Question

The 2-bit communication transmitter below is used to emit equally likely messages over AWGN channel with zero mean and two-sided PSD No/2 = 1 Watt/Hz. The inter-distance (in the signal space) between the signals of the BPSK modulator is 4 and the inter-distance between the signals of the OOK (ON-OFF Keying) modulator equals 2.

a) Write down the equations of the possible output signals.

b) Sketch to scale the output signals in signal space showing the bits assigned to each message point, and then define the decision regions (DRs) and decision boundaries (DBs).

c) Find the average energy of the transmitted signals.

d) Calculate the average probability of error.

Answer 1

To determine the molar concentration of cobalt in the diluted solution, you can use the Beer-Lambert law, which relates the absorbance (A), molar absorptivity (ε), path length (b), and concentration (C) of a solution:

A = ε * b * C

In this case, you are given the absorbance (A), the molar absorptivity (εCo = 36400 M^(-1)cm^(-1)), and the path length (b = 1.0 cm). You need to find the concentration (C) of cobalt.

(a) Calculate the molar concentration of cobalt (C):

A = ε * b * C 0.371 = (36400 M^(-1)cm^(-1)) * (1.0 cm) * C

Now, solve for C:

C = 0.371 / (36400 M^(-1)cm^(-1)) C ≈ 1.016 x 10^(-5) M

So, the molar concentration of cobalt in the diluted solution is approximately 1.016 x 10^(-5) M.

(b) To determine the concentration in ppm (parts per million) of cobalt in the sample, you need to consider the dilution and the mass of the sample.

Given:

• Sample mass (m) = 0.515 g

• Dilution factor (D) = V_final / V_aliquot = (50.0 mL) / (20.0 mL) = 2.5

The concentration in ppm can be calculated using the following formula:

Concentration (in ppm) = (g of solute / g of solution) x 10^6

First, calculate the mass of cobalt in the aliquot:

Mass of cobalt in the aliquot = C * V_aliquot = (1.016 x 10^(-5) M) * (20.0 mL) = 2.032 x 10^(-7) moles

Now, calculate the mass of cobalt in the entire sample:

Mass of cobalt in the sample = Mass in the aliquot / Dilution factor Mass of cobalt in the sample = (2.032 x 10^(-7) moles) / 2.5 = 8.128 x 10^(-8) moles

Now, convert the moles of cobalt to grams using the molar mass of cobalt:

Mass of cobalt in the sample = (8.128 x 10^(-8) moles) * (58.93 g/mol) = 4.807 x 10^(-6) g

Finally, calculate the concentration in ppm:

Concentration (in ppm) = (4.807 x 10^(-6) g / 0.515 g) x 10^6 Concentration (in ppm) ≈ 9,331.07 ppm

So, the concentration of cobalt in the sample is approximately 9,331.07 ppm.