An Introduction to Spread-Spectrum Communications
Abstract:This application note is a tutorial overview of spread-spectrum principles.The discussion covers both direct-sequence and fast-hopping methods.Theoretical equations are given to allow performance estimates.The following discussion of direct-sequence spread-spectrum(DSSS) and frequency-hopping spread-spectrum(FHSS) methods.As spread-spectrum techmiques become increasingly popular,electrical engineers outside the field are eager for understandable explanations of the technology.There are books and websites on the subject,but many are hard to understand or describe some aspects while ignoring others(e.g.,the DSSS technique with extensive focus on PRN-code generation).
The following discussion covers the full spectrum. Spread-spectrum communications technology was first described on paper by an actress and 1.A Short History a musician!In 1941 Hollywood actress Hedy Lamarr and pianist George Antheil described a secure radio link to control torpedos.They received U.S.Patent #2.292.387.The technology was not taken seriously at that time by the U.S.Army and was forgotten until the 1980s,when it became active.Since then the technology has become increasingly popular for application that involve radio links in hostile environments.
Typical applications for the resulting short-range data transceivers include satellite-positioning systemsGPS，3G mobile telecommunications,W-LAN(IEEE802.11a,IEEE 802.11b,IEEE 802.11g),and Bluetooth.Spread-spectrum techniques also aid in the endless race between communication needs and radio-frequency availability-situations where the radio spectrum is limited and is,therefore,an expensive resource.
2.Theoretical Justification for Spread Spectrum
Spread-spectrum is apparent in the Shannon and Hartley channel-capacity theorem:
C=B ×log 2(1+S/N) (Eq.1)
I n this equation,C is the channel capacity in bits per second(bps),which is the maximum data rate for a theoretical bit-error rate(BER).B is the required channel bandwidth in Hz,and S/N is the signal-to-nosie power ratio.To be more explicit,one assumes that C,which represents the amount of information allowed by the communication channel,also represents the desired performance.Bandwidth (B) is the price to be paid,bacause frequency is a limited resource.The S/N ratio expresses the environmental conditions or the physical characteristics (i.e., obstacles ,presence of jammers ,interferences,etc.).
There is an elegant interpretation of this equation,applicable for difficult environments,for
example,when a low S/N ratio is caused by noise and interference.This approach says that one can maintain or even increase communication performance (high C) by allowing or injecting more bandwidth (high B),even when signal power is below the noise floor. (The equation does not forbid that condition!)
Modify Equation 1 by changing the log base from 2 to e (the Napierian number) and by noting that In=loge.
Therefore:
C/B=(1/ln2)×ln(1+S/N)=1.443×ln(1+S/N) (Eq.2)
Applying the MacLaurin series development for
ln(1+x)=x-x2/2+x3/3-x4/4+…+(-1)k+1xk/k+…:
C/B=1.443×(S/N-1/2×(S/N)2+1/3×(S/N)3-…) (Eq.3)
S/N is usually low for spread-spectrum applications. (As just mentioned, the signal power density can even be below the noise level.) Assuming a noise level such that S/N
C/B≈1.443×S/N (Eq.4)
Very roughly:
C/N≈S/N (Eq.5)
Or:
N/S≈B/C (Eq.6)
To send error-free information for a given noise-to-signal ratio in the channel,therefore,one need only perform the fundamental spread-spectrum signal-spreading operation:increase the transmitted bandwidth.That principle seems simple and evident.Nonetheless,implementation is complex,mainly because spreading the baseband (by a factor that can be several orders of magnitude) forces the electronics to act and react accordingly,which,in turn,makes the spreading and despreading operations necessary.
3.Spread Spectrum definitions
Different spread-spectrum techniques are available,but all have one idea in common:the key (also called the code or sequence) attached to the communication channel.The manner of inserting this code defines precisely the spread-spectrum technique.The term "spread spectrum" refers to the expansion of signal bandwidth,by several orders of magnitude in some cases,which occurs when a key is attached to the communication channel.
