In this post, we make our neurons work a bit in the world of communication systems. We learn what the communication process is, discover some terms then attack modulation techniques.

I remember I learned most of the following theory in my network engineering studies at the university.

## The communication process

The communication process can be summarized in the following diagram:

The source of information delivers what is called the signal message. This is the message we want to transmit. It can be text, computer data, sounds, images or video.

At the transmitter, level, the message signal is converted into symbols, and symbols are then encoded into a form that is understandable by the communication channel.

At the receiver, the received signal is a set of encoded symbols. These are decoded and used to re-generate the original message signal. However, it is only an estimate of the original message signal, and that’s due to the noise in the communication channel. In fact, the communication channel is usually affected by internal or external -or both- noise signals, which alter some characteristics of the traversing signal, thus altering the content of the original message. This is why we can not be 100% that we received an exact copy of the emitted signal.

## Terms in communication systems

We need to define some terms before we get down further.

Channel bandwidth: refers to the range of frequencies that a communication channel provides for the transmission of a signal.

When defining signal bandwidth, pay attention that there is a difference between signal bandwidth and signal spectrum. The spectrum of a signal is the range of frequencies occupied by a signal. The signal bandwidth, however, is the upper limit over which the signal spectrum is negligible.

In communication systems design, we tend to maximize the signal power while leveraging the signal bandwidth and the channel bandwidth. Let’s consider the diagram below. The horizontal axis is the frequencies and the vertical axis is the signal power.

In legacy voice networks for example, we only consider the signal between 300 Hz and 3400kHz. It’s true that the spectrum of the signal energy -here the energy with which we speak- can go up to 7kHz. But the signal bandwidth -the bandwidth of the voice signal- is concentrated in the [300-3400]Hz interval, and the voice energy is at its higher level in that same interval. That’s why a communication channel with a bandwidth of  4 kHz is enough.

The frequency of doing something is the number of times it is done per a certain observation period. In the case of communication systems, frequency is the number of oscillations of a waveform per second. The frequency is measured in Hertz after its inventor Heinrich Hertz. So a frequency of 3000 Hz means 3000 oscillations of the waveform per second, or 3000 waves per second.

## Modulation Process

In the upper parts of the post, we learned that the transmitter should adapt the message signal to the communication channel, by converting it into symbols and encoding those symbols. This process is called modulation.

There are two big families of modulations in communication systems: Continuous Wave modulation and Pulse modulation.

## Time domain vs Frequency domain

To represent a signal, we can do it in either the time domain or the frequency domain. The following diagram is a representation of a signal in the time domain (on the left) and its correspondent in the frequency domain (on the right). The difference is, in the time domain, the signal evolves over time, while in the frequency domain, the signal is represented in terms of frequencies. Look how the shapes are different.

## High frequencies

In Telecommunication system, we tend to prefer higher frequencies over lower ones. For example, the frequencies used in 802.11 specifications are over 2GHz. Why?

Let’s take wireless communications as an example. In wireless, the frequency of the signal we want to transmit is inversely proportional to the length of the antenna. So the lower the frequency, the bigger the antenna should be. Imagine you wanted to transmit a signal at the speed of light, which is about 300 km/s, you would then design an antenna that is 30 km in length!

That’s why Telecom engineers opted to raise the signal frequency in multiples of 1GHz, so that manufacturers can produce reasonably-sized antennas.

Also, higher frequencies allow lower attenuation of the signal and better immunity against noise. Thus, higher frequencies allow better signal quality and longer traveled distance. ### Continuous Wave modulation (CW) This family of modulation techniques modifies the characteristics of a sine wave signal called the carrier, in accordance to the message signal. To simplify the concept of the carrier signal, let’s consider this example: you are a street painter. One passenger asks you to draw the street:

• the street is the message signal,
• the color pencils are the carrier, since the painter uses them to reproduce the shapes and colors of the street on paper
• The variation of lines, colors and shapes in the drawing are in accordance with the details of the street.

Usually we apply modulation techniques to signals that take a sine (or a cosine) waveform, which repeats itself over time, if no modulation technique is applied and no significant noise is present. We apply to these “basic form” signals what is called carrier signals because they “carry” the information we want to transmit (or receive).

