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# LAB SESSION 2 - AWC Course 2012-2013 Lab session on 22/02/2013 - Due date: 5/03/2013 Objective The goal of this lab is to explore wireless channel...

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LAB SESSION 2 - AWC Course 2012-2013 Lab session on 22/02/2013 - Due date: 5/03/2013 Objective The goal of this lab is to explore wireless channel modelling in complex baseband and to practice writing Matlab code from scratch for simple computations. Background There are two key diﬀerences between wireless and wireline communication. The ﬁrst is multipath propagation due to reﬂections of scatterers adding up at the receiver. This addition can be constructive or destructive, and is sensitive to small changes in the relative location of the transmitter and receiver. The resulting ﬂuctuations in signal strength are termed fading . The second is interference: wireless is a broadcast medium, so the receiver can also hear transmissions other than the one it is interested in. In this session, we explore the eﬀects of fading in some simple scenarios. Consider a passband transmitted signal at carrier frequency u p ( t ) = u c ( t ) cos 2 πf c t - u s ( t ) sin 2 πf c t = e ( t ) cos(2 πf c t + θ ( t )) , where u ( t ) = u c ( t ) + ju s ( t ) = e ( t ) e ( t ) is the complex baseband representation, or complex envelope. In order to model the propagation of this signal through a multipath environment, let us consider its propaga- tion through a path of length r . The propagation attenuates the ﬁeld by a factor of 1 /r , and introduces a delay of τ ( r ) = r/c , where c denotes the speed of light. Suppressing the dependence of τ on r , the received signal is given by v p ( t ) = A r e ( t - τ ) cos(2 πf c ( t - τ ) + θ ( t - τ ) - φ ) where we consider relative values (across paths) for the constants A and φ . For example, we may take A = 1, φ = 0 for a reference direct path from transmitter to receiver, while the corresponding values for a reﬂected path depend on the reﬂector material and angle of incidence. A grazing reﬂection would have A 1, φ = π . The complex envelope of v p ( t ) is given by v ( t ) = A r u ( t - τ ) e - j (2 πf c τ + φ ) 1
Generalizing this to multiple paths of length r 1 ,r 2 ,... , the complex envelope of the received signal is given by v ( t ) = X i A i r i u ( t - τ i ) e - j (2 πf c τ i + φ i ) where τ i = r i c and A i , φ i depend on the reﬂector characteristic and incidence angle for the i th ray. Channel delay spread : Let τ min and τ max denote the minimum and maximum of the delays { τ i } . The diﬀerence 4 τ = τ max - τ min is called the channel delay spread . The reciprocal of the delay spread is termed the channel coherence band- width , 4 f coh = 1 4 τ . A baseband signal is said to be narrowband if W 4 τ ± 1, or equivalently, if its bandwidth is smaller than the channel coherence bandwidth. Under the narrowband assumption, we can approximate the received signal v ( t ) by: v ( t ) = u ( t - τ min ) X i A i r i e - j (2 πf c τ i + φ i ) For a narrowband signal, the received complex baseband signal equals a delayed version of the transmitted signal, scaled by a complex number that we term the fading gain h = X i A i r i e - j (2 πf c τ i + φ i ) Modelling a lammpost based broadband network Consider a lamppost-based network supplying broadband access using unlicensed spectrum at 5 GHz. Figure 1 shows two kind of links: lamppost-to-lamppost for backhaul and lamppost-to-mobile for access, where we show nominal values of antenna heights and distances. We explore simple channel models for each case, consisting only of the direct path and the ground reﬂection. For simplicity, assume throughout that A 1 = 1, φ 1 = 0 for the direct path, and A 2 = 0 . 98, φ 2 = π for the ground reﬂection. Find the delay spread and coherence bandwidth for the lamppost-to-lamppost link. If the message signal has 20 MHz bandwidth, is it “narrowband” with respect to the channel? Find the delay spread for the lamppost-to-car link when the car is 100 m away from each lamppost. Is it “narrowband”? To explore the variation of the fading gain as a function of changes in the propa- gation geometry, assume that you send a single tone (zero bandwidth, narrowband signal) at the carrier frequency f c . That is, u p ( t ) = cos 2 πf c t and u ( t ) = 1. We consider both the lamppost-to-lamppost and lamppost-to-car links. 2
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