What is the bandwidth of communication channels. Bandwidth Calculation

Bandwidth

Bandwidth- metric characteristic showing the ratio maximum quantity passing units (information, objects, volume) per unit of time through a channel, system, node.

Used in various fields:

in communications and computer science, P.S. is the maximum achievable amount of passing information;
in transport PS - the number of transport units;
in mechanical engineering - the volume of passing air (oil, grease).

It can be measured in various, sometimes very specialized, units - pieces, bits/sec, tons, cubic meters, etc.

In computer science, the definition of throughput usually applies to a communication channel and is defined as the maximum amount of information transmitted or received per unit of time.
Bandwidth is one of the most important factors from a user's point of view. It is estimated by the amount of data that the network can, in the limit, transfer per unit of time from one device connected to it to another.

Channel capacity

The highest possible information transmission speed in a given channel is called its throughput. Channel capacity is the speed of information transmission when using the “best” (optimal) source, encoder and decoder for a given channel, so it characterizes only the channel.

Throughput of a discrete (digital) channel without interference

C = log(m) bits/symbol

where m is the base of the signal code used in the channel. Information transfer speed discrete channel without noise (ideal channel) is equal to its capacity when the symbols in the channel are independent and all m symbols of the alphabet are equally probable (used equally often).

Neural Network Bandwidth

The throughput of a neural network is the arithmetic average between the volumes of processed and created information neural network per unit of time.

throughput - highest speed data transmission equipment from which information enters the storage device without loss while maintaining the sampling speed and analogue digital transformation. for devices with parallel bus architecture, throughput... ... Dictionary of concepts and terms formulated in regulatory documents of Russian legislation

Parameter name	Meaning
Article topic:	Bandwidth
Rubric (thematic category)	Technologies

The main task for which any network is built is the rapid transfer of information between computers. For this reason, criteria related to the capacity of a network or part of a network are a good indicator of how well the network performs its primary function.

Exists a large number of options for defining criteria of this type, just as in the case of criteria of the “reaction time” class. These options may differ from each other: the selected quantity unit transmitted information, the nature of the data taken into account - only user data or user data together with service data, the number of measurement points of transmitted traffic, the method of averaging the results for the network as a whole. Let's consider various ways constructing the capacity criterion in more detail.

Criteria that differ in the unit of measurement of transmitted information. The unit of measurement of transmitted information is usually packets (or frames, later these terms will be used interchangeably) or bits. Accordingly, throughput is measured in packets per second or bits per second.

Because computer networks work on the principle of packet (or frame) switching, then measuring the amount of transmitted information in packets makes sense, especially since the throughput of communication equipment operating on link level and higher, also most often measured in packets per second. At the same time, due to the variable packet size (this is typical for all protocols except ATM, which has a fixed packet size of 53 bytes), measuring throughput in packets per second is associated with some uncertainty - packets of which protocol and of what size mean? Most often they mean packets of the Ethernet protocol, as the most common one, having a minimum protocol size of 64 bytes (without preamble). Packets of minimum length were chosen as reference packets due to the fact that they create the most difficult operating mode for communication equipment - the computational operations performed with each arriving packet depend very little on its size, and therefore processing per unit of transferred information A packet of minimum length requires many more operations to be performed than a packet of maximum length.

Bandwidth measurement in bits per second (for local networks speeds measured in millions of bits per second - Mb/s are more typical) gives a more accurate estimate of the speed of transmitted information than when using packets.

Criteria differing in consideration official information. Any protocol has a header that carries service information, and a data field that carries information considered for of this protocol custom. For example, in an Ethernet protocol frame of minimum size, 46 bytes (out of 64) represent the data field, and the remaining 18 are service information. When measuring throughput in packets per second, it is impossible to separate user information from service information, but when measuring bitwise, it is possible.

