and a and b are the signal levels corresponding to 0 and 1. The receiver measures the amplitude of the received signal and compares it with the mid-point value (a+b)/2. If the received signal amplitude is smaller than (a+b)/2 it determines that a 0 was transmitted, and if larger, a 1. This mid-point value is also known as the detection threshold. Modulated signal Figure 7.1 Binary amplitude modulation Amplitude Figure 7.2 Binary amplitude shift keying modulation signal detection threshold Digital Modulation Amplitude Figure 7.3 Noise signal and its distribution Probability Amplitude distribution Amplitude Amplitude Figure 7.4 Binary ASK signal with noise (a) and its distribution (b) As discussed in Chapter 3, digital telecommunication systems are robust against noise, however detection errors occur if noise and interference levels are large compared with received signal. That is, a transmitted 0 may be detected as 1 because of added noise and interference. Consider the ASK signal constellation in Figure 7.2. Additive thermal noise as discussed in Chapter 4 is a random process with a normal distribution. Typical noise signal points (a total of some 70 dots, each of which represent the noise signal at one sampling time) and their x-axis normal distribution are shown in Figure 7.3. These noise signals are added to the received signal amplitude (a or b) and as a result the total value of the received signal is different from the ASK signal constellation point. Errors occur if the (a+b)/2 boundary is crossed. This is illustrated in Figure 7.4. The received signal is the sum of the transmitted signal (a) and the noise values as shown in Figure 7.4(a). It can be observed that some signal points cross the (a+b)/2 boundary and as a result are detected erroneously. Figure 7.4(b) shows the distribution of the received signal, a normally distributed variable. The area under the distribution curve between -00 and (a+b)/2 is the probability that an error occurs. This is the probability that a signal transmitted as an a is dete