EE140 Introduction to Communication Systems Lecture 10

EE140 Introduction to

Communication Systems

Lecture 10

Instructor: Prof. Hua Qian

ShanghaiTech University, Spring 2019

Architecture of a (Digital) Communication System

©2019 Hua Qian EE140: Introduction to Communication Systems 2

Source A/Dconverter

Sourceencoder

Channelencoder Modulator

Channel

DetectorChanneldecoder

Sourcedecoder

D/Aconverter

User

Transmitter

Receiver

Absent ifsource isdigital

Noise

Contents

• Synchronization

– Carrier synchronization

– Symbol/Bit synchronization

– Frame synchronization

– Network Synchronization


Synchronization• Synchronization is one of the most critical functions

of a communication system with coherent receiver. To some extent, it is the basis of a synchronous communication system.– Carrier synchronization




Carrier Synchronization (载波同步)• Receiver needs estimate and compensate for

frequency and phase differences between a received signal’s carrier wave and the receiver’s local oscillator for the purpose of coherent demodulation


Phase-locked Loop (PLL)• PLL （锁相环）is used in carrier syn. and symbol

syn. It is a closed-loop control system consisting of– Phase detector (PD): generate the phase difference of vi(t)

and vo(t). – Voltage-controlled oscillator (VCO): adjust the oscillator

frequency based on the phase difference to eliminate the phase difference. At steady state, the output frequency will be exactly the same as the input frequency.

– Loop filter (LF)


Extract the Carrier• Pilot-tone insertion method

– Sending a carrier component at specific spectral-line along with the signal component. Since the inserted carrier component has high frequency stability, it is called pilot (导频).

• Direct extraction method– Directly extract the synchronization information from the

received signal component.


Insert Pilot to the Modulated Signal

• The pilot signal is generated by shifting the carrier by 90o and decrease by several dB, then adding to the modulated signal. Assume the modulated signal has 0 DC component, then the pilot is


Modulator

Bandpass filter

Add s(t)x(t)

π/2phase shift

-asin(ωct)

cos(ωct)

Thinking：Why 900 shift？

tsinatcos)t(f)t(s cc ωω −=

Contents

• Synchronization






Symbol/Bit Synchronization (符号/位同步)

• In digital systems, the output of the receiving filter (i.e. matched filter) must be sampled at the symbol rate and at the precise sampling time instants. Hence, we require a clock signal. The process of extracting such a clock signal at the receiver is called symbol/bit synchronization.


Symbol/Bit Synchronization (cont’d)• To perform this periodic sampling, we need a clock

signal at the receiver• The process of extracting such a clock signal is

called symbol synchronization or timing recovery• One method is for the transmitter to simultaneously

transmit the clock frequency along with the information signal. The receive can simply employ a narrowband filter or PLL to extract it. This method requires extra power and bandwidth and hence, but frequently used in telephone transmission systems.

• Another method is to extract the clock signal from the received data signal by using some kind of non-linear transformation.


Early-Late Gate Synchronization• Basic Idea: exploit the symmetry properties of the

output signal of matched filter or correlator


• Due to the symmetry, the values of the correlation function at the early samples and the late samples are equal.

• Thus, the proper sampling time is the midpoint between and

• Comments: works for linear modulations

TTt δ−=TTt δ+=

TTt δ−=TTt δ+=

Early-Late Gate Synchronization


Zero-Crossing Synchronization• The Zero-Crossing method is a decision-directed

technique that requires two samples per symbol at the synchronizer's input.


Zero-Crossing Synchronization (cont’d)• It performs well in low SNR conditions for all values

of excess bandwidth, and in moderate SNR conditions for moderate excess bandwidth factors (~0.4-0.6).

• For more information, check Matlab: comm.SymbolSynchronizer System object


Frame Synchronization (帧同步)• In frame-based digital systems, receiver also needs

to estimate the starting/stopping time of a data frame. The process of extracting such a clock signal is called frame synchronization. – Frame synchronization is to insert frame alignment signal

(distinctive bit sequence) and then detect the alignment symbol.

– Besides adding frame alignment bits, some code such as self-synchronizing code can be synchronized without adding extra bits.

• For more information, please check Matlab: comm.PreambleDetector System object


Contents

• Synchronization






Frame Synchronization (帧同步)• In frame-based digital systems, receiver also needs

to estimate the starting/stopping time of a data frame. The process of extracting such a clock signal is called frame synchronization. – Frame synchronization is to insert frame alignment signal

(distinctive bit sequence) and then detect the alignment symbol.

– Besides adding frame alignment bits, some code such as self-synchronizing code can be synchronized without adding extra bits.

