# Introduction – Digital Modulators and Demodulators – Passband Simulation Models – Chapter 2

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### In this chapter:

For a given modulation technique, there are two ways to implement the simulation model: passband model and equivalent baseband model. The passband model is also called waveform level simulation model. The waveform level simulation techniques, described in this chapter, are used to represent the physical interactions of the transmitted signal with the channel. In the waveform level simulations, the transmitted signal, the noise and received signal are all represented by samples of waveforms.

Typically, a waveform level simulation uses many samples per symbol. For the computation of error rate
performance of various digital modulation techniques, the value of the symbol at the symbol-sampling time instant is all the more important than the look of the entire waveform. In such a case, the detailed waveform level simulation is not required, instead equivalent baseband discrete-time model, described in chapter 3 can be used. Discrete-time equivalent channel model requires only one sample per symbol, hence it consumes less memory and yields results in a very short span of time.

In any communication system, the transmitter operates by modulating the information bearing baseband waveform on to a sinusoidal RF carrier resulting in a passband signal. The carrier frequency, chosen for transmission, varies for different applications. For example, FM radio uses $$88 -108 MHz$$ carrier frequency range, whereas for indoor wireless networks the center frequency of transmission is $$1.8\; GHz$$. Hence, the carrier frequency is not the component that contains the information, rather it is the baseband signal that contains the information that is being conveyed.

Actual RF transmission begins by converting the baseband signals to passband signals by the process of up-conversion. Similarly, the passband signals are down-converted to baseband at the receiver, before actual demodulation could begin. Based on this context, two basic types of behavioral models exist for simulation of communication systems – passband models and its baseband equivalent. In the passband model, every cycle of the RF carrier is simulated in detail and the power spectrum will be concentrated near the carrier frequency $$f_c$$. Hence, passband models consume more memory, as every point in the RF carrier needs to be stored in computer memory for simulation.

On the other hand, the signals in baseband models are centered near zero frequency. In baseband equivalent models, the RF carrier is suppressed and therefore the number of samples required for simulation is greatly reduced. Furthermore, if the behavior of the system is well understood, the baseband model can be further simplified and the system can be implemented entirely based on the samples at symbol-sampling time instants.

Conversion of passband model to baseband equivalent model is discussed in chapter 3 section 3.2.
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