Question

A binary digital communication system employs the signals

s₀(t)=0, 0≤tand
s₁(t)=A,0≤tfor transmitting the information. This is called on-off signaling. The demodulato cross correlates the received signal r(t) with s(t) and samples the output of thr correlator at t=T.
1. Determine the optimum detector for an AWGN channel and the optimum thresh old, assuming that the signals are equally probable.
2. Determine the probability of error as a function of the SNR. How does on-of signaling compare with antipodal signaling?

Answer 1

The optimum detector for an AWGN channel in an on-off signaling system is a matched filter, and the optimum threshold is usually set at the midpoint between the mean values of the noise-free signals. The probability of error in an AWGN channel can be determined using the Q-function, and it increases as the signal-to-noise ratio decreases. Antipodal signaling typically achieves lower probabilities of error compared to on-off signaling for the same SNR.

Step-by-step explanation:

An optimum detector for an AWGN (Additive White Gaussian Noise) channel in an on-off signaling system is a matched filter. The matched filter is a filter whose impulse response is a time-reversed and scaled version of the transmitted signal. The optimum threshold for detection is usually set at the midpoint between the mean values of the noise-free signals 0 and A. By adjusting the threshold, the receiver can control the trade-off between probability of detection and probability of false alarm.

The probability of error in an AWGN channel can be determined using the Q-function, which is the tail distribution of the Gaussian distribution. For on-off signaling, the probability of error increases as the signal-to-noise ratio (SNR) decreases. Antipodal signaling, on the other hand, uses two distinct signals (e.g., -A and A) and typically achieves lower probabilities of error compared to on-off signaling for the same SNR.