Expansion of the spectrum by frequency hopping. Direct serial spread spectrum. Code Division Multiple Access. Frequency hopping spectrum extension Frequency hopping spectrum extension (Fr

Initially, the spread spectrum method was created for intelligence and military purposes. The main idea of the method is to distribute the information signal over a wide radio band, which ultimately makes it much more difficult to suppress or intercept the signal. The first spread spectrum scheme developed is known as frequency hopping technique. A more modern spread spectrum scheme is the direct serial spread method. Both methods are used in various wireless standards and products.

Frequency Hopping Spread Spectrum (FHSS)

To ensure that radio traffic could not be intercepted or suppressed by narrow-band noise, it was proposed to transmit with a constant change of carrier within a wide frequency range. As a result, the signal power was distributed over the entire range, and listening to a specific frequency produced only a small noise. The sequence of carrier frequencies was pseudo-random, known only to the transmitter and receiver. An attempt to suppress a signal in a certain narrow range also did not degrade the signal too much, since only a small part of the information was suppressed.

The idea of this method is illustrated in Fig. 1.10.

For a fixed period of time, transmission is carried out on a constant carrier frequency. At each carrier frequency, standard modulation methods such as FSK or PSK are used to transmit discrete information. In order for the receiver to synchronize with the transmitter, sync bits are transmitted for a period of time to indicate the start of each transmission period. So the useful speed of this encoding method is less due to the constant synchronization overhead.

Rice. 1.10. Spectrum expansion by frequency hopping

The carrier frequency changes in accordance with the numbers of frequency subchannels generated by the pseudo-random number algorithm. The pseudorandom sequence depends on some parameter called initial number. If the receiver and transmitter know the algorithm and the value of the seed, then they change frequencies in the same sequence, called a pseudo-random frequency hopping sequence.

If the frequency of subchannel changes is lower than the data transmission rate in the channel, then this mode is called slow spectrum expansion(Fig. 1.11a); otherwise we are dealing with rapid spectrum expansion(Fig. 1.11b).

The fast spread spectrum method is more resistant to interference because the narrowband interference that suppresses the signal in a particular subchannel does not result in bit loss because its value is repeated several times in different frequency subchannels. In this mode, the effect of intersymbol interference does not appear, because by the time the signal delayed along one of the paths arrives, the system has time to switch to another frequency.

The slow spectrum spreading method does not have this property, but it is simpler to implement and involves less overhead.

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Rice. 1.11. Relationship between data rate and subchannel change frequency

FHSS methods are used in IEEE 802.11 and Bluetooth wireless technologies.

In FHSS, the approach to using the frequency range is different from other encoding methods - instead of economically using a narrow bandwidth, an attempt is made to occupy the entire available range. At first glance, this does not seem very effective - after all, only one channel is operating in the range at any given time. However, the latter statement is not always true - spread spectrum codes can also be used to multiplex multiple channels over a wide range. In particular, FHSS methods allow you to organize the simultaneous operation of several channels by selecting such pseudo-random sequences for each channel so that at each moment of time each channel operates at its own frequency (of course, this can only be done if the number of channels does not exceed the number of frequency subchannels).

Direct Sequence Spread Spectrum (DSSS)

Direct Sequential Spread Spectrum also uses the entire frequency range allocated to a single wireless link. Unlike the FHSS method, the entire frequency range is occupied not by constant switching from frequency to frequency, but by replacing each bit of information with N-bits, so that the clock speed of signal transmission increases by N times. And this, in turn, means that the signal spectrum also expands N times. It is enough to select the data rate and N value appropriately so that the signal spectrum fills the entire range.

The purpose of DSSS coding is the same as FHSS - to increase immunity to interference. Narrowband interference will distort only certain frequencies of the signal spectrum, so that the receiver is likely to be able to correctly recognize the transmitted information.

The code that replaces the binary unit of the original information is called spreading sequence, and each bit of such a sequence is a chip.

Accordingly, the transmission rate of the resulting code is called chip speed. A binary zero is encoded by the inverse of the spreading sequence. Receivers must know the spreading sequence that the transmitter uses in order to understand the information being transmitted.

The number of bits in the spreading sequence determines the spreading factor of the source code. As with FHSS, any type of modulation, such as BFSK, can be used to encode the bits of the result code.

The larger the spreading factor, the wider the spectrum of the resulting signal and the higher the degree of interference suppression. But at the same time, the spectrum occupied by the channel increases. Typically the expansion factor ranges from 10 to 100.

