Communication Systems/Print Version
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[edit] Introduction
This book will eventually cover a large number of topics in the field of electrical communications. The reader will also require a knowledge of Time and Frequency Domain representations, which is covered in-depth in the Signals and Systems book. This book will, by necessity, touch on a number of different areas of study, and as such is more than just a text for aspiring Electrical Engineers. This book will discuss topics of analog communication schemes, computer programming, network architectures, information infrastructures, communications circuit analysis, and many other topics. It is a large book, and varied, but it should be useful to any person interested in learning about an existing communication scheme, or in building their own. Where previous Electrical Engineering books were grounded in theory (notably the Signals and Systems book), this book will contain a lot of information on current standards, and actual implementations. It will discuss how current networks and current transmission schemes work, and may even include information for the intrepid engineer to create their own versions of each.
This book is still in an early stage of development. Many topics do not yet have pages, and many of the current pages are stubs. Any help would be greatly appreciated.
[edit] Table of Contents
[edit] Introduction
People are prone to take for granted the fact that modern technology allows us to transmit data at nearly the speed of light to locations that are very far away. 200 years ago, it would be deemed preposterous to think that we could transmit webpages from China to Mexico in less then a second. It would seem equally preposterous to think that people with cellphones could be talking to each other, clear as day, from miles away. Today, these things are so common, that we accept them without even asking how these miracles are possible.
[edit] What is Communications?
Communications is the field of study concerned with the transmission of information through various means. It can also be defined as technology employed in transmitting messages. It can also be defined as the inter-transmitting the content of data (speech, signals, pulses etc.) from one node to another.
[edit] Who is This Book For?
This book is for people who have read the Signals and Systems wikibook, or an equivalent source of the information. Topics considered in this book will rely heavily on knowledge of Fourier Domain representation and the Fourier Transform. This book can be used to accompany a number of different classes spanning the 3rd and fourth years in a study of electrical engineering. Knowledge of integral and differential calculus is assumed. The reader may benefit from knowledge of such topics as semiconductors, electromagnetic wave propagation, etc, although these topics are not necessary to read and understand the information in this book.
[edit] What this Book will Cover
This book is going to take a look at nearly all facets of electrical communications, from the shape of the electrical signals, to the issues behind massive networks. It makes little sense to be discussing these subjects outside the realm of current examples. We have the internet, so in discussing issues concerning digital networks, it makes good sense to reference these issues to the internet. Likewise, this book will attempt to touch on, at least briefly, every major electrical communications network that people deal with on a daily basis. From AM radio to the internet, from DSL to cable TV, this book will attempt to show how the concepts discussed apply to the real world.
This book also acknowledges a simple point: It is easier to discuss the signals and the networks simultaneously. For this kind of task to be undertaken in a paper book would require hundreds, if not thousands of printed pages, but through the miracle of wikimedia, all this information can be brought together in a single, convenient location.
This book would like to actively solicit help from anybody who has experience with any of these concepts: Computer Engineers, Communications Engineers, Computer Programmers, Network Administrators, IT Professionals. Also, this book may cover all these topics, but the reader doesn't need to have prior knowledge of all these disciplines to advance. Information will be developed as completely as possible in the text, and links to other information sources will be provided as needed.
[edit] Where to Go From Here
Since this book is designed for a junior and senior year of study, there aren't necessarily many topics that will logically follow this book. After reading and understanding this material, the next logical step for the interested engineer is either industry or graduate school. Once in graduate school, there are a number of different areas to concentrate study in. In industry, the number is even higher.
[edit] Division of Material
Admittedly, this is a very large topic, one that can span not only multiple printed books, but also multiple bookshelves. It could then be asked "Why don't we split this book into 2 or more smaller books?" This seems like a good idea on the surface, but you have to consider exactly where the division would take place. Some would say that we could easily divide the information between "Analog and Digital" lines, or we could divide up into "Signals and Systems" books, or we could even split up into "Transmissions and Networks" Books. But in all these possible divisions, we are settling for having related information in more then 1 place.
[edit] Analog and Digital
It seems most logical that we divide this material along the lines of analog information and digital information. After all, this is a "digital world", and aspiring communications engineers should be able to weed out the old information quickly and easily. However, what many people don't realize is that digital methods are simply a subset of analog methods with more stringent requirements. Digital transmissions are done using techniques perfected in analog radio and TV broadcasts. Digital computer modems are sending information over the old analog phone networks. Digital transmissions are analyzed using analog mathematical concepts such as modulation, SNR (signal to noise ratio), Bandwidth, Frequency Domain, etc... For these reasons, we can simplify both discussions by keeping them in the same book.
[edit] Signals and Systems
Perhaps we should divide the book in terms of the signals that are being sent, and the systems that are physically doing the sending. This makes some sense, except that it is impossible to design an appropriate signal without understanding the restrictions of the underlying network that it will be sent on. Also, once we develop a signal, we need to develop transmitters and receivers to send them, and those are physical systems as well.
[edit] About This Book
There are a few points about this book that are worth mentioning:
 |
Real-world examples will appear in these boxes |
- The programming parts of this book will not use any particular language, although we may consider particular languages in dedicated chapters.
This page will attempt to show some of the basic history of electrical communication systems.
[edit] Claude Shannon
| The Errata page contains additional information about this subject: |
[edit] Harry Nyquist
[edit] Section 1: Communications Basics
It is important to know the difference between a baseband signal, and a broad band signal. In the Fourier Domain, a baseband signal is a signal that occupies the frequency range from 0Hz up to a certain cutoff. It is called the baseband because it occupies the base, or the lowest range of the spectrum.
In contrast, a broadband signal is a signal which does not occupy the lowest range, but instead a higher range, 1MHz to 3MHz, for example. A wire may have only one baseband signal, but it may hold any number of broadband signals, because they can occur anywhere in the spectrum.
[edit] Wideband vs Narrowband
[edit] Frequency Spectrum
A graphical representation of the various frequency components on a given transmission medium is called a frequency spectrum.
