Question

A binary PSK signal in the presence of additive white Gaussian noise (AWGN) is detected by a correlation receiver. Assuming that the carrier recovery circuit has a phase error of 8, show that the bit error rate is given by: Ρ. = (1/2)erfe[VE, Ncoς ε] Where E, is the bit energy of the signal and N, is the power spectral density of the AWGN. Assume that the symbols occur with equal probability.

Answer 1

Ans:

The bit error rate (BER) is the number of bit errors per unit time.The bit error probability p_e is the expectation value of the bit error ratio.In a noisy channel, the Bit Error Rate  is often expressed as a function of the normalized carrier-to-noise ratio measure denoted Eb/N0, (energy per bit to noise power spectral density ratio), or Es/N0 (energy per modulation symbol to noise spectral density).

a bit mis interpretahion The Bit Emor rate (BER) OF due to electrical Noise wit) ,(t)= A+ Wit) fOr 1' Kolt) = AtWLt) for '0 considenng NRZ bipolan transmission. Noise has bilatenal spechral density No2 2,(t) is N "(^,) No T-time peniod 1. and, A No) 20lt) is N (-^ 2T Pe = P(011)P, + P(10) Po and P(Ol1)P. P(O11),=05 erfe AtA NOIT P(1/0) - 0.5 erfc No/T where, A- Threshold of decision P= Po0-5

Average Energy of signal E = A2T 10000 . substituting all valuee in egn O O.5 erfe Pe = CoS E A No