1.1. Brief description of the extension of the spectrum of signals by the frequency hopping method

1.1.1. Basic principles and methods of signal widening

In the case when researchers and developers of radio communication systems (RCS) are faced with the problem of ensuring reliable communication in conditions of organized and unintentional interference, multipath propagation of radio waves, as well as implementation of multiple access when working in packet radio networks, the best results can be obtained when used in RCS spread spectrum signals. The basic principles of known methods for spreading the spectrum of signals, which adequately reflect their physical essence, are given in: ...spreading the spectrum of a signal is a transmission method in which the signal occupies a frequency band that is wider than the band minimally necessary for transmitting information; extension of the signal frequency band is provided by a special code that does not depend on the transmitted information; for subsequent compression of the signal frequency band and data recovery, a special code is also used in the receiving device, similar to the code in the CPC transmitter and synchronized with it... Thus, the method of transmitting information with spread spectrum consists of: on the transmitting side - in simultaneous and independent modulation of parameters signal with a special code (spreading the spectrum function) and a transmitted message; on the receiving side - in synchronous demodulation of the signal in accordance with the spectrum spreading function and restoration of the transmitted message.

Despite the fact that the principles of expanding the spectrum of signals in general form were known already in the 20-30s of the 20th century, the theoretical basis for the development of SRS with such signals was the fundamental formula of K.E. Shannon

which, characterizing the limiting capabilities of a Gaussian channel, radically expands the understanding of the possibility of transmitting information over radio communication channels with band-limited additive white Gaussian noise (AWGN).

Thus, from (1.1) it follows that the capacity (bit/s) of a radio communication channel, after it is specified, under the influence of additive Gaussian interference (noise) with limited average power (W) can be ensured either by using a wide frequency band ( Hz) with a low signal-to-interference ratio, or - a narrow frequency band (Hz) with a higher signal-to-interference ratio, where is the average signal power. Therefore, there can be a trade-off between the channel bandwidth and the signal-to-interference ratio of that channel. In this case, in accordance with dependence (1.1), the most appropriate is to exchange the signal power for the channel bandwidth. For example, it is required to provide bit/s throughput with signal-to-noise ratio =. Based on (1.1), the radio communication channel must have a MHz bandwidth. With a larger signal-to-interference ratio, for example, the capacity of the radio communication channel bit/s can be realized in a fairly narrow kHz frequency band. Formula (1.1) also indicates that for a given signal-to-interference ratio in a radio communication channel with AWGN, the throughput can be increased by correspondingly expanding the signal spectrum.

For small signal-to-noise ratios, expression (1.1) takes the form:

(1.2a)

where 1.44 is the modulus of transition from binary logarithms to natural ones; in the case of large ratios, it follows from (1.1) with a good approximation that

. (1.2b)

The maximum capacity for a Gaussian radio communication channel is at

, (1.2v)

where is the one-way power spectral density of white noise.

Expression (1.2c) indicates that in a noisy channel, even in the limiting case at, the signal-to-interference ratio must exceed a certain threshold value. So, to transmit a bit of information, the required signal energy is (or).

If the throughput is equal to the required information transmission rate, then from (1.1) and (1.2) it is clear that the radio communication channel can operate with a significant excess of the interference power over the useful signal power. Therefore, methods for expanding the spectrum of signals are widely used in special SRS, which must provide reliable communication in conditions of electronic jamming (ERS).

Spread spectrum methods can be based on changing (modulating) the amplitude, phase, frequency and temporal position (delay) of the signal in accordance with a special code generated based on a pseudo-random sequence.

However, amplitude modulation is, as a rule, not used to generate a spread spectrum signal, since this produces a signal with a large peak (instantaneous) power, which is quite easily detected by simple receivers of radio reconnaissance stations (RTR).

Due to insufficient noise immunity, the method of expanding the spectrum by modulating the temporal position (delay) of the signal, the so-called pseudo-random time-pulse modulation (PVPM) method, does not find independent application in CRS. With the PVIM method, spectrum expansion is achieved by compressing the information signal in the time domain. Reducing the transmission time of each information signal by a factor leads to an expansion of the signal spectrum by a factor and reduces the total transmission time. Information is transmitted only at specified time intervals, which follow each other in accordance with the selected code. When using the PVIM method, as well as the method of spreading the spectrum due to amplitude modulation, a large crest factor occurs, which leads to wasted power consumption of the SRS transmitter.

