Auxiliary notes of "In-depth understanding of communication principles"

1.2.2, wireless analog communication system

1. What is distortion?

• In radio technology, the output signal is inconsistent with the input signal. Such as sound quality changes, image distortion, etc.

1.3.1, source and sink

1. What is Morse code?

• Morse code is a system composed of "dots" and "strokes" invented in 1838 by the American painter and telegraph inventor, Mr. Morse. It is determined by the different arrangement sequence of "dots" and "strokes" intervals. Express different English letters, numbers and punctuation marks. With the financial support of the U.S. Congress in 1844, Mr. Morse opened the first telegraph line from Baltimore, Maryland to Washington, the capital of the United States, using "Morse code" communications. In 1851, it was related to European countries. With the support of the parties, the Morse code has been simplified and has become an international standard communication code ever since. The invention of the telegraph and the use of Morse code changed the face of human society. With the progress of society and the development of science, there are more advanced communication methods waiting for us to use, but telegraph "Morse" code communication occupies an important position in amateur radio. The "Radio Regulations" formulated by the International Telecommunication Union clearly pointed out: Anyone who requests a license to use amateur radio equipment should prove that they can accurately receive messages composed of "Morse" code signals by hand and by ear. Although today's computer technology has created conditions for automatic or semi-automatic sending and receiving of telegrams, every righteous hobbyist still must and can master manual sending and receiving techniques through self-training. Morse code itself is not classified at all, it is just a tool.

1.4.1, wired channel

1. What is the core network?

• The core network is one of the three major components of the communication network.
  The core network is the "management hub", responsible for managing data, sorting the data, and then telling it where to go. The processing and distribution of data is actually "routing and switching", which is the essence of the core network.
  The core network is mainly related to call connection, billing, mobility management, supplementary service realization, intelligent triggering, etc. The main body is supported by the switch. As for softswitching, there are two obvious concepts, the separation of control and bearer, and the separation of control channels and data channels.

1.4.2, wireless channel

1. Description of frequency bands.

• Frequency band is a term related to waves and communications. In the communications field, frequency band refers to the frequency range of electromagnetic waves, in Hz.
• The frequency band used in wireless communication is only a small part of the electromagnetic wave frequency band, which defines the frequency range of radio waves.
• In order to use spectrum resources rationally and ensure that various industries and services do not interfere with each other when they use spectrum resources, the International Telecommunication Union Radio Committee (ITU-R) promulgated international radio regulations to control the wireless use of various services and communication systems. The frequency bands have carried out a unified frequency range regulation.
  The frequency range of these frequency bands will be slightly different in actual applications in various countries and regions, but they must all be within these ranges specified internationally.
  According to international radio regulations, the existing radio communications are divided into more than 50 different services such as aeronautical communications, maritime communications, terrestrial communications, satellite communications, broadcasting, television, radio navigation, positioning, and telemetry, remote control, and space exploration. Each kind of business has stipulated certain frequency band.

2. Explanation of sky wave, ground wave and space wave.

• There are basically three ways of electromagnetic waves from emission to reception: one is called "ground wave", which relies on the ground; the other is called "space wave", which relies on a straight line between two points in space; and the third is ionization above the earth. The single-hop or multi-hop propagation that reflects from the layer to the ground is called "sky wave".
• Ground waves propagating along the ground surface will be attenuated by improper conductors such as the ground due to the hopping electromagnetic waves propagating along the ground to generate induced currents. The higher the frequency, the greater the skin effect and the greater the loss. Therefore, ground waves are suitable for medium and long waves and medium waves (that is, hundreds of kilohertz to several megahertz). For example, the frequency band from 535kHz to 1605kHz (one program per 10kHz) for civil broadcasting is an example.
• The short wave (high frequency band) of several megahertz to tens of megahertz is suitable for sky wave propagation, and the distance between receiving and sending is far greater than that of ground wave, up to hundreds of kilometers to thousands of kilometers, which depends on the size of the antenna incident angle.
• If the wavelength is shorter, that is, a higher frequency band, such as hundreds of megahertz to several gigahertz (109MHz) or more, it enters the microwave band. Electromagnetic waves in this frequency band have little absorption in the ionosphere and are no longer reflected back to the ground. Such as satellite communications, electromagnetic waves can penetrate the ionosphere and travel to the satellite. This kind of space wave propagation is similar to light. Not only does it travel in a straight line, but electromagnetic waves also have a diffraction (diffraction) effect, which can bypass some local obstacles.