The formal definition of spread spectrum is more precise:an RF communications system in which the baseband signal bandwidth is intentionally spread over a larger bandwidth by injecting a higher frequency signal (Figure 1).As a direct consequence,energy used in transmitting the signal is spread over a wider bandwidth,and appears as noise.The ratio (in dB) between the
spread baseband and the original signal is called processing gain.Typical spread-spectrum processing gains run from 10dB to 60dB.
To apply a spread-spectrum technique,simply inject the corresponding spread-spectrum code somewhere in the transmitting chain before the antenna (receiver).Conversely,you can remove the spread-spectrum code (called a despreading operation) at a point in the receive chain before data retrieval.A despreading operation reconstitutes the information into its original bandwidth.Obviously,the same code must be known in advance at both ends of the transmission channel. (In some circumstances,the code should be known only by those two parties).Therefore, the impact caused by the bandwidth of the following:
Figure 1.Spread-spectrum communication system
（1）Bandwidth Effects of the Spreading Operation
Figure 2 illustrates the evaluation of signal bandwidths in a communication link.
Figure 2.Spreading operation spreads the signal energy over a wider frequency bandwidth. Spread-spectrum modulation is applies on top of a conventional modulation such as BPSK or direct conversion.One can demonstrate that all other signals not receiving the spread-spectrum code will remain ad they are,that is,unspread.
（2）Bandwidth Effects of the Despreading Operation
Similarly,despreading can be seen in Figure 3.
Figure 3. The despreading operation recovers the original signal.
Here a spread-spectrum demodulation has been made on top of the normal demodulation operations.One can also demonstrate that signals such as an interferer or jammer added during the transmission will be spread during the despreading operation!
（3）Waste of Bandwidth Due to Spreading Is Offset by Multiple Users
Spreading results directly in the use of a wider frequency band by a factor that corresponds exactly to the "processing gain" mentioned earlier.Therefore spreading does not spare the limited frequency resource.That overuse is well compensated,however,by the possibility that many
users will share the enlarged frequency band (Figure 4).
Figure 4. The same frequency band can be shared by multiple
users with spread-spectrum techniques.
4.Spread Spectrum Is a Wideband Technology
In contrast to regular narrowband technology,the spread-spectrum process is a wideband technology.For example ，W-CDMA and UMTS,are wideband technologies that require a relatively large frequency bandwidth, compared to narrowband radio.Benefits of Spread Spectrum ：
(1) Resistance to Interference and Antijamming Effects
There are many benefits to spread-spectrum technology.Resistance to interference is the most important advantage.Intentional or unintentional interference and jamming signals are rejected because they do not contain the spread-spectrum key.Only the desired signal,which has the key, will be seen at the receiver when the despreading operation is exercised.See Figure 5.
Figure 5. A spread-spectrum communication system.Note that the interferer’s energy
is spread while the data signal is despread in the receive chain.
You can practically ignore the interference,narrowband or wideband,if it does not include the key used in the dispreading operation.That rejection also applies to other spread-spectrum signals that do not have the right key.Thus different spread-spectrum communications can be active simultaneously in the same band,such as CDMA.Note that spread-spectrum is a wideband technology,but the reverse is not true:wideband techniques need not involve spread-spectrum technology.
(2) Resistance to Interception
Resistance to interception is the second advantage provided by spread-spectrum techniques.Because nonauthorized listeners do not have the key used to spread the original signal,those listeners cannot decode it.Without the right key,the spread-spectrum signal appears as noise or as an interferer.(Scanning methods can break the code,however,if the key is short.) Even better,signal levels can be below the noise floor,because the spreading operation reduces the spectral density.See Figure 6.(Total energy is the same,but it is widely spread in frequency.) The message is thus made invisible,an effect that is particularly strong with the direct-sequence spread-spectrum (DSSS) technique.(DSSS is discussed in greater detail below.) Other receivers cannot “see ”
the transmission;they only register a slight increase in the overall noise level!