• For more information, please check Matlab: comm.PreambleDetector System object


Frame Synchronization (Preamble Detection)

• Preamble Detection

– Start-stop method

– Bunched frame alignment signal

– Distributed frame alignment signal


Start-stop Method

• Start-stop method: It is widely used in teleprinter. Each symbol contains 5-8 data bits, a start bit and a stop bit.


start bit: “0’’, width = 𝑇𝑇𝑏𝑏stop bit: “1’’, width ≥ 𝑇𝑇𝑏𝑏System will keep sending stop bit when it is idle. When “1”→“0’’, the receiver will start to receive a data symbol

Start-stop Method

• Drawbacks:

– Low transmission efficiency

– Low timing accuracy


Bunched Frame Alignment Signal• Bunched frame alignment signal: inserts

synchronous code at a particular place in each frame. – The code should have a sharp self-correlation function. – The detector should be simple to implement.

• Frame synchronization code: – Barker code– optimal synchronous code– pseudo-random code


Barker Code(1)Barker code:

A n bits barker code 𝑥𝑥1, 𝑥𝑥2, 𝑥𝑥3, … , 𝑥𝑥𝑛𝑛 , 𝑥𝑥𝑖𝑖 = +1 or -1. Its self-correlation function satisfies:

𝑅𝑅𝑥𝑥 𝑗𝑗 = �𝑖𝑖=1

𝑛𝑛−𝑗𝑗𝑥𝑥𝑖𝑖𝑥𝑥𝑖𝑖+𝑗𝑗 = �

𝑛𝑛 𝑗𝑗 = 00 or ± 1 0 < 𝑗𝑗 < 𝑛𝑛0 𝑗𝑗 ≥ 𝑛𝑛

Barker code is not a periodic sequence. It is proved that when 𝑛𝑛 < 12100, we can only find barker code with 𝑛𝑛 = 2, 3, 4, 5, 7, 11, 13


Barker Code (cont’d)


n barker code2 + +

3 + + -

4 + + + - ，+ + - +

5 + + + - +

7 + + + - - + -

11 + + + - - - + - - + -

13 + + + + - - + + - + - +

Barker Code (cont’d)Example: A barker code with n=7, find its self-correlation

function𝑗𝑗 = 0: 𝑅𝑅𝑥𝑥 0 = 𝑥𝑥1𝑥𝑥1 + 𝑥𝑥2𝑥𝑥2 + ⋯+ 𝑥𝑥7𝑥𝑥7 = 7

𝑗𝑗 = 1: 𝑅𝑅𝑥𝑥 1 = 𝑥𝑥1𝑥𝑥2 + 𝑥𝑥2𝑥𝑥3 + ⋯ = 0

Similarly, we can determine 𝑅𝑅𝑥𝑥 𝑗𝑗 .The result is shown below, we can see it has a sharp peak

when 𝑗𝑗 = 0.


Barker Code (cont’d)• Barker code generator

– shift register

• Example：when n=7, a 7 bits shift register. The initial state is a barker code


Barker Code (cont’d)• Barker code detector


Barker Code (cont’d)• The barker code detector follows:

𝑖𝑖𝑛𝑛𝑖𝑖𝑖𝑖𝑖𝑖: "1" � +1−1

𝑖𝑖𝑛𝑛𝑖𝑖𝑖𝑖𝑖𝑖: "0" � −1+1

If the output of the shift register is the same with a barker code, then when the input is a barker code, the output of the shift register is “1111111”. The detector will send a synchronous impulse.


Distributed Frame Alignment Signal• Distributed frame alignment signal: the

synchronous code is distributed in the data signal. That means between each n bits, a synchronous bit is inserted.

• Design criteria of synchronous code:– Easy to detect. For example: “11111111”or ”10101010”– Easy to separate synchronous code from data code. For

example: In some digital telephone system，all ”0” stands for ring, so synchronous code can only use “10101010”.


Performance• Performance of frame synchronization system

(Bunched frame alignment signal)

• Probability of missing synchronization PL– Affected by noise, the detector may not be able to detect

the synchronous code. The probability of this situation is called probability of missing synchronization PL.

– Assume the length of synchronous code is n，bit error rate is Pe. The detector will not be able to detect if more than m bit errors happen, then:


( )∑=

−−

−=

m

x

xne

xeL PP

xn

P0

11

Performance (cont’d)• Probability of false synchronization PF

– Since data code can be arbitrary, it may be the same with synchronous code. The probability of this situation is called probability of false synchronization PF.

– PF equals to the probability of appearance of synchronous code in the data code.

• In a binary code, assume 0 and 1 appears with the same probability. There are 2n combinations of a n bit code.

• Assume when there are more than m bit errors, the data code will also be detected as synchronous code.