The way we are going to transfer (or receive) information is by manipulating one or more of the three characteristics of the signal (amplitude, phase or wavelength)

The characteristics of a carrier signal -and any other signal- are:

• amplitude (A)
• phase (theta): measured in degrees or in multiples of π
• wavelength (T)

Here is a sample form of the carrier: And here is another graph that shows the phase:

We can modify the amplitude, the frequency or the phase of the carrier signal over time.

• If we modify the amplitude of the carrier in accordance with the message signal, we get the Amplitude Modulation technique (AM)
• If we modify the frequency of the carrier in accordance with the message signal, we get the Frequency Modulation technique (FM)
• If we modify the phase of the carrier in accordance with the message signal, we get the Phase Modulation technique (PM)

Both FM and PM are also called angle modulations.

Here is a visual example of amplitude modulation: When modulation occurs, the carrier signal goes in accordance with the message signal: the envelope in red is the original signal to which we applied a carrier. copyright http://hoytech.github.io/

### Pulse modulation

There are two categories for Pulse Modulation: analog pulse modulation and digital pulse modulation. Analog pulse modulation techniques are :

• PAM: Pulse Amplitude Modulation
• PDM: Pulse Division Modulation
• PPM: Pulse Position Modulation

This diagram summarizes the different modulation families and techniques:

## Digital modulation

Digital modulation techniques are also called Pulse Code Modulation (PCM).

As part of the whole digital communication system, digital modulation occurs immediately before the physical transmission of the signal:

### Digital modulation techniques

Digital modulation techniques manipulate the phase, the amplitude -or both- of the carrier signal. In fact, we consider the frequency as constant and only amplitude and phase can be functions of time.

Some popular digital modulation methods are:

#### 1. Phase Shift Keying PSK

Phase Shift Keying is a type of angle modulation. As its name implies, this technique manipulates the phase of the carrier signal.

This technique is ideal in the cases where the signal strength is variable. PSK is used in cable modems, DSL and wireless. We distinguish different flavors among which we have BPSK and QPSK.

Binary Phase Shift Keying BPSK: At one time we have a carrier signal with 0° phase, and at another time the signal shifts with 180° phase.

Quadrature Phase Shift Keying QPSK: also called 4-PSK, this method uses two bits to code symbols (so four symbols in total) and the carrier signal is shifted by 90°.

QPSK uses the concept of quadrature signals. At the input of the QPSK modulator, we have two carrier signals as follow:

• one In-phase signal
• one “quadrature” signal, or a “90°-shifted” signal.

Two signals are called in quadrature when one signal’s phase is different by 90° from the other signal. For example, the sine wave and the cosine wave are by nature quadrature signals.

#### 2. Amplitude Shift Keying ASK

It is used in wired networks such as 100Base-T, 1000Base-T and 10GBase-T. In this type of modulation we have the On-Off Keying method (OOK).

This technique applies both phase modulation and amplitude modulation. QAM allows for denser alphabet of symbols.

### Digital modulation: symbols

A symbol (M) is a set of bits. If a modulation type defines a symbol on k bits, the number of possible symbols is given by this formula:

M = 2 power k

We call the list of possible symbols the Symbol alphabet.

[box type=”note” align=”aligncenter” ]When you have a computer and want to connect to Internet through a DSL connection, you will need to have a DSL modem. This intermediate device performs analog-to-digital and digital-to-analog conversion of the signal.[/box]

What’s the relation between symbols and modulation? Digital modulation techniques allow to send&receive symbols,  instead of bits, at the physical layer. Some modulation schemes allow two symbols, some allow four symbols, etc. For example:

• In BPSK, we can transmit/receive only two symbols (0 and 1),
• in QPSK, we can transmit/receive four symbols (00, 01, 10 and 11),
• In 16-QAM however, we can have up to 16 symbols.

The symbol alphabet for each modulation type becomes easier to determine with the concept of (I,Q) constellations.

### Digital modulation: (I,Q) Constellation

The (I,Q) constellation diagram gives a pictorial representation of the symbol alphabet that can be carried by a particular signal. The construction of the (I,Q) constellation is only possible when the frequency of the signal is constant, such as with PSK, ASK and QAM modulation techniques.

By convention:

• I is the amplitude the In-phase signal, and is put on the horizontal axis
• Q is the amplitude of the “90°-shifted” signal, and is put on the vertical axis.

