produce QPSK, MPSK or QAM carriers.

ss T D / 1

= input symbol (baud) rate.

Serial-to-parallel converter reads in N input serial symbols at a time and holds theirvalues (elements of w) on the parallel output lines for T = NT s seconds, where T =

time span of IFFT.

IFFT uses w to evaluate output IFFT vector g that contains elements representingsamples of the complex envelope.

The parallel-to-serial converter shifts out the element values of g.

These are the samples of OFDM complex envelope described by Eq. (5-117), where x(t ) and y(t ) are the I and Q components of complex envelope.

OFDM signal is produced by I-Q modulators as shown in figure.

At the receiver, the serial data are recovered from received OFDM signal by:

1) demodulating the signal to produce serial I and Q data



2) converting the serial data to parallel data

3) evaluating the FFT, and

5) converting the FFT vector (parallel data) to serial output data.

The length of FFT vector determines the resistance of OFDM errors caused bymultipath channels.

N is chosen so that T = NT s is much larger than the maximum delay time of echocomponents in the received multipath signal.

OFDM signal is used in Europe digital broadcast systems (radio and television).

Chap 2 Bandpass Signaling-Notes

Documents

Transcript of Chap 2 Bandpass Signaling-Notes