Performance (cont’d)• When 𝑚𝑚 = 0, only 1(𝐶𝐶𝑛𝑛0) code will be detected as

synchronous code; When 𝑚𝑚 = 1, there are 𝐶𝐶𝑛𝑛1 codes will be detected as

synchronous code;……

Therefore, the probability of false synchronization is:

𝑃𝑃𝐹𝐹 =∑𝑥𝑥=0𝑚𝑚 𝐶𝐶𝑛𝑛𝑥𝑥

2𝑛𝑛=

12

𝑛𝑛

�𝑥𝑥=0

𝑚𝑚

𝐶𝐶𝑛𝑛𝑥𝑥

𝑃𝑃𝐿𝐿 and 𝑃𝑃𝐹𝐹 depends on the length of synchronous code n and the maximum bit error m. When n ↑,𝑃𝑃𝐹𝐹 ↓,𝑃𝑃𝐿𝐿 ↑; when m ↑,𝑃𝑃𝐿𝐿 ↓,𝑃𝑃𝐹𝐹 ↑


Performance (cont’d)• Average build time 𝑖𝑖𝑠𝑠

Assume both 𝑃𝑃𝐿𝐿 and 𝑃𝑃𝐹𝐹 will not happen, the worst case is that we need one frame to build frame synchronization. Assume each frame contains N bits, each bit a width 𝑇𝑇𝑏𝑏 , then one frame costs N𝑇𝑇𝑏𝑏.

Now assume a missing synchronization or a false synchronization also needs N𝑇𝑇𝑏𝑏 to rebuild the synchronization, then:

𝑖𝑖1𝑠𝑠 = N𝑇𝑇𝑏𝑏(1 + 𝑃𝑃𝐿𝐿 + 𝑃𝑃𝐹𝐹)Besides, the average build time of using the distributed frame alignment signal is:

𝑖𝑖2𝑠𝑠 = 𝑁𝑁2T𝑏𝑏(𝑁𝑁 ≫ 1)Apparently, 𝑖𝑖1𝑠𝑠 < 𝑖𝑖2𝑠𝑠, so the previous method is more widely used.


Contents

• Synchronization






Network Synchronization (网同步)• Network synchronization purposes: make the whole

network stations can be interconnected, correctly receive information symbols– One-way(单向) communication system: Generally, the

receiving device adjusts its own clock to synchronize with the transmitting device’s clock

– Two-way(双向) communication system

• Synchronous network: all stations have a unified time standard

• Asynchronous or quasi-synchronous network: allow clock error in each station, but make the whole network coordinately work by adjusting the symbol rate


Reference Time and Reference Frequency• The prediction time error ∆𝑖𝑖 and the prediction

frequency error ∆𝑓𝑓 are usually caused by random fluctuations of the reference frequency.

• The reference time of the transmitter or receiver is usually derived from the period of the reference frequency, so the reference time is related to the accuracy of the reference frequency.

• The fluctuation of the reference frequency is difficult to express statistically and usually specifies a daily maximum permissible error

𝛿𝛿 =∆𝑓𝑓𝑓𝑓0

(Hz/Hz/day)


Range of 𝛿𝛿 Values• Cheap crystal oscillator: 10-5 to 10-6

• High-quality crystal oscillator: 10-9 to 10-11

• Rubidium(铷) atomic clock: 10-12

• Cesium(铯) atomic clock: 10-13


Synchronization Method of Synchronous Network

• May be responsible for receiving equipment to solve, may need both transmit and receive to solve

• A satellite communication network has four earth (terminal) stations, in the satellite (central station) S1 to receive earth station TDMA signal


Satellite Communication Network


• the slot arrangement

Open-loop Method

• Open loop method: The open loop method does not rely on any information about the arrival time of the received signal at the central station.

• The terminal station can correct its transmission time in advance based on information such as the link length that it stores. The information stored in the terminal station is provided from the concerned unit, but may also be modified in accordance with a signal sent back from the central station.


Open-loop Method (cont’d)• The open-loop method relies on accurate parameter

information such as the link length. When the path of the link is determined, this method works well. However, when the path of the link is not deterministic, or the terminal station is intermittently accessed, this method is difficult to use effectively.

• The main advantage of the open-loop method is capture quickly, can work without reverse link and real-time computing is small.

• The disadvantage is the need for external units to provide the required link parameter, and the lack of flexibility.


Closed-loop Method• Closed-loop method: In the closed-loop method,

the central station needs to measure the synchronization accuracy of the signal from the terminal station and send the measurement result to the terminal station through the reverse channel.

• Therefore, the closed-loop method requires a reverse channel to transmit the measurement result, and the terminal station needs to adjust its clock appropriately according to this feedback information.


Closed-loop Method (cont’d)• Advantages of the closed-loop method: It is not

necessary to know the link parameter in advance. And can easily adapt to the change of path and link situation by using reverse link in time.

• The shortcomings of the closed-loop method: terminal stations require a higher real-time processing capability. And there must be a two-way link between each terminal station and the central station. In addition, it takes a long time to capture synchronization


EE140 Introduction to Communication Systems Lecture 10

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