1.5.1, source coding

1. What is GSM?

• Global System for Mobile Communications (Global System for Mobile Communications), abbreviated as GSM, is a digital mobile communication standard formulated by the European Telecommunications Standards Organization ETSI.
• The Global System for Mobile Communications (GSM) is by far the most successful global mobile communications system. Its development began in 1982. The European Telecommunications Management Conference (CEPT), the predecessor of the European Telecommunications Standards Institute (ETSI), established the Groupe Speciale Mobile (Groupe Speciale Mobile), which has been authorized to improve many of the recommendations related to the pan-European digital mobile communication system. The two goals that I tried to accomplish were:
  First, better and more effective technical solutions for wireless communications—At that time, digital systems had to be in terms of user capacity, ease of use, and the number of possible additional services. It was obvious that it was superior to the analog system that was still popular at the time.
  Second, to achieve a unified standard across Europe to support roaming across national borders. This was impossible in the past because all countries use incompatible analog systems.

1.5.4, modulation

1. What is ADSL?

• Asymmetric Digital Subscriber Line (ADSL, Asymmetric Digital Subscriber Line) is the most popular type of digital subscriber line (xDSL, Digital Subscriber Line) service.
• The so-called asymmetry is mainly reflected in the asymmetry between the uplink rate and the downlink rate. It uses digital coding technology to obtain the maximum data transmission capacity from the existing copper telephone line without interfering with conventional voice services on the same line. The reason is that it uses frequencies other than telephone voice transmission to transmit data. Users can make calls or send faxes while surfing the Internet, and this will not affect the call quality or reduce the speed of downloading Internet content. In fact, in the ADSL transmission technology, ADSL uses its unique modem hardware to connect each end of the existing twisted pair connection. It creates a channel with three channels, as shown in the following figure:
  
  It has a high-speed downlink channel (Downstream) to the user side, an upstream channel (Upstream) and a POTS channel (4kHz), the POTS channel is used to ensure that even if the ADSL connection fails, the voice communication can still operate normally. Both high-speed and medium-speed channels can use multiplexing technology to create multiple low-speed channels. The key concept of ADSL is also the key to the simultaneous transmission of digital and analog signals on the telephone line, because the upstream and downstream bands are asymmetrical. That is, the transmission bandwidth from the ISP to the client (downlink channel) is relatively high, and the transmission bandwidth from the client to the ISP (uplink channel) is relatively low. On the one hand, this design is to be compatible with the existing telephone network spectrum, and on the other hand, it is also in line with the habits and characteristics of using the Internet (the amount of data received is much larger than the amount of data sent).
• Main features:
  High-speed transmission: Provides asymmetrical transmission bandwidth for uplink and downlink.
  Internet access and phone calls do not interfere with each other: Data signals and phone audio signals are modulated in their respective frequency bands based on the principle of frequency division multiplexing and do not interfere with each other. You can make or receive calls while surfing the Internet, avoiding the trouble of not being able to use the phone when dialing up.
  Exclusive bandwidth, safe and reliable: each node adopts broadband switches to process and exchange information, and information transmission is fast and safe.

2.2.2 Characteristics of sine signal

1. What is fundamental wave? What are harmonics?

• The fundamental wave refers to the sine wave component equal to the longest period of the oscillation in a complex periodic oscillation, and the frequency corresponding to this period is called the fundamental wave frequency.
  The sine wave components whose frequency is equal to an integer multiple of the fundamental frequency are called harmonics.
• For example, suppose the set of sinusoidal signals is [{sin2πf0t, cos2πf0t, sin4πf0t, cos4πf0t, sin6πf0t, cos6πf0t,...}].
  The fundamental wave is a subset of all the signals with the longest period in this sinusoidal signal set, that is, the set [{sin2πf0t, cos2πf0t}], then the fundamental frequency is [f0], and the rest of the sinusoidal signals if their frequencies are fundamental frequency Integer multiples of, then they are called harmonics, that is, the harmonic frequency satisfies [nf0], and it is called the second harmonic when n=2. The corresponding subset in the example is [{sin4πf0t, cos4πf0t}], n= 3, 4, 5... are called the third harmonic, the fourth harmonic, and the fifth harmonic... respectively.

2. Explanation on the verification of the orthogonality of two sine functions.

• If the dot product of two vectors is equal to 0, then the two vectors are orthogonal.
• The verification of the orthogonality of the two functions can also be explained by the idea of ​​vector. The two functions are cut into the areas of small rectangles according to the idea of ​​differentiation, and the areas of the rectangles of these two functions are regarded as two respectively. The vector element of an infinite dimensional vector, let these two infinite dimensional vectors do the dot product, you can get the accumulative formula of a1b1+a2b2+..., if the accumulative formula is equal to 0, then it can indicate that the two vectors are positive Intersection, then these two functions are also orthogonal. Since this cumulative formula has infinite terms, it was cut according to the idea of ​​differentiation, so they were written in the form of integrals, so that if the two functions are Orthogonal, then the integral of the product of these two functions is equal to zero.

