ata modulators, especially those intended to produce constantenvelope output signals, are “high-leverage” components in that even very small deviations from ideal in their behavior can lead to large degradations in overall system performance. Therefore, successful simulation of wireless communication systems depends upon the use of modulator models that capture all of the signiﬁcant deviations from ideal behavior.
In the “usual” development of data modulation techniques as presented in most communications texts, the various techniques are presented in order of complexity, starting with the simplest. Thus BPSK would be presented ﬁrst, then QPSK followed by m-PSK, and so on. Because of its relationship to complex-envelope representations of signals, quadrature modulation plays a central role in simulation of wireless communication systems and models for quadrature modulators, and demodulators serve as building blocks for most other types of data modulators and demodulators. Therefore, this chapter begins with a discussion of quadrature phase shift keying (QPSK) and uses this discussion as a vehicle for development of generic models for quadrature modulation and demodulation. The discussion then moves to binary phase shift keying (BPSK) and shows how this simpler format is modeled using the generic quadrature modulation models. A similar approach is then taken for developing models for multiple phase shift keying (m-PSK), minimum shift keying (MSK), and frequency shift keying (FSK).
The tasks of carrier recovery and symbol-clock regeneration, which are usually considered part of the demodulation process, are an essential part of any data communication system. There are a number of different techniques for accomplishing these 262
tasks, and these techniques can be used across a wide range of modulation formats and demodulation schemes. If we were to implement every possible combination of demodulation algorithm, carrier-recovery technique, and clock regeneration as a distinct model, the combinatorial explosion of different models would become unmanageable. Therefore, it is a common practice to implement the demodulation, carrier recovery, and clock regeneration as separate models that can be put together in any desired combination in a simulation. In some particular situations (such as a cross-strapped Costas loop demodulator) it still makes sense to combine all three tasks into a single demodulator model.
Using the Recovered Carrier
When a signal passes through a nonideal channel, it is subjected to a certain amount of phase shift. For bandpass simulations, the recovered carrier can be used directly as a phase reference mimicking the way most real-world demodulators operate. For complex baseband simulations, the recovered carrier consists of a phase angle which, in general, may be slowly time-varying. We have several choices with regard to how such a carrier is used in simulations:
1. Use a model external to the modulator to rotate the phase of the received signal so that the reference phase effectively becomes zero. The rotated signal can then be input to a demodulator model that assumes a reference phase of zero. The phase rotation requires one complex multiplication for each sample of the received signal. The external model must fetch each sample of the signal and each sample of the reference from memory, perform the rotation, and then store the result back into memory. The demodulator must then fetch each sample of the rotated signal from memory.
2. Pass the recovered carrier phase into the demodulator model where it can be used to rotate the phase of the received signal so that the reference phase effectively becomes zero. This phase rotation requires one complex multiplication for each sample of the received signal, regardless of whether the recovered carrier phase is constant or...
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