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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

The SNR is used for analog signals where the signal $(S)$ is the signal power of the analog signal, and noise $(N)$ is the amount of noise power in the required bandwidth for sending the analog signal. For digital modulation, square pulses or bits are used to send information from the transmitter to the receiver. The amount of energy in a single bit is denoted as $E_b$. The bit rate or the number of bits per second is denoted as $R_b$. The signal power for a digital modulation system is equal to the energy in a single bit times the bit rate:
$$S=E_b * R_b$$
The noise power $(N)$ is equal to the noise power spectral density $\left(N_o\right.$, which is the amount of noise per $\mathrm{Hz}$, or in other words, the amount of noise in a $1 \mathrm{~Hz}$ bandwidth), times the bandwidth $(B)$ of the digital system:
$$N=N_o * B$$
Therefore, the SNR for the digital system is equal to
\begin{aligned} S &=E_b * R_b \ N &=N_o * B \ S N R &=E_b / N_o * R_b / B \end{aligned}

The bandwidth for a basic digital system is equal to the bit rate. In this case, the SNR is equal to
$$S N R=E_b / N_o$$
For more complex digital communications, the bandwidth may not equal the bit rate, so the entire equation needs to be carried out.

For example, one method of digital modulation is to change the phase of a frequency in accordance with the digital signal, a digital ” 0 ” is $0^{\circ}$ phase and a digital ” 1 ” is $180^{\circ}$ phase. This is known as binary phase-shift keying (BPSK). (The types of digital modulation are discussed later in this book). For BPSK, the bandwidth is equal to the bit rate:
\begin{aligned} &S N R=E_b / N_o * R_b / B \ &S N R=E_b / N_o \end{aligned}
However, if a more complex digital modulation waveform is used that contains four phase states- $0^{\circ}, 90^{\circ}, 180^{\circ},-90^{\circ}$ – such as quadrature phase-shift keying (QPSK), then the bit rate is twice as fast as the bandwidth required because there are two bits of information for one phase shift. Further explanation is provided in Chapter 2. Consequently, the SNR is equal to
\begin{aligned} &S N R=E_b / N_o * 2 R_b / B \ &S N R=2 E_b / N_o \end{aligned}

The link budget a method used to determine the necessary parameters for successful transmission of a signal from a transmitter to a receiver. The term link refers to linking or connecting the transmitter to the receiver, which is done by sending out RF waves through space (Figure 1-11). The term budget refers to the allocation of RF power, gains, and losses and tracks both the signal and the noise levels throughout the entire system, including the link between the transmitter and the receiver. The main items that are included in the budget are the required power output level from the transmitter power amplifier, the gains and losses throughout the system and link, and the SNR for reliable detection; the $E_b / N_o$ to produce the desired bit error rate (BER); or the probability of detection and probability of false alarm at the receiver. Therefore, when certain parameters are known or selected, the link budget allows the system designer to calculate unknown parameters.

Several of the link budget parameters are given or chosen during the process and the rest of the parameters are calculated. There are many variables and trade-offs in the design of a transceiver, and each one needs to be evaluated for each system design. For example, there are trade-offs between the power output required from the power amplifier and the size of the antenna. The larger the antenna (producing more gain), the less power is required from the power amplifier. However, the cost and size of the antenna may be too great for the given application. On the other hand, the cost and size of the power amplifier increase as the power output increases, which may be the limiting factor. If the power output requirement is large enough, a solid-state amplifier may not be adequate, and therefore a traveling-wave tube amplifier (TWTA) may be needed. The TWTA requires a special high-voltage power supply, which generally increases size and cost. So by making these kinds of trade-off studies, an optimum data link solution can be designed for a specific application.

Before starting the link budget, all fixed or specified information concerning the transceiver needs to be examined to determine which parameters to calculate in the link budget. These concessions need to be evaluated before the link budget is performed and then must be reevaluated to ensure that the right decisions have been made. The parameters for a link budget are described previously in this chapter.

Proper transceiver design is critical in the cost and performance of a data link. To provide the optimal design for the transceiver, a link budget is used to allocate the gains and losses in the link and to perform trade-offs of various parts of the system. The link budget also uses the required SNR or the ratio of bit energy to noise spectral density $\left(E_b / N_o\right)$ for a given probability of error. These required levels are derived by using probability of error curves given a certain type of modulation. Probability of error curves are discussed in Chapter 6. Generally, since there are both known and unknown variances in the link budget, a link budget will provide an additional SNR or $E_b / N_o$, which is referred to as the link margin. The link margin is equal to
Link margin for analog systems $=$ SNR (calculated) $-$ SNR (required)
Link margin for digital systems $=E_b / N_o$ (calculated) $-E_b / N_o$ (required)

# 数字系统设计代考

SNR 用于模拟信号，其中信号 $(S)$ 是模拟信号的信号功率，噪声 $(N)$ 是发送模拟信号所需带宽中的噪声功率量。对于数字调制，方脉冲或比特用于将
$$S=E_b * R_b$$

$$N=N_o * B$$

$$S=E_b * R_b N \quad=N_o * B S N R=E_b / N_o * R_b / B$$

$$S N R=E_b / N_o$$

$$S N R=E_b / N_o * R_b / B \quad S N R=E_b / N_o$$

$$S N R=E_b / N_o * 2 R_b / B \quad S N R=2 E_b / N_o$$

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MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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