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How to calculate the error rate of a QAM symbol?
In this post let us derive the equation for probability of symbol being in error for a general M-QAM constellation, given that the signal (symbol) to noise ratio is . The number of points in the constellation is defined as, where is the number of bits in each constellation symbol.
Why is probability in quantum mechanics is given by the wave?
Wave functions evolve in time according to the Schrödinger equation. The act of measuring a quantum system returns a number, known as the eigenvalue of the quantity being measured. The probability of getting any particular eigenvalue is equal to the square of the amplitude for that eigenvalue.
Which is a quadrature amplitude modulation ( QAM ) scheme?
Quadrature Amplitude Modulation (QAM) schemes like 16-QAM, 64-QAM are used in typical wireless digital communications specifications like IEEE802.11a , IEEE802.16d. In this post let us derive the equation for probability of symbol being in error for a general M-QAM constellation, given that the signal (symbol) to noise ratio is .
What is the scaling factor of 16 QAM and 64 QAM?
From the above explanations, it is reasonably intuitive to guess that the scaling factor of , which is seen along with 16-QAM, 64-QAM constellations respectively is for normalizing the average transmit power to unity.
Is there an inherent symbol rate for any modulation type?
There is no inherent symbol rate for any modulation type. 64 QAM symbols transmit 6 bits per symbol, and 256 QAM symbols transmit 8 bits per symbol. If the bit rate were to stay constant, then the 256 QAM symbol rate would be 6/8 of the 64 QAM symbol rate, but it appears that that is not the case (assuming your numbers are correct).
How can I find the symbol rate of a signal?
If you take an FFT of the signal and measure the width of the first lobe of the data (or 2x the lobe at baseband), that will be your symbol rate. An early-late gate symbol synchronizer can easily be implemented, but you’ll need to first run the data through a matched filter, which will require at least an estimate of the symbol rate.
Is the symbol rate the same as the bit rate?
So for example, when BPSK modulation is used the symbol rate is the same as the bit rate because 1 bit of data is transmitted per symbol. The rate at which symbols are transmitted is the baud rate. SR – Symbol Rate. FEC – Forward Error Correction. DR – Data Rate. m – Modulation Factor. sps – Symbols per second.