Another diagram that displays the same information as the (I,Q) constellation diagram is the Phasor diagram. Looking at the figure below, the difference between the two is that the (I,Q) constellation diagram displays points (see b), while the Phasor diagram displays vectors (see a):

Now, given an (I,Q) constellation, it is possible to quickly determine the number of possible symbols we can send&receive at the physical layer. some (I,Q) constellations. Notice how we can easily determine the symbol alphabet for each modulation technique  – copyright cp.literature.agilent.com

Using the (I,Q) constellation diagram -or the Phasor diagram- we can determine if a modulation scheme is dense in symbols or not. The more dense the symbol alphabet is, the less immune to noise the signal is.

### Shannon Capacity

The Shannon capacity, or the Shannon Limit, defines the maximum amount of information a communication channel can transmit without errors, when noise is present on the channel. (We interchangeably refer to the communication media as the communication channel).

C = B * Log_base2 (1 + S/N)

where

• C: the maximum capacity of the communication channel, expressed in bits per seconds,
• B: the channel bandwidth, expressed in Hz,
• S: the average strength of the received signal, expressed in Watt,
• N: the average received noise, expressed in Watt too.

Both S and N must be measured at the same time.

The quotient S/N is also called the signal-to-noise ratio SNR. SNR can be expressed as a ratio (without a unit) or in Decibel dB. If we want to express the SNR in dB, we use this formula:

SNR_dB = 10 * Log_base10 (SNR)

But we have the Shannon Limit calculated in Log_base2. Remember the following formula to convert between Log_base2 and Log_base10:

Log_base2 (X) = Log_base10 (X) / Log_base10 (2)

To increase the number of bits a media can transmit we have to increase the bandwidth and/or the signal-to-noise ratio. So we either:

• increase the signal strength in terms of voltage
• reduce the noise, which is expensive in hardware

### Bit Error Rate (BER)

This is the ratio between the number of transmitted bits by the number of bits received correctly.

### Coding

Coding is adding redundancy to the physical layer, in order to improve the link layer throughput.

We said that modulation techniques use symbols. What coding does is it assigns to each symbol a longer -yet fixed- set of bits called a chip. The length of the chip is determined by what we call the coding gain. For example:

• a coding gain of 1/8 means : for each bit at the link layer we code 8 bits at the physical layer.

There is a formula that ties the bit rate to the coding gain:

Bit rate = symbol rate * bits per symbol * coding gain

## Multiplexing & Demultiplexing

One interesting benefit of modulation is the ability to transmit many signals on the same communication channel. this process is called Multiplexing. At the receiver side, demultiplexing occurs to separate signals.

The multiplexing techniques you need to know are:

• FDM
• CDM
• TDM
• WDM

TDM -or Time Division Multiplexing- is a technique that allows two functions:

• aggregating multiple input signals onto the same communication media, and this is called Multiplexing
• chunking a transmitted signal into many output signals, and this is called Demultiplexing.

These two functions are performed consecutively by a Multiplexer and a Demultiplexer.

How can we transmit many signals onto the same media, without having some sort of collision? And how can we distinguish the output signals at the receiver side? That’s the power of timeslots.

Over a period of time T, we divide the time into time slots. Each time slot is used to carry a portion of a signal X. T is repeated over time and that means another portion of signal X is transmitted, etc … until all input signals are completely transmitted. Out in the world, there are TDM links that use this TDM technology. These TDM links are used for example in these scenarios:

• connecting a PABX to a Cisco voice gateway,
• connecting two PABXs together,
• connecting a voice gateway to the PSTN

## Baseband and Passband in communication systems Baseband communication is when the encoded signal is sent at its original low frequencies. Such examples are voice telephony (not voice over IP) and analog video camera output.

Passband communication is when the encoded signal is “modulated” to a higher range of frequencies. And it can be analog modulation or digital modulation. It allows to multiplex different signals together on the same physical media, given that de-multiplexing occurs at the receiver side to distinguish the various signals. Wired and wireless technologies operate on a passband basis.

## Clocks

The cadence of signal transmission is regulated by a regular type of signals called the clock signal. The transmitter uses a flip flop circuit to generate the clock. Both the clock signal and the data signal are put on the medium.

When both the transmitter and the receiver in communication systems have the same clock signal, then it is easy to regenerate the sent signal at the receiver level. However, in communication systems, receivers do not know which clock transmitters are using. Thus, we need a system that “tries” to guess the clock.

This is the job of the clock recovery circuits. They take as input the received signal and they estimate the clock at their output.

References

• Communication Systems, Haykin&Mohner
• http://www.chem.tamu.edu/class/fyp/mathrev/mr-log.html