Block diagram of a digital data transmission Data

Block diagram of a digital data transmission

Data compression : - correlation - redundancy PCM : 64 Kbps ==> ADPCM : 32 Kbps vocoder : 8 Kbps, 13 Kbps QCELP, EVRC ==> CDMA 휴대폰 vocoder MPEG 4(Motion Picture Expert Group 4) MP 3 : audio compression A 2 b : audio compression

M-ary Modulation ASK FSK PSK Coherent / Noncoherent (oscillator) Synchronous /Asynchronous (clock) “ The primary measure of system performance for digital data communication systems is the probability of error Pe ”

System model and waveforms for synchronous baseband digital data transmission Transmitter Receiver

Receiver structure and integrator output

Linear systems and random processes • The autocorrelation function of the output of a linear system in terms of the input autocorrelation function 평균 전력

Cross-correlation function between input and output The cross-correlation function of input with output is the autocorrelation function of the input convolved with the impulse response

Fourier transform From the time-reversal theorem 다음 page Inverse fourier transform

7. 2 Binary Synchronous Data Transmission with Arbitrary Signal Shapes Receiver Structure and Error Probability

h(t) Threshold H(f) k

The task now is to minimize this error probability by adjusting the threshold k and the impulse response h(t)

Because of the equal a priori probabilities for the symmetrical shapes of and Resonable choice

The Matched Filter that maximizes distances between two signals decreases with increasing distance

Since the input noise is stationary, To maximize the above equation, we employ Schwarz’s inequality Equality is holds if and only equals

Equality condition Optimum choice for setting

Considering the case of two complex functions Inner product and

Matched filter receiver for binary signaling in white Gaussian Ex. 7. 3 Matched filter

Ex. 7. 4 The condition of A, B for the same signal to noise at the matched filter output, is the same for both cases

Error probability for the matched filter receiver From (7. 30) page 465 <= (7. 39) Using Parseval’s theorem, frequency domain to time domain

antipodal

Correlator implementation of the matched filter receiver Same result

Optimum threshold Refer to (7. 29) page 465

Nonwhite(colored) noise background white noise bandlimiting filter such as passband filter following intermediate frequency amplifier colored noise Prewhitening filter ISI generation white noise