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# Noise in Communication System

Noise in Communication System

Contents

Recall Noise and its Types 1

Identify Sources of Noise 2

Define dB in Communications Systems 3

Recall Power Spectral Density of White Noise affecting: Message Signal and AM Signal and DSB-SC and SSB-SC Signal 4

Describe Mathematical representation of Noise and Narrowband Noise 5

Describe Power Spectral Density of In-phase component of noise affecting different Modulated Signals 6

Describe Noise Figure and Noise Factor 7

Describe Noise Figure Measurement 8

Recall figure-of-merit 8

Recall SNR at the Input of the DSB-SC Receiver 9

Recall SNR at the Output of the DSB-SC Receiver 10

Calculate the Figure-of-Merit of DSB-SC 11

Identify SNR Improvement in DSB-SC 12

Recall SNR at the Input of the SSB-SC Receiver 13

Recall SNR at the Output of the SSB-SC Receiver 14

Calculate the Figure-of-Merit of SSB-SC 14

Identify SNR Improvement in SSB-SC 14

Recall SNR at the Input of the AM Receiver 14

Recall SNR at the Output of the AM Receiver 14

Calculate figure-of-merit of AM 14

Identify SNR Improvement in AM 14

Recall SNR at the Input of the FM Receiver 14

Recall SNR at the Output of the FM Receiver 14

Calculate the figure-of-merit of FM 14

Identify SNR Improvement in FM 14

Recall the Threshold Effect in FM 14

# Recall Noise and its Types

Noise is an unwanted or undesired electrical or electromagnetic disturbance that can affect the performance of electronic systems. It can be classified into several types based on its origin and characteristics:

1. Thermal noise: This type of noise is produced by the random motion of electrons in a conductor or resistor. It is also known as Johnson noise or white noise, and has a flat frequency spectrum. Thermal noise is present in all electronic systems, and its intensity increases with temperature.

2. Intermodulation noise: This type of noise is produced by the nonlinearities in electronic components, such as transistors and diodes. It occurs when two or more signals are mixed together, and results in the generation of sum and difference frequencies that were not present in the original signals. Intermodulation noise can be a problem in systems that use a wide range of frequencies, and can be difficult to eliminate.

3. Crosstalk: This type of noise is produced when an undesired signal is coupled from one circuit or channel to another. It can occur due to proximity, capacitive coupling, or inductive coupling. Crosstalk can be a problem in systems that use multiple channels or circuits, and can be reduced by proper circuit layout and shielding.

4. Radio frequency interference (RFI): This type of noise is produced by electromagnetic radiation from sources such as radio transmitters, power lines, and motors. It can affect the performance of electronic systems, particularly those that operate at or near the frequency of the interference. RFI can be reduced by proper shielding and filtering.

5. Shot noise: This type of noise is produced by the random motion of charge carriers in a semiconductor or other active device. It is characterized by a frequency spectrum that is inversely proportional to the frequency, and is typically more significant at higher frequencies. Shot noise is a fundamental noise source, and cannot be completely eliminated.

6. Flicker noise: This type of noise is produced by the random fluctuation of the current or voltage in a device or circuit. It is also known as 1/f noise or pink noise, and has a frequency spectrum that decreases with frequency. Flicker noise is typically more significant at lower frequencies, and can be reduced by proper circuit design and device selection.

# Identify Sources of Noise

There are many sources of noise in electronic systems, including:

1. Thermal noise: This type of noise is produced by the random motion of electrons in a conductor or resistor. It is present in all electronic systems, and its intensity increases with temperature.

2. Intermodulation noise: This type of noise is produced by the nonlinearities in electronic components, such as transistors and diodes. It occurs when two or more signals are mixed together, and results in the generation of sum and difference frequencies that were not present in the original signals.

3. Crosstalk: This type of noise is produced when an undesired signal is coupled from one circuit or channel to another. It can occur due to proximity, capacitive coupling, or inductive coupling.

4. Radio frequency interference (RFI): This type of noise is produced by electromagnetic radiation from sources such as radio transmitters, power lines, and motors. It can affect the performance of electronic systems, particularly those that operate at or near the frequency of the interference.

5. Shot noise: This type of noise is produced by the random motion of charge carriers in a semiconductor or other active device. It is characterized by a frequency spectrum that is inversely proportional to the frequency, and is typically more significant at higher frequencies.

6. Flicker noise: This type of noise is produced by the random fluctuation of the current or voltage in a device or circuit. It is also known as 1/f noise or pink noise, and has a frequency spectrum that decreases with frequency. Flicker noise is typically more significant at lower frequencies.

Other sources of noise in electronic systems include mechanical vibrations, atmospheric noise, cosmic noise, and man-made noise from sources such as electrical appliances and industrial equipment. Noise can also be introduced by the transmission media, such as cables, connectors, and transmission lines.

