The best replacement for qpsk is qam.

The best alternatives to qpsk are rated as following:
★★★★★  qam
★★★★  8psk
★★★  bpsk
★★  16 qam
★★  oqpsk
★  4 qam
★  qpsk
★  psk
★  64 qam
★  bpsk ber
★  dqpsk
  gmsk
  16qam
  dpsk
  ofdm
  16-qam
  pi 4 dqpsk

Your alternative for qpsk is not listed? Suggest!
Speaking about qpsk, one probably shouldn't forget about ofdm.

Other search terms related to qpsk and their ratings are:
★★★★★ ofdm
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Google Trends

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qpsk
qam
8psk