<P> The first rectangular QAM constellation usually encountered is 16 - QAM, the constellation diagram for which is shown here . A Gray coded bit - assignment is also given . The reason that 16 - QAM is usually the first is that a brief consideration reveals that 2 - QAM and 4 - QAM are in fact binary phase - shift keying (BPSK) and quadrature phase - shift keying (QPSK), respectively . Also, the error - rate performance of 8 - QAM is close to that of 16 - QAM (only about 0.5 dB better), but its data rate is only three - quarters that of 16 - QAM . </P> <P> Expressions for the symbol - error rate of rectangular QAM are not hard to derive but yield rather unpleasant expressions . For M - ary square QAM exact expressions are available . They are most easily expressed in a per carrier sense: </P> <Dl> <Dd> P s c = 2 (1 − 1 M) Q (3 M − 1 E s N 0) (\ displaystyle P_ (sc) = 2 \ left (1 - (\ frac (1) (\ sqrt (M))) \ right) Q \ left ((\ sqrt ((\ frac (3) (M - 1)) (\ frac (E_ (s)) (N_ (0))))) \ right)) </Dd> </Dl> <Dd> P s c = 2 (1 − 1 M) Q (3 M − 1 E s N 0) (\ displaystyle P_ (sc) = 2 \ left (1 - (\ frac (1) (\ sqrt (M))) \ right) Q \ left ((\ sqrt ((\ frac (3) (M - 1)) (\ frac (E_ (s)) (N_ (0))))) \ right)) </Dd>

What is quadrature amplitude modulation (qam) and how does it work