Introduction to Communication Systems Simulation

Simulating the demodulator is considerably more difficult than simulating the transmitter. At the receiver, parameters such as frequency offset, bit timing, and symbol block time become significant. In this chapter we shall develop some basic demodulation procedures that are commonly and nearly universally employed. The last section is devoted to the concept of baseband simulation that eliminates the transmitted carrier frequency from consideration. This process can significantly increase the simulation speed.
In Chapter 6 we showed that a transmitted signal can be represented by the form
where f 0 is the transmitted carrier frequency, and the information is conveyed by the in-phase signal I (t) and the quadrature signal Q (t). The receiver tunes to f 0 filters the signal and usually produces the result to an intermediate frequency (IF). This is called a heterodyne receiver. There are several standard IF frequencies in use: commercial AM uses 455 kHz and commercial FM uses 10.7 MHz. Other well-known IF frequencies are 70 MHz and 21.4 MHz, and there are others.
The I/Q down conversion process is straightforward. The operation is shown in Figure 7.1. The output of this process is called I and Q, but they are not the information I and Q we started with. We label them I ? (t), Q ? (t), and the development below relates them to the original I (t), Q (t). The mathematical operations for I ?