# Define dB in Communications Systems

The decibel (dB) is a unit used to express the ratio of two quantities in logarithmic scale. It is commonly used in communications systems to express the gain or loss of a signal, or the level of a noise or interference.

In communications systems, the decibel is often used to express the power or voltage of a signal relative to a reference level. The reference level is usually chosen based on the sensitivity of the system or the desired signal-to-noise ratio. For example, in radio systems, the reference level is often taken as the power or voltage required to produce a certain signal-to-noise ratio at the receiver.

The decibel scale is logarithmic, which means that a change of one decibel represents a change in the ratio of the two quantities by a factor of 10. For example, a change of 10 dB represents a change in the ratio by a factor of 10, a change of 20 dB represents a change in the ratio by a factor of 100, and so on. This logarithmic scale allows for more convenient representation of large changes in signal level, as the range of possible signal levels can be very large in communications systems.

The decibel is often abbreviated as dB, and the symbol “dB” is used to indicate that the ratio of two quantities is expressed in decibels. For example, the power gain of an amplifier can be expressed as “Gain = 10 dB”, which means that the output power of the amplifier is 10 dB higher than the input power.

The decibel is a dimensionless unit, which means that it does not have an inherent unit of measurement. It is used to express the ratio of two quantities with the same units, such as watts, volts, or amperes. In order to express the decibel in terms of a specific unit of measurement, it is necessary to specify the reference level and the type of quantity being measured. For example, the decibel can be used to express the power of a signal relative to a reference level, in which case it is called the dBm (decibel relative to one milliwatt). Similarly, the decibel can be used to express the voltage of a signal relative to a reference level, in which case it is called the dBV (decibel relative to one volt).

# Recall Power Spectral Density of White Noise affecting: Message Signal and AM Signal and DSB-SC and SSB-SC Signal

The power spectral density (PSD) of white noise is constant over all frequencies. White noise is a type of noise that has equal power at all frequencies, and it is assumed to be additive and independent of the signal of interest. Therefore, the effect of white noise on different signals depends on the frequency range of the signal and the amount of noise power present.

Here are the effects of white noise on different signals:

1. Message signal: White noise affects the message signal by adding noise power to it. The amount of noise power added depends on the frequency range of the message signal and the noise power density. The noise power is proportional to the bandwidth of the message signal, and it is given by:
Pnoise = kTB
where k is the Boltzmann constant, T is the temperature, and B is the bandwidth of the message signal. Therefore, the higher the bandwidth of the message signal and the noise power density, the higher the noise power added to the signal.
2. AM signal: White noise affects the AM signal by adding noise power to both the carrier and the message signal. The amount of noise power added depends on the frequency range of the AM signal and the noise power density. The noise power added to the carrier signal is proportional to the carrier frequency, while the noise power added to the message signal is proportional to the message bandwidth.
3. DSB-SC signal: White noise affects the DSB-SC signal by adding noise power to both the carrier and the message signal. The amount of noise power added depends on the frequency range of the DSB-SC signal and the noise power density. The noise power added to the carrier signal is proportional to the carrier frequency, while the noise power added to the message signal is proportional to the message bandwidth.
4. SSB-SC signal: White noise affects the SSB-SC signal by adding noise power to the message signal only. The amount of noise power added depends on the frequency range of the SSB-SC signal and the noise power density. The noise power added to the message signal is proportional to the message bandwidth.
In all cases, the effect of white noise can be reduced by using techniques such as filtering and modulation techniques like phase-locked loop (PLL) or frequency synthesizer to improve signal-to-noise ratio (SNR) and reduce noise power in the frequency band of interest.

# Describe Mathematical representation of Noise and Narrowband Noise

Noise is a random or unpredictable electrical or electromagnetic disturbance that can affect the performance of electronic systems. It can be represented mathematically as a random process, which is a sequence of random variables that evolve over time.

The mathematical representation of noise depends on the type of noise and the characteristics of the system in which it is present. Some common methods for representing noise include:

1. Probability density function (PDF): This is a function that describes the probability of a noise variable taking on a particular value. For example, the PDF of Gaussian noise (also known as white noise) is given by:

PDF = (1 / √(2πσ2)) * exp(-x2 / (2σ2))

where x is the value of the noise variable, and σ is the standard deviation of the noise. The PDF of Gaussian noise is a bell-shaped curve, with the most probable value being zero.

2. Power spectral density (PSD): This is a function that describes the power per unit frequency band that is contained in the noise. The PSD is typically plotted as a function of frequency, and can be used to characterize the frequency content of the noise. For example, the PSD of white noise (a type of noise with a flat frequency spectrum) is constant across all frequencies.

3. Autocorrelation function (ACF): This is a function that describes the correlation between different samples of the noise at different times. The ACF is typically plotted as a function of the time lag between the samples, and can be used to characterize the temporal properties of the noise. For example, the ACF of white noise is zero at all time lags, which means that the noise is uncorrelated in time.

