# 电气工程代写|数字系统设计作业代写Digital System Design代考|ECE4110

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

The most common form of digital modulation is changing the phase of the carrier frequency in accordance with the digital signal that is being sent. This is known as phase-shift keying (PSK) or direct sequence digital modulation. This digital sequence can be either the digitized data or a combination of digitized data and a spread spectrum sequence. There are many different levels and types of PSK; only basic modulation methods are discussed here. However, the principles can be extended to higher order PSK modulations. The basic form of digital communication is shown in Figure 2-10. This shows the carrier frequency and the digital data being fed into a modulator. The modulator is binary phase-shift keying (BPSK) and changes the phase between $0^{\circ}$ and $180^{\circ}$ according to the digital data being sent.

The BPSK modulator and phasor diagram is shown in Figure 2-11. BPSK is defined as shifting the carrier $0^{\circ}$ or $180^{\circ}$ in phase, depending on the digital waveform. For example, a binary ” $0 “$ gives $0^{\circ}$ phase of the carrier, and a binary ” $1 “$ shifts the carrier by $180^{\circ}$.

To produce the digital waveform, the data or information signal is digitized, encoded, and sent out in a serial bit stream (if not already). The end result is a serial modulating digital waveform representing the data to be transmitted. This digital output contains 0 and 1 and often needs to be changed to $\pm 1$ to directly modulate the carrier frequency in a typical mixer application. However, certain forms of hardware can bypass this step and modulate the mixer directly. The output of the mixer is a BPSK modulated carrier signal that is transmitted and sent over to the receiver for demodulation and detection. As the carrier phase changes $180^{\circ}$, the hardware does not allow for an instantaneous change in phase, so the amplitude goes to zero, which produces $100 \%$ amplitude modulation (Figure 2-11). This is called the zero crossover point and is an unwanted characteristic of BPSK and can cause degradation to the waveform and performance.

A high-speed pseudo-noise (PN) code and modulo-2 adder/exclusive-or functions are added to the basic BPSK modulator to produce a spread spectrum waveform (Figure 2-12). The high-speed code generates a wider spectrum than the data spectrum needed for communications, which is known as a spread spectrum.

Applying minus voltage to an actual RF mixer reverses the current through the balun of the mixer and causes the current to flow in the opposite direction, creating a net $180^{\circ}$ phase shift of the carrier. Thus, the carrier is phase shifted between $0^{\circ}$ and $180^{\circ}$ depending on the input waveform. A simple way of generating BPSK spread spectrum is shown in Figure 2-13. The LO is modulated by this digital sequence producing a $0^{\circ}$ or $180^{\circ}$ phase shift on the output of the mixer. Other devices such as phase modulators and phase shifters can create the same waveform as long as one digital level compared with the other digital level creates a $180^{\circ}$ phase difference in the carrier output.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Differential Phase-Shift Keying

The BPSK waveform above can be sent out as absolute phase (i.e., a $0^{\circ}$ phase shift is a ” 1 ” and a $180^{\circ}$ phase shift is a “0”). This type of system is known as a coherent system, or coherent BPSK. Another way to perform this function is to use differential phase-shift keying (DPSK), which generates and detects a change of phase. A change of phase $\left(0^{\circ}\right.$ to $180^{\circ}$ or $180^{\circ}$ to $\left.0^{\circ}\right)$ represents a ” $1 “$ “, and no change $\left(0^{\circ}\right.$ to $0^{\circ}$ or $180^{\circ}$ to $\left.180^{\circ}\right)$ represents a ” 0. .” This scheme is easier to detect because the absolute phase does not need to be determined; just the change of phase is monitored. The differential mode can be applied to various phase shifting schemes and higher order phase shift schemes. DPSK results in a degradation of the signal, compared with using the absolute phase or coherent BPSK. However, it is much easier to demodulate and detect the data and generally is less costly due to the demands of keeping the phase constant over a longer period of time. Note that differential techniques can be applied in higher order PSK systems such as differential quadrature phaseshift keying (DQPSK) and differential 8-level phase-shift keying (D8PSK).

Quadrature phase-shift keying (QPSK) is generated by quadrature phase shifting the LO so that four possible phase states are produced at the output. One method of producing these phasors is by using two channels: one channel containing an LO that is in phase and the output of the mixer is BPSK modulated to produce $0^{\circ}$ or $180^{\circ}$; and the other channel containing the same LO that is shifted by $90^{\circ}$ so that the output of the mixer is BPSK modulated to produce $90^{\circ}$ or $270^{\circ}$. These two channels are then combined to produce the four phase states (Figure 2-13). The two BPSK systems are summed together, which gives four possible resultant phasors $-45^{\circ}, 135^{\circ},-135^{\circ}$, and $-45^{\circ}$-which are all in quadrature, as shown in Figure 2-13. Since the digital transitions occur at the same time, changes hetween any four resultant phasors can necur.

Depending on the input of both bit streams, the phase of the resultant can be at any of the four possible phases. For example, if both bit streams are 0 , then the phasor would be $45^{\circ}$. If both bit streams changed to 1 , then the phasor would be at $-135^{\circ}$, giving a change of carrier phase of $180^{\circ}$. If only the first channel changes to 1 , then the phasor would be at $-45^{\circ}$, giving a change of $90^{\circ}$. Therefore, the four possible phase states are $45^{\circ}, 135^{\circ},-135^{\circ}$, or $-45^{\circ}$. The phasor diagram can be rotated, since it is continually rotating in time and only a snapshot is shown, and then the phasors would be at $0^{\circ}, 90^{\circ},-90^{\circ}$, and $180^{\circ}$ for QPSK generation. QPSK has the capability of $180^{\circ}$ phase shifts depending on the code and the previous phase state, so it often goes through the zero crossover point, which produces $100 \%$ amplitude modulation during the phase transition as shown in Figure 2-13. This causes unwanted characteristic of QPSK and can cause degradation to the waveform and performance.

Usually, the LO contains the $90^{\circ}$ phase shift that is used to provide the two quadrature channels of the BPSK phasors instead of trying to provide the $90^{\circ}$ phase shift of the actual hinary input. Fither way it would provide the $90^{\circ}$ quadrature phase rotation that is required. However, quadrature rotation of the binary input requires phase shifting all of the frequency components by $90^{\circ}$. This requires a more sophisticated and expensive phase shifter that is broadband. Shifting only the carrier to produce the quadrature channels requires a phase shift at one frequency, which is much simpler to build. In fact, in the latter case, a longer piece of cable cut to the right length can provide this $90^{\circ}$ quadrature phase shift.

# 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|Digital Modulation

BPSK 调制器和相量图如图 2-11 所示。BPSK被定义为移动载波0∘或者180∘同相，取决于数字波形。例如，二进制“0“给0∘载波的相位，以及一个二进制“1“将载体转移180∘.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Differential Phase-Shift Keying

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