2.3.1 Euler's formula

1. An explanation of the three representation methods of complex numbers and some operations of complex numbers.
Reference video: https://www.icourse163.org/learn/SCU-1206674841?tid=1207010274#/learn/content?type=detail&id=1212330013&cid=1215609017&replay=true.

• The complex number [z=x+iy] has a one-to-one correspondence with the ordered real number pair [(x, y)]. After the rectangular coordinate system is established on the plane, the points on the plane can also use the ordered real number pair [(x, y) 】, so a rectangular coordinate system with y as the imaginary axis and x as the real axis can be used to represent a complex number z . This kind of plane used to represent the complex number is called the complex plane. In the complex plane, the complex number z can also be called the point z. In the rectangular coordinate system, z=x+iy is used to represent a complex number, which is called the algebraic representation of complex numbers. In addition, there are trigonometric representations and exponential representations , which are introduced as follows.
• In the complex plane of the rectangular coordinate system, the complex number z corresponds to the vector with the origin pointing to the point z (z=x+iy) one-to-one. Therefore, the complex number z=x+iy can also be represented by the vector oz , as shown in the figure below.
  
• The position of the complex number z can also be represented by the polar coordinates r and θ of the point z. When the vector oz is used to represent the complex number z=x+iy, the length of the vector oz is called the modulus or absolute value of the complex number z, denoted as |z| Or r, which is the equation in the figure below.
  
  In the case of z≠0, the number of radians θ with the positive real axis as the starting edge and the vector oz representing the point z (or the complex number z) as the ending angle is called the argument of z, denoted as [Arg z=θ].
  Note that any non-zero complex number z has an infinite number of arguments. If θ is one of its arguments, then all arguments of z are [Arg z = θ + 2kπ]
• The triangle inequality of complex numbers is shown in the figure below.
  
  Both z1 and z2 in the figure above are complex numbers.
• The distance formula of the two points z1 and z2 on the rectangular coordinate system corresponding to two complex numbers is shown in the figure below.
  
  The distance formula in the figure above is derived in Euclidean space (Euclidean distance).
• Using the relationship between the rectangular coordinate system and the polar coordinate system, x=rcosθ, y=rsinθ, and the non-zero complex number z can be expressed as z=r (cosθ + isinθ ). In particular, when the modulus of the point z is 1, that is, r= 1, z=cosθ+isinθ is the unit complex number. This is called the triangular representation of the complex number z in the polar coordinate system.
• Using Euler's formula, the exponent can be connected with the triangular representation of the point z in the polar coordinate system, and the exponential representation of the complex number z in the polar coordinate system can be obtained. As shown below.
  
  The algebraic representation of the complex number z in the rectangular coordinate system, the triangular representation of the complex number z in the polar coordinate system, and the exponential representation of the complex number z in the polar coordinate system can be transformed into each other. You can choose the appropriate complex number representation to calculate according to the actual problem.
• The product and quotient of complex numbers are explained in exponential notation in polar coordinates, as shown in the figure below.
  
  [Arg(z1z2)] in the above figure refers to the argument of the complex number after the product of the complex number z1 and the complex number z2. The geometric meaning of the multiplication of the above two complex numbers is shown in the figure below.
  
  In the above figure, the complex number z1z2 rotates counterclockwise compared to the complex number z1, then the argument of the complex number z2 is positive, and if it is rotated clockwise, the argument of z2 is negative.
• The powers and square roots of complex numbers are explained by exponential and trigonometric representations in polar coordinates, as shown in the figure below.
  
  It can be concluded from the figure above that the modulus of the complex number z^n is equal to the nth power of the modulus of the complex number z, and the argument of the complex number z^n is equal to n times the argument of the complex number z. The last circled equation in the above figure is obtained through the triangular representation in the polar coordinate system and Euler's formula. The square root of a complex number is shown in the figure below.
  
  
  
  
  The w0 in the above figure seems to be wrong, and I feel that the e index in the root sign should not have [1/n]. The above figure is the conclusion obtained by using the exponent of the complex number in the polar coordinate system to express the geometric meaning of the product. A complex number multiplied by a complex number with a modulus of 1 is equivalent to the change of the complex argument. The image is shown below.
  
