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扩频通信系统
的介绍
摘要：本应用笔记概述了扩频技术的原理，讨论了涵盖直接序列和快速跳频的方法。

相关理论方程的性能估算。

以及讨论直接序列扩频（DSSS）和跳频（FHSS）这两种扩频方式。

简介
扩频技术越来越受欢迎，就连这一领域以外的电器工程师都渴望能够深入理解这一技术。

很多书和网站上都有关于这方面的书，但是，很多都很难理解或描述的不够详尽。

（例如，直接序列扩频技术广泛关注的是伪随机码的产生）。

下面讨论扩频技术（双关语意）。

简史
一名女演员和一名音乐家首次以书面形式描述了扩频通信技术。

1941年，好莱坞女星Hedy Lamarr和钢琴家George Antheil描述一个安全的无线链路来控制鱼雷。

他们获得了美国专利#2.292.387。

但这一技术被遗忘了，没有在当时受到美军的重视，直到20世纪80年代它才开始活跃起来。

从那时起，这一技术在有关恶劣环境中的收音机链接方面越来越受欢迎。

最典型的扩频技术应用是数据收发器包括卫星定位系统（GPS）、3G移动通信、无限局域网(符合IEEE®802.11a,IEEE 802.11b,IEEE 802.11g标准)，还有蓝牙技术也帮助了那些通讯落后和无线电通信条件有限的地方，因此，它是一种昂贵的资源。

扩频通信的原理
扩频是香农定理的典型：
C=B×log2(1+S/N) 公式（1）
在公式中，C为信道容限，单位是比特/秒(bps),意指单位时间内信道中无差
错传输的最大信息量。

B为信号频带宽度，单位是Hz，S/N为信噪比。

也就是说，
C为信道允许通过的信息量，也代表了扩频的性能。

带宽(B)是代价，因为频率
是一个有限的资源。

信噪比体现了环境条件或物理特性（如障碍、干扰器、干扰
等）。

上式说明，的情况下，在无差错传输的信息速率C不变时，如果信噪比很低，
则可以用足够宽的带宽来传输信号，即使信号功率密度低于噪音水平。

（公式可
用！）
改变公式（1）中对数的底数，2改为e，则为In=loge。

因此，
C/B=(1/ln2)×ln(1+S/N)=1.443×ln(1+S/N)公式
（2）
根据MacLaurin扩展公式
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-…) 公式
（3）
在扩频应用中，通常S/N很低。

（正如刚才提到的，信号功率密度甚至低于
噪音水平。

）假定噪音水平即S/N<<1，香农公式可简单表示为：
C/B≈1.443×S/N公式
（4）
简化为：
C/N≈S/N 公式
（5）
或者：
N/S≈B/C 公式
（6）
向固定了信噪比的信道发送错误的信息，只要执行基本扩频信号的传播操
作：增加传输带宽。

尽管这一原则看起来很简单明确，但实现她却很复杂，主要
是因为展宽基带的电子设备必须同时存在展宽和解扩的操作过程。

定义
不同的扩频技术都有一个共同之处：密钥（也称为代码或序列）依附于传输
信道。

以插入代码的形式准确地定义扩频技术，术语“频谱扩展”是指扩频信号的几个数量级的带宽在有密钥的传输信道中的扩展。

以传统的方式定义扩频更为精确：在射频通信系统中，将基带信号扩展为比原有信号的带宽宽得多的高频信号（如图1）。

在此过程中，传输宽带信号产生的损耗，表现为噪声。

扩频信号带宽与信息带宽之比称为处理增益。

扩频过程的处理增益大都在10dB 到60dB 之间。

要应用扩频技术，只需在天线（接收器）之前加入相应的扩频码。

相反，你可以删除一个点的扩频码（称为解扩操作）接收发射链路数据恢复。

解扩过程是重新恢复原始带宽的过程。

很明显，同样的代码必须在事先知道在传输通道两端的信息。

（在某些情况下，在调制和解调的过程中代码应该是知道的）。

图1.扩频通信系统
传播工作带宽的影响
图2说明了信号带宽的通信链路评估
图2.扩频操作遍及一个更宽的频率带宽的信息能量
扩频调制是一种适用于如BPSK 或直接转换。

