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# mt03 - Lecture 13 EE 359 Wireless Communications Fall 2003...

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Lecture 13 - EE 359: Wireless Communications - Fall 2003 MIDTERM This exam is open book and notes, and calculators are needed. Graded exams and solutions will be available next week. Good Luck! Problem 1 (40 points): Wireless Channels. This problem illustrates the impact of channel delay spread on wireless system performance when T s T M , as well as the impact of Doppler. Consider a channel with impulse response c ( τ, t ) = δ ( τ )+ . 5 δ ( τ - 10 μ sec)+ . 5 δ ( τ - 40 μ sec) . (a) Is the channel time-varying or time-invariant? Explain. (b) For what data rates does a BPSK signal sent over this channel experience ISI? (c) Define rect t T s = ( 1 | t | < T s / 2 0 else . Suppose we transmit the signal s ( t ) consisting of two pulses, s ( t ) = rect t T s + rect t - T s T s through the channel with impulse response c ( τ, t ). Sketch the received signal for T s = 20 μ sec. Does the received signal exhibit ISI (why or why not)? (d) Repeat (c) for T s = 2 μ sec. (e) Suppose now that c ( τ, t ) = α 1 ( t ) δ ( τ ) + α 2 ( t ) δ ( τ - 10 μ sec) + α 3 ( t ) δ ( τ - 40 μ sec) , where the α i ( t ) are independent Rayleigh fading processes with average power of 1 Watt.

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