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Unformatted text preview: 1 Chapter 4 Receiver Design 2 So far we have considered the frequency domain properties of digital systems. In this chapter we consider transmitting such signals through a noisy channel. We first focus on the baseband, which refers to the transmission without modulation. We will discuss the modulated signals later. We are interested in designing receivers to recover information. The following issues are important in this case. optimal receiver structure,  bit error rate (BER) due to noise, how to improve BER performance? Overview 3 Detection and Detection Error Any channel is subject to noise and distortion, such as the situation shown below. We will focus on an additive white Gaussian noise (AWGN) channel. In this case the received signal r ( t ) can be expressed as the sum of the transmitted signal and a Gaussian noise. The receiver need to recover the original information from r ( t ). One method is to select a sampling point and make decision according to the sampled value. This is not a good choice. For example, in the above figure, at the bad sampling point as indicated, the sampled value has opposite sign of the transmitted pulse and so it can lead to an error. channel transmitted signal received signal s ( t ) r ( t )= s ( t )+ n ( t ) bad sampling point τ τ A 4 Integral Detection We can observe that using area as the decision variable is more reliable. For example, if the positive area is much larger than the negative area during the pulse period, then we can guess that the transmitted signal is a positive pulse. To realize this idea, integration is needed. An obvious advantage of the area method is that it utilizes more information, so in principle it should be better than the single sample based method. channel transmitted signal received signal s ( t ) r ( t )= s ( t )+ n ( t ) bad sampling point τ τ A 5 Integrator Receiver We now consider the structure of integrator receiver. Assume that the transmitted waveform is bs (t), where b ={1,1} is the information and s ( t ) is a rectangular pulse function with amplitude A . Our task is to estimate b from the received signal. We will only consider the detection of the first pulse and the remaining is similar. Suppose that the first pulse interval is [0, τ ]. Denote by n ( t ) the channel noise....
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This note was uploaded on 01/11/2011 for the course EE 3008 taught by Professor Pingli during the Fall '08 term at City University of Hong Kong.
 Fall '08
 PingLi
 Frequency

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