i i i in Software Use EAN13 in Software i i i barcode for .NET

i i i generate, create none none in none projectsprint barcode .net i i TranterBook 2003/11/ none for none 18 16:12 page 499 #517. Developing with Visual Studio .NET Section 13.1. Introduction Channel Attenuation Time - seconds Figure 13.1 Snapshots of a slowly varying time-varying channel. corresponding to unsatisfact none for none ory system performance, BER> 10 3 , for example, then the outage probability is (100/10, 000) = 0.01 for this speci c BER threshold. As a second example, consider a mobile communication system consisting of a xed base station and a mobile user.

The characteristics of the communication channel between the transmitter and the receiver will be time varying, since the parameters of the channel, such as the attenuation and delay, are changing due to relative motion between the base station and the mobile user. In addition, changes in atmospheric conditions will also contribute to the time-varying nature of the channel. If the mobile user is rapidly moving and if the symbol rate is of the order of 10, 000 symbols per second, the rate at which channel conditions are changing might be comparable to the symbol rate.

In this case a time-varying channel model would be required. While a time-varying model may or may not be needed for BER estimation, such a model will be necessary to study the behavior of receiver subsystems such as synchronizers and equalizers..

Modeling and Simulation Approach As with LTIV systems, LTV sy none none stems can be modeled and simulated in either the time domain or in the frequency domain. The time-domain approach leads to a model consisting of a tapped delay-line structure with time-varying tap gains. This model is very easy to implement for simulation purposes and is computationally very e cient if the time-varying impulse response is relatively short.

Many of the modeling and simulation concepts previously discussed for LTIV systems apply to LTV systems, but with some important di erences. Particular attention must be paid to the sampling rate used in the simulation, since an increase in the sampling rate will be required because of bandwidth expansion resulting from underlying time variations. One source of bandwidth expansion is the doppler spreading in a mobile communications system.

In addition, caution. i i i i i TranterBook 2003/11/ none none 18 16:12 page 500 #518. Modeling and Simulation of Time-Varying Systems 13 . must be exercised in simplif ying the block diagrams of LTV systems, since LTV blocks do not obey commutative properties and hence the order of computations cannot be interchanged between LTV blocks as with LTIV blocks. However, as long as the time-varying system is linear in nature, superposition and convolution apply, and many of the time-domain and frequency-domain analysis techniques developed for LTIV systems can be used, with slight modi cations, to model and simulate LTV systems. We will also use equivalent lowpass signal and system representations as we develop simulation models and techniques for timevarying systems.

. Models for LTV Systems In the time domain, a linear time-invariant system is described by a complex envelope impulse response h( ), where h( ) is de ned as the response of the system at time to an impulse applied at the input at time t = 0. The variable represents the elapsed time, which is the di erence between the time at which the impulse response is measured and the time at which the impulse is applied at the system input. The complex envelope input-output relationship for a LTIV system is given by the familiar convolution integral.

y(t) =. h( )x(t ) d (13.1). where x(t) and y(t) represen t the complex envelopes of the system input and output, respectively. Taking the Fourier transform of (13.1) gives the input-output relationship for the LTIV system in the frequency domain.

This is Y (f ) = X(f )H(f ) (13.2). where H(f ) is the transfer none none function of the system, and X(f ) and Y (f ) are the Fourier transforms of the input and output, respectively. The output y(t) is obtained by taking the inverse transform of Y (f ). This gives.

y(t) =.
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