If throughput is measured without dividing information into user and service, then in this case You cannot set the task of choosing a protocol or protocol stack for a given network. This is explained by the fact that even if when replacing one protocol with another we get higher network throughput, this does not mean that the network will work faster for end users - if the share of service information per unit of user data for these protocols are different (and in general this is true), then you can choose a slower network option as the optimal one. If the protocol type does not change when setting up the network, then you can use criteria that do not separate user data from the general flow.

When testing network throughput on application level The easiest way to measure throughput is by user data. To do this, it is enough to measure the time it takes to transfer a file of a certain size between the server and the client and divide the file size by the resulting time. To measure the overall throughput, special measurement tools are required - protocol analyzers or SNMP or RMON agents built into operating systems, network adapters or communications equipment.

Criteria that differ in the number and location of measurement points. Bandwidth can be measured between any two nodes or points on the network, for example, between client computer 1 and server 3 in the example shown in Figure 1.2. In this case, the resulting throughput values will change under the same network operating conditions based on the two points between which measurements are taken. Since the network simultaneously works big number user computers and servers, then full description network throughput gives a set of throughputs measured for various combinations interacting computers - the so-called traffic matrix of network nodes. Exist special means measurements that record the traffic matrix for each network node.

Since in networks data on the way to the destination node usually passes through several transit intermediate processing stages, the throughput of an individual intermediate network element - a separate channel, segment or communication device - can be considered as an efficiency criterion.

Knowing the total throughput between two nodes cannot provide complete information O possible ways its increase, since from the total figure it is impossible to understand which of the intermediate stages of packet processing slows down the network to the greatest extent. For this reason, throughput data individual elements networks can be useful for deciding how to optimize it.

In the example under consideration, packets on the path from client computer 1 to server 3 pass through the following intermediate network elements:

Segment AR SwitchR Segment BR Router R Segment CR RepeaterR Segment D.

Each of these elements has a certain throughput, therefore the total network throughput between computer 1 and server 3 will be equal to the minimum throughput of the route components, and the transmission delay of one packet (one of the options for determining the response time) will be is equal to the sum of the delays introduced by each element. To increase the throughput of a multipart path, you need to first pay attention to the slowest elements - in this case, such an element will most likely be the router.

It makes sense to define the total network throughput as the average amount of information transmitted between all network nodes per unit of time. Total network throughput can be measured in either packets per second or bits per second. When dividing a network into segments or subnets, the total network capacity is equal to the sum of the subnets' capacities plus the capacity of inter-segment or inter-network links.

Throughput - concept and types. Classification and features of the category "Throughput" 2017, 2018.

- A 30 MB file is transferred over the network in 24 seconds. The network capacity is

About 10 Mbit/s 261. A photograph of the CD reader is shown in the figure. O 4 O 1 O 2 O +3 X 228. Chronological sequence of appearance operating systems : a) MS DOS b) Windows XP c) Windows "98 d) Windows Vista

O +a), c), b), d) The characteristics of the field in the databases are not... .

It is determined by the distance between adjacent moving trains. The shorter this distance, the greater the line capacity. On this moment There are two types of metro lines: lines with automatic blocking and protective sections of the line with normal... .

O +a), c), b), d) The characteristics of the field in the databases are not... .

It is determined by the distance between adjacent moving trains. The shorter this distance, the greater the line capacity. At the moment, there are two types of metro lines: lines with automatic blocking and protective sections of the line with normal... [read more].

- Road capacity, models and calculation methods

Throughput – the number that can be passed by the AD, providing the necessary safety and convenience for movement.

PS can be: - theoretical; -practical.

Theoretical PS is defined as the ratio of the time period T under consideration to the time that... .

- Capacity of export gas pipelines on the former border of the USSR, billion cubic meters per year Gas pipeline Capacity Export direction Through Ukraine: Orenburg-Western border (Uzhgorod) Slovakia, Czech Republic, Austria, Germany, France, Switzerland, Slovenia, Italy Urengoy-Uzhgorod Slovakia, Czech Republic, Austria,... . The channel capacity is called

maximum value

the speed of information transmission over this channel. That is, throughput characterizes the potential for transmitting information. Channel throughput is measured in bits per second (bps).