Narrowband noise is a type of noise that is concentrated within a narrow frequency band. It can be represented mathematically using the same methods as for noise in general, but with the frequency range restricted to the narrowband.

# Describe Power Spectral Density of In-phase component of noise affecting different Modulated Signals

The power spectral density (PSD) of the in-phase component of noise is a measure of the power per unit frequency band that is contained in the in-phase component of the noise. The in-phase component of noise is the part of the noise that is in phase with the carrier signal of a modulated signal.

The PSD of the in-phase component of noise can affect different types of modulated signals in different ways.

For an AM (amplitude modulation) signal, the in-phase component of noise can mask or distort the message, as well as introduce additional noise into the demodulated signal. The PSD of the in-phase component of noise is added to the PSD of the message signal during demodulation, which increases the overall noise level and reduces the signal-to-noise ratio.

For a DSB-SC (double sideband suppressed carrier) signal, the in-phase component of noise can also mask or distort the message, as well as introduce additional noise into the demodulated signal. The PSD of the in-phase component of noise is added to the PSD of the message signal during demodulation, which increases the overall noise level and reduces the signal-to-noise ratio.

For an SSB-SC (single sideband suppressed carrier) signal, the in-phase component of noise can also mask or distort the message, as well as introduce additional noise into the demodulated signal. The PSD of the in-phase component of noise is added to the PSD of the message signal during demodulation, which increases the overall noise level and reduces the signal-to-noise ratio.

For a QAM (quadrature amplitude modulation) signal, the in-phase component of noise can also mask or distort the message, as well as introduce additional noise into the demodulated signal. The PSD of the in-phase component of noise is added to the PSD of the message signal during demodulation, which increases the overall noise level and reduces the signal-to-noise ratio. The effect of the in-phase component of noise on QAM signals may be more severe than on other types of modulated signals, as QAM signals are more sensitive to noise.

# Describe Noise Figure and Noise Factor

Noise figure is a measure of the degradation in the signal-to-noise ratio (SNR) of a communication system or component due to the presence of noise. It is defined as the ratio of the output noise power to the input noise power of the system or component, normalized to a reference temperature and impedance.

Noise figure is typically expressed in decibels (dB), and is calculated using the following equation:

Noise Figure (dB) = 10 * log(Output Noise Power / Input Noise Power)

The noise figure of a system or component is a measure of the amount of noise that is introduced by the system or component. A system or component with a low noise figure will introduce less noise than a system or component with a high noise figure.

Noise factor is another measure of the degradation in the SNR of a communication system or component due to the presence of noise. It is defined as the ratio of the output noise power to the input noise power of the system or component, normalized to the noise power at the input.

Noise factor is typically expressed as a ratio, and is calculated using the following equation:

Noise Factor = Output Noise Power / Input Noise Power

The noise factor is related to the noise figure by the following equation:

Noise Figure (dB) = 10 * log(Noise Factor)

Like noise figure, the noise factor is a measure of the amount of noise that is introduced by the system or component. A system or component with a low noise factor will introduce less noise than a system or component with a high noise factor.

# Describe Noise Figure Measurement

Noise figure is a measure of the degradation in the signal-to-noise ratio (SNR) of a communication system or component due to the presence of noise. It is typically measured in decibels (dB), and is calculated using the following equation:

Noise Figure (dB) = 10 * log(Output Noise Power / Input Noise Power)

There are several methods for measuring the noise figure of a communication system or component, including:

1. Direct measurement: This method involves measuring the output noise power and input noise power of the system or component, and calculating the noise figure using the equation above. This method requires the use of specialized measurement equipment, such as noise generators, noise figure meters, and spectrum analyzers.

2. Noise parameter measurement: This method involves measuring the noise parameters of the system or component, such as the noise temperature, noise bandwidth, and noise resistance, and using these values to calculate the noise figure. This method requires the use of specialized measurement equipment, such as noise generators, noise temperature meters, and impedance analyzers.

3. Noise temperature measurement: This method involves measuring the noise temperature of the system or component, and using this value to calculate the noise figure. The noise temperature is defined as the temperature of a resistor that would produce the same amount of noise power as the system or component under test. This method requires the use of specialized measurement equipment, such as noise generators and noise temperature meters.

4. Noise-figure-dependent measurement: This method involves measuring a parameter that is dependent on the noise figure of the system or component, such as the signal-to-noise ratio or the output-to-input power ratio, and using this value to calculate the noise figure. This method requires the use of specialized measurement equipment, such as signal generators, spectrum analyzers, and power meters.

# Recall figure-of-merit

Figure of merit (FoM) is a measure of the performance of a communication system or component. It is a dimensionless quantity that is used to compare different systems or components based on their performance characteristics.

