mohatta2015.pdf

CHAPTER 1
INTRODUCTION
In this chapter we will define the problem we are solving and give mathematical
models of the problem, based on the physical laws of nature. Before we do this,
let's jump in with an example.
Alice and Bob
Alice has just sent Bob a question in a game of Truth or Dare. The question is
represented by two digital symbols (si and s 2 ) as shown in Table 1.1. After sending
an initial symbol so, the symbols are sent one at a time. Each is modified as it
travels along a direct path to the receiver, so that it gets multiplied by —10. The
symbols also travel along a second path, bouncing off a building, as shown in Fig.
1.1. The signal along this path gets multiplied by 9 and delayed so that it arrives
at the same time as the next symbol arrives along the direct path. There is also
noise which is added to the received signal.
At Bob's phone, the received values can be modeled as
Π = — 10si+9so + rci
r 2 = -10s2+9si+«2
(1.1)
Suppose the actual received values are
ri = 1, r 2 = -7. (1.2)
Channel Equalization for Wireless Communications: From Concepts to Detailed 1
Mathematics, First Edition. Gregory E. Bottomley.
© 2011 Institute of Electrical and Electronics Engineers, Inc. Published 2011 by John Wiley & Sons, Inc.