From the relationship it is clear that if the signal power were not limited, then the throughput would be infinitely large. Bandwidth is zero when the signal-to-noise ratio P s / P w is equal to zero. As this ratio increases, the throughput increases indefinitely. This is impossible. Here H"(a) is the performance of a source with a given speed or the performance of a transmitter for a controlled source. Therefore, in order for the discrete information transmission system to be economical (effective), it is necessary to coordinate the source of the message with the channel. Since the performance of the information source H"(a ) is usually given, then two cases are of greatest interest: H"(a)C and H"(a)

In the first case, the transmitter and receiver can be very simple, and therefore cheap, since if the channel capacity greatly exceeds the source performance, you can limit yourself to the simplest methods of transmission (coding, modulation) and reception (decision circuits) and obtain sufficient fidelity . However, this uses a very expensive channel, since a wide frequency band or a high signal-to-noise ratio is expensive.

In the second case, a cheaper channel with lower capacity can be used, but more advanced transmission and reception methods are required, i.e. more expensive transmitter and receiver. From the above it follows that there must be an optimal ratio of C and H"(a), at which the total cost of the discrete information transmission system is minimal. When determining this minimum, it should be taken into account that, with the development of electronic technology, the cost of transceivers decreases faster than the cost of communication channels , i.e., over time the ratio C/H"(a) decreases.

In this case, the channel capacity is greater than the source capacity, so this channel can be used to transmit analog and digital signals. The channel capacity reserve, compared to the source capacity, could be used to apply statistical or noise-resistant coding.

There are many factors that can distort or damage a signal. The most common of these is interference or noise, which is any unwanted signal that mixes with and distorts the signal intended to be transmitted or received. For digital data, the question arises: to what extent do these distortions limit the possible data transfer rate? The maximum possible speed under certain conditions at which information can be transmitted along a specific communication path, or channel, is called pass ability channel.

There are four concepts that we will try to tie together.

Data transfer rate - the speed in bits per second (bit/s) at which you can

transmit data;

Bandwidth - the bandwidth of the transmitted signal, limited by transmission to ohms and the nature of the transmitting medium.

It is expressed in periods in seconds, or hertz (Hz).

Noise. Average noise level in the communication channel.

Error level – frequency of occurrence of errors and side effects.

An error is considered to be the reception of 1 and the transmission of 0 and vice versa.

The problem is this: communications are not cheap and, in general, the wider their bandwidth, the more expensive they are. Moreover, all transmission channels of practical interest have limited bandwidth. Limitations are caused by the physical properties of the transmission medium or by deliberate bandwidth limitations in the transmitter itself, made to prevent interference with other sources.

Naturally, we would like to make the most efficient use of the available bandwidth. For digital data, this means that for a certain band it is desirable to obtain the maximum possible data rate given the existing error level. The main limitation in achieving such efficiency is interference.

Methods of accessing the medium in wireless networksOne of the main problems in building wireless systems is solving the problem of access of many users to a limited resource of the transmission medium. There are several basic access methods (also called multiplexing or multiplexing methods), based on the division of parameters such as space, time, frequency and code between stations. The purpose of multiplexing is to allocate space, time, frequency and/or code to each communication channel with a minimum of mutual interference and maximum use of the characteristics of the transmission medium.Seal

with spatial division Based on the separation of signals in space when the transmitter sends a signal using a code With , time t and frequency f in area

For example, if a radio station broadcasts on a strictly defined frequency in its assigned territory, and some other station in the same area also starts broadcasting on the same frequency, then radio listeners will not be able to receive a “clean” signal from any of these stations . It’s another matter if radio stations operate on the same frequency in different cities. There will be no distortion of the signals of each radio station due to the limited range of propagation of the signals of these stations, which eliminates their overlap with each other. A typical example is cellular telephone systems.