There are several different types of FoM, each of which is used to measure a specific aspect of system performance. Some common examples of FoM include:

1. Noise figure: This is a measure of the degradation in the signal-to-noise ratio (SNR) of a system or component due to the presence of noise. It is typically expressed in decibels (dB), and is a measure of the amount of noise that is introduced by the system or component.

2. Gain: This is a measure of the amplification or attenuation of a system or component. It is typically expressed in decibels (dB), and is a measure of the ratio of the output power or voltage to the input power or voltage.

3. Bandwidth: This is a measure of the range of frequencies over which a system or component can operate. It is typically expressed in hertz (Hz), and is a measure of the width of the frequency response of the system or component.

4. Efficiency: This is a measure of the amount of power that is lost in a system or component due to resistance, dissipative processes, or other factors. It is typically expressed as a percentage, and is a measure of the ratio of the output power to the input power.

5. Sensitivity: This is a measure of the minimum input power or voltage required to produce a specified output signal or performance. It is typically expressed in decibels (dB), and is a measure of the ability of the system or component to detect weak signals.

The choice of FoM depends on the specific application and the performance requirements of the system or component. Different FoM may be used to optimize different aspects of system performance, and trade-offs may be necessary to achieve the desired overall performance.

# Recall SNR at the Input of the DSB-SC Receiver

The signal-to-noise ratio (SNR) at the input of a DSB-SC (double sideband suppressed carrier) receiver is a measure of the strength of the desired signal relative to the level of noise present at the input. It is defined as the ratio of the power of the desired signal to the power of the noise, and is typically expressed in decibels (dB).

The SNR at the input of a DSB-SC receiver can be affected by a variety of factors, including the transmitter power, the transmission distance, the receiver sensitivity, the receiver noise figure, and the presence of interference or noise sources.

In a DSB-SC receiver, the SNR at the input is an important factor in determining the performance of the receiver. A higher SNR at the input results in a higher SNR at the output of the receiver, which can improve the performance of the demodulation process and result in a clearer and more accurate demodulated signal.

The SNR at the input of a DSB-SC receiver can be improved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver. It can also be improved by reducing the level of interference or noise present in the system, or by using techniques such as filtering or frequency-selective amplification to remove or reduce the effect of interference or noise.

# Recall SNR at the Output of the DSB-SC Receiver

The signal-to-noise ratio (SNR) at the output of a DSB-SC (double sideband suppressed carrier) receiver is a measure of the strength of the demodulated signal relative to the level of noise present at the output. It is defined as the ratio of the power of the demodulated signal to the power of the noise, and is typically expressed in decibels (dB).

The SNR at the output of a DSB-SC receiver is determined by the SNR at the input, as well as the performance of the demodulation process. In general, a higher SNR at the input results in a higher SNR at the output, and a lower SNR at the input results in a lower SNR at the output.

The SNR at the output of a DSB-SC receiver can be improved by increasing the SNR at the input, or by using techniques such as filtering or signal processing to remove or reduce the effect of noise. It can also be improved by using more advanced demodulation techniques that are better able to extract the desired signal from the noise.

The SNR at the output of a DSB-SC receiver is an important factor in determining the performance of the receiver. A higher SNR at the output results in a clearer and more accurate demodulated signal, which can improve the overall performance of the communication system.

# Calculate the Figure-of-Merit of DSB-SC

The Figure-of-Merit (FOM) of a communication system is a metric used to evaluate its performance based on parameters such as power efficiency, bandwidth utilization, and signal quality. To calculate the FOM of a Double-Sideband Suppressed Carrier (DSB-SC) modulation scheme, we need specific values for these parameters. Let’s consider an example to illustrate the calculation.

Example:

Suppose we have a DSB-SC system with the following parameters:

• Peak amplitude of the modulating signal (m): 2 V
• Carrier frequency (fc): 1 MHz
• Modulating signal frequency (fm): 10 kHz
• Total power of the modulating signal (Pm): 1 W

To calculate the FOM, we’ll consider power efficiency as the ratio of the modulating signal power to the total transmitted power, and bandwidth utilization as the ratio of the bandwidth occupied by the DSB-SC signal to the total available bandwidth.

1. Power Efficiency:

The power efficiency is calculated using the formula:

Power efficiency = (Pm / Pt) * 100%

where Pm is the power of the modulating signal, and Pt is the total transmitted power.

In our example, Pm = 1 W, and the DSB-SC modulation does not transmit a carrier, so the total transmitted power consists only of the power in the sidebands.

Pt = Power in sidebands = (m^2/2) * Pc

where m is the peak amplitude of the modulating signal, and Pc is the power of the carrier.

