what is the relation between complex envelope and zero crossing (qpsk,offset qpsk and MSK)?
Dear Sultan,
The constellation of the QPSK is four points consisting of ordered pairs of QI as 11, 10,00, and 01. These are four vectors as we all know every vector has also an amplitude and phase. The input data to the QPSK modulator is taken two bits by two bits since every QPSK symbol have two bits at a time. So if the data pairs are sequenced as 00 after 11 there will be a transition of the envelope through the origin of the constellation. Zero transitions occurs also when we have the symbols 10 after 01 and vice verse. In order to prevent the the ZERO point transition of the envelope at the symbol boundary the transition is accomplished only circumstantially by affecting only change in one bit very bit time. This is realized by offsetting the I bits from the Q bits by half symbol time. This is called OQPSK. This helps reduce the out of band emission by reducing the sharp transitions at the symbol boundary. In minimum shift keying MSK instead of circulating the the circumference of the constellation by jumping from one point to the other adjacent one, one moves at a circumference of the constellation circles continuously making the envelope constant as the case in frequency modulation. In this way the out of band emission is reduced further than that of the OQPSK.
For more information please refer to Glover and Grant: https://www.google.com.eg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjtlZ-XhIzLAhXGaQ8KHZ6OAgYQFggbMAA&url=http%3A%2F%2F213.55.83.214%3A8181%2FComputer%2520Science%2FNetworks%2F01589.pdf&usg=AFQjCNFo--Rhr2dqUcznri05XKMqnH5a2w&sig2=FfwUyNYqgd0xDIHxSAgrZg
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