Methods of accessing the medium in wireless networkswith frequency sectionltion(Frequency Division Multiplexing, FDM)

Each device operates at a strictly defined frequency, thanks to which several devices can transmit data in one territory (Figure 3.2.6). This is one of the most well-known methods, one way or another used in the most modern wireless communication systems.

Figure 3.2.6 – Principle of frequency division of channels

A clear illustration of a frequency multiplexing scheme is the operation of several radio stations operating at different frequencies in one city. To reliably detune from each other, their operating frequencies must be separated by a protective frequency interval to prevent mutual interference.

This scheme, although it allows the use of multiple devices in a given area, itself leads to unnecessary waste of usually scarce frequency resources, since it requires the allocation of a separate frequency for each wireless device.

Methods of accessing the medium in wireless networkswith temporary sectionelaziness(Time Division Multiplexing, TDM)

In this scheme, the distribution of channels occurs in time, i.e. each transmitter broadcasts a signal at the same frequency t in area f, but at different periods of time With i (usually cyclically repeating) with strict requirements for synchronization of the transmission process (Figure 3.2.7).

Figure 3.2.7 – Principle of time division of channels

This scheme is quite convenient, since time intervals can be dynamically redistributed between network devices. Devices with more traffic are assigned longer intervals than devices with less traffic.

The main disadvantage of time multiplex systems is the instant loss of information when synchronization in the channel is lost, for example, due to strong interference, accidental or intentional. However, successful experience in operating such famous TDM systems as GSM cellular telephone networks indicates the sufficient reliability of the time multiplex mechanism.

Methods of accessing the medium in wireless networkscode-separated(Code Division Multiplexing, CDM)

In this scheme, all transmitters transmit signals at the same frequency t , in area f and during With, but with different codes c i.

The name of the CDM-based channel separation mechanism (CDMA, CDM Access)

the IS-95a cellular telephone standard has even been named, as well as a number of standards for the third generation of cellular communication systems (cdma2000, WCDMA, etc.).

In the CDM scheme, each transmitter replaces each bit of the original data stream with a CDM symbol - a code sequence of length 11, 16, 32, 64, etc. bits (they are called chips). The code sequence is unique for each transmitter. As a rule, if a certain CDM code is used to replace “1” in the original data stream, then to replace “0” the same code is used, but inverted.

The receiver knows the CDM code of the transmitter whose signals it must receive. It constantly receives all signals and digitizes them. Then, in a special device (correlator), it performs the operation of convolution (multiplication with accumulation) of the input digitized signal with the CDM code known to it and its inversion. In a somewhat simplified form, this looks like the operation of the scalar product of the input signal vector and the vector with the CDM code.

If the signal at the correlator output exceeds a certain set threshold level, the receiver considers that it has received a 1 or 0. To increase the probability of reception, the transmitter can repeat sending each bit several times. In this case, the receiver perceives signals from other transmitters with other CDM codes as additive noise.

Moreover, due to high redundancy (each bit is replaced by dozens of chips), the received signal power can be comparable to the integrated noise power. The similarity of CDM signals to random (Gaussian) noise is achieved using CDM codes generated by a pseudorandom sequence generator. Therefore, this method is also called the method of spreading the signal spectrum using direct sequence (DSSS - Direct Sequence Spread Spectrum), spectrum spreading will be discussed below.

The strongest aspect of this seal lies in the increased security and secrecy of data transmission: without knowing the code, it is impossible to receive a signal, and in some cases, to detect its presence. In addition, the code space is incomparably larger compared to the frequency multiplexing scheme, which makes it possible to assign each transmitter its own individual code without any problems.

Until recently, the main problem of code multiplexing was the complexity of the technical implementation of receivers and the need to ensure accurate synchronization of the transmitter and receiver to ensure guaranteed receipt of the packet.

