Quiz_Chpt4-3_Q

# Quiz_Chpt4-3_Q - CHAPTER 4 Problem Consider a communication...

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C HAPTER 4 Problem: Consider a communication system, modeled as y = xC + n , where y is the received signal, x is the input signal and takes values on {–3, –1, +1, +3}, C is a known positive constant used for power control, and n is the additive noise modeled as a Gaussian random variable with zero mean and variance σ 2 . As x takes on 4 values, for every transmission x can carry 2 information bits. Here, the following mapping from two information bits, b 0 b 1 , to an input signal, x , is adopted (see the following figure), 10 Æ –3, 11 Æ –1 01 Æ +1, 00 Æ +3 Upon receiving y , the receiver makes a hard decision on x and recovers the transmitted two information bits. Answer the following question regarding this communication system. 1. When transmitting two information bits ( b 0 b 1 ) = (01), what is the error probability? (a) Q ( C / σ ) (b) 2 Q ( C / σ ) (c) Q (2 C / σ ) (d) 2 Q (2 C / σ )

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