Signal Encoding Techniques (信号编码技术) 张宝贤：无线网络技术——第三次课程 Signal Encoding Techniques (信号编码技术) 《无线通信与网络》第六章

Reasons for Choosing Encoding Techniques Digital data, digital signal Equipment less complex and expensive than digital-to-analog modulation equipment Analog data, digital signal Permits use of modern digital transmission and switching equipment 模拟信号先要进行数字化再在导向或非导向的媒质上传输，可以改善传输质量并可以利用TDM方式。对于无线传输来说，得到的数字信号必须调制到一个模拟载波上去。

Reasons for Choosing Encoding Techniques Digital data, analog signal Some transmission media will only propagate analog signals E.g., optical fiber and unguided media （也就是说在无线传输环境下，数据数据必须先转换成模拟信号） Analog data, analog signal Analog data in electrical form can be transmitted easily and cheaply Done with voice transmission over voice-grade lines 也可以把模拟信号调制到高频载波上进行传输

Signal Encoding Criteria What determines how successful a receiver will be in interpreting an incoming signal? Signal-to-noise ratio Data rate Bandwidth An increase in data rate increases bit error rate An increase in SNR decreases bit error rate An increase in bandwidth allows an increase in data rate （但根据汕农信道容量公式，这是有上限的）

（关键数字传输术语） （信号元素）

Factors Used to Compare Encoding Schemes Signal spectrum With lack of high-frequency components, less bandwidth required （如果一个信号没有高频成分） With no dc component, ac coupling via transformer possible （如果没有直流成分，那么通过变压器的交流偶合——可以进行电气隔离，降低干扰） Transfer function of a channel is worse near band edges （频带边缘的信道传输能力较差） Clocking （计时） Ease of determining beginning and end of each bit position 通过独立的时钟信道——成本高 通过发送信号的同步机制——通过适当的编码技术可以做到

Factors Used to Compare Encoding Schemes Signal interference and noise immunity Performance in the presence of noise 某些码元在噪声环境下性能很好 抗噪声能力通常用“误码率”来表示 Cost and complexity The higher the signal rate to achieve a given data rate, the greater the cost 后面将会看到，某些码元要求信号速率>实际数据速率

Basic Encoding Techniques Digital data to analog signal Amplitude-shift keying (ASK) （幅移键控） Amplitude difference of carrier frequency Frequency-shift keying (FSK) （频移键控） Frequency difference near carrier frequency Phase-shift keying (PSK) （相移键控） Phase of carrier signal shifted

Basic Encoding Techniques

Amplitude-Shift Keying One binary digit represented by presence of carrier, at constant amplitude Other binary digit represented by absence of carrier where the carrier signal is Acos(2πfct)

Amplitude-Shift Keying Susceptible to sudden gain changes （受突发的增益变化影响严重） Inefficient modulation technique On voice-grade lines, used up to 1200 bps (话音级链路上，最高能到1200 bps) Used to transmit digital data over optical fiber 发光二极管发送光信号，方式如下 激光发送器通常有一个固定的偏流(bias)，它可以使器件发射出亮度较低的光信号。 用这个较低的亮度表示一个信号 用振幅较高的光波表示另一个信号

Binary Frequency-Shift Keying (BFSK) 二元频移键控 Two binary digits represented by two different frequencies near the carrier frequency where f1 and f2 are offset from carrier frequency fc by equal but opposite amounts

双方向上的频谱没什么交叠， 也就没什么干扰 2125 1170

Binary Frequency-Shift Keying (BFSK) Less susceptible to error than ASK 这是因为ASK空号时不传信号，因此信号功率比FSK低 50% (振幅相同时） On voice-grade lines, used up to 1200bps Used for high-frequency (3 to 30 MHz) radio transmission Can be used at higher frequencies on LANs that use coaxial cable 易于实现——早期Modem都采用移频键控技术

