GATE EC 2014 Set 1 Q51 — Digital Communications

Let $Q(\sqrt{\gamma})$ be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density $N_{0}/2.$ The parameter $\gamma$ 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 $N_{0}/2$ is shown in the figure. The BPSK demodulator receives the sum of outputs of both the channels.

If the BER of this system is $Q( b \sqrt{\gamma})$ then the value of $b$ is _____.