传统的调制可以证明所有其他
信号接收不到扩频代码将保持它们原有的信息，极没有被扩展。

输入的扩频码
频率
数据的处理增益
数据输入宽度 扩频调制
数据输入
能量
能量
PF 载体 输电链
扩频代码
接收链
扩频代码
数据输入
射频输出
射频输入
射频连接
相同的配置序列
数据输出
解扩过程中带宽的影响
同样，解扩过程如图3。

图3,在解扩过程中恢复的原有信号
在这里，解扩调制已经取得了正常解调操作，也表明了干扰或干扰信号在解
扩传输过程中被扩展！
由于带宽的浪费抵消了传播的多用户
扩频结果直接在一个更宽的频带使用，完全对应之前的“处理增益”。

因此扩频并没有节约有限的频率资源。

过度的使用虽然得到了补偿，但是可能有很多用户共享这一扩大频率波段（如图4）。

图4.在相同的频带多个用户共享扩频技术。

扩频是宽带技术
相对于常规窄带技术，扩频过程是一种宽带技术。

例如，W - CDMA 和UMTS 都是宽带技术，与窄带广播相比，它需要一个比较大的频率带宽。

扩频的优点
抗干扰性能和抗干扰的影响
扩频技术有很多优点。

.抗干扰性是最重要的一个优点。

有意或无意的干扰和
用户1+用户2+用户3+…+用户N
数据输入获得的扩频增益
能量
数据输入宽度
数据输入
解扩调制
能量
输入的扩频码
数据的处理增益
PF 载体
频率
干扰信号都是不希望存在的因为它们不包含扩频密钥。

只有期望信号才有密钥，在解扩过程中才会被接收器接收，如图5。

图5.扩频通信系统。

注意，解扩链路中数据信号被传输的同时干扰能源也被传输。

无论在窄带或宽带中，如果它不涉及解扩过程，你几乎可以忽略干扰。

这种抑制反应也适用于其他没有正确密钥的扩频信号。

因此不同的扩频通信系统可以工作在同一频段，例如CDMA 。

值得注意的是，扩频是宽带技术，但反之则不然：宽带技术不涉及扩频技术。

抗截获
抗截获是扩频通信技术的第二个优势。

由于非法的听众没有密钥用于原始信号传播，这些听众无法解码。

没有合适的钥匙，扩频信号会出现噪音或干扰。

（扫描方法可以打破的这些密钥，但是密钥是短暂的。

）甚至更好，信号电平可以低于噪声水平，因为扩频传输降低了频谱密度，如图6。

（总能量是相同的，但它是广泛存在于频率的。

）因此信息是无形的，这一影响在直接序列扩频（DSSS ）技术上有充分的体现。

（在下文的DSSS 作更详细说明。

）其他接收机无法“看到”这种传输，它们只能出现在整体噪音水平略有增加的情况下！
图 6.在被噪音水平之下的扩频频谱信号。

在没有正确的扩频传输密钥的情况下，接收器不能“看到”传输过程。

抗衰落（多径效应）
噪声基准
扩展后的数据
噪声基准
数据传播之前
输电链
扩频代码
接收链
扩频代码
数据输入
射频输出
射频输入
射频连接
数据输出
数据 干扰
数据扩展和 干扰扩展
数据扩展 数据扩展和干扰
无线信道通常具有多径传播，即有一个以上的信号从发射机传到接收器（如图7）。

