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Let Q(√γ) be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density N0/2. The parameter γ is a function of bit energy and noise power spectral density. A system with two independent and identical AWGN channels with noise power spectral density N0/2 is shown in the figure. The BPSK demodulator receives the sum of outputs of both the channels. If the BER of this system is Q(b√γ), then the value of b is _____.

1. 1
2. √2
3. 2
4. 4

Correct answer: √2

Solution

The correct option is √2 because when two independent AWGN channels are combined, the effective signal-to-noise ratio (SNR) is increased by a factor of 2, leading to an improvement in the BER performance. This results in the argument of the Q-function being scaled by √2, hence the BER becomes Q(b√γ) with b equal to √2.

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