The main, basic methods for expanding the spectrum of signals, widely used in modern SRS, control and information distribution systems, are:

Method of direct modulation of a carrier by a pseudo-random sequence (PSR);

Method of pseudo-random tuning of operating frequency (PRFC);

Method of joint (integrated) use of various methods; for example, the method of direct modulation of the PSP carrier and the frequency hopping method; the PPRF method and the PVIM method and other combinations.

In the first method, broadening the signal spectrum is achieved through direct modulation of the PSP carrier frequency, the elements of which are generated at a speed significantly higher than the transmission rate of elements of the information sequence, and then superimposed on each information symbol. A typical example of such signals are phase-shift keyed wideband signals (WWPS). With a rectangular shape of the elements of the information sequence and using the PSP, which ensures expansion of the signal spectrum, the binary PMSHPS can be described by the expression

Figure 1.4, a, b shows in an idealized form the spectral power densities of the signal and narrow-band interference at characteristic points of the structural diagrams of the transmitter and receiver of the SRS with FMSPS.

In Fig. Figure 1.4 shows how the spectrum of the useful signal is converted and the spectrum of narrowband interference is expanded in the transmitting and receiving devices of the SRS with FMSPS.

Spread Spectrum Methods

Initially, spread spectrum methods (PC or SS - Spread-Spectrum) were used in the development of military control and communications systems. During World War II, spread spectrum was used in radar to combat intentional interference. In recent years, the development of this technology is explained by the desire to create effective radio communication systems to ensure high noise immunity when transmitting narrow-band signals over noisy channels and complicating their interception.

The communication system is a spread spectrum system in the following cases:

The frequency band used during transmission is much wider than the minimum required for transmitting current information. In this case, the energy of the information signal expands over the entire frequency band with a low signal-to-noise ratio, making the signal difficult to detect, intercept, or interfere with its transmission by introducing interference. Although the total signal power can be large, the signal-to-noise ratio in any frequency range is small, making the spread spectrum signal difficult to detect over radio communications and, in the context of information hiding by steganographic techniques, difficult to discern by humans.

Spreading the spectrum is performed using a so-called spreading (or code) signal, which is independent of the information being transmitted. The presence of signal energy in all frequency ranges makes the spread spectrum radio signal resistant to interference, and the information embedded in the container using the spread spectrum method is resistant to its elimination or removal from the container. Compression and other attacks on a communications system can remove signal energy from some portions of the spectrum, but because the energy has been spread across the entire spectrum, there is still enough data in other bands to recover the information. As a result, if, of course, you do not disclose the key that was used to generate the code signal, the likelihood of unauthorized persons extracting information is significantly reduced.

Reconstruction of the primary information (that is, “narrowing of the spectrum”) is carried out by comparing the received signal and a synchronized copy of the code signal.

There are three main methods of spectrum extension used in radio communications:

Using direct PSP (RSPP);

Using frequency hopping;

Using compression using linear frequency modulation (LFM).

When spreading the spectrum by direct sequence, the information signal is modulated by a function that takes pseudo-random values within established limits and is multiplied by a time constant - the frequency (speed) of repetition of elementary parcels (signal elements). This pseudo-random signal contains components at all frequencies, which, when expanded, modulate the signal energy over a wide range.

In the frequency hopping spread spectrum method, the transmitter instantly changes one frequency of the carrier signal to another. The secret key in this case is the pseudo-random law of frequency changes.

With chirp compression, the signal is modulated by a function whose frequency varies over time.

It is obvious that any of these methods can be extended to use in the spatial domain when constructing steganographic systems.

Let's consider one of the options for implementing the RSPP method, the authors of which are J.R. Smith and V.O. Comiskey. The modulation algorithm is as follows: each bit of the message is represented by some basis function, dimension, multiplied, depending on the value of the bit (1 or 0), by +1 or -1:

(11.7)

The modulated message received in this case is summed pixel-by-pixel with a container image, which is a halftone image of size . The result is a steched image, with .

