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

## 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.

# 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。

## 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

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