Noise in DSBSC Receivers

Double-sideband suppressed carrier (DSBSC) receivers are also susceptible to various types of noise that can degrade the quality of the received signal. The most common types of noise in DSBSC receivers are thermal noise and intermodulation distortion (IMD).

1. Thermal noise: As mentioned earlier, thermal noise is generated by the random motion of electrons in a conductor at a finite temperature. In DSBSC receivers, thermal noise is present in the receiver components such as amplifiers and mixers, and it can degrade the quality of the received signal.

2. Intermodulation distortion: Intermodulation distortion (IMD) is a type of distortion that occurs when two or more signals are mixed in a nonlinear device. In DSBSC receivers, IMD can be caused by nonlinearities in the receiver components such as mixers, amplifiers, and filters. IMD can create unwanted signals that interfere with the received signal and degrade its quality.

To minimize the effect of noise and distortion in DSBSC receivers, various techniques such as filtering, equalization, and modulation schemes can be used. For example, using a low noise amplifier (LNA) at the beginning of the receiver chain can help amplify the received signal and minimize the effect of thermal noise. Using high-Q filters can help minimize the effect of IMD by rejecting unwanted signals. Additionally, using a high-quality carrier recovery circuit can help extract the carrier signal and improve the receiver's overall performance.

Let the transmitted signal is
u(t)=𝐴𝑐𝑚(𝑡) cos(2𝜋𝑓𝑐t)
The received signal at the output of the receiver noise- limiting filter : Sum of this signal and filtered noise .A filtered noiseprocess can be expressed in terms of its in-phase and quadrature components as

where nc(t) is in-phase component and ns(t) is quadrature component Received signal (Adding the filtered noise to the modulated signal)
r(t)=u(t)+n(t)=𝐴𝑐𝑚(𝑡) cos(2𝜋𝑓𝑐t)+ 𝑛𝑐(𝑡)cos(2π𝑓𝑐t)- 𝑛𝑠(𝑡)sin(2π𝑓𝑐t )

Demodulate the received signal by first multiplying r(t) by a locally generated sinusoid cos(2𝜋fct + ∅),where is the phase of the sinusoid.Then passing the product signal through an ideal lowpass filter having a bandwidth W.

the effect of a phase difference between the received carrier and a locally generated carrier at the receiveris a drop equal to 𝑐𝑜𝑠2(∅) in the received signal power.
Phase-locked loop
The effect of a phase-locked loop is to generate phase of the received carrier at the receiver. If a phase-locked loop is employed, then = 0 and the demodulator is called a coherent or synchronous demodulator.

In our analysis in this section, we assume that we are employing a coherent demodulator. With this assumption, we assume that = 0
Y(t)=1 [𝐴2𝑚(𝑡) + 𝑛𝑐 (t)]
Therefore, at the receiver output, the message signal and the noise components are additive and we are able to define a meaningful SNR. The message signal power is given by 𝐴2