Idea of the method frequency hopping spectrum extension Frequency Hopping Spread Spectrum (FHSS) originated during World War II, when radio was widely used for secret communications and control of military assets such as torpedoes. To ensure that radio traffic could not be intercepted or suppressed by narrow-band noise, it was proposed to transmit with a constant change of carrier within a wide frequency range. As a result, the signal power was distributed over the entire range, and listening to a specific frequency produced only a small amount of noise. The sequence of carrier frequencies was chosen pseudo-randomly, known only to the transmitter and receiver. An attempt to suppress a signal in a certain narrow range also did not degrade the signal too much, since only a small part of the information was suppressed.

The idea of this method is illustrated in Fig. 10.12.

Rice. 10.12. Spectrum expansion by frequency hopping

During a certain fixed time interval, transmission is carried out on a constant carrier frequency. At each carrier frequency, standard modulation methods such as FSK or PSK are used to transmit discrete information. To keep the receiver synchronized with the transmitter, sync bits are transmitted for a period of time to indicate the start of each transmission period. So the useful speed of this encoding method is less due to the constant synchronization overhead.

The carrier frequency changes in accordance with the numbers of frequency subchannels generated by the pseudo-random number algorithm. The pseudorandom sequence depends on some parameter called starting number. If the receiver and transmitter know the algorithm and the value of the initial number, then they change frequencies in the same sequence, called sequence of pseudo-random frequency tuning.

If the frequency of subchannel changes is lower than the data transmission rate in the channel, then this mode is called slow spectrum expansion(Fig. 10.13, a); otherwise we are dealing with rapid spectrum expansion(Fig. 10.13, b).

Rice. 10.13. Relationship between data rate and subchannel change frequency

The slow spectrum spreading method does not have this property, but it is easier to implement and has lower overhead costs.

FHSS methods are used in IEEE 802.11 and Bluetooth wireless technologies. In FHSS methods, the approach to using the frequency range is different from other coding methods - instead of economically using a narrow bandwidth, an attempt is made to occupy the entire available range. At first glance, this does not seem very effective - after all, only one channel is operating in the range at any given time. However, the latter statement is not always true, since spread spectrum codes can also be used to multiplex multiple channels over a wide range. In particular, FHSS methods make it possible to organize the simultaneous operation of several channels by selecting for each channel such pseudo-random sequences that at each moment of time give each channel the opportunity to operate at its own frequency (of course, this can only be done if the number of channels does not exceed the number of frequency subchannels) .

In order to send a high-power radio signal in the microwave range, you need an expensive transmitter with an amplifier and an expensive large-diameter antenna. In order to receive a low-power signal without interference, you also need an expensive large antenna and an expensive receiver with an amplifier.

This is the case when using a conventional “narrowband” radio signal, when transmission occurs at one specific frequency, or more precisely, in a narrow band of the radio spectrum surrounding this frequency (frequency channel). The picture is further complicated by various mutual interferences between high-power narrowband signals transmitted close to each other or at similar frequencies. In particular, a narrowband signal can simply be jammed (accidentally or intentionally) by a transmitter of sufficient power tuned to the same frequency.

It was this vulnerability to interference from conventional radio signals that led to the development, initially for military applications, of a completely different radio transmission principle called Spread Spectrum or Spread Spectrum technology. After many years of successful defense use, this technology has found civilian applications, and it is in this capacity that it will be discussed here.

It was found that in addition to its characteristic properties (its own noise immunity and low level of generated interference), this technology turned out to be relatively cheap for mass production. Cost-effectiveness occurs due to the fact that all the complexity of broadband technology is programmed into several microelectronic components (“chips”), and the cost of microelectronics in mass production is very low. As for the remaining components of broadband devices - microwave electronics, antennas - they are cheaper and simpler than in the usual “narrowband” case, due to the extremely low power of the radio signals used.

The idea of Spread Spectrum is that a much wider frequency band is used to transmit information than is required for conventional (in a narrow frequency channel) transmission. Two fundamentally different methods for using such a wide frequency band have been developed - the Direct Sequence Spread Spectrum (DSSS) method and the Frequency Hopping Spread Spectrum (FHSS) method. Both of these methods are provided by the 802.11 (Radio-Ethernet) standard.

The current state of wireless communications is determined by the situation with the IEEE 802.11 standard. The standard is being developed and improved by the Working Group for Wireless Local Area Networks of the Institute of Electrical and Electronic Engineers (IEEE) Standards Committee, chaired by Vic Hayes of Lucent Technologies. . The group has about a hundred members with a decisive vote and about fifty with an advisory vote; they represent virtually all equipment manufacturers, as well as research centers and universities. Four times a year, the group meets in plenary sessions and makes decisions to improve the standard.

