Telecomunicações
Digital Communication
System Overview
• Overview of a point-to-point digital
communication system:
Digital Communication
System Overview
• The signal from an analog source, located at the transmitting site, is converted into a digital signal by the analog-to-digital (A/D) converter;
• The encoder encodes the input digital signal into another digital signal, which in turn is used by the modulator to generate a modulated carrier output;
• The modulated signal is transmitted through the communication channel to the remotely located receiving site, where the corresponding inverse functions are performed by the demodulator, decoder, and digital-to-analog (D/A) converter.
Digital Communication
System Overview
• For a TDM telemetry system, each sensor
channel may be considered a single channel
of the point-to-point digital communication
system described.
Digital Communication
System Overview
• In such a system, the output bit sequence is
usually the result of sampling, digitizing, and
combining the outputs from a number of
different sensors;
• The commutators’s purpose is to sequentially
sample the output of the sensors and produce an
amplitude-modulated pulse for each sample;
• The encoder quantizes the samples and converts
each into an n-bit binary word;
• Hence, the commutator and the encoder behave
as the single A/D converter and encoder.
Digital Communication
System Overview
• The purpose of the multiplexer (MUX) is to
insert
the
minor
and
major
frame
synchronization words into the bit stream, and to
perhaps add computer data words from an
onboard computer;
• The MUX basically builds the frame structure
along with the frame synchronization timing.
• A lowpass filter is inserted between the digital
MUX
and
the
transmitter
to
limit
the
Communication System
Signals
• Analog Signals:
– An analog signal may be described as a continuous-amplitude (CA) and continuous-time (CT) signal. That is, the signal amplitude is continuous between the maximum and minimum values, and is continuously changing in time.
Communication System
Signals
Communication System
Signals
• Analog Signals:
– Two metrics describe this signal — an amplitude metric and a time metric;
– Typical amplitude metrics are peak-to-peak voltage and RMS voltage;
– The time metric is usually given in terms of the maximum frequency or bandwidth;
– For the signal shown, the amplitude is 20V peak-to-peak, and the maximum frequency is 2,000 Hz.
Communication System
Signals
• Digital Signals:
– A digital signal is a discrete amplitude (DA) and discrete time (DT) signal;
– The signal amplitude may assume one of a finite number of discrete levels between the maximum and minimum values, and may only change at discrete times.
Communication System
Signals
Communication System
Signals
• Digital Signals:
– The amplitude metric is the number of discrete levels the signal may assume, with each level corresponding to a unique symbol;
– The time metric is usually given in terms of the number of symbols per second, which is also known as the baud rate.
Communication System
Signals
• Digital Signals:
We define the following parameters:
• E ≡ the number of levels the signal amplitude may assume;
• B ≡ baud rate = the maximum number of signal symbols per second.
– A numeric representation of the E levels requires a binary number of n bits, where
𝑛 = 𝑙𝑜𝑔2𝐸
– Since n is the number of bits of information required to represent one change (or symbol) of the signal, and there are baud rate symbols per second, we have:
I ≡ information rate = baud rate (𝑙𝑜𝑔2𝐸) bps, or
Communication System
Signals
• Digital Signals:
Example:
In figure in slide 12, the signal may assume one of four levels specifying that E = 4. The time between changes is T = 0.0002 seconds, and B = 1/ T = 5,000 symbols/second.
Thus we have I = B(log2E) = (5,000) (log24) = 10,000 bps.
Quantization and A/D
Conversion
• The quantization process changes the
continuously
varying
pulse
amplitudes
created by sampling an analog signal into a
finite number of levels.
• Each level is assigned an n-bit binary word by
the A/D converter.
Quantization and A/D
Conversion
• Quantization Errors:
– The numbers of leves E, is giveen by 𝐸 = 2𝑛
where n is the length in bits of the binary word. – In telemetering, n is nominally 8.
Quantization and A/D
Conversion
• Quantization Errors:
– If 𝑉𝑝𝑝 is the peak-to-peak voltage and the peak voltage 𝑉𝑝 is 𝑉𝑝𝑝 /2 of the signal being quantized, the voltage separation between each level is given by
𝑞 = 𝑉𝑝𝑝
𝐸 = 2𝑉𝑝/𝐸
– The quantization error is the difference between the quantized signal and the continuous signal.