Consider a situation where there are multiple signals which would all like to use the same wire (or medium). For instance, a telephone company wants multiple signals on the same wire at the same time. It certainly would save a great deal of space and money by doing this, not to mention time by not having to install new wires. How would they be able to do this? One simple answer is known as Time-Division Multiplexing.
[edit] What is TDM?
In Time-Division Multiplexing (TDM), each signal is transmitted for a certain period of time, and is then "turned off". When one signal has been turned off, another signal is "turned on". On the other end of the wire is a switch that will then move each signal to its correct destination.
[edit] Benefits of TDM
TDM is all about cost: fewer wires and simpler receivers are used to transmit data from multiple sources to multiple destinations. TDM also uses less bandwidth than Frequency-Division Multiplexing (FDM) signals, unless the bitrate is increased, which will subsequently increase the necessary bandwidth of the transmission.
[edit] Synchronous TDM
Synchronous TDM is a system where the transmitter and the receiver both know exactly which signal is being sent. Consider the following diagram:
Signal A ---> |---| |A|B|C|A|B|C| |------| ---> Signal A Signal B ---> |TDM| --------------> |De-TDM| ---> Signal B Signal C ---> |---| |------| ---> Signal C
In this system, starting at time-slice 0, every third time-slice is reserved for Signal A; starting at time-slice 1, every third time-slice is reserved for Signal B; and starting at time-slice 2, every third time-slice is reserved for Signal C. In this situation, the receiver (De-TDM) needs only to switch after the signal on each time-slice is received.
[edit] Statistical TDM
Synchronous TDM is beneficial because the receiver and transmitter can both cost very little. However, consider the most well-known network: the Internet. In the Internet, a given computer might have a data rate of 1kbps when hardly anything is happening, but might have a data rate of 100kbps when downloading a large file from a fast server. How are the time-slices divided in this instance? If every time slice is made big enough to hold 100Kbps, when the computer isn't downloading any data, all of that time and electricity will be wasted. If every time-slice is only big enough for the minimum case, the time required to download bigger files will be greatly increased.
The solution to this problem is called Statistical TDM, and is the solution that the Internet currently uses. In Statistical TDM, each data item, known as the payload (we used time-slices to describe these earlier), is appended with a certain amount of information about who sent it, and who is supposed to receive it (the header). The combination of a payload and a header is called a packet. Packets are like envelopes in the traditional "snail mail" system: Each packet contains a destination address and a return address as well as some enclosed data. Because of this, we know where each packet was sent from and where it is going.
The downside to statistical TDM is that the sender needs to be smart enough to write a header, and the receiver needs to be smart enough to read the header and (if the packet is to be forwarded,) send the packet toward its destination.
[edit] Packets
Packets will be discussed in greater detail once we start talking about digital networks (specifically the Internet). Packet headers not only contain address information, but may also include a number of different fields that will display information about the packet. Many headers contain error-checking information (checksum, Cyclic Redundancy Check) that enables the receiver to check if the packet has had any errors due to interference, such as electrical noise.
[edit] Duty Cycles
Duty cycle is defined as " the time that is effectively used to send or receive the data, expressed as a percentage of total period of time." The more the duty cycle , the more effective transmission or reception.
We can define the pulse width, τ, as being the time that a bit occupies from within it's total alloted bit-time Tb. If we have a duty cycle of D, we can define the pulse width as:
- τ = DTb
Where:
The pulse width is equal to the bit time if we are using a 100% duty cycle.
[edit] Introduction
It turns out that many wires have a much higher bandwidth than is needed for the signals that they are currently carrying. Analog Telephone transmissions, for instance, require only 3 000 Hz of bandwidth to transmit human voice signals. Over short distances, however, twisted-pair telephone wire has an available bandwidth of nearly 100 000 Hz!
[edit] What is FDM?
Frequency Division Multiplexing (FDM) allows engineers to utilize the extra space in each wire to carry more than one signal. By frequency-shifting some signals by a certain amount, engineers can shift the spectrum of that signal up into the unused band on that wire. In this way, multiple signals can be carried on the same wire, without having to divy up time-slices as in Time-Division Multiplexing schemes.
[edit] Benefits of FDM
FDM allows engineers to transmit multiple data streams simultaneously over the same channel, at the expense of bandwidth. To that extent, FDM provides a trade-off: faster data for more bandwidth. Also, to demultiplex an FDM signal requires a series of bandpass filters to isolate each individual signal. Bandpass filters are relatively complicated and expensive, therefore the receivers in an FDM system are generally expensive.
[edit] Examples of FDM
As an example of an FDM system, Commercial broadcast radio (AM and FM radio) simultaneously transmits multiple signals or "stations" over the airwaves. These stations each get their own frequency band to use, and a radio can be tuned to receive each different station. Another good example is cable television, which simultanously transmits every channel, and the TV "tunes in" to which channel it wants to watch.
[edit] Orthogonal FDM
Orthogonal Frequency Division Multiplexing (OFDM) is a more modern variant of FDM that uses orthogonal sub-carriers to transmit data that does not overlap in the frequency spectrum and is able to be separated out using frequency methods. OFDM has a similar data rate to traditional FDM systems, but has a higher resilience to disruptive channel conditions such as noise and channel fading.
[edit] Voltage Controlled Oscillators (VCO)
A voltage-controlled oscillator (VCO) is a device that outputs a sinusoid of a frequency that is a function of the input voltage. VCOs are not time-invariant, linear components. A complete study of how a VCO works will probably have to be relegated to a book on electromagnetic phenomena. This page will, however, attempt to answer some of the basic questions about VCOs.
A basic VCO has input/output characteristics as such:
v(t) ----|VCO|----> sin(a[f + v(t)]t + O)
VCOs are often implemented using a special type of diode called a "Varactor". Varactors, when reverse-biased, produce a small amount of capacitance that varies with the input voltage.
[edit] Phase-Locked Loops
If you are talking on your cellphone, and you are walking (or driving), the phase angle of your signal is going to change, as a function of your motion, at the receiver. This is a fact of nature, and is unavoidable. The solution to this then, is to create a device which can "find" a signal of a particular frequency, negate any phase changes in the signal, and output the clean wave, phase-change free. This device is called a Phase-Locked Loop (PLL), and can be implemented using a VCO.