Figure 6.Spread-spectrum signal is buried under noise level.The receiver cannot “see ”
the transmission without the right spread-spectrum keys.
(3) Resistance to Fading (Multipath Effects)
Wireless channels often include multiple-path propagation in which the signal has more than one path from the transmitter to the receiver (Figure 7).Such multipaths can be caused by
atmospheric reflection or refraction, and by reflection from the ground or from objects such as
buildings.
Figure 7.Illustration of how the signal can reach the receiver over multiple paths. The reflected path (R) can interfere with the direct path (D) in a phenomenon called fading.Because the dispreading process synchronizes to signal D,signal R is rejected even though it contains the same key. Methods are available to use the reflected-path signals by dispreading them and adding the extracted results to the main one.
5.Spread Spectrum Allows CDMA
Note that spread spectrum is not a modulation scheme,and should not be confused with other types of modulation.One can,for example,use spread-spectrum techniques to transmit a signal modulated by PSK or BPSK.Thanks to the coding basis,spread spectrum can also be used as another method for implementing multiple access (i.e.,the real or apparent coexistence of multiple and simultaneous communication links on the same physical media).So far,three main methods are available.
a. FDMA-Frequency Division Multiple Access
FDMA allocates a specific carrier frequency to a communication channel.The number of different users is limited to the number of “slices ” in the frequency spectrum (Figure 8).Of the three methods for enabling multiple access,FDMA is the least efficient in term of frequency-band usage.Methods of FDMA access include radio broadcasting,TV
,AMPS,and TETRAPOLE.
Figure 8.Carrier-frequency allocations among different users in a FDMA system.
b. TDMA-Time Division Multiple Access
With TDMA the different users speak and listen to each other according to a defined allocation of time slots (Figure 9).Different communication channels can then be established for a unique carrier frequency.Examples of TDMA are GSM,DECT,TETRA,and IS-136.
Figure 9. Time-slot allocations among different users in a TDMA system.
c. CDMA-Code Division Multiple Access
CDMA access to the air is determined by a key or code (Figure 10).In that sence,spread spectrum is a CDMA access.The key must be defined and known in advance at the transmitter
and receiver ends.Growing examples are IS-95 (DS),IS-98,Bluetooth,and WLAN.
Figure 10.CDMA systems access the same frequency band with unique keys or codes.
One can,of course,combine the above access methods.GSM,for instance,combines TDMA and FDMA.GSM defines the topological areas (cells) with different carrier frequencies,and sets time slots within each cell.
6.Spread Spectrum and coding “Keys ”
At this point,it is worth restating that the main characteristic of spread spectrum is the presence of a code or key,which must be known in advance by the transmitter and receiver (s).In modern communications the codes are digital sequences that must be as long and as random as possible to appear as “noise-like ” as possible.But in any case,the codes must remain reproducible.or the receiver cannot extract the message that has been sent.Thus,the sequence is “nearly random”.Such a code is called a pseudo-random number (PRN) or sequence.The method most frequently used to generate pseudo-random codes is based on a feedback shift register.
Many books are available on the generation of PRNs and their characteristics,but that development is outside the scope of this basic tutorial.Simply note that the construction or
selection of proper sequences,or sets of sequences,is not trivial.To guarantee efficient spread-spectrum communications,the PRN sequences must respect certain rules,such as length, autocorrelation,cross-correlation,orthogonality,and bits balancing.The more popular PRN sequences have names:Barker,M-Sequence,Gold,Hadamard-Walsh,etc.Keep in mind that a more complex sequence set provides a more robust spread-spectrum link.But there is a cost to this: more complex electronics both in speed and behavior,mainly for the spread-spectrum despreading operations.Purely digital spread-spectrum despreading chips can contain more than several million equivalent 2-input NAND gates,switching at several tens of megahertz.