  
  In the above figure, w=e^(i*2kπ/n). The properties of w are as follows.
  

2.4.3. Phases and phases of the moon

1. A summary of the phases of the moon and the moon.

• The concept of the phase of the moon in astronomy refers to the part of the moon that is illuminated by the sun as seen on the earth. Since the moon revolves around the earth, the moon, the sun and the earth change regularly in a month, so the moon phase It also changes regularly.
• The phase of the moon can be represented by the lunar calendar. There are 30 days in the lunar calendar, and each day corresponds to a phase of the moon. According to the definition of phase (the part of the complete cycle measured from the designated reference point), the reference point is the first month of the lunar calendar. Phase (new moon), when it reaches the first day of the lunar calendar of the next month, it is considered a complete cycle. Assuming that it is the fifteenth day of the lunar calendar at this time, the moon phase at this time is the full moon, which is exactly half of the lunar phase cycle. The corresponding aspect of the time and month is the fifteenth of the lunar calendar.

2.6.1. Definition of Fourier series expansion

1. A brief description of the definition and related properties of the series.

• Reference: https://pan.baidu.com/s/1dIjhmWZCy9VRl15F9lKLBQ. Extraction code: 1688.

2. Explanation about Fourier series.
Reference course 1: https://www.icourse163.org/learn/NUDT-42003?tid=1458933442#/learn/content?type=detail&id=1233948094&cid=1253381261&replay=true.
Reference Course 2: https://www.icourse163.org/learn/NUDT-42003?tid=1458933442#/learn/content?type=detail&id=1233948094&cid=1253381262.
Reference course 3: https://www.icourse163.org/learn/NUDT-42003?tid=1458933442#/learn/content?type=detail&id=1233948094&cid=1253381264&replay=true.
Reference course 4: https://www.icourse163.org/learn/NUDT-42003?tid=1458933442#/learn/content?type=detail&id=1233948094&cid=1253381266.

• The concept of trigonometric series is explained as follows.
  
  The function [f(x)] discussed by the sum function approximate approximation of the trigonometric series in the above figure is a periodic function with a period of 2π. The convergence range of the trigonometric series is [-π, π].
• The description of the orthogonal characteristic of the trigonometric series and the derivation of the coefficient formula are as follows.
  
  The derivation of the above three formulas requires the transformation of product and difference formulas.
  
  The derivation of a0, an and bn in the above figure is shown in the following figure.
  
  
  
  All the above derivations need to use the orthogonal characteristics of trigonometric functions.
  
• The concept of Fourier series coefficients and Fourier series.
  
  
  Function [f(x)] is an even function bk is equal to 0. The function [f(x)] is an odd function ak is equal to 0.
  The following two examples are to find the Fourier series of a function whose period is 2pi.
  See the solution process: https://www.icourse163.org/learn/NUDT-42003?tid=1458933442#/learn/content?type=detail&id=1233948094&cid=1253381266&replay=true.
  
  
• The Fourier series is transformed from triangular form to complex exponential form. As shown below.
  
  
  In the above figure, F(nw1), F(nw2), and F(0) can be combined. The expression of F(nw1) where n is from 1 to positive infinity and F(-) where n is from positive infinity to -1 The expression of nw1) is the same, so when n is equal to 0, the two are also equal, so it can be directly combined to get the exponential form of the Fourier series.

2.8.2 Continuous spectrum of non-periodic rectangular pulse signal

1. A summary of solving the continuous spectrum of non-periodic rectangular signals.

• To require a continuous spectrum of aperiodic rectangular signal, the first step is to extend the aperiodic signal into a periodic signal with a period T. As shown below.
  
• After that, the Fourier coefficient ck of this periodic rectangular signal after the continuation can be obtained according to the Fourier series. The spectral line length of the amplitude spectrum of this periodic rectangular signal is ck (the ck of the periodic rectangular signal is a real number, and it is After taking the modulus as a complex number, it is still ck itself), in order to facilitate the observation of the change law of ck after extending the non-periodic rectangular signal into a periodic rectangular signal according to different periods, use a f0 as the bottom side of ck and ck/f0 as high , The area of ​​this rectangle is exactly ck, so you will get a stepped broken line with frequency f as the horizontal axis and ck/f0 as the vertical axis. By drawing the stepped fold line diagram of the periodic rectangular signal after extension with different periods, it can be found that as the period increases, the stepped fold line infinitely approximates the curve of X(f)=tsinc(tf), and t is the pulse width of the rectangular signal , F is the frequency (horizontal axis). When the continuation period T tends to positive infinity, the continuous spectrum function of the non-periodic rectangular signal can be obtained, that is, X(f)=tsinc(tf).
• The above transformation to find the continuous spectrum of the non-periodic rectangular wave is the Fourier transform, and the transform to find the discrete spectrum of the periodic rectangular wave is called the Fourier series. Both the Fourier transform and the Fourier series transform the signal from the time domain. The coordinate system (with t as the independent variable) is transformed into a frequency domain (with f as the independent variable) coordinate system, which makes it more convenient to process the signal.