[edit] Purpose of VCO and PLL
VCO and PLL circuits are highly useful in modulating and demodulating systems. We will discuss the specifics of how VCO and PLL circuits are used in this manner in future chapters.
[edit] Varactors
As a matter of purely professional interest, we will discuss varactors here. (VCO)
[edit] What is an Envelope Filter?
The envelope detector is a simple analog circuit that can be used to find the peaks in a quickly-changing waveform. Envelope detectors are used in a variety of devices, specifically because passing a sinusoid through an envelope detector will supress the sinusoid.
[edit] Circuit Diagram
In essence, an envelope filter has the following diagram:
o------+------+------o
+ | | +
\ (c)
vin /R | vout
\ |
- | | -
o------+------+------o
Where (c) represents a capacitor, and R is a resistor. Under zero input voltage (vin = 0), the capacitor carries no charge, and the resistor carries no current. When vin is increased, the capacitor stores charge until it reaches capacity, and then the capacitor becomes an open circuit. At this point, all current in the circuit is flowing through the resistor, R. As voltage decreases, the capacitor begins to discharge it's stored energy, slowing down the state change in the circuit from high voltage to low voltage.
[edit] Positive Voltages
By inserting a diode at the beginning of this circuit, we can negate the effect of a sinusoid, dipping into negative voltage, and forcing the capacitor to discharge faster:
diode
o-->|--+------+------o
+ | | +
\ (c)
vin /R | vout
\ |
- | | -
o------+------+------o
[edit] Purpose of Envelope Filters
Envelope filters help to find the outer bound of a signal that is changing in amplitude.
|
Envelope Filters are generally used with AM demodulation, discussed later. |
(Envelope Detectors)
Modulation is a term that is going to be used very frequently in this book. So much in fact, that we could almost have renamed this book "Principals of Modulation", without having to delete too many chapters. So, the logical question arises: What exactly is modulation?
[edit] Definition
Modulation is a process of mixing a signal with a sinusoid to produce a new signal. This new signal, conceivably, will have certain benefits of an un-modulated signal, especially during transmission. If we look at a general function for a sinusoid:
- f(t) = Asin(ωt + φ)
we can see that this sinusoid has 3 parameters that can be altered, to affect the shape of the graph. The first term, A, is called the magnitude, or amplitude of the sinusoid. The next term, ω is known as the frequency, and the last term, φ is known as the phase angle. All 3 parameters can be altered to transmit data.
The sinusoidal signal that is used in the modulation is known as the carrier signal, or simply "the carrier". The signal that is being modulated is known as the "data signal". It is important to notice that a simple sinusoidal carrier contains no information of it's own.
[edit] Types of Modulation
There are 3 different types of modulation: Amplitude modulation, Frequency modulation, and Phase modulation. We will talk about the differences and uses of all three in a later chapter.
[edit] Why Use Modulation?
Clearly the concept of modulation can be a little tricky, especially for the people who don't like trigonometry. Why then do we bother to use modulation at all? To answer this question, let's consider a channel that essentially acts like a bandpass filter: The lowest frequency components and the highest frequency components are attenuated or unusable, in some way. If we can't send low-frequency signals, then we need to shift our signal up the frequency ladder. Modulation allows us to send a signal over a bandpass frequency range. If every signal gets it's own frequency range, then we can transmit multiple signals simultaneously over a single channel, all using different frequency ranges. Another use of modulation is that it allows the efficient use of antenna, a baseband signal to be transmitted will need an antenaa of huge length, whereas once modulated the antenna length will be reduced dramatically (antenna length almost equal 1/10 of the signal wavelength
[edit] Examples
Think about your car radio. There are more then a dozen (or so) channels on the radio at any time, each with a given frequency: 100.1MHz, 102.5MHz etc... Each channel gets a certain range (usually about 0.2MHz), and the entire station gets transmitted over that range. Modulation makes it all possible, because it allows us to send voice and music (which are essentiall baseband signals) over a bandpass (or "Broadband") channel.
[edit] non-sinusoidal modulation
A sine wave at one frequency can separated from a sine wave at another frequency (or a cosine wave at the same frequency) because the two signals are "orthogonal".
There are other sets of signals, such that every signal in the set is orthogonal to every other signal in the set.
A simple orthogonal set is time multiplexed division (TDM) -- only one transmitter is active at any one time.
Other more complicated sets of orthogonal waveforms -- Walsh codes and various pseudonoise codes such as Gold codes and maximum length sequences -- are also used in some communication systems.
The process of combining these waveforms with data signals is sometimes called "modulation", because it is so very similar to the way modulation combines sine waves are with data signals.
[edit] further reading
- Data Coding Theory/Spectrum Spreading
- Wikipedia:Walsh code
- Wikipedia:Gold code
- Wikipedia:pseudonoise code
- Wikipdia:maximum length sequence
There is lots of talk nowadays about buzzwords such as "Analog" and "Digital". Certainly, engineers who are interested in creating a new communication system should understand the difference. Which is better, analog or digital? What is the difference? What are the pros and cons of each? This chapter will look at the answers to some of these questions.
[edit] What are They?
What exactly is an analog signal, and what is a digital signal?
- Analog
- Analog signals are signals with continuous values. Analog signals are used in many systems, although the use of analog signals has declined with the advent of cheap digital signals.
- Digital
- Digital signals are signals that are represented by binary numbers, "1" or "0". The 1 and 0 values can correspond to different discrete voltage values, and any signal that doesnt quite fit into the scheme just gets rounded off.
[edit] What are the Pros and Cons?
Each paradigm has it's own benefits and problems.
- Analog
- Analog systems are very tolerant to noise, make good use of bandwidth, and are easy to manipulate mathematically. However, analog signals require hardware receivers and transmitters that are designed to perfectly fit the particular transmission. If you are working on a new system, and you decide to change your analog signal, you need to completely change your transmitters and receivers.
