Rf and if digitization in Radio Receivers: Theory, Concepts, and Examples
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Chương-3, tham-số-hiệu-năng, OFDM vs OFDMA
| 2.1.2 Out-of-Band Energy
Two practical problems arise when sampling at the 2f
rate: defining what a bandlimited signal is for real systems and analog filtering before the ADC stage. A theoretically defined bandlimited signal is a signal with no frequency components above a certain frequency. When considering real signals such as an RF signal at the input of a radio receiver, however, signals of all frequencies are always present. While all frequencies are always present, it is the amplitude of these frequencies that is the important factor. In particular, the relative amplitude of the undesired signals to the desired signal is important. When digitizing an RF or IF signal at the 2f
rate in a radio receiver, undesired signals (above one-half the sampling rate) of a sufficient amplitude can create spectrum overlap and distort the desired signal. This phenomenon is
5 illustrated in Figure 2. Figure 2(a) shows the spectrum of the analog input signal with its desired and undesired components. If this signal is sampled at two times the highest frequency in the desired signal f d , the resulting spectrum of the sampled signal F s (f) is shown in Figure 2(b). Note that spectrum overlap has occurred here (i.e., the spectrum of the undesired signal occurs within the spectrum of the desired signal). This causes distortion in the reconstructed desired signal.
Figure 2. Spectrum of: (a) a continuous-time analog signal with a desired and undesired component and (b) the signal sampled at f s =2f d
This effect raises an important question: “How large do signals occurring above f s /2 need to be for the distortion of the desired signal to be caused predominantly by spectrum overlap and not ADC nonlinearities?” Nonlinearities in the ADC cause spurious responses in the ADC output spectrum. Distortion due to spectrum overlap can be said to predominate distortion due to ADC nonlinearities when the undesired signals appearing in the frequency band from 0 to f s /2 due to spectrum overlap exceed the largest spurious response of the ADC due to nonlinearities. Therefore, undesired signals appearing in the frequency band from 0 to f s /2 due to spectrum overlap must be lower in power than the largest spurious response of the ADC. In other words, distortion of the desired signal is predominated by ADC nonlinearities (and not spectrum overlap) if signals higher in frequency than f
/2 are lower in power than the largest spurious response of the ADC. This can be quite a stringent requirement. Depending upon the details of the radio system, this requirement may be eased. To determine ways to “ease” this requirement, the following questions should be asked: “How much distortion of the desired signal is tolerable?” “Do the bandwidth and frequency content of both the desired signal in the frequency band from 0 to f
/2 and the undesired signals above the frequency band from 0 to f
/2 effect the distortion of the desired signal?” These questions are best answered by considering the details of the specific radio system such as the type of source
6 information (voice, data, video, etc.); the desired signal bandwidth; the modulation and coding techniques; the undesired signal characteristics (bandwidth, power, and type of signal); and the performance criterion used to evaluate the reception quality of the desired signal. System simulation is a valuable tool for providing answers to these questions for specific radio systems and operating environments. tải về 0.99 Mb. Chia sẻ với bạn bè của bạn:
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