0195136047.pdf

726 COMMUNICATION SYSTEMS

Sampler

Sample at time Tb for bit interval 0 < t ≤ Tb

Waveform formatter Channel Demodulator and code generator of receiver

and modulator

Ac cos (ωct + φc)

a(t − Tb)

Broad-band system noise

Differential encoder

Digital

signal d(t) sR(t)

si(t) + noise

sd(t) + noise

sDPSK(t)

a(t) R

If D ≥ 0 choose 1

If D < 0 choose 0

... Σ

+

+

Matched

filter

WBLPF

Wide-band

low-pass filter

Coherent detector

D

Delay Tb

Delay Tb

Figure 15.3.17Functions of a DPSK system.

say, the DPSK waveform in a given bit interval serves as its own local-oscillator signal in the

following bit interval.

In Figure 15.3.17,si(t) is the signal component of the matched filter output, andsd(t)isthe

signal component of the detector output. If the phases of bothsi(t) andsi(t−Tb) are the same,

sd(t) is then a positive voltage; if their phases differ byπradians,sd(t) will then be a negative

voltage. These voltages will have maximum amplitudes at the sample time at the end of the bit

interval. Because the sign of the voltage at the sampler depends upon the phase relationship

betweensi(t) and its delayed replica, and the sign ofsd(t) is of the same form asd(t), the

original digital bit sequence can be determined by sampling to decide the sign of the detector

output.

Figure 15.3.18 illustrates an example sequence of message binary digits, modulator wave-

forms in DPSK, and phase and polarity relationships as applied to DPSK message recovery.

FREQUENCY-SHIFTKEYING(FSK)

Digital transmission by FSK is a nonlinear modulation method that is appropriate for channels

that lack the phase stability needed to perform carrier-phase estimation. Figure 15.3.19 shows

the functions of a coherent FSK system in which the transmitted signalsFSK(t) is generated by

frequency modulation of a voltage-controlled oscillator (VCO). The digital signald(t) has a polar

format with amplitudes±1, corresponding to binary digits 1 and 0, respectively. Modulation keys

the VCO’s angular frequency between two values, such that

ω 2 =ωc+ω whend(t)= 1 (15.3.21)

ω 1 =ωc−ω whend(t)=− 1 (15.3.22)

whereωis the frequency deviation from a nominal or carrier angular frequencyωc. In order

to conserve the bandwidth in the signalsFSK(t),ωis usually selected not much larger than the

minimum allowable value given by

ω=

π

Tb

=

ωb

2

(15.3.23)