- Digital
- Digital signals are very intolerant to noise, and digital signals can be completely corrupted in the presence of excess noise. In digital signals, noise could cause a 1 to be interpreted as a 0 and vice versa, which makes the received data different than the original data. Imagine if the army transmitted a position coordinate to a missile digitally, and a single bit was received in error? This single bit error could cause a missile to miss its target by miles. Luckily, there are systems in place to prevent this sort of scenario, such as checksums and CRCs, which tell the receiver when a bit has been corrupted and ask the transmitter to resend the data. The primary benefit of digital signals is that they can be handled by simple, standardized receivers and transmitters, and the signal can be then dealt with in software (which is comparatively cheap to change).
- The Difference between Digital and Discrete
Digital quantity may be either 0 or 1, but discrete may be any numerical value i.e 0,1....9.
[edit] Which is Better?
There is no way to say which type of signal is better or worse. Modern digital systems often require more expensive components (consider the difference in price between old TV sets, and new HDTV sets), although lower-end digital systems can be moderately priced. Analog systems need to be built with a complex array of Op Amps, resistors, capacitors, diodes, etc, while a digital system can be implemented with a generic microcontroller, and some quick programming.
[edit] Sampling and Reconstruction
The process of converting from analog data to digital data is called "sampling". The process of recreating an analog signal from a digital one is called "reconstruction". This book will not talk about either of these subjects in much depth beyond this, although other books on the topic of EE might, such as A-level Physics (Advancing Physics)/Digitisation.
[edit] further reading
Signals need a channel to follow, so that they can move from place to place. These Communication Mediums, or "channels" are things like wires and antennae that transmit the signal from one location to another. Some of the most common channels are listed below:
[edit] Twisted Pair Wire
Twisted Pair is a transmission medium that uses two conductors that are twisted together to form a pair. The concept for the twist of the conductors is to prevent interference. Ideally, each conductor of the pair basically receives the same amount of interference, positive and negative, effectively cancelling the effect of the interference. Typically, most inside cabling has four pairs with each pair having a different twist rate. The different twist rates help to further reduce the chance of crosstalk by making the pairs appear electrically different in reference to each other. If the pairs all had the same twist rate, they would be electrically identical in reference to each other causing crosstalk, which is also referred to as capacitive coupling. Twisted pair wire is commonly used in telephone and data cables with variations of categories and twist rates.
Other variants of Twisted Pair are the Shielded Twisted Pair cables. The shielded types operate very similar to the non-shielded variety, except that Shielded Twisted Pair also has a layer of metal foil or mesh shielding around all the pairs or each individual pair to further shield the pairs from electromagnetic interference. Shielded twisted pair is typically deployed in situations where the cabling is subjected to higher than normal levels of interference.
[edit] Coaxial Cable
Another common type of wire is Coaxial Cable. Coaxial cable (or simply, "coax") is a type of cable with a single data line, surrounded by various layers of padding and shielding. The most common coax cable, common television cable, has a layer of wire mesh surrounding the padded core, that absorbs a large amount of EM interference, and helps to ensure a relatively clean signal is transmitted and received. Coax cable has a much higher bandwidth than a twisted pair, but coax is also significantly more expensive than an equal length of twisted pair wire. Coax cable frequently has an available bandwidth in excess of hundreds of megahertz (in comparison with the hundreds of kilohertz available on twisted pair wires).
Originally, Coax cable was used as the backbone of the telephone network because a single coaxial cable could hold hundreds of simultaneous phone calls by a method known as "Frequency Division Multiplexing" (discussed in a later chapter). Recently however, Fiber Optic cables have replaced Coaxial Cable as the backbone of the telephone network because Fiber Optic channels can hold many more simultaneous phone conversations (thousands at a time), and are less susceptible to interference, crosstalk, and noise then Coaxial Cable.
[edit] Fiber Optics
Fiber Optic cables are thin strands of glass that carry pulses of light (frequently infrared light) across long distances. Fiber Optic channels are usually immune to common RF interference, and can transmit incredibly high amounts of data very quickly. There are 2 general types of fiber optic cable: single frequency cable, and multi-frequency cable. single frequency cable carries only a single frequency of laser light, and because of this there is no self-interference on the line. Single-frequency fiber optic cables can atain incredible bandwidths of many gigahertz. Multi-Frequency fiber optics cables allow a Frequency-Division Multiplexed series of signals to each inhabit a given frequency range. However, interference between the different signals can decrease the range over which reliable data can be transmitted.
[edit] Wireless Transmission
In wireless transmission systems, signals are propagated as Electro-Magnetic waves through free space. Wireless signals are transmitted by a transmitter, and received by a receiver. Wireless systems are inexpensive because no wires need to be installed to transmit the signal, but wireless transmissions are susceptable not only to EM interference, but also to physical interference. A large building in a city, for instance can interfere with cell-phone reception, and a large mountain could block AM radio transmissions. Also, WiFi internet users may have noticed that their wireless internet signals don't travel through walls very well.
There are 2 types of antennas that are used in wireless communications, isotropic, and directional.
[edit] Isotropic
People should be familiar with isotropic antennas because they are everywhere: in your car, on your radio, etc... Isotropic antennas are omni-directional in the sense that they transmit data out equally (or nearly equally) in all directions. These antennas are excellent for systems (such as FM radio transmission) that need to transmit data to multiple receivers in multiple directions. Also, Isotropic antennas are good for systems in which the direction of the receiver, relative to the transmitter is not known (such as cellular phone systems).
[edit] Directional
Directional antennas focus their transmission power in a single narrow direction range. Some examples of directional antennas are satellite dishes, and wave-guides. The downfall of the directional antennas is that they need to be pointed directly at the receiver all the time to maintain transmission power. This is useful when the receiver and the transmitter are not moving (such as in communicating with a geo-synchronous satellite).
[edit] Receiver Design
It turns out that if we know what kind of signal to expect, we can better receive those signals. This should be intuitive, because it is hard to find something if we don't know what precisely we are looking for. How is a receiver supposed to know what is data and what is noise, if it doesnt know what data looks like?
Coherent transmissions are transmissions where the receiver knows what type of data is being sent. Coherency implies a strict timing mechanism, because even a data signal may look like noise if you look at the wrong part of it. In contrast, noncoherent receivers don't know exactly what they are looking for, and therefore noncoherent communication systems need to be far more complex (both in terms of hardware and mathematical models) to operate properly.
