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P31Q
DIGITAL COMMUNICATIONS
LECTURE 7 |
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P31Q
DIGITAL COMMUNICATIONS
LECTURE 7 |
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BANDPASS MODULATION
Channel: Telephone channel, microwave link, satellite channel, or an optical fiber.
Modulation process: Switching or keying the amplitude, frequency, or phase of the carrier in accordance with the information binary digits.
Three basic modulation techniques: Amplitude Shift Keying (ASK), frequency shift keying (FSK), and phase Shift Keying (PSK).
PHASE-SHIFT KEYING (PSK)
Constant A, f. Compared to other schemes, PSK has excellent protection against noise, because the information is contained within its phase. Noise mainly affects the amplitude of the carrier.
We shall first consider the Binary Phase Shift Keying (BPSK) modulation scheme, in which a binary digit is mapped to a high frequency carrier sinusoidal waveform of a given phase as shown below.
Signal  represents binary digit
1 |
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Signal  represents binary digit
0 |
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where the amplitude  ,  , and  is the transmitted signal
energy per binary digit. The duration of this sinusoidal waveform is
 . The proof of is a student exercise
later in this lecture. | |
The diagram below illustrates the Binary Phase Shift Keying (BPSK) signal waveform (shown in green) for the binary sequence 1001011. The corresponding baseband signal is shown in red.
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To ensure that each transmitted binary digit contains and
integral number of cycles, the carrier frequency 
, where 
is a fixed integer. For
above diagram, = 2.
A pair of signal which differ in phase by 180 degrees are referred to as antipodal signals
Why use a high freq. carrier ?
Consider the transmission of electromagnetic waves (EM) through
space using antennas. The wavelength of a EM is given by 
. It can be shown that
the length of the antenna required to efficiently transmit this EM wave is
approximately 
.
For voice at a frequency f = 3kHz, is 100000m !
However if f = 300 MHz, length of antenna required is 1 m.
The higher the frequency carrier, the smaller the length of the antenna required. For example, a cellular phone.
High frequency EM waves can propagate through atmosphere without much attenuation. For space satellites use carrier frequency typically of 4 and 6 GHz.
![[Student Excercise]](Modulationpsk_archivos/stuexer.gif)
ENERGY IN SIGNALS
From basic electronic circuit theory, the power P
dissipated in a resistor R, is given by 
, where V is the
voltage across the resistor.
Based on this expression, the power in a signal is given by
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The area under power time curve is the energy in the signal i.e
since 
, then 
Hence, the energy E contained within a signal is given by
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Show
that the energy contained within a BPSK signal 
If
, then the amplitude . Compare this with the
BPSK signals and defined earlier.
Notice that can be increased either by
increasing the duration of the signal
and/or the amplitude A of the signal.
The time duration of a BPSK signal
is often referred to as the symbol time, because it
represents the time duration occupied by a symbol,
which in this case happens to be a binary digit. In TCM, we will find
that a bandpass signal typically represents more than one binary
digit.