Multiple Frequency-Shift Keying (MFSK)多元频移键控 More than two frequencies are used More bandwidth efficient but more susceptible to error f i = f c + (2i – 1 – M)f d f c = the carrier frequency （载波频率） f d = the difference frequency （差分频率） M = number of different signal elements = 2 L L = number of bits per signal element

Multiple Frequency-Shift Keying (MFSK) To match data rate of input bit stream, each output signal element is held for: Ts=LT seconds where T is the bit period (data rate = 1/T) So, one signal element encodes L bits

Multiple Frequency-Shift Keying (MFSK) Total bandwidth required 2Mfd Minimum frequency separation required 2fd=1/Ts , Ts指信号周期 Therefore, modulator requires a bandwidth of Wd=2 M fd=M/Ts

Multiple Frequency-Shift Keying (MFSK)

Phase-Shift Keying (PSK) Two-level PSK (BPSK) （二元相移键控） Uses two phases to represent binary digits

Phase-Shift Keying (PSK) Differential PSK (DPSK) Phase shift with reference to previous bit Binary 0 – signal burst of same phase as previous signal burst Binary 1 – signal burst of opposite phase to previous signal burst

Phase-Shift Keying (PSK) Differential PSK (DPSK) （Cont’d) 避免了接收端要有一个与发送端精确匹配的本地震荡器相位的要求。 只要前面的相位接收正确，那么参照相位就是精确的

Phase-Shift Keying (PSK) Four-level PSK (QPSK)（四元相移键控） Each element represents more than one bit

Phase-Shift Keying (PSK) Multilevel PSK Using multiple phase angles with each angle having more than one amplitude, multiple signals elements can be achieved D = modulation rate, baud R = data rate, bps M = number of different signal elements = 2L L = number of bits per signal element 在标准的9600 bps的调制解调器中，使用了12个相位角度，其中有四个具有两种振幅值，因而总共有16个不同的信号元素

Performance [来自COUC01] Bandwidth of modulated signal (BT) ASK, PSK BT=(1+r)R FSK BT=2DF+(1+r)R R = bit rate 0 < r < 1; related to how signal is filtered DF = f2-fc=fc-f1

Performance Bandwidth of modulated signal (BT) MPSK MFSK L = number of bits encoded per signal element M = number of different signal elements

Performance (Cont’d)

最小频移键控（Minimum Shift Keying: MSK) 在某些移动通信系统中采用 仅在差错性能有限损伤的情况下，提供了比BFSK更优的带宽效率 Eb: 每比特信号能量； Tb是每比特持续时间 MSK的一个重要特征：连续相位移频键控

最小频移键控（续） MSK满足如下条件 以上两频率之间的这段空隙可以允许接收器能成功地检测信号的最小值。这也是MSK 中Minimum的含义

Quadrature Amplitude Modulation QAM is a combination of ASK and PSK Two different signals sent simultaneously on the same carrier frequency 从ASK or PSK简单的一维编码方式变换为二维编码，信号稳定性强，码间距离加大 用于ADSL传输等

Quadrature Amplitude Modulation 2比特串并转换

Reasons for Analog Modulation Modulation of digital signals When only analog transmission facilities are available, digital to analog conversion required Modulation of analog signals A higher frequency may be needed for effective transmission。直接传送基带信号是不可能的——需要使用的天线的直径是几千米！ Modulation permits frequency division multiplexing

Basic Encoding Techniques Analog data to analog signal Amplitude modulation (AM) Angle modulation Frequency modulation (FM) Phase modulation (PM)

Amplitude Modulation Amplitude Modulation cos2fct = carrier x(t) = input signal na = modulation index Ratio of amplitude of input signal to carrier a.k.a double sideband transmitted carrier (DSBTC) （双边带发射载波）

Carrier Modulating Sine-wave signal Amplitude-modulated (DSBTC) wave

Spectrum of AM signal 上下边带都是原始 信号的副本 比如如果信号带宽 300—3000Hz 载频：60 kHZ 则上边带 60.3-63kHz 下边带 57-59.7kHz