The standard defines one type of MAC layer media access protocol and three different protocols for physical (PHY) links.

The MAC layer defines the basic components of the network architecture and the list of services provided by this layer. There are two typical wireless network architectures:

Independent “ad-hoc” configuration, where stations can communicate directly with each other. The area of such a network and functionality are limited.

An infrastructure configuration in which stations communicate through an access point, either operating stand-alone or connected to a cable network. The standard defines the radio channel interface between stations and the access point. Access points can be connected to each other using radio bridges or cable network segments.

The standard establishes a protocol for using a single transmission medium, called Carrier Sense Multiple Access Collision Avoidance (CSMA/CA). The likelihood of conflicts for wireless nodes is minimized by first sending all nodes a short message (ready to send, RTS) about the destination and the duration of the upcoming transmission. Nodes delay transmission for a time equal to the advertised message duration. The receiving station responds to the RTS with a message (CTS), which tells the sending node whether the medium is clear and whether the node is ready to receive. After receiving a data packet, the node sends an acknowledgment (ACK) of error-free reception. If the ACK is not received, the data packet will be retransmitted.

The specification provided by the standard requires the data to be divided into packets equipped with control and addressing information. This information, which takes up about 30 bytes, is followed by an information block up to 2048 bytes long. This is followed by a 4-byte CRC code of the information block. The standard recommends using packets of 400 bytes in length for an FHSS physical channel and 1500 or 2048 for a DSSS channel.

The standard provides for data security, including authentication (to verify that a node entering the network is authorized in it) and data encryption using the RC4 algorithm with a 40-bit key. For laptop computers, the standard provides for a power saving mode: putting the device into a “sleep” mode and bringing it out of this state for a short time necessary to receive a service signal from network nodes starting transmission. There is also a roaming mode that allows a mobile subscriber to move between access points without losing connection.

Spectrum extension

At the physical layer, the standard allows the use of one of two types of radio channels and one type of infrared channel. Both types of radio channels use spread spectrum technology, which reduces the average power spectral density of the signal by distributing energy over a wider frequency band than is necessary to provide a given transmission rate. This technology reduces the level of interference generated and provides increased reception immunity to interference.

The first type of radio channel is Frequency Hopping Spread Spectrum (FHSS) Radio PHY. A transfer rate of 1 Mbit/s is provided (optional 2 Mbit/s). The 1 Mbit/s version uses two-level Gaussian frequency modulation (2GFSK), while the 2 Mbit/s version uses four-level Gaussian frequency modulation (4GFSK). At a speed of 1 Mbit/s, the signal frequency changes over a message symbol duration of 1 μs, according to the Gaussian law, from the nominal value to a value of +170 kHz and returns to the nominal value. To transmit zero, the signal frequency is changed to –170 kHz. For 2 Mbps there are four levels of frequency offset (+225, +75, –75, –225 kHz), so each chip (symbol) carries two message bits. The signal spectrum width with such modulation is 1 MHz, regardless of the transmission speed. This makes it possible to use 79 frequency positions for transmission in the range from 2402 to 2480 MHz in 1 MHz steps. To expand the spectrum, the signal frequency changes according to a pseudo-random law at least once every 400 ms.

The second type of radio channel is Direct Sequence Spread Spectrum (DSSS) Radio PHY. This option provides for transmission at speeds of 1 and 2 Mbit/s. At a transfer rate of 1 Mbit/s, binary phase shift keying (BPSK) is used. The one bit is represented by an 11-element Barker code of the form 11100010010, and the zero bit is represented by an inverse Barker code. Elementary symbols of the Barker code do not carry information; bits are transmitted at once by the entire Barker code - direct or inverse. This allows you to give the signal noise properties that provide noise immunity. The spectrum width of such a signal is 22 MHz. For speeds of 2 Mbit/s, the standard provides quadrature phase shift keying - QPSK. In this case, two bits are transmitted during the duration of the message symbol. To do this, you need not two, but four different signals. Therefore, together with the main carrier vibration, an additional one is used, shifted in phase by 90° relative to it. The phase of each of these oscillations is controlled by a direct or inverse Barker sequence, and both oscillations are added. Thus, over the duration of a symbol, the signal has four degrees of freedom, allowing two bits to be transmitted. In this case, the transmission speed is doubled while maintaining the same frequency band as with binary transmission. The DSSS signal uses one of 14 overlapping frequency bands defined by the standard within the overall 83.5 MHz frequency band.