3.3, channel capacity

1. The relationship between the signal-to-noise ratio and the ratio of signal power to noise power.

• Signal-to-noise ratio (dB) = 10 * log10(S/N) (dB)
  For example: when S/N=10, the signal-to-noise ratio is 10dB; when S/N=1000, the signal-to-noise ratio is 30dB

3.4.2, large-scale fading

1. The difference between large-scale fading and small-scale fading.

• The causes are different.
  Small-scale fading is caused by the rapid fluctuation of the received signal in a short period of time when the mobile station moves a small distance.
  Large-scale fading is caused by the shadow of obstacles on the communication road.
• The impact on the signal is different.
  Small-scale fading has a large impact on the signal and will cause the signal to deteriorate.
  Large-scale fading has a small effect on the signal and can be eliminated.
• Fading speed is different
  Small scale fading speed is fast, time is short and rapid.
  Large-scale fading is slow and takes a long time.

4.1.2, quantification

1. Explanation of the principle of using compressor, uniform quantizer and expander to achieve non-uniform quantization.

• The essence of compression is shown in the figure below.
  
  From the above figure, it can be seen that after the large signal passes through the compressor, the amplitude is almost unchanged compared to the original one, while the amplitude of the small signal has been greatly amplified compared to before. This reduces the amplitude difference between large and small signals, which also weakens the problem of low quantized signal-to-noise ratio of uniformly quantized small signals, because small signals are amplified. The specific compression and enlargement process is shown in the figure below.
  

6. Transmission and reception of baseband signals

1. What is a baseband signal?

• The original electrical signal from the source (information source, also called the sending end) without modulation (spectrum shifting and transformation) is characterized by a low frequency, and the signal spectrum starts near zero frequency and has a low-pass form. According to the characteristics of the original electrical signal, the baseband signal can be divided into a digital baseband signal and an analog baseband signal (correspondingly, the signal source is also divided into a digital signal source and an analog signal source.) It is determined by the signal source.

7.2.3, QAM modulation

1. What is a code element?

• A symbol is a pulse signal, a pulse signal may carry 1bit data, it may also carry 2bit data, 4bit data! If you send a pulse signal, if you can carry 4bit data, the sending rate must be faster! So how can one pulse signal carry multiple bits of data? Certain techniques are required, such as setting the frequency, phase, and amplitude of the signal in the analog signal. For example: Divide the amplitude into four types, low (00), medium (01), high (10), and high (11). Then I send a pulse signal, and its amplitude is low, which means that the transmission is 00 (that is, 2bit), its amplitude is medium (01), and 01 (that is, 2bit) is sent... It also realizes a pulse signal that carries the function of 2bit... (I give an inappropriate example for everyone to understand That’s it, just understand what it means)
• Again, a symbol is a pulse signal! The baud rate refers to how many symbols can be sent in 1 second, that is, how many pulse signals can be sent in 1 second! One symbol can carry 1bit data, then bit rate = baud rate! One symbol can carry 2bit data, then the bit rate = 2 times the baud rate! One symbol can carry 4bit data, then the bit rate = 4 times the baud rate.

8.6.2 、 ​​MIMO

1. The relationship between the rank of the matrix and the system of equations

• The relationship between the rank of a matrix and a system of non-homogeneous linear equations.
  The coefficient matrix r(A), the augmented matrix r(A,b), and the number of unknowns n of the equation system.
  r(A)<r(A,b), then the equation system has no solution, then the equation system has no solution;
  r(A)=r(A,b)<n, then the equation system has multiple solutions, then the equation system has Multiple solutions.
  r(A)=r(A,b)=n, then the equation system has a unique solution, then the equation system has a unique solution.
• The ranks of the coefficient matrix and the augmented matrix can be used to judge whether the linear equation system has a solution, infinite solution or a unique solution.
  ①When the rank of the coefficient matrix<the rank of the augmented matrix, there is no solution;
  ②When the rank of the coefficient matrix=increase When the rank of the broad matrix = the number of unknowns, there is a unique solution
  ③When the rank of the coefficient matrix = the rank of the augmented matrix <the number of unknowns, there is an infinite solution