Amplitude Modulation Transmitted power Pt = total transmitted power in s(t) Pc = transmitted power in carrier na 越大，用来传送有用信息的能量越大 但 na必须<1,否则将发生信息丢失

Single Sideband (SSB) Variant of AM is single sideband (SSB) Sends only one sideband Eliminates other sideband and carrier Advantages Only half the bandwidth is required Less power is required Disadvantages Suppressed carrier can’t be used for synchronization purposes

Angle Modulation 调频和调相是角度调制的特例 Angle modulation Phase modulation Phase is proportional to modulating signal np = phase modulation index

Angle Modulation Frequency modulation Derivative of the phase is proportional to modulating signal （相位的导数与受调信号成正比） nf = frequency modulation index

载波 调制正弦信号 调幅DSBTC 调相 跳频

Angle Modulation Compared to AM, FM and PM result in a signal whose bandwidth: is also centered at fc but has a magnitude that is much different Angle modulation includes cos( (t)) which produces a wide range of frequencies 注意：频率可以定义成为相位变化的速率 Thus, FM and PM require greater bandwidth than AM

Angle Modulation Carson’s rule The formula for FM becomes where Am是输入信号的最大值， nf, np是调频、调幅指数

Basic Encoding Techniques Analog data to digital signal Pulse code modulation (PCM) 脉冲编码调制，或称脉码调制 Delta modulation (DM) 增量调制

Analog Data to Digital Signal Once analog data have been converted to digital signals, the digital data: (1) can be transmitted using NRZ-L. In this case, we have gone directly from analog data to digital signal (2) can be encoded as a digital signal using a code other than NRZ-L (3) can be converted to an analog signal, using previously discussed modulation techniques （3）的目的如下图所示

Pulse Code Modulation Based on the sampling theorem 如果采样频率高于信号最大主频的两倍，那么采样样本包含原始信号的所有信息。利用低通滤波器可以从这些样本中复原原始信号 Each analog sample is assigned a binary code Analog samples are referred to as pulse amplitude modulation (脉幅调制PAM) samples The digital signal consists of block of n bits, where each n-bit number is the amplitude of a PCM pulse

Pulse Code Modulation

Pulse Code Modulation By quantizing the PAM pulse, original signal is only approximated Leads to quantizing noise Signal-to-noise ratio for quantizing noise　[GIBS93] Thus, each additional bit increases SNR by 6 dB, or a factor of 4

Pulse Code Modulation 线性编码：每个量化阶间隔距离相同 对振幅较低的信号失真相对严重 非线性编码： 对低振幅信号采用较多的量化阶 对高振幅信号采用较少的量化阶 图6.16

Delta Modulation （增量调制） Analog input is approximated by staircase function　（阶梯函数） Moves up or down by one quantization level () at each sampling interval The bit stream approximates derivative of analog signal (rather than amplitude) 1 is generated if function goes up 0 otherwise 注意：这样的结果是每个抽样值只编码为一位

Delta Modulation

Delta Modulation Two important parameters Size of step assigned to each binary digit () Sampling rate Accuracy improved by increasing sampling rate However, this increases the data rate Advantage of DM over PCM is the simplicity of its implementation

带宽／数据率分析 采用128位量化电平或7位编码 话音信号占4kHz, 那么采样速率8000次/秒 采用PCM编码的话，数据速率为56kbps 根据Nyquist定理，56kbps数据速率可能需要的带宽的量级为28kHz. 而如果采用10-bit PCM编码那么４.6ＭHz的电视信号将需要92Mbps的速率

为什么我们还使用数字化技术？ Growth in popularity of digital techniques for sending analog data Repeaters are used instead of amplifiers No additive noise （噪声积累） TDM is used instead of FDM No intermodulation noise Conversion to digital signaling allows use of more efficient digital switching techniques

作业 (1) 什么是差分编码 (2) 考虑一个频谱成分在300-3000Hz的音频信号，假设使用7kHz的采样频率来生成PCM信号． 当SNR=30dB时，需要多少个均匀的量化值？ 所需的数据率是多少？