For the infrared channel (Infrared PHY), the standard provides a speed of 1 Mbit/s (optional 2 Mbit/s) with pulse-position modulation. This type of channel is not of great interest, since the transmission range provided for by the standard does not exceed 20 m.

There are several different spread spectrum technologies, but to further understand the 802.11 protocol, we only need to take a closer look at Direct Sequence Spread Spectrum (DSSS).

DSSS technology

With potential coding, information bits - logical zeros and ones - are transmitted as rectangular voltage pulses. A rectangular pulse of duration T has a spectrum whose width is inversely proportional to the pulse duration. Therefore, the shorter the duration of the information bit, the larger the spectrum occupied by such a signal.

To deliberately broaden the spectrum of an initially narrow-band signal, DSSS technology literally embeds a sequence of so-called chips into each transmitted information bit (logical 0 or 1). If information bits - logical zeros or ones - during potential information encoding can be represented as a sequence of rectangular pulses, then each individual chip is also a rectangular pulse, but its duration is several times less than the duration of the information bit. The sequence of chips is a sequence of rectangular pulses, that is, zeros and ones, but these zeros and ones are not informational. Since the duration of one chip is n times less than the duration of the information bit, the width of the spectrum of the converted signal will be n times greater than the width of the spectrum of the original signal. In this case, the amplitude of the transmitted signal will decrease by n times.

The chip sequences embedded in the information bits are called noise-like codes (PN-sequences), which emphasizes the fact that the resulting signal becomes noise-like and is difficult to distinguish from natural noise.

It is clear how to broaden the signal spectrum and make it indistinguishable from natural noise. To do this, in principle, you can use an arbitrary (random) chip sequence. However, the question arises: how to receive such a signal? After all, if it becomes noise-like, then isolating a useful information signal from it is not so easy, if not impossible. It turns out that it is possible, but for this you need to select the chip sequence accordingly. Chip sequences used to broaden the signal spectrum must satisfy certain autocorrelation requirements. The term autocorrelation in mathematics refers to the degree of similarity of a function to itself at different points in time. If you select a chip sequence for which the autocorrelation function will have a pronounced peak for only one point in time, then such an information signal will be possible to isolate at the noise level. To do this, the received signal is multiplied in the receiver by the same chip sequence, that is, the autocorrelation function of the signal is calculated. As a result, the signal again becomes narrowband, so it is filtered in a narrow frequency band and any interference that falls within the band of the original broadband signal, after multiplying by the chip sequence, on the contrary, becomes broadband and is cut off by filters, and only part of the interference falls into the narrow information band, according to power is significantly less than the interference acting at the receiver input (Fig. 7.1).

Barker codes

There are quite a lot of chip sequences that meet the specified autocorrelation requirements, but the so-called Barker codes are of particular interest to us, since they are used in the 802.11 protocol.

Barker codes have the best noise-like properties among known pseudo-random sequences, which has led to their widespread use.

The 802.11 family of protocols uses a Barker code that is 11 chips long (11100010010).

In order to transmit a signal, a logical one is transmitted by a direct Barker sequence, and a logical zero by an inverse sequence.

Speed 1 Mbps

The 802.11 standard provides two speed modes: 1 and 2 Mbit/s. To encode data at the physical layer, the DSSS method with 11-chip Barker codes is used. With an information speed of 1 Mbit/s, the speed of individual Barker sequence chips is 11×106 chip/s, and the spectrum width of such a signal is 22 MHz. Considering that the width of the frequency range is 83.5 MHz, we find that a total of 3 non-overlapping frequency channels can fit in this frequency range. The entire frequency range, however, is usually divided into 11 overlapping frequency channels of 22 MHz, spaced 5 MHz from each other. For example, the first channel occupies the frequency range from 2400 to 2423 MHz and is centered relative to the frequency of 2412 MHz. The second channel is centered at 2417 MHz, and the last, channel 11, is centered at 2462 MHz. When viewed this way, the first, sixth and 11th channels do not overlap with each other and have a 3 megahertz gap relative to each other. It is these three channels that can be used independently of each other.

Differential Binary Phase Shift Key (DBPSK) is used to modulate a sinusoidal carrier signal (a process necessary to inform the carrier signal). In this case, information encoding occurs due to a phase shift of the sinusoidal signal relative to the previous signal state. Binary phase modulation provides two possible phase shift values - 0 and π. Then a logical zero can be transmitted by an in-phase signal (the phase shift is 0), and a logical one can be transmitted by a signal that is phase shifted by π.

