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电气工程代写|数字系统设计作业代写Digital System Design代考|Differential 8-Level PSK

The D8PSK type of modulation is the same as $\pi / 4$ DQPSK but includes the phase-shift possibilities of $0^{\circ}, 90^{\circ},-90^{\circ}$, and $180^{\circ}$, thus providing $0^{\circ}, 45^{\circ},-45^{\circ}, 90^{\circ},-90^{\circ}, 135^{\circ}$, $-135^{\circ}$, and $180^{\circ}$ phase shifts. This provides eight possible phase shifts, or 3 bits $\left(2^3\right)$ of information, as shown in Figure 2-15. Since this is a differential system, these phase shifts are referenced to the previous bit, not the absolute phase. Therefore, the previous bit is mapped to the reference phasor with zero degrees for every bit received, and the next bit is shown to have one of the eight possible phase shifts referenced to $0^{\circ}$. If this was not a differential system, then the phasors would be absolute, not referenced to the previous bit.
Thus, for the same bandwidth as BPSK, the D8PSK can send three times as many bits (i.e., the bit rate is three times the bit rate of BPSK); however, it requires a higher $E_b / N_o$. The actual phase shifting occurs at the same rate as BPSK. The rate of the phase shifts is called the symbol rate. The symbol is the rate at which the phase is shifted, but the actual bit rate in this case is three times the symbol rate since there are 3 bits of information in each phase shift or symbol. The symbol rate is important because it describes the spectral waveform of the signal in space. For example, if the symbol rate is $3 \mathrm{ksps}$ ( 1000 samples per second), then the null-to-null bandwidth would be $6 \mathrm{kHz}$ wide ( 2 times the symbol rate), which would decode into 9 kbps. Note that this type of modulation allows a $180^{\circ}$ phase shift, which experiences AM.

Another common modulation scheme is 16-offset quadrature amplitude modulation (16-OQAM), which is very similar to OQPSK. In 16-OQAM, each of the phasors has two amplitude states before summation. The resultant phasor in one quadrant has four possible states (R1, R2, R3, and R4), as shown in the phasor diagram in Figure 2-16. Offset is used here for the same reasons as in OQPSK – to prevent transitions through zero amplitude and to reduce the AM on the output.

Since there are 4 possible amplitude/phase positions in one quadrant and a total of four quadrants, there are 16 possible amplitude/phase positions in this modulation scheme (Figure 2-16). These 16 states equates to 4 bits of information for each change in state or symbol, which provides four times the data rate compared with BPSK. However, a higher $E_b / N_o$ is required.

Since this is 16-offset QAM, the “offset” means that the phasors in the defined quadrant can change only to the adjacent quadrants. For example, the phasors shown in quadrant 1 can change only to quadrants 2 and 4 . These phasors cannot change from quadrant 1 to quadrant 3 . In other words, only the I or $\mathrm{Q}$ channel can change in phase at one time, not both at the same time (Figure 2-16).

电气工程代写|数字系统设计作业代写Digital System Design代考|Phasor Constellations and Noise Immunity

A phasor constellation is a technique used to determine the quality of phase modulated waveforms and to distinguish between phase states. A phasor constellation shows the magnitude and phase of the resultant phasor, including noise. A vector analyzer is used to display the constellations. The constellation diagram for a 16-OQAM signal is shown in Figure 2-16. The 16 phasors appear as points in a two-dimensional display representing both phase and amplitude and with no noise in the system. These constellation points show the amount of separation between one phasor state point and another. The data rate of the 16-state quadrature amplitude modulation (16-QAM) is four times higher than BPSK, as shown in Figure 2-17.

To understand the noise immunity of different modulation types, Figure 2-17b shows two types of phase modulations, including noise, which varies the phasor’s end points for BPSK and 16-OQAM modulated signals. For BPSK, the constellations are close enough together that it is very easy to detect which value of phase was sent, $0^{\circ}$ or $180^{\circ}$. Therefore, BPSK is much more resistant to noise and variations in phasor values. Although the 16-OQAM signal contains more bits per phasor value or symbol, which provides a faster data rate for a given bandwidth, the actual phasor value is more susceptible to noise, and it is much more difficult to separate the noisy phasor values, which results in more bit errors. This is a trade-off between noise resistance and higher data rates.

The quality of the phasor values can also be measured by determining the error vector magnitude (EVM). An error vector is a vector in the I- $\mathrm{Q}$ plane between the ideal vector or constellation point and the received vector or constellation point (Figure 2-18). The constellation points are the ends of the vectors and appear as points on a vector analyzer. These points represent the magnitude and phase of the vectors. The average length or magnitude of the error vector, defined as the distance between these two points, is the EVM. The ratio of the EVM (the distance between constellation points) and the ideal vector magnitude multiplied by 100 provides the EVM as a percentage. For example, if the ideal phasor magnitude is equal to 10 and the EVM is equal to 3, then the EVM in percent would be $3 / 10 \times 100=30 \%$ EVM (Figure 2-18). The smaller the percentage EVM, the less noise and the higher the probability of detecting the correct signal phase and amplitude.

