0.2 The six elements  (Page 10/10)

The sixth element: adaptation

Adaptation is a primitive form of learning. Adaptive elements in telecommunication systems find approximatevalues for unknown parameters in an attempt to compensate for changing conditions or to improve performance.A common strategy in parameter estimation problems is to guess a value, to assess how good the guess is, and to refine the guessesover time. With luck, the guesses converge to a useful estimate of the unknown value.

[link] shows an adaptive element containing two parts. The adaptive subsystem parameterized by $a$ changes the input into the output. The quality assessment mechanism monitors the output (and other relevant signals)and tries to determine whether $a$ should be increased or decreased. The arrow through the system indicates thatthe $a$ value is then adjusted accordingly.

Adaptive elements occur in a number of places in the communication system, including the following:

• In an automatic gain control, the “adaptive subsystem” is multiplication by a constant $a$ . The quality assessment mechanism gauges whether the power at the output of the AGC is too large or too small,and adjusts $a$ accordingly.
• In a phase-locked loop, the “adaptive subsystem” contains a sinusoid with an unknown phase shift $a$ . The quality assessment mechanism adjusts $a$ to maximize a filtered version of the product of the sinusoid and its input.
• In a timing recovery setting, the “adaptive subsystem” is a fractional delay given by $a$ . One mechanism for assessing quality monitors the power of the output, and adjusts $a$ to maximize this power.
• In an equalizer, the “adaptive subsystem” is a linear filter parameterized by a set of $a$ 's. The quality assessment mechanism monitors the deviation of the output of the system froma target set and adapts the $a$ 's accordingly.

Chapter  [link] provides an introduction to adaptive elements in communication systems, and a detailed discussion of theirimplementation is postponed until then.

Summary

The bewildering array of blocks and acronyms in a typical communication system diagram really consists of just ahandful assuming a six-fingered hand. of simple elements: oscillators, linear filters,samplers, static nonlinearities, mixers, and adaptive elements. For the most part, these are ideas that the readerwill have encountered to some degree in previous studies, but they have been summarized here in orderto present them in the same form and using the same notation as in later chapters.In addition, this chapter has emphasized the “how-to” aspects by providing a series of M atlab exercises, which will be useful when creating simulations of the variousparts of a receiver.

For further reading

The intellectual background of the material presented here is often called Signals and Systems . One of the most accessible books is

• J. H. McClellan, R. W. Schafer, and M. A. Yoder, Signal Processing First , Pearson Prentice Hall, NJ, 2003.

Other books provide greater depth and detail about the theory and uses of Fourier transforms. We recommend these as bothbackground and supplementary reading:

• A. V. Oppenheim, A. S. Willsky, and S.H. Nawab, Signals and Systems, Second Edition, Prentice Hall, 1997.
• S. Haykin and B. Van Veen, Signals and Systems , Wiley, 2002.

There are also many wonderful new books about digital signal processing, and these provide both depth and detailabout basic issues such as sampling and filter design. Some of the best are the following:

• A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing , Prentice Hall, 1999.
• B. Porat, A Course in Digital Signal Processing , Wiley, 1997.
• S. Mitra, Digital Signal Processing: A Computer-Based Approach , McGraw-Hill, 2005.

Finally, since M atlab is fundamental to our presentation, it is worth mentioning some books that describethe uses (and abuses) of the M atlab language. Some are:

• A. Gilat, MATLAB: An Introduction with Applications , Wiley, 2007.
• B. Littlefield and D. Hanselman, Mastering M atlab 7 , Prentice Hall, 2004.