This section will talk about coherent receivers, first discussing the "Simple Receiver" case, and then going into theory about what the optimal case is. Once we know mathematically what an optimal receiver should be, we then discuss two actual implementations of the optimal receiver.
It should be noted that the remainder of this book will discuss optimal receivers. After all, why would a communication's engineer use anything that is less then the best?
[edit] The Simple Receiver
A simple receiver is just that: simple. A general simple receiver will consist of a low-pass filter (to remove excess high-frequency noise), and then a sampler, that will select values at certain points in the wave, and interpolate those values to form a smooth output curve. In place of a sampler (for purely analog systems), a general envelope filter can also be used, especially in AM systems. In other systems, different tricks can be used to demodulate an input signal, and acquire the data. However simple receivers, while cheap, are not the best choice for a receiver. Occcasionally they are employed because of their price, but where performance is an issue, a better alternative receiver should be used.
[edit] The Optimal Receiver
Mathematically, Engineers were able to predict the structure of the optimal receiver. Read that sentence again: Engineers are able to design, analyze, and build the best possible receiver, for any given signal. This is an important development for several reasons. First, it means that no more research should go into finding a better receiver. The best receiver has already been found, after all. Second, it means any communications system will not be hampered (much) by the receiver.
[edit] Derivation
here we will attempt to show how the coherent receiver is derived.
[edit] Matched Receiver
The matched receiver is the logical conclusion of the optimal receiver calculation. The matched receiver convolutes the signal with itself, and then tests the output. Here is a diagram:
s(t)----->(Convolve with r(t))----->
This looks simple enough, except that convolution modules are often expensive. An alternative to this approach is to use a correlation receiver.
[edit] Correlation Receiver
The correlation receiver is similar to the matched receiver, instead with a simple switch: The multiplication happens first, and the integration happens second.
Here is a general diagram:
r(t)
|
v
s(t) ----->(X)----->(Integrator)--->
In a digital system, the integrator would then be followed by a threshold detector, while in an analog receiver, it might be followed by another detector, like an envelope detector.
[edit] Conclusion
To do the best job of receiving a signal, we need to know the form of the signal that we are sending. This should seem obvious, we can't design a receiver until after we've decided how the signal will be sent. This method poses some problems however, in that the receiver must be able to line up the received signal with the given reference signal to work the magic: If the received signal and the reference signal are out of sync with each other, either as a function of an error in phase or an error in frequency, then the optimal receiver will not work.
[edit] Section 2: Analog Modulation
[edit] Analog Modulation Overview
Let's take a look at a generalized sinewave:
- x(t) = As(t)sin(2π[fc + kfm(t)]t + αφ(t))
[edit] Types of Analog Modulation
We can see 3 parameters that can be changed in this sine wave to send information:
- As(t). This term is called the "Amplitude", and changing it is called "Amplitude Modulation" (AM)
- kfm(t) This term is called the "Frequency Shift", and changing it is called "Frequency Modulation"
- αφ(t). this term is called the "Phase angle", and changing it is called "Phase Modulation".
[edit] The Breakdown
Each term consists of a coefficient (called a "scaling factor"), and a function of time that corresponds to the information that we want to send. The scaling factor out front, A, is also used as the transmission power coefficient. When a radio station wants their signal to be stronger (regardless of whether it is AM, FM, or PM), they "crank-up" the power of A, and send more power out onto the airwaves.
[edit] How we Will Cover the Material
We are going to go into separate chapters for each different type of modulation. This book will attempt to discuss some of the mathematical models and techniques used with different modulation techniques. It will also discuss some practical information about how to construct a transmitter/receiver, and how to use each modulation technique effectively.
This page will talk about Amplitude modulation.
[edit] Amplitude Modulation
Amplitude modulation (AM) occurs when the amplitude of a carrier wave is modulated, to correspond to a source signal. In AM, we have an equation that looks like this:
- Fsignal(t) = A(t)sin(ωt)
We can also see that the phase of this wave is irrelevant, and does not change (so we dont even include it in the equation).
|
AM Radio uses AM modulation |
AM Double-Sideband (AM-DSB for short) can be broken into two different, distinct types: Carrier, and Suppressed Carrier varieties (AM-DSB-C and AM-DSB-SC, for short, respectively). This page will talk about both varieties, and will discuss the similarities and differences of each.
[edit] AM-DSB-SC
AM-DSB-SC is characterized by the following transmission equation:
- v(t) = As(t)cos(2πfct)
It is important to notice that s(t) can contain a negative value. AM-DSB-SC requires a coherent receiver, because the modulation data can go negative, and therefore the receiver needs to know that the signal is negative (and not just phase shifted). AM-DSB-SC systems are very susceptable to frequency shifting and phase shifting on the receiving end. In this equation, A is the transmission amplitude.
[edit] AM Transmitter
A typical AM-DSB-SC transmitter looks like this:
cos(...)
|
Signal ---->(X)----> AM-DSB-SC
[edit] AM Receiver
To demodulate AM-DSB-SC, you need to have a correlation receiver, with a tightly synchronized reference signal.
[edit] AM-DSB-C
In contrast to AM-DSB-SC is AM-DSB-C, which is categorized by the following equation:
- v(t) = A[s(t) + c]cos(2πfct)
Where c is a positive term representing the carrier. If the term [s(t) + c] is always non-negative, we can receive the AM-DSB-C signal non-coherently, using a simple envelope detector to remove the cosine term. The +c term is simply a constant DC signal and can be removed by using a blocking capacitor.
It is important to note that in AM-DSB-C systems, a large amount of power is wasted in the transmission sending a "boosted" carrier frequency. since the carrier contains no information, it is considered to be wasted energy. The advantage to this method is that it greatly simplifies the receiver design, since there is no need to generate a coherent carrier signal at the receiver. For this reason, this is the transmission method used in conventional AM radio.