An Introduction to Spread-Spectrum Communications
Abstract:This application note is a tutorial overview of spread-spectrum principles.The discussion covers both direct-sequence and fast-hopping methods.Theoretical equations are given to allow performance estimates.The following discussion of direct-sequence spread-spectrum(DSSS) and frequency-hopping spread-spectrum(FHSS) methods.As spread-spectrum techmiques become increasingly popular,electrical engineers outside the field are eager for understandable explanations of the technology.There are books and websites on the subject,but many are hard to understand or describe some aspects while ignoring others(e.g.,the DSSS technique with extensive focus on PRN-code generation).
The following discussion covers the full spectrum. Spread-spectrum communications technology was first described on paper by an actress and 1.A Short History a musician!In 1941 Hollywood actress Hedy Lamarr and pianist George Antheil described a secure radio link to control torpedos.They received U.S.Patent #2.292.387.The technology was not taken seriously at that time by the U.S.Army and was forgotten until the 1980s,when it became active.Since then the technology has become increasingly popular for application that involve radio links in hostile environments.
Typical applications for the resulting short-range data transceivers include satellite-positioning systemsGPS，3G mobile telecommunications,W-LAN(IEEE802.11a,IEEE 802.11b,IEEE 802.11g),and Bluetooth.Spread-spectrum techniques also aid in the endless race between communication needs and radio-frequency availability-situations where the radio spectrum is limited and is,therefore,an expensive resource.
2.Theoretical Justification for Spread Spectrum
Spread-spectrum is apparent in the Shannon and Hartley channel-capacity theorem:
C=B ×log 2(1+S/N) (Eq.1)
I n this equation,C is the channel capacity in bits per second(bps),which is the maximum data rate for a theoretical bit-error rate(BER).B is the required channel bandwidth in Hz,and S/N is the signal-to-nosie power ratio.To be more explicit,one assumes that C,which represents the amount of information allowed by the communication channel,also represents the desired performance.Bandwidth (B) is the price to be paid,bacause frequency is a limited resource.The S/N ratio expresses the environmental conditions or the physical characteristics (i.e., obstacles ,presence of jammers ,interferences,etc.).
There is an elegant interpretation of this equation,applicable for difficult environments,for
example,when a low S/N ratio is caused by noise and interference.This approach says that one can maintain or even increase communication performance (high C) by allowing or injecting more bandwidth (high B),even when signal power is below the noise floor. (The equation does not forbid that condition!)
Modify Equation 1 by changing the log base from 2 to e (the Napierian number) and by noting that In=loge.
Therefore:
C/B=(1/ln2)×ln(1+S/N)=1.443×ln(1+S/N) (Eq.2)
Applying the MacLaurin series development for
ln(1+x)=x-x2/2+x3/3-x4/4+…+(-1)k+1xk/k+…:
C/B=1.443×(S/N-1/2×(S/N)2+1/3×(S/N)3-…) (Eq.3)
S/N is usually low for spread-spectrum applications. (As just mentioned, the signal power density can even be below the noise level.) Assuming a noise level such that S/N
C/B≈1.443×S/N (Eq.4)
Very roughly:
C/N≈S/N (Eq.5)
Or:
N/S≈B/C (Eq.6)
To send error-free information for a given noise-to-signal ratio in the channel,therefore,one need only perform the fundamental spread-spectrum signal-spreading operation:increase the transmitted bandwidth.That principle seems simple and evident.Nonetheless,implementation is complex,mainly because spreading the baseband (by a factor that can be several orders of magnitude) forces the electronics to act and react accordingly,which,in turn,makes the spreading and despreading operations necessary.
3.Spread Spectrum definitions
Different spread-spectrum techniques are available,but all have one idea in common:the key (also called the code or sequence) attached to the communication channel.The manner of inserting this code defines precisely the spread-spectrum technique.The term "spread spectrum" refers to the expansion of signal bandwidth,by several orders of magnitude in some cases,which occurs when a key is attached to the communication channel.