Since DSB-SC suppresses the carrier, the power in the sidebands is given by:

Pc = (m^2/2) / 2 = m^2/4

Substituting the values:

Pt = (2^2/2) * (2^2/4) = 1 W

Power efficiency = (Pm / Pt) * 100% = (1 / 1) * 100% = 100%

1. Bandwidth Utilization:

The bandwidth utilization is calculated by dividing the occupied bandwidth of the DSB-SC signal by the total available bandwidth.

In DSB-SC, the occupied bandwidth is twice the bandwidth of the modulating signal.

Occupied Bandwidth = 2 * fm

In our example, fm = 10 kHz, so the occupied bandwidth is:

Occupied Bandwidth = 2 * 10 kHz = 20 kHz

Assuming we have a total available bandwidth of 100 kHz,

Bandwidth utilization = (Occupied Bandwidth / Total Available Bandwidth) * 100% = (20 kHz / 100 kHz) * 100% = 20%

1. Signal Quality:

The signal quality aspect of the FOM can be subjective and may require specific parameters or metrics based on the system requirements. For example, it could include metrics such as signal-to-noise ratio (SNR), bit error rate (BER), or other relevant measures.

Once you define the specific signal quality metric, you can incorporate it into the FOM calculation by assigning a weight to it and combining it with the power efficiency and bandwidth utilization values.

The overall FOM can be calculated by combining the power efficiency, bandwidth utilization, and signal quality components based on the specific weights assigned to each factor.

It’s important to note that the FOM calculation can be customized based on the requirements and priorities of the system being evaluated.

# Identify SNR Improvement in DSB-SC

The signal-to-noise ratio (SNR) at the output of a DSB-SC (double sideband suppressed carrier) receiver is a measure of the strength of the demodulated signal relative to the level of noise present at the output. It is defined as the ratio of the power of the demodulated signal to the power of the noise, and is typically expressed in decibels (dB).

There are several ways to improve the SNR at the output of a DSB-SC receiver, including:

1. Increase the SNR at the input: The SNR at the output of a DSB-SC receiver is determined, in part, by the SNR at the input. Increasing the SNR at the input can result in an improvement in the SNR at the output. This can be achieved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver.

2. Use signal processing techniques: Techniques such as filtering or signal processing can be used to remove or reduce the effect of noise on the demodulated signal. This can improve the SNR at the output of the receiver.

3. Use advanced demodulation techniques: More advanced demodulation techniques, such as coherent detection or maximum likelihood detection, can be more effective at extracting the desired signal from the noise. Using these techniques can result in an improvement in the SNR at the output of the receiver.

4. Reduce the level of interference or noise: Reducing the level of interference or noise present in the system can also improve the SNR at the output of the receiver.

# Recall SNR at the Input of the SSB-SC Receiver

The signal-to-noise ratio (SNR) at the input of a SSB-SC (single sideband suppressed carrier) receiver is a measure of the strength of the desired signal relative to the level of noise present at the input. It is defined as the ratio of the power of the desired signal to the power of the noise, and is typically expressed in decibels (dB).

The SNR at the input of a SSB-SC receiver can be affected by a variety of factors, including the transmitter power, the transmission distance, the receiver sensitivity, the receiver noise figure, and the presence of interference or noise sources.

In a SSB-SC receiver, the SNR at the input is an important factor in determining the performance of the receiver. A higher SNR at the input results in a higher SNR at the output of the receiver, which can improve the performance of the demodulation process and result in a clearer and more accurate demodulated signal.

The SNR at the input of a SSB-SC receiver can be improved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver. It can also be improved by reducing the level of interference or noise present in the system, or by using techniques such as filtering or frequency-selective amplification to remove or reduce the effect of interference or noise.

# Recall SNR at the Output of the SSB-SC Receiver

The Signal-to-Noise Ratio (SNR) at the output of the SSB-SC receiver is an important parameter that determines the quality of the received signal. In SSB-SC systems, the receiver has to extract the modulating signal from the received single sideband signal. This process can be affected by noise, interference, and distortion, which can degrade the quality of the received signal and reduce the SNR.
The SNR at the output of the SSB-SC receiver can be defined as the ratio of the power of the received modulating signal to the power of the noise at the receiver output. The SNR can be expressed in decibels (dB) using the following formula:
SNR (dB) = 10 log10 (Psignal / Pnoise)
where Psignal is the power of the received modulating signal and Pnoise is the power of the noise at the receiver output.The SNR can be affected by several factors, including the quality of the receiver components, the strength of the received signal, the bandwidth of the receiver, and the level of interference and noise in the transmission channel. In SSB-SC systems, the SNR can be improved by using high-quality filters and amplifiers, by increasing the received signal strength using a larger antenna or a higher transmitting power, and by reducing the interference and noise in the transmission channel.

In addition to the SNR, other parameters such as the Bit Error Rate (BER) and the Carrier-to-Noise Ratio (CNR) can also be used to measure the quality of the received signal in SSB-SC systems. The BER is a measure of the number of bit errors in the received signal, while the CNR is the ratio of the power of the received carrier signal to the power of the noise at the receiver output. All of these parameters are important in evaluating the performance of the SSB-SC system and ensuring high-quality communication.