AM-DSB-SC and AM-DSB-C both suffer in terms of bandwidth from the fact that they both send two identical (but reversed) frequency "lobes", or bands. These bands (the upper band and the lower band) are exactly mirror images of each other, and therefore contain identical information. Why can't we just cut one of them out, and save some bandwidth? The answer is that we can cut out one of the bands, but it isn't always a good idea. The technique of cutting out one of the sidebands is called Amplitude Modulation Single-Side-Band (AM-SSB). AM-SSB has a number of problems, but also some good aspects. A compromise between AM-SSB and the two AM-DSB methods is called Amplitude Modulation Vestigial-Side-Band (AM-VSB), which uses less bandwidth then the AM-DSB methods, but more than the AM-SSB.
[edit] Transmitter
A typical AM-DSB-C transmitter looks like this:
c cos(...)
| |
Signal ---->(+)---->(X)----> AM-DSB-C
which is a little more complicated than an AM-DSB-SC transmitter.
[edit] Receiver
An AM-DSB-C receiver is very simple:
AM-DSB-C ---->|Envelope Filter|---->|Capacitor|----> Signal
The capacitor blocks the DC component, and effectively removes the +c term.
[edit] AM-SSB
To send an AM-SSB signal, we need to remove one of the sidebands from an AM-DSB signal. This means that we need to pass the AM-DSB signal through a filter, to remove one of the sidebands. The filter, however, needs to be a very high order filter, because we need to have a very agressive roll-off. One sideband needs to pass the filter almost completely unchanged, and the other sideband needs to be stopped completely at the filter.
To demodulate an AM-SSB signal, we need to perform the following steps:
- Low-pass filter, to remove noise
- Modulate the signal again by the carrier frequency
- Pass through another filter, to remove high-frequency components
- Amplify the signal, because the previous steps have attenuated it significantly.
AM-SSB is most efficient in terms of bandwidth, but there is a significant added cost involved in terms of more complicated hardware to send and receive this signal. For this reason, AM-SSB is rarely seen as being cost effective.
[edit] SSB Transmitter
AM-SSB transmitters are a little more complicated:
cos(...)
|
Signal ---->(X)---->|Low-Pass Filter|----> AM-SSB
The filter must be a very high order, for reasons explained in that chapter.
[edit] SSB Receiver
An AM-SSB receiver is a little bit complicated as well:
cos(...)
|
AM-SSB ---->(X)---->|Low-Pass Filter|---->|Amplifier|----> Signal
This filter doesnt need to be a very high order, like the transmitter has.
[edit] AM-VSB
As a compromise between AM-SSB and AM-DSB is AM-VSB. To make an AM-VSB signal, we pass an AM-DSB signal through a lowpass filter. Now, the trick is that we pass it through a low-order filter, so that some of the filtered sideband still exists. This filtered part of the sideband is called the "Vestige" of the sideband, hence the name "Vestigial Side Band".
AM-VSB signals then can get demodulated in a similar manner to AM-SSB. We can see when we remodulate the input signal, the two vestiges (the positive and negative mirrors of each other) over-lap each other, and add up to the original, unfiltered value!
AM-VSB is less expensive to implement then AM-SSB because we can use lower-order filters.
|
Broadcast television in North America uses AM-VSB |
[edit] Transmitter
here we will talk about an AM-VSB transmitter circuit.
[edit] Receiver
here we will talk about an AM-VSB receiver circuit.
[edit] AM Demodulation
When trying to demodulate an AM signal, it seems like good sense that only the amplitude of the signal needs to be examined. By only examining the amplitude of the signal at any given time, we can remove the carrier signal from our considerations, and we can examine the original signal. Luckily, we have a tool in our toolbox that we can use to examine the amplitude of a signal: The Envelope Detector. (AM)
[edit] Frequency Modulation
If we make the frequency of our carrier wave a function of time, we can get a generalized function that looks like this:
- sFM = Acos(2π[fc + ks(t)]t + φ)
We still have a carrier wave, but now we have the value ks(t) that we add to that carrier wave, to send our data.
As an important result, ks(t) must be less then the carrier frequency always, to avoid ambiguity and distortion.
[edit] FM Transmission Power
Since the value of the amplitude of the sine wave in FM does not change, the transmitted power is a constant. As a general rule, for a sinusoid with a constant amplitude, the transmitted power can be found as follows:
Where A is the amplitude of the sine wave, and RL is the resistance of the load. In a normalized system, we set RL to 1.
[edit] FM Transmitters
FM Transmitters can be easily implemented using a VCO (see why we discussed Voltage Controlled Oscillators, in the first section?), because a VCO converts an input voltage (our input signal) to a frequency (our modulated output).
Signal ----->|VCO|-----> FM Signal
[edit] FM Receivers
Any angle modulation receiver needs to have several components:
- A limiter, to remove abnormal amplitude values
- bandpass filter, to separate the out-of-band noise.
- A Discriminator, to change a frequency back to a voltage
- A lowpass filter, to remove noise added by the discriminator.
A discriminator is essentially a differentiator in line with an envelope detector:
FM ---->|Differentiator|---->|Envelope Filter|----> Signal
Also, you can add in a blocking capacitor to remove any DC components of the signal, if needed. (FM)
[edit] What is Phase Modulation?
Similar to FM (frequency modulation), is Phase modulation. (We will show how they are the same in the next chapter.) If we alter the value of the phase according to a particular function, we will get the following generalized PM function:
sPM = Acos(2πfct + αs(t))
It is important to note that the fact that 
for all values of t. If this relationship is not satisfied, then the phase angle is said to be wrapped.
[edit] Wrapped/Unwrapped Phase
The phase angle is a circular quantity, with the restriction 0 = 2π. Therefore, if we wrap the phase a complete 360 degrees around, the receiver will not know the difference, and the transmission will fail. When the phase exceeds 360 degrees, the phase value is said to be wrapped. It is highly difficult to construct a communication system that can detect and decode a wrapped phase value.
[edit] PM Transmitter
PM signals can be transmitted using a technique very similar to FM transmitters. The only difference is that we need to add a differentiator to it:
Signal ---->|Differentiator|---->|VCO|----> PM Signal
[edit] PM Receiver
PM receivers have all the same parts as an FM receiver, except for the 3rd step:
- A limiter, to remove abnormal amplitude values
- bandpass filter, to separate the out-of-band noise.
