A digital radio  (Page 7/8)

These channel imperfections are all incorporated in the channel model shown in [link] , which sits in the communication system between Figures  [link] and [link] .

Many of these imperfections in the channel can be mitigated by clever use of filtering at the receiver.Narrowband inference can be removed with a notch filter that rejects frequency components in the narrow range of theinterferer without removing too much of the broadband signal. Out-of-band interference andbroadband noise can be reduced using a bandpass filter that suppresses the signal in the out-of-band frequencyrange and passes the in-band frequency components without distortion.With regard to [link] , it is reasonable to wonder if it is better to perform such filteringbefore or after the sampler (i.e., by an analog or a digital filter).In modern receivers, the trend is to minimize the amount of analog processing since digital methodsare (often) cheaper and (usually) more flexible since they can be implemented as reconfigurable softwarerather than fixed hardware.

Analog or digital processing?

Conducting more of the processing digitally requires moving the sampler closer to the antenna.The sampling theorem (discussed in [link] ) says that no information is lostas long as the sampling occurs at a rate faster than twice the highest frequency of the signal.Thus, if the signal has been modulated to (say) the band from $20B$ to $25B$ Hz, then the sampler must be able to operate at least as fast as $50B$ samples per second in order to be able to exactly reconstruct the value ofthe signal at any arbitrary time instant. Assuming this is feasible,the received analog signal can be sampled using a free-running sampler.Interpolation can be used to figure out values of the signal at any desired intermediate instant,such as at time $\eta +kT$ (recall [link] ) for a particular $\eta$ that is not an integer multiple of $T$ . Thus, the timing synchronization can be incorporatedin the post-sampler digital signal processing box, which is shown generically in [link] . Observe that [link] is one particular version of [link] .

How exactly does interpolation work?

However, sometimes it is more cost effective to perform certain tasks in analog circuitry.For example, if the transmitter modulates to a very high frequency, then it may cost too much to sample fast enough.Currently, it is common practice to perform some frequency translation and some out-of-band signal reductionin the analog portion of the receiver. Sometimes the analog portion may translate the received signalall the way back to baseband. Other times, the analog portion translates to some intermediatefrequency, and then the digital portion finishes the translation. The advantage of this (seemingly redundant) approach is thatthe analog part can be made crudely and, hence, cheaply. The digital processing finishes the job, and simultaneouslycompensates for inaccuracies and flaws in the (inexpensive) analog circuits.Thus, the digital signal processing portion of the receiver may need to correct for signal impairments arisingin the analog portion of the receiver as well as from impairments caused by the channel.