Problem 1. Consider a 2-branch diversity system using BPSK with coherent detecti

Question

Problem 1. Consider a 2-branch diversity system using BPSK with coherent detection. The channel gain in each branch can take on the values of 1.0 and 0.05. The channel gains in the two branches are correlated with the joint probability distribution given by P(?,-1 .0, ?,-1.0,-P(?,-0.05, ?,-0.05,-0.4, P(a1-1.0, a2-0.05)- P(a0.05, a2 1.0) 0.1 (a) For maximal ratio combining, calculate the probability of a bit error as a function of EyN (b) For selection combining, calculate the probab?lity of a bit error as a function of ENo. (c) Compare the probabilities of a bit error in parts (a) and (b).

Explanation / Answer

Binary Phase-shift keying (BPSK) is a digital modulation scheme that conveys data by changing, or modulating, two different phase?s of a reference signal (the carrier wave). The constellation points chosen are usually positioned with uniform angular spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the moduli of the complex numbers they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves.

COHERENT DETECTION::

A “coherent” optical transmission system is characterized by its capability to do “coherent detection,” which means that an optical receiver can track the phase of an optical transmitter (and hence “phase coherence”) so as to extract any phase and frequency information carried by a transmitted signal.

The bit error rate (BER) is the number of bit errors per unit time. The bit error ratio (also BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. Bit error ratio is a unitless performance measure, often expressed as a percentage

The bit error probability pe is the expectation value of the bit error ratio. The bit error ratio can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long time interval and a high number of bit errors

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