The formal definition of spread spectrum is more precise:an RF communications system in which the baseband signal bandwidth is intentionally spread over a larger bandwidth by injecting a higher frequency signal (Figure 1).As a direct consequence,energy used in transmitting the signal is spread over a wider bandwidth,and appears as noise.The ratio (in dB) between the
spread baseband and the original signal is called processing gain.Typical spread-spectrum processing gains run from 10dB to 60dB.
To apply a spread-spectrum technique,simply inject the corresponding spread-spectrum code somewhere in the transmitting chain before the antenna (receiver).Conversely,you can remove the spread-spectrum code (called a despreading operation) at a point in the receive chain before data retrieval.A despreading operation reconstitutes the information into its original bandwidth.Obviously,the same code must be known in advance at both ends of the transmission channel. (In some circumstances,the code should be known only by those two parties).Therefore, the impact caused by the bandwidth of the following:
Figure 1.Spread-spectrum communication system
（1）Bandwidth Effects of the Spreading Operation
Figure 2 illustrates the evaluation of signal bandwidths in a communication link.
Figure 2.Spreading operation spreads the signal energy over a wider frequency bandwidth. Spread-spectrum modulation is applies on top of a conventional modulation such as BPSK or direct conversion.One can demonstrate that all other signals not receiving the spread-spectrum code will remain ad they are,that is,unspread.
（2）Bandwidth Effects of the Despreading Operation
Similarly,despreading can be seen in Figure 3.
Figure 3. The despreading operation recovers the original signal.
Here a spread-spectrum demodulation has been made on top of the normal demodulation operations.One can also demonstrate that signals such as an interferer or jammer added during the transmission will be spread during the despreading operation!
（3）Waste of Bandwidth Due to Spreading Is Offset by Multiple Users
Spreading results directly in the use of a wider frequency band by a factor that corresponds exactly to the "processing gain" mentioned earlier.Therefore spreading does not spare the limited frequency resource.That overuse is well compensated,however,by the possibility that many
users will share the enlarged frequency band (Figure 4).
Figure 4. The same frequency band can be shared by multiple
users with spread-spectrum techniques.
4.Spread Spectrum Is a Wideband Technology
In contrast to regular narrowband technology,the spread-spectrum process is a wideband technology.For example ，W-CDMA and UMTS,are wideband technologies that require a relatively large frequency bandwidth, compared to narrowband radio.Benefits of Spread Spectrum ：
(1) Resistance to Interference and Antijamming Effects
There are many benefits to spread-spectrum technology.Resistance to interference is the most important advantage.Intentional or unintentional interference and jamming signals are rejected because they do not contain the spread-spectrum key.Only the desired signal,which has the key, will be seen at the receiver when the despreading operation is exercised.See Figure 5.
Figure 5. A spread-spectrum communication system.Note that the interferer’s energy
is spread while the data signal is despread in the receive chain.
You can practically ignore the interference,narrowband or wideband,if it does not include the key used in the dispreading operation.That rejection also applies to other spread-spectrum signals that do not have the right key.Thus different spread-spectrum communications can be active simultaneously in the same band,such as CDMA.Note that spread-spectrum is a wideband technology,but the reverse is not true:wideband techniques need not involve spread-spectrum technology.
(2) Resistance to Interception
Resistance to interception is the second advantage provided by spread-spectrum techniques.Because nonauthorized listeners do not have the key used to spread the original signal,those listeners cannot decode it.Without the right key,the spread-spectrum signal appears as noise or as an interferer.(Scanning methods can break the code,however,if the key is short.) Even better,signal levels can be below the noise floor,because the spreading operation reduces the spectral density.See Figure 6.(Total energy is the same,but it is widely spread in frequency.) The message is thus made invisible,an effect that is particularly strong with the direct-sequence spread-spectrum (DSSS) technique.(DSSS is discussed in greater detail below.) Other receivers cannot “see ”
the transmission;they only register a slight increase in the overall noise level!