– The error is random, has a maximum value of q/2 and is uniformly distributed such that
𝑝 𝑒 = 1 𝑞 , − 𝑞 2 < 𝑒 < 𝑞 2
Quantization and A/D
Conversion
• Quantization Errors:
– The variance or noise power is given by 𝜎𝑞2 = 1 𝑞 −𝑞/2 𝑞/2 𝑒2𝑑𝑒 = 𝑞 2 12
– In terms of the number of levels, the quantization noise power is
𝜎𝑞2 = 𝑉𝑝
2
Quantization and A/D
Conversion
• Quantization Errors:
– If 𝑚(𝑡)2 is the RMS power of the message, 𝑚(𝑡),
being quantized, the signal-to-noise power ratio out of the quantizer is given by
𝑆 𝑁 = 𝑚 𝑡 2 𝜎𝑞2 = 𝑚 𝑡 2 𝑞2/12 Or 𝑆 𝑁 = 3𝐸2𝑚 𝑡 2 𝑉𝑝2 Exemplo quadro
Encoding
– Encoding methods are often classified into one of two categories:
• source encoding; • channel encoding.
– Source encoding techniques attempt to remove redundant information from the source signal, and thus reduce the information rate of the signal;
– Channel encoding techniques transform the source digital signal into another digital signal that better matches the bandwidth and signal-to-noise characteristics of the channel.
– Now we will introduce the concept of channel encoding, assuming that any required source encoding has been implemented.
Encoding
– The encoder input digital signal e(t) is encoded into a digital output signal m(t) as shown in figure below.
Encoding
– For each input symbol (change), the encoder generates N output symbols, (changes), each representing one of M possibilities.
– Thus we have
𝐵𝑚 = 𝑁𝐵𝑒
Where the encoder rate is defined as 1/N.
– At the encoder input the information rate is 𝐼𝑒 = 𝐵𝑒𝑙𝑜𝑔2𝐸
where 𝐵𝑒 is the input baud rate, and 𝐸 is the number of levels of the input digital signal.
Encoding
– In a similar way, at the encoder output, the information rate is
𝐼𝑚 = 𝐵𝑚𝑙𝑜𝑔2𝑀
where 𝐵𝑚 is the output baud rate, and M is the number of levels of the output digital signal.
– If there is a one-to-one correspondence between the encoder input combinations and output combinations, we have
Encoding
– Encoders that map the input signal to the output signal have the property that 𝐼𝑚 = 𝐼𝑒;
– This is desirable in the sense that the encoder preserves the original information and adds no redundant information to the original signal;
– As N is increased, the output baud rate 𝐵𝑚 increases, while the number of output signal levels M decreases.
Encoding
– Furthermore, an increase (decrease) in 𝐵𝑚 requires an increase (decrease) in channel bandwidth;
– and an increase (decrease) in M requires an increase (decrease) in channel signal-to-noise ratio at the receiver;
– Therefore, we have the following principle:
The channel encoder allows the designer to ‘‘match’’ the digital signal to the channel
characteristics by trading off channel bandwidth requirements with receiver signal-to-noise ratio
Encoding
• Design Example:
Design an encoder to transform a four-level digital signal into a two-level digital signal.
Encoding
• Design Example:
Design an encoder to transform a four-level digital signal into a two-level digital signal.
Thus, there are 2 two-level output symbols for every four-level input symbol.
Encoding
• Design Example:
Design an encoder to transform a four-level digital signal into a two-level digital signal.
A representative encoder input signal e(t), and the corresponding encoder output signal m(t), for this mapping is shown in next figure.
The output baud rate is twice the input baud rate, while the input and output information rates are equal.
Encoding
Modulation
– For each input symbol, the carrier output from the modulator is a sinusoidal time signal s(t) given by
𝑠 𝑡 = 𝐴𝑐𝑜𝑠(2𝜋𝑓𝑡 + 𝜙)
where A is the amplitude of the transmitted signal, f is the frequency of the transmitted signal, and 𝜙 is the phase of the transmitted signal.
– Basic digital modulation methods will vary one of the above parameters in proportion to the input signal amplitude, while holding the other two parameters constant;
– The modulator input signal m(t) comes from the encoder output.
