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Telecommunications Engineering DISCUSSION
I understand that QPSK carries 2 bits per symbol, 16-QAM carries 4 and 64-QAM carries 6, so for a fixed symbol rate the higher orders give more throughput in the same bandwidth. What I do not see is why radios fall back to QPSK when the signal gets weak instead of always using 64-QAM.
How much more signal-to-noise ratio does each step need, and how do symbol rate, bandwidth and bit rate fit together for, say, 5 Msymbol/s?
Think of the constellation diagram. Each symbol is one point in the I/Q plane, and the receiver decides which point was sent by picking the nearest one. For the same average transmit power, 64 points have to be packed much closer together than 4 points. Noise moves the received point away from its ideal position, and when the points are close a small amount of noise is enough to push it into a neighbour's decision region.
More bits per symbol therefore means less distance between points and more SNR needed for the same error rate.
The size of the step can be put in numbers. For square QAM at equal average power, the squared distance between neighbouring points scales as 1 / (M - 1). Going from QPSK (M = 4) to 16-QAM costs a factor of 15 / 3 = 5, which is 7 dB; 16-QAM to 64-QAM costs 63 / 15 = 4.2, about 6.2 dB; 64 to 256 is again about 6 dB.
So each two extra bits per symbol cost roughly 6 dB. As a guide, uncoded QPSK needs about 13.5 dB of SNR per symbol for a bit error rate of 1 in a million, 16-QAM about 20.5 dB and 64-QAM about 26.5 dB. Error-correcting codes lower all of these by several dB.
For your 5 Msymbol/s: the bit rates before coding are 10, 20 and 30 Mbit/s for QPSK, 16-QAM and 64-QAM. The occupied bandwidth is set by the symbol rate and the pulse-shaping filter, not by the modulation order: about symbol rate × (1 + roll-off). With a roll-off of 0.25 that is 6.25 MHz in all three cases.
That is the whole attraction of high-order QAM, three times the data in the same spectrum, and the price is paid in SNR, exactly as the Shannon limit says it must be.
Noise is not the only thing that closes the gaps between points. Dense constellations are also sensitive to transmitter and receiver imperfections: phase noise rotates the constellation and hits the outer points hardest, and a power amplifier driven near saturation compresses the outer points inward. QAM has a high peak-to-average power ratio, so the amplifier has to be backed off, which reduces the available output power just when more SNR is wanted.
The combined effect is measured as error vector magnitude, and standards specify a tighter EVM limit for each higher modulation order.
This is why practical radios use adaptive modulation and coding. The receiver reports channel quality, and the link picks the densest constellation and the lightest error-correction code that the current SNR supports. Close to the base station or access point that may be 64-QAM or 256-QAM; at the edge of coverage it falls back to QPSK with a strong code.
Throughput changes but the connection survives, which is a better trade than a fixed 64-QAM link that simply fails when the SNR drops by 10 dB.
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