电气工程代写|数字系统设计作业代写Digital System Design代考|EE301

数字系统设计代考

电气工程代写|数字系统设计作业代写Digital System Design代考|Differential 8-Level PSK

D8PSK 调制类型与圆周率/4DQPSK,但包括相移的可能性0∘,90∘,−90∘, 和180∘,从而提供0∘,45∘,−45∘,90∘,−90∘,135∘, −135∘, 和180∘相移。这提供了八种可能的相移,或 3 位(23)信息,如图 2-15 所示。由于这是一个差分系统,因此这些相移参考前一位,而不是绝对相位。因此,对于接收到的每一位,前一位都映射到具有零度的参考相量,并且下一位显示为具有参考的八种可能相移之一0∘. 如果这不是一个差分系统,那么相量将是绝对的,不参考前一位。
因此,对于与BPSK相同的带宽,D8PSK可以发送3倍的比特(即比特率是BPSK的3倍);但是,它需要更高的和b/ñ○. 实际相移发生的速率与 BPSK 相同。相移的速率称为符号率。符号是相移的速率,但在这种情况下,实际比特率是符号率的三倍,因为每个相移或符号中有 3 位信息。符号率很重要,因为它描述了空间信号的频谱波形。例如,如果符号率是3ķsps(每秒 1000 个样本),那么零到零带宽将为6ķH和宽(符号率的 2 倍),将解码为 9 kbps。请注意,这种类型的调制允许180∘相移,经历 AM。

另一种常见的调制方案是 16 偏移正交幅度调制 (16-OQAM),它与 ​​OQPSK 非常相似。在 16-OQAM 中,每个相量在求和之前都有两个幅度状态。一个象限中的合成相量有四种可能的状态(R1、R2、R3 和 R4),如图 2-16 中的相量图所示。此处使用偏移的原因与在 OQPSK 中的原因相同 – 以防止通过零幅度的转换并减少输出上的 AM。

由于一个象限有 4 个可能的幅度/相位位置,总共有 4 个象限,因此该调制方案有 16 个可能的幅度/相位位置(图 2-16)。这 16 个状态相当于状态或符号的每个变化的 4 位信息,与 BPSK 相比,它提供了四倍的数据速率。然而,更高的和b/ñ○是必须的。

由于这是 16 偏移 QAM,“偏移”意味着定义的象限中的相量只能改变到相邻的象限。例如,象限 1 中所示的相量只能更改为象限 2 和 4。这些相量不能从象限 1 变为象限 3。换句话说,只有 I 或问通道可以同时改变相位,不能同时改变(图 2-16)。

电气工程代写|数字系统设计作业代写Digital System Design代考|Phasor Constellations and Noise Immunity

相量星座是一种用于确定相位调制波形质量和区分相位状态的技术。相量星座图显示了合成相量的幅度和相位,包括噪声。矢量分析仪用于显示星座。16-OQAM 信号的星座图如图 2-16 所示。16 个相量显示为二维显示中的点,代表相位和幅度,系统中没有噪声。这些星座点显示了一个相量状态点与另一个相量状态点之间的分离量。16 态正交幅度调制(16-QAM)的数据速率是 BPSK 的 4 倍,如图 2-17 所示。

为了了解不同调制类型的抗噪性,图 2-17b 显示了两种类型的相位调制,包括噪声,它改变了 BPSK 和 16-OQAM 调制信号的相量端点。对于 BPSK,星座足够接近,很容易检测到哪个相位值被发送,0∘或者180∘. 因此,BPSK 对噪声和相量值变化的抵抗力更强。尽管 16-OQAM 信号的每个相量值或符号包含更多位,这为给定带宽提供了更快的数据速率,但实际相量值更容易受到噪声的影响,并且分离有噪声的相量值要困难得多,这导致更多的位错误。这是抗噪性和更高数据速率之间的权衡。

相量值的质量也可以通过确定误差矢量幅度 (EVM) 来测量。误差向量是 I- 中的向量问理想矢量或星座点与接收矢量或星座点之间的平面(图 2-18)。星座点是矢量的末端,在矢量分析仪上显示为点。这些点代表向量的幅度和相位。误差向量的平均长度或幅度,定义为这两点之间的距离,是 EVM。EVM(星座点之间的距离)与理想矢量幅度的比率乘以 100 提供了以百分比形式的 EVM。例如,如果理想相量幅度等于 10 且 EVM 等于 3,则以百分比表示的 EVM 将是3/10×100=30%EVM(图 2-18)。EVM 百分比越小,噪声越少,检测到正确信号相位和幅度的概率就越高。

电气工程代写|数字系统设计作业代写Digital System Design代考

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