Multiplexing mechanism via orthogonal carrier frequencies (OrthogonalFrequencyDivisionMultiplexing, OFDM)

The entire available frequency range is divided into quite a few subcarriers (from several hundred to thousands). One communication channel (receiver and transmitter) is assigned for transmission several such carriers, selected from the entire set according to a certain law. Transmission is carried out simultaneously on all subcarriers, i.e. in each transmitter the outgoing data stream is divided into N substreams, where N– the number of subcarriers assigned to this transmitter.

The distribution of subcarriers can change dynamically during operation, which makes this mechanism no less flexible than the time multiplexing method.

The OFDM scheme has several advantages. First, only some subchannels will be subject to selective fading, not the entire signal. If the data stream is protected by forward error correction code, then this fading is easy to combat. But more importantly, OFDM allows intersymbol interference to be suppressed. Intersymbol interference has a significant impact at high data rates because the distance between bits (or symbols) is small.

In the OFDM scheme, the data transmission rate is reduced by N times, which allows you to increase the symbol transmission time by N once. Thus, if the symbol transmission time for the source stream is T s , then the period of the OFDM signal will be equal to NT s. This allows you to significantly reduce the impact of intersymbol interference. When designing a system N is chosen so that the value NT s significantly exceeded the root-mean-square spread of channel delays.

Throughput of information transmission systems

One of the main characteristics of any information transmission system, in addition to those listed above, is its throughput.

Bandwidth – the maximum possible amount of useful information transmitted per unit of time:

c = max(Imax) / TC ,

c = [bit/s].

Sometimes the information transmission rate is defined as the maximum amount of useful information in one elementary signal:

s = max(Imax) / n,

s = [bit/element].

The considered characteristics depend only on the communication channel and its characteristics and do not depend on the source.

Throughput of a discrete communication channel without interference. In a communication channel without interference, information can be transmitted using a non-redundant signal. In this case, the number n = m, and the entropy of the elementary signal HCmax = logK.

max(IC) = nHCmax= mHCmax .

Duration of an elementary signal, where is the duration of an elementary signal.

where FC is the signal spectrum.

Communication channel capacity without interference

Let us introduce the concept of the rate of generation of an elementary signal by a source of information:

Then, using the new concept, we can transform the formula for the information transmission speed:

The resulting formula determines the maximum possible speed of information transmission in a discrete communication channel without interference. This follows from the assumption that the entropy of the signal is maximum.

If H.C.< HCmax, то c = BHC и не является максимально возможной для данного канала связи.

Capacity of a discrete communication channel with interference. In a discrete communication channel with noise, the situation shown in Fig. 6.

Taking into account the property of additivity, as well as Shannon’s formulas for determining the amount of information discussed above, we can write

IC = TC FC log(AK PC),

IPOM = TP FP log(APP).

For the recipient, the source of useful information and the source of interference are equivalent, therefore, on the receiving side it is impossible to isolate the interference component in the signal with the resulting information

IRES = TC FC log(AK (PP + PC)), if TC = TP, FC = FP.

The receiver may be narrowband, and the interference may be in other frequency ranges. In this case, it will not affect the signal.

We will determine the resulting signal for the most “unpleasant” case, when the signal and noise parameters are close to each other or coincide. Useful information is determined by the expression

This formula was obtained by Shannon. It determines the speed of information transmission over a communication channel if the signal has PC power and the interference has PP power. All messages at this speed will be transmitted with absolute reliability. The formula does not answer the question of how to achieve such a speed, but it gives the maximum possible value of c in a communication channel with interference, that is, the value of the transmission speed at which the received information will be absolutely reliable. In practice, it is more economical to allow a certain amount of error in the message, although the transmission speed will increase.