Figure 6.Spread-spectrum signal is buried under noise level.The receiver cannot “see ”
the transmission without the right spread-spectrum keys.
(3) Resistance to Fading (Multipath Effects)
Wireless channels often include multiple-path propagation in which the signal has more than one path from the transmitter to the receiver (Figure 7).Such multipaths can be caused by
atmospheric reflection or refraction, and by reflection from the ground or from objects such as
buildings.
Figure 7.Illustration of how the signal can reach the receiver over multiple paths. The reflected path (R) can interfere with the direct path (D) in a phenomenon called fading.Because the dispreading process synchronizes to signal D,signal R is rejected even though it contains the same key. Methods are available to use the reflected-path signals by dispreading them and adding the extracted results to the main one.
5.Spread Spectrum Allows CDMA
Note that spread spectrum is not a modulation scheme,and should not be confused with other types of modulation.One can,for example,use spread-spectrum techniques to transmit a signal modulated by PSK or BPSK.Thanks to the coding basis,spread spectrum can also be used as another method for implementing multiple access (i.e.,the real or apparent coexistence of multiple and simultaneous communication links on the same physical media).So far,three main methods are available.
a. FDMA-Frequency Division Multiple Access
FDMA allocates a specific carrier frequency to a communication channel.The number of different users is limited to the number of “slices ” in the frequency spectrum (Figure 8).Of the three methods for enabling multiple access,FDMA is the least efficient in term of frequency-band usage.Methods of FDMA access include radio broadcasting,TV
,AMPS,and TETRAPOLE.
Figure 8.Carrier-frequency allocations among different users in a FDMA system.
b. TDMA-Time Division Multiple Access
With TDMA the different users speak and listen to each other according to a defined allocation of time slots (Figure 9).Different communication channels can then be established for a unique carrier frequency.Examples of TDMA are GSM,DECT,TETRA,and IS-136.
Figure 9. Time-slot allocations among different users in a TDMA system.
c. CDMA-Code Division Multiple Access
CDMA access to the air is determined by a key or code (Figure 10).In that sence,spread spectrum is a CDMA access.The key must be defined and known in advance at the transmitter
and receiver ends.Growing examples are IS-95 (DS),IS-98,Bluetooth,and WLAN.
Figure 10.CDMA systems access the same frequency band with unique keys or codes.
One can,of course,combine the above access methods.GSM,for instance,combines TDMA and FDMA.GSM defines the topological areas (cells) with different carrier frequencies,and sets time slots within each cell.
6.Spread Spectrum and coding “Keys ”
At this point,it is worth restating that the main characteristic of spread spectrum is the presence of a code or key,which must be known in advance by the transmitter and receiver (s).In modern communications the codes are digital sequences that must be as long and as random as possible to appear as “noise-like ” as possible.But in any case,the codes must remain reproducible.or the receiver cannot extract the message that has been sent.Thus,the sequence is “nearly random”.Such a code is called a pseudo-random number (PRN) or sequence.The method most frequently used to generate pseudo-random codes is based on a feedback shift register.
Many books are available on the generation of PRNs and their characteristics,but that development is outside the scope of this basic tutorial.Simply note that the construction or
selection of proper sequences,or sets of sequences,is not trivial.To guarantee efficient spread-spectrum communications,the PRN sequences must respect certain rules,such as length, autocorrelation,cross-correlation,orthogonality,and bits balancing.The more popular PRN sequences have names:Barker,M-Sequence,Gold,Hadamard-Walsh,etc.Keep in mind that a more complex sequence set provides a more robust spread-spectrum link.But there is a cost to this: more complex electronics both in speed and behavior,mainly for the spread-spectrum despreading operations.Purely digital spread-spectrum despreading chips can contain more than several million equivalent 2-input NAND gates,switching at several tens of megahertz.