Question

An FSK system transmits binary data at the rate of 2.5%106 bits per second. During the course of transmission, white Gaussian noise of zero mean and power spectral density 1020 watts per hertz is added to the signal. In the absence of noise, the amplitude of the received sinusoidal wave for digit 1 or 0 is 1 microvolt. De termine the average probability of symbol error for the following system configurations

a. Coherent binary FSK.
b. Coherent MSK.
c. Noncoherent binary FSK.

Answer 1

The average probability of symbol error for FSK systems can be calculated using different formulas for coherent binary FSK, coherent MSK, and noncoherent binary FSK.

Step-by-step explanation:

a. The average probability of symbol error for coherent binary FSK can be calculated using the formula:

Pe = Q ( √ (2Es1) / N0, ⁄ (2Es0) / N0)

Where:

• Pe is the average probability of symbol error
• Q is the Q-function
• Es1 and Es0 are the energies of the signals for digit 1 and 0, respectively
• N0 is the one-sided power spectral density of the white Gaussian noise

b. The average probability of symbol error for coherent MSK can be calculated using a different formula, which depends on the modulation index.

c. The average probability of symbol error for noncoherent binary FSK can be calculated using another formula, which considers the signal-to-noise ratio.

Answer 2

The average probability of symbol error for different FSK system configurations can be determined using specific formulas. The formulas take into account parameters such as the energy of each symbol, the power spectral density of the noise, and the bandwidth of the system. By calculating the average probability of symbol error, we can compare the performance of different FSK system configurations and determine their reliability in the presence of noise.

Step-by-step explanation:

a. Coherent binary FSK:

The average probability of symbol error for a coherent binary FSK system can be determined using the formula:

P(e) = Q(sqrt((4 * Es) / (N0 * B)))

Where:

• P(e) is the average probability of symbol error
  
• Q is the Q-function, which is a mathematical function used in probability theory and statistics
  
• Es is the energy of each symbol, given by Es = A² / 2, where A is the amplitude of the received sinusoidal wave for digit 1 or 0
  
• N0 is the power spectral density of the white Gaussian noise
  
• B is the bandwidth of the system, given by B = 2 * R, where R is the rate of transmission
  

Using the given values, we can calculate the average probability of symbol error for a coherent binary FSK system.

b. Coherent MSK:

The average probability of symbol error for a coherent MSK system can also be determined using the same formula as above.

c. Noncoherent binary FSK:

The average probability of symbol error for a noncoherent binary FSK system can be determined using a different formula:

P(e) = Q(sqrt((Es) / (N0 * B)))

Where the values of Es, N0, and B are the same as in the previous formula.

By calculating the average probability of symbol error for each system configuration, we can compare their performance and determine which one is more reliable in the presence of white Gaussian noise.