A digital radio  (Page 6/8)

At the receiver, the signal can be returned to its original frequency (demodulated)by multiplying by another high frequency sinusoid (and then low pass filtering).These frequency translations are described in more detail in [link] , where it is shown that the modulating sinusoid and the demodulating sinusoid musthave the same frequencies and the same phases in order to return the signal to its original form.Just as it is impossible to align any two clocks exactly,it is also impossible to generate two independent sinusoids of exactly the same frequency and phase.Hence there will ultimately need to be some kind of “carrier synchronization,” a way of aligningthese oscillators.

How can the frequencies and phases of these two sinusoids be aligned?

Adding frequency translation to the transmitter and receiver of [link] and [link] produces the transmitter in [link] and the associated receiver in [link] . The new block in the transmitteris an analog component that effectively adds the same value (in Hz) to the frequencies of all of the components of thebaseband pulse train. As noted, this can be achieved with multiplicationby a “carrier” sinusoid with a frequency equal to the desired translation.The new block in the receiver of [link] is an analog component that processes the received analog signal prior to sampling in order to subtract the same value(in Hz) from all components of the received signal. The output of this blockshould be identical to the input to the sampler in [link] .

This process of translating the spectrum of the transmitted signal to higher frequencies allows many transmitters tooperate simultaneously in the same geographic area. But there is a price.Since the signals are not completely bandlimited to within their assigned $5B$ -wide slot, there is some inevitable overlap.

Thus the residual energy of one transmitter (the energy outside its designated band) acts as an interference toother transmissions. Solving the problem of multiple transmissions has thus violated one of the assumptionsfor an ideal transmission. A common theme throughout Software Receiver Design is that a solution to one problem often causes another!

There is no free lunch. How much does the fix cost?

In fact, there are many other ways that the transmission channel can deviate from the ideal, and these will be discussedin detail later on (for instance, in [link] and throughout [link] ). Typically, the cluttered electromagnetic spectrumresults in a variety of distortions and interferences:

• in-band (within the frequency band allocated to the user of interest)
• out-of-band (frequency components outside the allocated band such as the signals of other transmitters)
• narrowband (spurious sinusoidal-like components)
• broadband (with components at frequencies across the allocated band and beyond, including thermal noise introduced by the analog electronics in the receiver)
• fading (when the strength of the received signal fluctuates)
• multipath (when the environment contains many reflective and absorptive objects at different distances, the transmission delay willbe different across different paths, smearing the received signal and attenuating some frequencies more than others)