这种多路径可以通过空气的反射或折射以及从地面反射或物体如这些路径建筑物引起。

图7.信号是如何通过多个路径到达接收器的。

这种反射路径（R ）可干扰直接路径（D ）的现象称为解扩过程的同步衰落。

因为解扩过程使信号D 与信号R 的同步被拒绝，即使它们包含了相同的密钥。

将反射路径的信号应用于解扩是个有用的方法。

扩频技术在CDMA 的应用
请注意，扩展频谱不是一个扩频调制方案，不应与其他调制方式相混淆。

例如我们可以使用扩频技术发射一个由PSK 或BPSK 的已调信号。

.感谢调制的信号的编码基础，使扩频频谱也可用于其他类型的多址实现（即可以同时进行多个通讯联系和实际或表面上相同的物理介质共存）。

到目前为止，有三个主要的方法可用。

FDMA-频分多址
FDMA 分配一个特定的载波频率给通信信道。

不同用户使用频谱的切片数是受到限制的（如图8）。

在已有的三种多路存取方法中，FDMA 在频带利用方面是效率最低的。

FDMA 的方法包括Methods 包括无线电广播，电视，高级移动电话系统AMPS 等。

图8. FDMA 系统中不同的用户的载波频率分配。

TDMA-时分多址
用户1 用户2 用户3 用户N
频率
(kHz,MHz,GHz)
Fc1 Fc2 Fc3 FcN
Rx
R
D
Tx
TDMA 的不同用户彼此间发言和听取信息时，是根据定义的时隙分配来处理的（如图9）。

不同的通信信道可以建立一个唯一的载波频率。

TDMA 的例子有全球移动通信系统GSM ，DECT ，TETRA 和IS - 136。

图9.在TDMA 系统中不同用户的时隙分配。

CDMA-码分多址
CDMA 的传播是由密钥或代码决定的（如图10）。

在这个意义上说，扩频就是一种CDMA 。

在发射器和接收器密钥必须提前被定义和确定。

它的例子有IS - 95(DS)，IS- 98，蓝牙和无线局域网。

图10.CDMA 系统中相同频带有独特的钥匙或代码。

当然，人们可以结合上述存取方法，例如，全球移动通信系统GSM 结合了TDMA 和FDMA 。

GSM 定义了不同的载波频率（细胞）的拓扑领域，并设定时段内每一个细胞。

扩频和（的）编码密钥
在这一点上，值得重申的是扩频的主要特点是一个代码或密钥必须在发射器和接收器之前就是已知的。

现代通讯的代码是数字序列必须长期存在和随机出现的，尽可能地显示为“噪音像”。

在任何情况下，代码必须确保是可再生的。

或者接收器不能提取已发出去的消息。

因此，该序列是几乎是随机的 。

这样的代码被称为伪随机数（PRN ）或序列。

最常用的方法来产生伪随机是基于反馈移位
用户1
用户5
用户4
用户3 用户2
用户1 用户2 用户3 用户N 用户1 用户2 用户3 用户N
时间段 时间段
时间
(ms,us)
寄存器的。

许多书籍都在介绍伪随机码的发展与特征，但是，实际的发展已超出了这些教材所叙述的。

注意的是，建立或选择适当的序列或序列集并不是微不足道的。

为了保证有效的扩频通信，伪随机序列必须尊重一定的规律如长度、自相关、互相关、正交。

比较受欢迎伪随机序列有Barker码，M序列码，Gold码，Walsh 码等。

考虑到存在更复杂的序列集，给它提供了一个更强大的扩展频谱链路。

但是这产生了成本问题：扩频和解扩都需要在速度和性能都更复杂的电子产品，数字扩频解扩芯片包含几百万个等效的2输入与非门在几十兆赫间切换。

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.Relation direct-sequence spread-spectrum(DSSS) and frequency-hopping spread-spectrum(FHSS) methods.
Introduction
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(pun intended).
A Short History
Spread-spectrum communications technology was first described on paper by an actress and 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(IEEE®802.11a,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.
Theoretical Justification for Spread Spectrum
Spread-spectrum is apparent in the Shannon and Hartley channel-capacity
theorem:
C=B×log2(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 <<1,Shannon's expression becomes simply:
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.
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.)
Figure 1.Spread-spectrum communication system
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.
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!
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.
Spread Spectrum Is a Wideband Technology
In contrast to regular narrowband technology,the spread-spectrum process is a wideband technology.W-CDMA and UMTS, for example,are wideband technologies that require a relatively large frequency bandwidth, compared to narrowband radio.
Benefits of Spread Spectrum
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.
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.
Resistance to Fading (Multipath Effects)
Wireless channels often include multiple-path propagation in which the signal has more that 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.
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.
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.
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.
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.
Spread Spectrum and (De) 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.。