# Calculate the Figure-of-Merit of SSB-SC

The figure-of-merit (FoM) of a SSB-SC (single sideband suppressed carrier) receiver is a measure of the performance of the receiver. It is a dimensionless quantity that is used to compare different receivers based on their performance characteristics.

There are several different types of FoM that can be used to measure the performance of a SSB-SC receiver, including:

1. Noise figure: This is a measure of the degradation in the signal-to-noise ratio (SNR) of the receiver due to the presence of noise. It is typically expressed in decibels (dB), and is a measure of the amount of noise that is introduced by the receiver.

2. Gain: This is a measure of the amplification or attenuation of the receiver. It is typically expressed in decibels (dB), and is a measure of the ratio of the output power or voltage to the input power or voltage.

3. Bandwidth: This is a measure of the range of frequencies over which the receiver can operate. It is typically expressed in hertz (Hz), and is a measure of the width of the frequency response of the receiver.

4. Efficiency: This is a measure of the amount of power that is lost in the receiver due to resistance, dissipative processes, or other factors. It is typically expressed as a percentage, and is a measure of the ratio of the output power to the input power.

5. Sensitivity: This is a measure of the minimum input power or voltage required to produce a specified output signal or performance. It is typically expressed in decibels (dB), and is a measure of the ability of the receiver to detect weak signals.

The choice of FoM depends on the specific application and the performance requirements of the receiver. Different FoM may be used to optimize different aspects of receiver performance, and trade-offs may be necessary to achieve the desired overall performance.

To calculate the FoM of a SSB-SC receiver, the values of the relevant performance parameters must be measured or calculated, and the FoM formula must be applied. For example, to calculate the noise figure of a SSB-SC receiver, the output noise power and input noise power of the receiver must be measured or calculated, and the noise figure formula must be applied. The formula for noise figure is:
Noise Figure (dB) = 10 * log(Output Noise Power / Input Noise Power)

# Identify SNR Improvement in SSB-SC

The signal-to-noise ratio (SNR) at the output of a SSB-SC (single sideband suppressed carrier) receiver is a measure of the strength of the demodulated signal relative to the level of noise present at the output. It is defined as the ratio of the power of the demodulated signal to the power of the noise, and is typically expressed in decibels (dB).

There are several ways to improve the SNR at the output of a SSB-SC receiver, including:

1. Increase the SNR at the input: The SNR at the output of a SSB-SC receiver is determined, in part, by the SNR at the input. Increasing the SNR at the input can result in an improvement in the SNR at the output. This can be achieved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver.

2. Use signal processing techniques: Techniques such as filtering or signal processing can be used to remove or reduce the effect of noise on the demodulated signal. This can improve the SNR at the output of the receiver.

3. Use advanced demodulation techniques: More advanced demodulation techniques, such as coherent detection or maximum likelihood detection, can be more effective at extracting the desired signal from the noise. Using these techniques can result in an improvement in the SNR at the output of the receiver.

4. Reduce the level of interference or noise: Reducing the level of interference or noise present in the system can also improve the SNR at the output of the receiver.

# Recall SNR at the Input of the AM Receiver

The signal-to-noise ratio (SNR) at the input of an AM (amplitude modulated) receiver is a measure of the strength of the desired signal relative to the level of noise present at the input. It is defined as the ratio of the power of the desired signal to the power of the noise, and is typically expressed in decibels (dB).

The SNR at the input of an AM receiver can be affected by a variety of factors, including the transmitter power, the transmission distance, the receiver sensitivity, the receiver noise figure, and the presence of interference or noise sources.

In an AM receiver, the SNR at the input is an important factor in determining the performance of the receiver. A higher SNR at the input results in a higher SNR at the output of the receiver, which can improve the performance of the demodulation process and result in a clearer and more accurate demodulated signal.

The SNR at the input of an AM receiver can be improved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver. It can also be improved by reducing the level of interference or noise present in the system, or by using techniques such as filtering or frequency-selective amplification to remove or reduce the effect of interference or noise.

# Recall SNR at the Output of the AM Receiver

The signal-to-noise ratio (SNR) at the output of an AM (amplitude modulated) receiver is a measure of the strength of the demodulated signal relative to the level of noise present at the output. It is defined as the ratio of the power of the demodulated signal to the power of the noise, and is typically expressed in decibels (dB).

The SNR at the output of an AM receiver is determined by the SNR at the input, as well as the performance of the demodulation process. In general, a higher SNR at the input results in a higher SNR at the output, and a lower SNR at the input results in a lower SNR at the output.

