Communication Equations

Question 1

Symbol rate Rs

Answer 1

R_s =1/T_s

T_s is the symbol interval, i.e. the duration of a symbol.

Question 2

Bit Rate R_b

Answer 2

T_b =1 / R_b

T_b is the bit interval, i.e. the duration of a bit.

Question 3

How are Symbol & Bit Rate / Duration related?

Answer 3

Question 4

Average power associated with the digital signal

Answer 4

Question 5

Average energy per symbol is:

Answer 5

Question 6

Average Energy per bit:

Answer 6

Question 7

Average energy associated with a unipolar signaling scheme

Answer 7

Question 8

Average energy associated with a polar signaling scheme

Answer 8

Question 9

Average energy per symbol and per bit- for a common m-ary scheme

Answer 9

Question 10

How is thermal noise generated and what shape can it be modeled by?

Answer 10

Thermal noise is generated in electric devices by the vibration (thermal agitation) of electrons.

Thermal noise can be modelled by a zero-mean stationary white Gaussian process with spectral density

S_N(f) = N₀/2 = kT/2

Question 11

Baseband Digital Reciever: How is the signal component of a Matched Filter determined?

Answer 11

Question 12

Baseband Digital Reciever: How is the noise component of a Matched Filter determined?

Answer 12

Question 13

Baseband Digital Reciever: What is the maximum possible output signal-to-noise ratio of a Matched Filter?

Answer 13

maximum possible SNR is equal to 2*Ɛ_p/N₀

Question 14

Baseband Digital Reciever: What is the signal component output of a correlation and dump filter?

Answer 14

Question 15

Baseband Digital Reciever: What is the noise component output of a correlation and dump filter?

Answer 15

Note how the noise component of a Correlation and Dump filter is equivalent to a Matched Filter

Question 16

What is the probability density function of Noise N_k ?

Answer 16

Question 17

What is the probability density function of Y_k given X_k ?

What is it useful for?

Answer 17

You can determine the distribution of Y_k for all the values of X_k .

Question 18

MAP Detector/Decision Rule

What is it ‘optimal’ and what are its equations?

Answer 18

MAP decision rule is optimal in the sense that it minimizes the (symbol) error probability.

Question 19

ML Detector/Decision Rule

Answer 19

Question 20

Cauchy-Schwartz inequality states…

Answer 20

Question 21

Impulse response and the frequency response of the filter that maximizes the output signal-to-noise ratio at time t=τ is…

Answer 21

Question 22

Maximum possible output signal-to-noise ratio of matched filter…

Answer 22

Question 23

What does ∀ mean ?

Answer 23

“forall” (for all) symbol

Question 24

Topic 3/4: Overall Error Probability of a polar binary transmission scheme

Answer 24

Question 25

Topic 3/4: Overall Error Probability of a quaternary transmission scheme

Answer 25

Question 26

Topic 3/4: Overall Error Probability of a binary unipolar transmission scheme

Answer 26

Question 27

Topic 5: Binary Amplitude-Shift Keying Average energy per bit Distance between constellation points

Answer 27

Question 28

Topic 5: Binary Phase-Shift Keying Average energy per bit Distance between constellation points

Answer 28

Question 29

Topic 5: M-ary Amplitude-Shift Keying Average energy per bit Average energy per symbol Distance between constellation points

Answer 29

Assumed that the symbols A₁ , A₂ ,…,A_M are equally likely.

Question 30

Topic 5: Quadrature Amplitude Modulation Average energy per bit Average energy per symbol Distance between constellation points

Answer 30

Question 31

Topic 5: Power spectral density of the passband signal S_x(f)

Answer 31

So the power spectral density of the passband is based on the baseband calculation l stands for low pass