Introduction to Communication Systems

Digital modulation is the process of translating bits to analog waveforms that can be sent over a physical channel. Figure 4.1 shows an example of a baseband digitally modulated waveform, where bits that take values in {0, 1} are mapped to symbols in {+1, −1}, which are then used to modulate translates of a rectangular pulse, where the translation corresponding to successive symbols is the symbol interval T. The modulated waveform can be represented as a sequence of symbols (taking values ±1 in the example) multiplying translates of a pulse (rectangular in the example). This is an example of a widely used form of digital modulation termed linear modulation, where the transmitted signal depends linearly on the symbols to be sent. Our treatment of linear modulation in this chapter generalizes this example in several ways. The modulated signal in Figure 4.1 is a baseband signal, but what if we are constrained to use a passband channel (e.g., a wireless cellular system operating at 900 MHz)? One way to handle this to simply translate this baseband waveform to passband by upconversion; that is, send up(t) = u(t)cos(2πfct), where the carrier frequency fc lies in the desired frequency band. However, what if the frequency occupancy of the passband signal is strictly constrained? (Such constraints are often the result of guidelines from standards or regulatory bodies, and serve to limit interference between users operating in adjacent channels.) Clearly, the timelimited modulation pulse used in Figure 4.1 spreads out significantly in frequency.