Which is the best digital modulation techniques : ASK, FSK, PSK or QAM ? and why ?

Every modulation technique has it's advantage and disadvantage.But if you are asking which is the best to use I would definetly go with the QAM as it has higher data rates among all techniques but you should maitain a good channel specs as the effect of error increases as the order of QAM increases.

QAM is the best :-

QAM is a combination ASK & PSK - Means using both systems ability to achieve better bit rate in same power as ASK.

QAM can allow bit rate optimization according to the power strength between4 ~64 QAM.

QAM  can use4 bits to64 bits combination to represent a symbol.

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ASK-PSK-QAM Example

QAM is the best one from them because it has high rate of data and good performance and high BER