Digital Communication Pulse Shaping - Digital Communication

What is Digital Communication Pulse Shaping?

To have a reliable communication, we have an idea on the preventive measures to be taken through various types of coding techniques.

We are going to discuss on very important distortion that can occur, known as Inter-Symbol Interference (ISI).

Inter Symbol Interference

This distortion of a signal in which one or more symbols interfere with subsequent signals cause noise giving out poor output.

Causes of ISI

The main causes of ISI are −

  • Multi-path Propagation
  • Non-linear frequency in channels
  • To have good output, ISI should be removed completely. In order to lessen the effect, the causes of ISI should also be resolved.

Consider representing ISI in a mathematical form which is in receiver output.

The receiving filter output y(t)y(t) is sampled at time ti=iTb (with i taking on integer values), yielding −

Pulse Shaping

From above, the first term μai is generated by the ith transmitted bit. While the second term determines the residual effect of all remaining transmitted bits on the decoding of the ith bit. This sort of residual effect is known as Inter Symbol Interference.

If ISI is not present, the output will be −

Pulse Shaping

Above equation depicts that the ith bit transmitted is generated correctly Even though the presence of ISI will lead to bit errors and disturbances in the output.

Transmitter or receiver should be designed in order to minimize the effects of ISI as to get the output with least error rate.

Correlative Coding

Even though the ISI degrades the signal, but when used in controlled manner can achieve a bit rate of 2W bits per second in a channel of bandwidth W Hertz. This is known as Correlative Coding or Partial response signaling schemes.

As the amount of ISI is predictive, it is very easy to design the receiver as per the requirement to avoid the ISI effect on the signal. Consider the Duo-binary Signaling example for the idea of correlative coding.

Duo-binary Signaling

The name implies doubling the binary system’s transmission capability. To get a clear understanding on this, consider a binary input sequence {ak} having uncorrelated binary digits each having duration of Ta seconds. Here, signal 1 is shown as a+1 volt and signal 0 by a-1 volt.

The duo-binary coder output ck is the sum of present binary digit ak and the previous value ak-1 as shown in the below equation.

Pulse Shaping

From above, it states that the uncorrelated binary sequence {ak} is changed to a sequence of three level pulses {ck}.

Eye Pattern

One way to study the effects of ISI is the Eye Pattern. Name was given as it resembles the human eye for binary waves. The interior region of the eye pattern is termed as eye opening. Below diagram shows the eye-pattern image.

Eye Pattern

  • The short term variation of the instant of digital signal from its ideal position is known as Jitter which leads to data errors.
  • The traces from the upper portion to the lower portion of the eye opening increases when the effect of ISI increases leading to closing the eye completely.
  • An eye pattern provides the following information about a particular system.
  • Used to estimate the bit error rate and the signal-to-noise ratio.
  • The eye width defines the time interval over which the received wave can be sampled without error from ISI.
  • Preferred time for sampling is the instant of time when the eye opening is wide.
  • The sensitivity of the system to the timing error is determined by the rate of the closure of the eye.
  • The height of the eye opening determines the margin over noise.

Hence, the interpretation of eye pattern is an important consideration.

Equalization

To establish reliable communication, we need a quality output. The transmission losses of the channel and various factors that affect the signal quality have to be treated. ISI is the most occurring loss.

Equalization is implemented to make the signal free from ISI and to ensure a high signal to noise ratio. Below diagram shows an equalizer in the receiver portion of the communication system.

Equalization

During transmission, the noise and the interferences will occur. Transmission losses can be shaped with the equalizer circuit.

Error Probability and Figure-of-merit

Data rate is the rate at which data is communicated. Bit Error Rate (BER) is the rate at which error occurs in the bits while transmission.

Error probability is the probability of the occurrence of BER. More the Signal to Noise Ratio, less the BER. Hence the Error Probability also gets decreased.

The ratio of output SNR to the input SNR in an analog receiver is the figure of merit at the detection process. It is an advantage to have high value of figure-of-merit.

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