Consider the case PC >> PP. If we introduce the concept of signal-to-noise ratio

PC >> PP means that . Then

The resulting formula reflects the maximum speed of a powerful signal in the communication channel. If PC<< PП, то с стремится к нулю. То есть сигнал принимается на фоне помех. В таком канале в единицу времени сигнал получить не удается. В реальных ситуациях полностью помеху отфильтровать нельзя. Поэтому приемник получает полезную информацию с некоторым набором ошибочных символов. Канал связи для такой ситуации можно представить в виде, изображенном на рис. 7, приняв источник информации за множество передаваемых символов {X}, а приемник – за множество получаемых символов {Y}.

Fig.7 Graph of transition probabilities of a K-ary communication channel

There is a certain one-to-one correspondence between. If there is no interference, then the probability of a one-to-one match is equal to one, otherwise it is less than one.

If qi is the probability of mistaking yi for xi, and pij = p(yi / xi) is the probability of error, then

The transition probability graph reflects the final result of the influence of interference on the signal. As a rule, it is obtained experimentally.

Useful information can be estimated as IPOL = nH(X · Y), where n is the number of elementary symbols in the signal; H(X Y) – mutual entropy of source X and source Y.

In this case, source X is the source of useful information, and source Y is the receiver. The relationship that determines useful information can be obtained based on the meaning of mutual entropy: the shaded section of the diagram determines the messages transmitted by source X and received by receiver Y; unshaded areas represent signals from source X that did not reach the receiver and extraneous signals received by the receiver that were not transmitted by the source.

B is the rate of generation of elementary symbols at the source output.

To obtain max, you need to increase H(Y) and decrease H(Y/X) if possible. Graphically, this situation can be represented by combining circles on the diagram (Fig. 2d).

If the circles do not intersect at all, X and Y exist independently of each other. In the following we will show how the general expression for the maximum transmission rate can be used when analyzing specific communication channels.

When characterizing a discrete channel, two concepts of speed are used: technical and information.

The technical transmission rate RT, also called the keying rate, refers to the number of symbols (elementary signals) transmitted over a channel per unit time. It depends on the properties of the communication line and the speed of the channel equipment.

Taking into account differences in the duration of symbols, the technical speed is determined as

where is the average symbol duration time.

The unit of measurement is "baud" - this is the speed at which one character is transmitted per second.

Information speed or information transmission rate is determined by the average amount of information that is transmitted over a channel per unit of time. It depends both on the characteristics of a particular channel (such as the volume of the alphabet of symbols used, the technical speed of their transmission, the statistical property of interference in the line), and on the probabilities of symbols arriving at the input and their statistical relationship.

With a known manipulation speed, the speed of information transmission over the channel is given by the relation:

where is the average amount of information carried by one symbol.

For practice, it is important to find out to what extent and in what way the speed of information transmission over a specific channel can be increased. The maximum capabilities of a channel for transmitting information are characterized by its throughput.

The channel capacity with given transition probabilities is equal to the maximum transmitted information over all input symbol distributions of source X:

From a mathematical point of view, searching for the capacity of a discrete channel without memory comes down to searching for the probability distribution of input symbols of source X, which ensures maximum transmitted information. At the same time, a restriction is imposed on the probabilities of input symbols: , .

In general, determining the maximum under given restrictions is possible using Lagrange's multiplicative method. However, such a solution is prohibitively expensive.

In the particular case of discrete symmetric channels without memory, the throughput (maximum ) is achieved with a uniform distribution of input symbols of the source X.

Then for a DSC without memory, considering the error probability ε as given and for equally probable input symbols = = = =1/2, we can obtain the capacity of such a channel using the well-known expression for:

where = is the entropy of a binary symmetric channel for a given error probability ε.

Boundary cases are of interest:

1. Transmission of information over a silent channel (without interference):

, [bit/character].

With fixed basic technical characteristics of the channel (for example, frequency band, average and peak transmitter power), which determine the value of the technical speed, the throughput of the channel without interference will be equal to [bit/sec].

What is the bandwidth of communication channels. Bandwidth Calculation

see also

Borkolabovskaya Icon of the Mother of God

Throughput of information transmission systems