Communication Equations Flashcards
Symbol rate Rs
Rs =1/Ts
Ts is the symbol interval, i.e. the duration of a symbol.
Bit Rate Rb
Tb =1 / Rb
Tb is the bit interval, i.e. the duration of a bit.
How are Symbol & Bit Rate / Duration related?
Average power associated with the digital signal
Average energy per symbol is:
Average Energy per bit:
Average energy associated with a unipolar signaling scheme
Average energy associated with a polar signaling scheme
Average energy per symbol and per bit- for a common m-ary scheme
How is thermal noise generated and what shape can it be modeled by?
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
SN(f) = N0/2 = kT/2
Baseband Digital Reciever: How is the signal component of a Matched Filter determined?
Baseband Digital Reciever: How is the noise component of a Matched Filter determined?
Baseband Digital Reciever: What is the maximum possible output signal-to-noise ratio of a Matched Filter?
maximum possible SNR is equal to 2*Ɛp/N0
Baseband Digital Reciever: What is the signal component output of a correlation and dump filter?
Baseband Digital Reciever: What is the noise component output of a correlation and dump filter?
Note how the noise component of a Correlation and Dump filter is equivalent to a Matched Filter
What is the probability density function of Noise Nk ?
What is the probability density function of Yk given Xk ?
What is it useful for?
You can determine the distribution of Yk for all the values of Xk .
MAP Detector/Decision Rule
What is it ‘optimal’ and what are its equations?
MAP decision rule is optimal in the sense that it minimizes the (symbol) error probability.
ML Detector/Decision Rule
Cauchy-Schwartz inequality states…
Impulse response and the frequency response of the filter that maximizes the output signal-to-noise ratio at time t=τ is…
Maximum possible output signal-to-noise ratio of matched filter…
What does ∀ mean ?
“forall” (for all) symbol
Topic 3/4: Overall Error Probability of a polar binary transmission scheme
Topic 3/4: Overall Error Probability of a quaternary transmission scheme
Topic 3/4: Overall Error Probability of a binary unipolar transmission scheme
Topic 5: Binary Amplitude-Shift Keying
Average energy per bit
Distance between constellation points
Topic 5: Binary Phase-Shift Keying
Average energy per bit
Distance between constellation points
Topic 5: M-ary Amplitude-Shift Keying
Average energy per bit
Average energy per symbol
Distance between constellation points
Assumed that the symbols A1 , A2 ,…,AM are equally likely.
Topic 5: Quadrature Amplitude Modulation
Average energy per bit
Average energy per symbol
Distance between constellation points
Topic 5: Power spectral density of the passband signal Sx(f)
So the power spectral density of the passband is based on the baseband calculation
l stands for low pass
