0.8 Stuff happens  (Page 2/14)

"Other Impairments: More “What Ifs”" presents a series of “what if” questions concerning the various assumptionsmade in the construction of the ideal system, focusing on performance degradationscaused by synchronization loss and various kinds of distortions:

• What if there is channel noise? (The ideal system is noise free.)
• What if the channel has multipath interference? (There are no reflections or echoes in the ideal system.)
• What if the phase of the oscillator at the transmitter is unknown (or guessed incorrectly) at the receiver? (The ideal systemknows the phase exactly.)
• What if the frequency of the oscillator at the transmitter is off just a bit from its specification? (In the ideal system,the frequency is known exactly.)
• What if the sample instant associated with the arrival of top-dead-center of the leading pulse isinaccurate so that the receiver samples at the “wrong” times? (The sampler in the ideal system is never fooled.)
• What if the number of samples between symbols assumed by the receiver is different from that used at the transmitter? (These are the samein the ideal case.)

These questions are investigated via a series of experiments that require onlymodest modification of the ideal system simulation. These simulations will show (as with the time-varying channel gain)that small violations of the idealized assumptions can often be tolerated.However, as the operational conditions become more severe (as more stuff happens),the receiver must be made more robust.

Of course, it is not possible to fix all these problems in one chapter. That's what the rest of the book is for!

• Chapter [link] deals with methods to acquire and track changes in the carrier phase and frequency.
• Chapter [link] describes better pulse shapes and corresponding receive filters that perform wellin the presence of channel noise.
• Chapter [link] discusses techniques for tracking the symbol clock so that the samples can be taken at the best possibletimes.
• Chapter [link] designs a symbol-spaced filter that undoes multipath interference and can reject certain kinds ofin-band interference.
• Chapter [link] describes simple coding schemes that provide protection against channel noise.

Simulating the ideal system

The simulation of the digital communication system in [link] divides into two parts just as the figure does.The first part creates the analog transmitted signal, and the second part implements the discrete-time receiver.

The message consists of the character string

In order to transmit this important message, it is first translated into the 4-PAM symbol set $\pm 1,\pm 3$ (which is designated $m\left[i\right]$ for $i=1,2,...,N$ ) using the subroutine letters2pam.m . This can be represented formally asthe analog pulse train ${\sum }_{i=0}^{N-1}m\left[i\right]\delta (t-iT)$ , where $T$ is the time interval between symbols. The simulation operates with an oversampling factor $M$ , which is the speed at which the “analog” portion of the system evolves.The pulse train enters a filter with pulse shape $p\left(t\right)$ . By the sifting property [link] , the output of the pulse shaping filteris the analog signal ${\sum }_{i=0}^{N-1}m\left[i\right]p(t-iT)$ , which is then modulated (by multiplication with acosine at the carrier frequency $f_c$ ) to form the transmitted signal