Statistical properties of digital signals
Statistical properties of noise n(t)
Statistical characteristics of received voltage r(t)
Best reception of digital signals
Total bit error rate Pe
Judgment rules
Called the "maximum likelihood criterion", it can minimize the bit error rate
maximum posterior probability criterion
Under the condition of Gaussian white noise: the maximum likelihood criterion is equivalent to the maximum posterior probability criterion
The best receiver for digital signals
Optimum receiver structure for binary known signals
Principle block diagram of the best receiver for M-ary, equal-general, and known signals:
Determine the bit error rate for optimal reception of digital signals
Best receiver error performance for binary known signals
The total bit error rate of a binary communication system
Calculation of bit error rate when P(0)=P(1)=1/2
Cross-correlation coefficient ρ
Bit error rate of multi-digit communication system
Best reception of phase-following digital signals
Best receiver architecture
The bit error rate of the best receiver for following signals
Best baseband transmission system
The best baseband system under ideal channel
Two conditions for optimization:
(1)H(ω) should satisfy the frequency domain condition of no inter-code crosstalk, that is
(2) Minimize the system output error probability
The best baseband transmission system consists of:
Error performance of optimal baseband transmission systems:
Optimal baseband system under non-ideal channels
optimal transmission conditions
(1) Minimize the bit error rate
(2) Eliminate inter-code crosstalk
Matched filter reception method of digital signals
Transmission characteristics of matched filter - H(ω)
It is a linear filter that can obtain the maximum output signal-to-noise ratio at the sampling time.
Impulse response of matched filter—— h(t)↔H(f)
The output signal of the matched filter - so(t)
Best receiver in the form of matched filtering
Performance comparison of actual receivers and optimal receivers
Best reception of fluctuating digital signals
Best receiver architecture