The SNR at the output of an AM receiver can be improved by increasing the SNR at the input, or by using techniques such as filtering or signal processing to remove or reduce the effect of noise. It can also be improved by using more advanced demodulation techniques that are better able to extract the desired signal from the noise.

The SNR at the output of an AM receiver is an important factor in determining the performance of the receiver. A higher SNR at the output results in a clearer and more accurate demodulated signal, which can improve the overall performance of the communication system.

# Calculate figure-of-merit of AM

The figure-of-merit (FoM) of an AM (amplitude modulated) receiver is a measure of the performance of the receiver. It is a dimensionless quantity that is used to compare different receivers based on their performance characteristics.

There are several different types of FoM that can be used to measure the performance of an AM receiver, including:

1. Noise figure: This is a measure of the degradation in the signal-to-noise ratio (SNR) of the receiver due to the presence of noise. It is typically expressed in decibels (dB), and is a measure of the amount of noise that is introduced by the receiver.

2. Gain: This is a measure of the amplification or attenuation of the receiver. It is typically expressed in decibels (dB), and is a measure of the ratio of the output power or voltage to the input power or voltage.

3. Bandwidth: This is a measure of the range of frequencies over which the receiver can operate. It is typically expressed in hertz (Hz), and is a measure of the width of the frequency response of the receiver.

4. Efficiency: This is a measure of the amount of power that is lost in the receiver due to resistance, dissipative processes, or other factors. It is typically expressed as a percentage, and is a measure of the ratio of the output power to the input power.

5. Sensitivity: This is a measure of the minimum input power or voltage required to produce a specified output signal or performance. It is typically expressed in decibels (dB), and is a measure of the ability of the receiver to detect weak signals.

The choice of FoM depends on the specific application and the performance requirements of the receiver. Different FoM may be used to optimize different aspects of receiver performance, and trade-offs may be necessary to achieve the desired overall performance.

To calculate the FoM of an AM receiver, the values of the relevant performance parameters must be measured or calculated, and the FoM formula must be applied. For example, to calculate the noise figure of an AM receiver, the output noise power and input noise power of the receiver must be measured or calculated, and the noise figure formula must be applied. The formula for noise figure is:

Noise Figure (dB) = 10 * log(Output Noise Power / Input Noise Power)

# Identify SNR Improvement in AM

There are several ways to improve the signal-to-noise ratio (SNR) at the output of an AM (amplitude modulated) receiver, including:

1. Increase the SNR at the input: The SNR at the output of an AM receiver is determined, in part, by the SNR at the input. Increasing the SNR at the input can result in an improvement in the SNR at the output. This can be achieved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver.

2. Use signal processing techniques: Techniques such as filtering or signal processing can be used to remove or reduce the effect of noise on the demodulated signal. This can improve the SNR at the output of the receiver.

3. Use advanced demodulation techniques: More advanced demodulation techniques, such as coherent detection or maximum likelihood detection, can be more effective at extracting the desired signal from the noise. Using these techniques can result in an improvement in the SNR at the output of the receiver.

4. Reduce the level of interference or noise: Reducing the level of interference or noise present in the system can also improve the SNR at the output of the receiver.

# Recall SNR at the Input of the FM Receiver

The signal-to-noise ratio (SNR) at the input of an FM (frequency modulated) receiver is a measure of the strength of the desired signal relative to the level of noise present at the input. It is defined as the ratio of the power of the desired signal to the power of the noise, and is typically expressed in decibels (dB).

The SNR at the input of an FM receiver can be affected by a variety of factors, including the transmitter power, the transmission distance, the receiver sensitivity, the receiver noise figure, and the presence of interference or noise sources.

In an FM receiver, the SNR at the input is an important factor in determining the performance of the receiver. A higher SNR at the input results in a higher SNR at the output of the receiver, which can improve the performance of the demodulation process and result in a clearer and more accurate demodulated signal.

The SNR at the input of an FM receiver can be improved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver. It can also be improved by reducing the level of interference or noise present in the system, or by using techniques such as filtering or frequency-selective amplification to remove or reduce the effect of interference or noise.

# Recall SNR at the Output of the FM Receiver

The signal-to-noise ratio (SNR) at the output of an FM (frequency modulated) receiver is a measure of the strength of the demodulated signal relative to the level of noise present at the output. It is defined as the ratio of the power of the demodulated signal to the power of the noise, and is typically expressed in decibels (dB).

The SNR at the output of an FM receiver is determined by the SNR at the input, as well as the performance of the demodulation process. In general, a higher SNR at the input results in a higher SNR at the output, and a lower SNR at the input results in a lower SNR at the output.

The SNR at the output of an FM receiver can be improved by increasing the SNR at the input, or by using techniques such as filtering or signal processing to remove or reduce the effect of noise. It can also be improved by using more advanced demodulation techniques that are better able to extract the desired signal from the noise.