- A Phase detector, to convert a phase back into a voltage
- A lowpass filter, to remove noise added by the discriminator.
Phase detectors can be created using a Phase-Locked-Loop (again, see why we discussed them first?). (PM)
[edit] Concept
We can see from our initial overviews that FM and PM modulation schemes have a lot in common. Both of them are altering the angle of the carrier sinusoid according to some function. It turns out that we can go so far as to generalize the two together into a single modulation scheme known as angle modulation. Note that we will never abbreviate "angle modulation" with the letters "AM", because Amplitude modulation is completely different from angle modulation.
[edit] Instantaneous Phase
Let us now look at some things that FM and PM have of common:
- sFM = Acos(2π[fc + ks(t)]t + φ)
- sPM = Acos(2πfct + αs(t))
What we want to analyze is the argument of the sinusoid, and we will call it Psi. Let us show the Psi for the bare carrier, the FM case, and the PM case:
- Ψcarrier(t) = 2πfct + φ
- ΨFM(t) = 2π[fc + ks(t)]t + φ
- ΨPM(t) = 2πfct + αs(t)
- s(t) = Acos(Ψ(t))
This Psi value is called the Instantaneous phase of the sinusoid.
[edit] Instantaneous Frequency
Using the Instantaneous phase value, we can find the Instantaneous frequency of the wave with the following formula:
We can also express the instantaneous phase in terms of the instantaneous frequency:
Where the greek letter "lambda" is simply a dummy variable used for integration. Using these relationships, we can begin to study FM and PM signals further.
[edit] Determining FM or PM
If we are given the equation for the instantaneous phase of a particular angle modulated transmission, is it possible to determine if the transmission is using FM or PM? it turns out that it is possible to determine which is which, by following 2 simple rules:
- In PM, instantaneous phase is a linear function.
- In FM, instantaneous frequency minus carrier frequency is a linear function.
For a refresher course on Linearity, there is a chapter on the subject in the Signals and Systems book worth re-reading.
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FM radio uses generalized "Angle Modulation" |
[edit] Bandwidth
In a PM system, we know that the value αs(t) can never go outside the bounds of ( − π,π]. Since sinusoidal functions oscillate between [-1, 1], we can use them as a general PM generating function. Now, we can combine FM and PM signals into a general equation, called angle modulation:
- v(t) = Asin(2πfct + βsin(2πfmt))
If we want to analyze the spectral components of this equation, we will need to take the Fourier transform of this. But, we can't integrate a sinusoid of a sinusoid, much less find the transform of it. So, what do we do?
It turns out (and the derivation will be omitted here, for now) that we can express this equation as an infinite sum, as such:
![v(t) = A \sum_{n = -\infty}^{\infty}J_n(\beta) \sin [2 \pi(nf_m + f_c)t]](http://upload.wikimedia.org/math/9/c/0/9c087e2676b352e9783d16c84477a284.png)
But, what is the term Jn(β)? J is the Bessel function, which is a function that exists only as an open integral (it is impossible to write it in closed form). Fortunately for us, there are extensive tables tabulating Bessle function values.
[edit] The Bessel Function
The definition of the Bessel function is the following equation:
![J_n(\beta) = \frac{1}{2\pi} \int_{-\pi}^\pi e^{j[\beta sin(\theta - n\theta)]} d\theta](http://upload.wikimedia.org/math/2/6/1/261a98e2ae909b2714dfdbca6560c017.png)
The bessel function is a function of 2 variables, N and β.
Bessel Functions have the following properties:
- If n is even:
- J − n(β) = Jn(β)
- If n is odd:
- J − n(β) = − Jn(β)
.
The bessel function is a relatively advanced mathematical tool, and we will not analyze it further in this book.
[edit] Carson's Rule
If we have our generalized function:
- v(t) = Asin(2πfct + βsin(2πfmt))
We can find the bandwidth BW of the signal using the following formula:
- BW = 2(β + 1)fm = 2(Δf + fm)
where Δf is the maximum frequency deviation, of the transmitted signal, from the carrier frequency. It is important to note that Carson's rule is only an approximation (albeit one that is used in industry frequently).
what?
[edit] Demodulation: First Step
Now, it is important to note that FM and PM signals both do the same first 2 steps during demodulation:
- Pass the signal through a limiter, to remove amplitude peaks
- Pass the signal through a bandpass filter to remove low and high frequency noise (as much as possible, without filtering out the signal).
Once we perform these two steps, we no longer have white noise, because we've passed the noise through a filter. Now, we say the noise is colored.
here is a basic diagram of our demodulator, so far:
channel
s(t) ---------> r(t) --->|Limiter|--->|Bandpass Filter|---->z(t)
Where z(t) is the output of the bandpass filter.
[edit] Filtered Noise
To denote the new, filtered noise, and new filtered signal, we have the following equation:
- z(t) = γAcos(Ψ(t)) + n0(t)
Where we call the additive noise n0(t) because it has been filtered, and is not white noise anymore. n0(t) is known as narrow band noise, and can be denoted as such:
Now, once we have it in this form, we can use a trigonometric identity to make this equation more simple:
Where
Here, the new noise parameter R(t) is a rayleigh random variable, and is discussed in the next chapter.
[edit] Noise Analysis
R(t) is a noise function that affects the amplitude of our received signal. However, our receiver passes the signal through a limiter, which will remove amplitude fluctuations from our signal. For this reason, R(t) doesnt affect our signal, and can be safely ignored for now. This means that the only random variable that is affecting our signal is the variable 
, "Theta". Theta is a uniform random variable, with values between pi and -pi. Values outside this range "Wrap around" because phase is circular.
[edit] Section 3: Transmission
This page will discuss some of the fundamental basics of EM wave propagation.
[edit] EM Waves
EM radiation, for the purposes of this book, can be treated like waves. EM waves satisfy the following equation:
- c = λf
where c is the speed of light (approximately 300,000,000 m/s in vacuum), f is the frequency of the wave, and λ is the wavelength of the wave.
