Details

A QPSK signal constellation represents the possible signal points used in a QPSK modulation. In QPSK, each symbol represents two bits of information. Two bits are transmitted each symbol time, .

For one symbol time, the transmitted QPSK signal on a carrier frequency of is one of the following four symbols [1]:

The energy/symbol is and the energy/bit . In practical scenarios, noise and intersymbol interference are present, causing random variations in the received signal points. Receiving a large set of symbols results in a "noise cloud" [1] centered around each ideal signaling point as shown in this Demonstration. An error occurs when the received symbol is outside its associated decision region, shown here by a colored area. The presence of noise and intersymbol interference introduces bit errors. Employing an optimum detector [1–3] with additive flat Gaussian noise and no intersymbol interference results in a probability of a bit error (BER) of

,

where is the noise power spectral density and .

The BER is calculated in the Demonstration.

References

[1] S. Haykin and M. Moher, Introduction to Analog and Digital Communications, 2nd ed., Hoboken, NJ: Wiley, 2012.

[2] L. W. Couch, Digital and Analog Communications Systems, 7th ed., Upper Saddle River, NJ: Pearson/Prentice Hall, 2007.

[3] H. Taub and D. L. Schilling, Principles of Communication Systems, 2nd ed., New York: McGraw-Hill, 1986.

[4] V. S. Frost. "Introduction to Communication Systems: An Interactive Approach Using the Wolfram Language." University of Kansas Libraries. (Jul 5, 2023) kuscholarworks.ku.edu/bitstream/handle/1808/31779/Introduction-to-Communication-Systems-Deployed-V3.cdf?sequence=5&isAllowed=y.