The SNR at the output of an FM receiver is an important factor in determining the performance of the receiver. A higher SNR at the output results in a clearer and more accurate demodulated signal, which can improve the overall performance of the communication system.

# Calculate the figure-of-merit of FM

The figure-of-merit (FoM) of an FM (frequency modulated) receiver is a measure of the performance of the receiver. It is a dimensionless quantity that is used to compare different receivers based on their performance characteristics.

There are several different types of FoM that can be used to measure the performance of an FM receiver, including:

1. Noise figure: This is a measure of the degradation in the signal-to-noise ratio (SNR) of the receiver due to the presence of noise. It is typically expressed in decibels (dB), and is a measure of the amount of noise that is introduced by the receiver.

2. Gain: This is a measure of the amplification or attenuation of the receiver. It is typically expressed in decibels (dB), and is a measure of the ratio of the output power or voltage to the input power or voltage.

3. Bandwidth: This is a measure of the range of frequencies over which the receiver can operate. It is typically expressed in hertz (Hz), and is a measure of the width of the frequency response of the receiver.

4. Efficiency: This is a measure of the amount of power that is lost in the receiver due to resistance, dissipative processes, or other factors. It is typically expressed as a percentage, and is a measure of the ratio of the output power to the input power.

5. Sensitivity: This is a measure of the minimum input power or voltage required to produce a specified output signal or performance. It is typically expressed in decibels (dB), and is a measure of the ability of the receiver to detect weak signals.

The choice of FoM depends on the specific application and the performance requirements of the receiver. Different FoM may be used to optimize different aspects of receiver performance, and trade-offs may be necessary to achieve the desired overall performance.

To calculate the FoM of an FM receiver, the values of the relevant performance parameters must be measured or calculated, and the FoM formula must be applied. For example, to calculate the noise figure of an FM receiver, the output noise power and input noise power of the receiver must be measured or calculated, and the noise figure formula must be applied. The formula for noise figure is:

Noise Figure (dB) = 10 * log(Output Noise Power / Input Noise Power)

# Identify SNR Improvement in FM

There are several ways to improve the signal-to-noise ratio (SNR) at the output of an FM (frequency modulated) receiver, including:

In FM (frequency modulation), the signal-to-noise ratio (SNR) can be improved by increasing the deviation of the carrier frequency from its center frequency, which is also known as the modulation index (m). The modulation index is defined as the ratio of the frequency deviation (Δf) to the maximum frequency of the modulating signal (fm), i.e.,

m = Δf/fm

When the modulation index is small, the FM signal is less affected by noise, but the frequency spectrum of the signal is narrow. On the other hand, when the modulation index is large, the FM signal is more affected by noise, but the frequency spectrum of the signal is wide.

To improve the SNR of an FM signal, the modulation index can be increased to some optimal value. At this optimal value, the FM signal has a wider frequency spectrum but still maintains a reasonable level of noise tolerance. The increase in modulation index results in an increase in the signal power and hence an increase in the SNR.

However, it should be noted that increasing the modulation index beyond the optimal value will result in a decrease in the SNR, as the FM signal becomes more affected by noise. Therefore, it is essential to find the optimal modulation index for a given system and signal-to-noise ratio requirements.

Additionally, other techniques such as pre-emphasis and de-emphasis can also be used to improve the SNR of FM signals. Pre-emphasis is used to boost the high-frequency components of the modulating signal before modulation, while de-emphasis is used to attenuate the high-frequency components of the demodulated signal after demodulation. This technique can improve the SNR by reducing the noise power in the frequency band of interest.

# Recall the Threshold Effect in FM

The threshold effect in FM (frequency modulated) refers to the phenomenon where the demodulated signal quality in an FM receiver begins to degrade as the signal-to-noise ratio (SNR) at the input falls below a certain level. This threshold level, also known as the threshold of hearing, is determined by the characteristics of the demodulation process and the human auditory system.

At SNR levels above the threshold, the demodulated signal quality is relatively unaffected by noise. However, as the SNR falls below the threshold, the demodulated signal quality begins to degrade rapidly, even in the presence of relatively low levels of noise. This phenomenon is known as the threshold effect.

The threshold effect in FM is a consequence of the non-linear behavior of the demodulation process. At low SNR levels, the demodulation process is more susceptible to noise, and the demodulated signal becomes distorted or corrupted. This can result in a significant reduction in the quality of the demodulated signal, which can be perceived as a reduction in the intelligibility or clarity of the received message.

To minimize the impact of the threshold effect in FM, it is important to maintain a high SNR at the input of the receiver. This can be achieved by increasing the transmitter power, reducing the transmission distance, increasing the receiver sensitivity, or reducing the noise figure of the receiver. It can also be achieved by reducing the level of interference or noise present in the system, or by using techniques such as filtering or frequency-selective amplification to remove or reduce the effect of interference or noise.