0.1 A telecommunication system  (Page 15/15)

The problem of reducing the sensitivity to noise is addressed in [link] using the idea of linear block codes , which cluster a number of symbols together, and then add extra bits.A simple example is the (binary) parity check, which adds an extra bit to each character. If there are aneven number of ones then a 1 is added, and if there are an odd number of ones, a 0 is added.The receiver can always detect that a single error has occurred by counting the number of 1's received.If the sum is even, then an error has occurred, while if the sum is odd then no single error can have occurred.More sophisticated versions can not only detect errors, but can also correct them.

Like good equalization and proper synchronization, coding is an essential part of the operation of digital receivers.

A telecommunication system

The complete system diagram, including the digital receiver that will be built in this text, is shown in [link] . This system includes the following:

• A source coding that reduces the redundancy of the message.
• An error coding that allows detection and/or correction of errors that may occur during the transmission.
• A message sequence of $T$ -spaced symbols drawn from a finite alphabet.
• Pulse shaping of the message, designed (in part) to conserve bandwidth.
• Analog upconversion to the carrier frequency (within specified tolerance).
• Channel distortion of transmitted signal.
• Summation with other FDM users, channel noise, and other interferers.
• Analog downconversion to intermediate frequency (including bandpass prefiltering aroundthe desired segment of the FDM passband).
• A/D impulse sampling (preceded by antialiasing filter) at a rate of $\frac{1}{T_s}$ with arbitrary start time. The sampling rate is assumed to be at least asfast as the symbol rate $\frac{1}{T}$ .
• Downconversion to baseband (requiring carrier phase and frequency synchronization).
• Lowpass (or pulse-shape-matched) filtering for the suppression of out-of-band users and channel noise.
• Downsampling with timing adjustment to $T$ -spaced symbol estimates.
• Equalization filtering to combat intersymbol interference and narrowband interferers.
• Decision device quantizing soft decision outputs of equalizer to nearest memberof the source alphabet (i.e. the hard decision).
• Source and error decoders.

Of course, permutations and variations of this system are possible, but we believe that [link] captures the essence of many modern transmission systems.

Stairway to radio

The path taken by Software Receiver Design is to break down the telecommunication system into its constituent elements:the modulators and demodulators, the samplers and filters, the coders and decoders.In the various tasks within each chapter, you are asked to build a simulation of therelevant piece of the system. In the early chapters, the parts need to operate onlyin a pristine, idealized environment, but as we delve deeper into the onion, impairments and noises inevitablyintrude. The design evolves to handle the increasingly realistic scenarios.

Throughout this text, we ask you to consider a variety of small questions, some of which aremathematical in nature, most of which are “what if” questions best answered by trial and simulation.We hope that this combination of reflection and activity will be a useful in enlarging your understandingand in training your intuition.

For further reading

There are many books about various aspects of communication systems. Here are some of our favorites.Three basic texts that utilize probability from the outset, and that also pay substantial attention to pragmatic design issues(such as synchronization) are the following:

[1] J. B. Anderson, Digital Transmission Engineering,IEEE Press, 1999. [2]J. G. Proakis and M. Salehi, Communication Systems Engineering, Prentice Hall, 1994. [This textalso has a Matlab-based companion, Introduction to Communication Systems Using Matlab, Brooks-ColePubs., 1999.] [3]S. Haykin, Communication Systems, 4th edition, John Wiley and Sons, 2001.Three introductory texts that delay the introduction of probability until the latter chapters are the following:[4] L. W. Couch III, Digital and Analog CommunicationSystems, 6th edition, Prentice Hall, 2001. [5]B. P. Lathi, Modern Digital and Analog Communica- tion Systems, 3rd edition, Oxford University Press, 1998.[6] F. G. Stremler, Introduction to CommunicationSystems, 3rd edition, Addison Wesley, 1990. These final three references are probably the mostcompatible with Software Receiver Design in terms of the assumed mathematical background.