Speed 2 Mbps

An information speed of 1 Mbit/s is mandatory in the IEEE 802.11 standard (Basic Access Rate), but a speed of 2 Mbit/s (Enhanced Access Rate) is optionally possible. To transmit data at this speed, the same DSSS technology with 11-chip Barker codes is used, but Differential Quadrature Phase Shiftey is used to modulate the carrier wave. With relative quadrature phase modulation, the phase shift can take four different values: 0, π/2, π and 3π/2. Using four different signal states, it is possible to encode a sequence of two information bits (dibits) in one discrete state and thereby double the information transmission rate. For example, dibit 00 may correspond to a phase shift of 0; dibit 01 - phase shift equal to π/2; dibit 11 - phase shift equal to π; dibit 10 - phase shift equal to 3π/2.

In conclusion, considering the physical layer of the 802.11 protocol, we note that at an information speed of 2 Mbit/s, the speed of individual chips of the Barker sequence remains the same, that is, 11 × 10 6 chip/s, and therefore the width of the spectrum of the transmitted signal does not change.

7.2 7.2 Physical layer of the 802.11b/b+ protocol

The IEEE 802.11b protocol, adopted in July 1999, is a kind of extension of the basic 802.11 protocol and, in addition to speeds of 1 and 2 Mbit/s, provides speeds of 5.5 and 11 Mbit/s. To operate at speeds of 1 and 2 Mbit/s, spectrum spreading technology using Barker codes is used, and for speeds of 5.5 and 11 Mbit/s so-called complementary codes (Complementary Code Keying, CCK) are used.

CCK sequences

Complementary codes or CCK sequences have the property that the sum of their autocorrelation functions for any cyclic shift other than zero is always zero.

The IEEE 802.11b standard deals with complex complementary 8-chip sequences defined on a set of complex elements.

Here it is worth making a small lyrical digression so as not to alienate the reader by the complexity of the mathematical apparatus used. The mathematics of complex numbers can evoke a lot of negative memories, being associated with something completely abstract. But in this case everything is quite simple. A complex representation of a signal is just a convenient mathematical apparatus for representing a phase-modulated signal.

Using a set of complex elements (1, –1, j, –j), it is possible to form eight complex numbers that are identical in magnitude but differ in phase. That is, the elements of the 8-chip CCK sequence can take one of the following eight values: 1, –1, j, –j, 1+j, 1–j, –1+j, –1–j. The main difference between CCK sequences and the previously discussed Barker codes is that there is not a strictly defined sequence through which either a logical zero or a one could be encoded, but a whole set of sequences. Considering that each element of an 8-sip sequence can take one of eight values depending on the phase value, it is clear that 8 8 =16777216 sequence options can be combined, however, not all of them will be complementary. But even taking into account the requirement of complementarity, a fairly large number of different CCK sequences can be formed. This circumstance makes it possible to encode several information bits in one transmitted symbol and thereby increase the information transmission rate.

Generally speaking, using CCK codes allows you to encode 8 bits per character at 11 Mbit/s and 4 bits per character at 5.5 Mbit/s. In both cases, the symbolic transmission rate is 1.385 × 10 6 symbols per second (11/8 = 5.5/4 = 1.385), and taking into account that each character is specified by an 8-chip sequence, we obtain that in both cases the transmission rate individual chips is 11×10 6 chips per second. Accordingly, the signal spectrum width at both speeds of 11 Mbit/s and 5.5 Mbit/s is 22 MHz.

Considering the possible transmission speeds of 5.5 and 11 Mbit/s in the 802.11b protocol, we have so far left without addressing the question of why a speed of 5.5 Mbit/s is needed if the use of CCK sequences allows data to be transmitted at a speed of 11 Mbit/s . Theoretically, this is true, but only if you do not take into account the interference environment. In real conditions, the noise level of transmission channels and, accordingly, the ratio of noise and signal levels may be such that transmission at a high information speed, that is, when many information bits are encoded in one symbol, may be impossible due to their erroneous recognition. Without going into mathematical details, we only note that the higher the noise level of communication channels, the lower the information transmission speed. It is important that the receiver and transmitter correctly analyze the interference environment and select an acceptable transmission rate.

Related information.