[edit] Polarization
[edit] Reflection
[edit] Diffraction
[edit] Path Loss
[edit] Rayleigh Fading
[edit] Rician Fading
[edit] Doppler Shift
This page is going to talk about the effect of noise on transmission systems.
[edit] Noise Temperature
The amount of noise in a given transmission medium can be equated to thermal noise. Thermal noise is well-studied, so it makes good sense to reuse the same equations when possible. To this end, we can say that any amount of radiated noise can be approximated by thermal noise with a given effective temperature. Effective temperature is measured in Kelvin. Effective temperature is frequently compared to the standard temperature, To, which is 290 Kelvin.
[edit] Noise Figure
The noise figure of a given system, is denoted with a capital F. F is generally defined in terms of it's frequency characteristics. For any given system with frequency characteristic G(f), we can define the noise figure in terms of the noise spectrum as follows:
We can show that the noise figure and the equivalent temperature of a system are related through the following relationship:
[edit] Receiver Sensitivity
In a given bandwidth, W, we can show that the noise power N equals:
- N = F(kT0)W
From N, we can show that the sensitivity of the receiver is equal to
[edit] Cascaded Systems
This page will discuss the topic of signal propagation through physical mediums, such as wires.
This section of the Communication Systems book is a stub. You can help by expanding this section.
This page will discuss Wireless EM wave propagation, and some basics about antennas.
[edit] Isotropic Antennas
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In communication we talk about 'antennas'; insects have 'antennae' |
An isotropic antenna radiates it's transmitted power equally in all directions. This is an ideal model; all real antennas have at least some directionality associated with them. However, it is mathematically convenient, and good enough for most purposes.
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A radio antenna is an example of an isotropic antenna |
[edit] Power Flux Density
If the transmitted power is spread evenly across a sphere of radius R from the antenna, we can find the power per unit area of that sphere, called the Power Flux Density using the greek letter Φ (capital phi) and the following formula:
Where PT is the total transmitted power of the signal.
[edit] Effective Area
The effective area of an antenna is the equivalent amount of area of transmission power, from a non-ideal isotropic antenna that appears to be the area from an ideal antenna. For instance, if our antenna is non-ideal, and 1 meter squared of area can effectively be modeled as .5 meters squared from an ideal antenna, then we can use the ideal number in our antenna. We can relate the actual area and the effective area of our antenna using the antenna efficiency number, as follows:
The area of an ideal isotropic antenna can be calculated using the wavelength of the transmitted signal as follows:
[edit] Received Power
The amount of power that is actually received by a receiver placed at distance R from the isotropic antenna is denoted PR, and can be found with the following equation:
- PR = ΦRAe
Where ΦR is the power flux density at the distance R. If we plug in the formula for the effective area of an ideal isotropic antenna into this equation, we get the following result:
Where LP is the path-loss, and is defined as:
The amount of power lost across freespace between two isotropic antenna (a transmitter and a receiver) depends on the wavelength of the transmitted signal.
[edit] Directional Antennas
A directional antenna, such as a parabolic antenna, attempts to radiate most of it's power in the direction of a known receiver.
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A "satellite dish" is an example of a parabolic antenna |
Here are some definitions that we need to know before we proceed:
- Azimuth Angle
- The Azimuth angle, often denoted with a θ (greek lower-case Theta), is the angle that the direct transmission makes with respect to a given reference angle (often the angle of the target receiver) when looking down on the antenna from above.
- Elevation Angle
- The elevation angle is the angle that the transmission direction makes with the ground. Elevation angle is denoted with a φ (greek lower-case phi)
[edit] Directivity
Given the above definitions, we can define the transmission gain of a directional antenna as a function of θ and φ, assuming the same transmission power:
[edit] Effective Area
The effective area of a parabolic antenna is given as such:
[edit] Transmit Gain
If we are at the transmit antenna, and looking at the receiver, the angle that the transmission differs from the direction that we are looking is known as Ψ (greek upper-case Psi), and we can find the transmission gain as a function of this angle as follows:
Where 
denotes the first-order bessel function.
[edit] Friis Equation
The Friis Equation is used to relate several values together when using directional antennas:
The Friis Equation is the fundamental basis for link-budget analysis.
[edit] Link-Budget Analysis
If we express all quantities from the Friis Equation in decibels, and divide both sides by the noise-density of the transmission medium, N0, we get the following equation:
- C / N0 = EIRP − LP + (GR / Te) − k
Where C/N0 is the received carrier-to-noise ratio, and we can decompose N0 as follows:
- N0 = kTe
k is Boltzmann's constant, (-228.6dBW) and Te is the effective temperature of the noise signal (in degrees Kelvin). EIRP is the "Equivalent Isotropic Radiated Power", and is defined as:
- EIRP = GTPT
To perform a link-budget analysis, we add all the transmission gain terms from the transmitter, we add the receive gain divided by the effective temperature, and we subtract boltzman's constant and all the path losses of the transmission.
This page is all about Space-Division Multiplexing (SDM).
- What is SDM: When we want to transmit multiple messages, the goal is maximum reuse of the given resources: time and frequency. Time-Division Multiplexing (TDM), operates by dividing the time up into time slices, so that the available time can be reused. Frequency-Division Multiplexing (FDM), operates by dividing up the frequency into transmission bands, so that the frequency spectrum can be reused. However, if we remember our work with directional antennas, we can actually reuse both time and frequency, by transmitting our information along parallel channels. This is known as Space-Division Multiplexing.
[edit] Technical categorisations
[edit] Spatial beamforming
[edit] Spactial Coding
[edit] Multipathing
[edit] Application systems
[edit] MIMO Systems
[edit] Smart antenna
[edit] Section 4: Digital Modulation
[edit] Definition
What is PAM? Pulse-Amplitude Modulation is "pulse shaping". Essentially, communications engineers realize that the shape of the pulse in the time domain can positively or negatively affect the characteristics of that pulse in the frequency domain. There is no one way to shape a pulse, there are all sorts of different pulse shapes that can be used, but in practice, there are only a few pulse shapes that are worth the effort. These chapters will discuss some of the common pulses, and will develop equations for working with any generic pulse.